diff --git a/scripts/remove_unused_imports.py b/scripts/remove_unused_imports.py index c1c56aaa4c..14ad2f055f 100755 --- a/scripts/remove_unused_imports.py +++ b/scripts/remove_unused_imports.py @@ -115,7 +115,7 @@ def filter_agda_files(f): return utils.is_agda_file(pathlib.Path(f)) and os.path temp_dir = 'temp' status = 0 - agda_options = '--without-K --exact-split --no-import-sorts --auto-inline --no-caching' + agda_options = '--without-K --exact-split --no-import-sorts --auto-inline --no-caching -WnoPatternShadowsConstructor' temp_root = os.path.join(root, temp_dir) shutil.rmtree(temp_root, ignore_errors=True) diff --git a/src/category-theory.lagda.md b/src/category-theory.lagda.md index 5d426bb25d..419e26be15 100644 --- a/src/category-theory.lagda.md +++ b/src/category-theory.lagda.md @@ -11,165 +11,173 @@ ## Modules in the category theory namespace ```agda -module category-theory where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom -open import category-theory.adjunctions-large-categories public -open import category-theory.adjunctions-large-precategories public -open import category-theory.anafunctors-categories public -open import category-theory.anafunctors-precategories public -open import category-theory.augmented-simplex-category public -open import category-theory.categories public -open import category-theory.category-of-functors public -open import category-theory.category-of-functors-from-small-to-large-categories public -open import category-theory.category-of-maps-categories public -open import category-theory.category-of-maps-from-small-to-large-categories public -open import category-theory.commuting-squares-of-morphisms-in-large-precategories public -open import category-theory.commuting-squares-of-morphisms-in-precategories public -open import category-theory.commuting-squares-of-morphisms-in-set-magmoids public -open import category-theory.commuting-triangles-of-morphisms-in-precategories public -open import category-theory.commuting-triangles-of-morphisms-in-set-magmoids public -open import category-theory.complete-precategories public -open import category-theory.composition-operations-on-binary-families-of-sets public -open import category-theory.cones-precategories public -open import category-theory.conservative-functors-precategories public -open import category-theory.constant-functors public -open import category-theory.copresheaf-categories public -open import category-theory.coproducts-in-precategories public -open import category-theory.cores-categories public -open import category-theory.cores-precategories public -open import category-theory.coslice-precategories public -open import category-theory.dependent-composition-operations-over-precategories public -open import category-theory.dependent-products-of-categories public -open import category-theory.dependent-products-of-large-categories public -open import category-theory.dependent-products-of-large-precategories public -open import category-theory.dependent-products-of-precategories public -open import category-theory.discrete-categories public -open import category-theory.displayed-precategories public -open import category-theory.embedding-maps-precategories public -open import category-theory.embeddings-precategories public -open import category-theory.endomorphisms-in-categories public -open import category-theory.endomorphisms-in-precategories public -open import category-theory.epimorphisms-in-large-precategories public -open import category-theory.equivalences-of-categories public -open import category-theory.equivalences-of-large-precategories public -open import category-theory.equivalences-of-precategories public -open import category-theory.essential-fibers-of-functors-precategories public -open import category-theory.essentially-injective-functors-precategories public -open import category-theory.essentially-surjective-functors-precategories public -open import category-theory.exponential-objects-precategories public -open import category-theory.extensions-of-functors-precategories public -open import category-theory.faithful-functors-precategories public -open import category-theory.faithful-maps-precategories public -open import category-theory.full-functors-precategories public -open import category-theory.full-large-subcategories public -open import category-theory.full-large-subprecategories public -open import category-theory.full-maps-precategories public -open import category-theory.full-subcategories public -open import category-theory.full-subprecategories public -open import category-theory.fully-faithful-functors-precategories public -open import category-theory.fully-faithful-maps-precategories public -open import category-theory.function-categories public -open import category-theory.function-precategories public -open import category-theory.functors-categories public -open import category-theory.functors-from-small-to-large-categories public -open import category-theory.functors-from-small-to-large-precategories public -open import category-theory.functors-large-categories public -open import category-theory.functors-large-precategories public -open import category-theory.functors-nonunital-precategories public -open import category-theory.functors-precategories public -open import category-theory.functors-set-magmoids public -open import category-theory.gaunt-categories public -open import category-theory.groupoids public -open import category-theory.homotopies-natural-transformations-large-precategories public -open import category-theory.indiscrete-precategories public -open import category-theory.initial-category public -open import category-theory.initial-objects-large-categories public -open import category-theory.initial-objects-large-precategories public -open import category-theory.initial-objects-precategories public -open import category-theory.isomorphism-induction-categories public -open import category-theory.isomorphism-induction-precategories public -open import category-theory.isomorphisms-in-categories public -open import category-theory.isomorphisms-in-large-categories public -open import category-theory.isomorphisms-in-large-precategories public -open import category-theory.isomorphisms-in-precategories public -open import category-theory.isomorphisms-in-subprecategories public -open import category-theory.large-categories public -open import category-theory.large-function-categories public -open import category-theory.large-function-precategories public -open import category-theory.large-precategories public -open import category-theory.large-subcategories public -open import category-theory.large-subprecategories public -open import category-theory.limits-precategories public -open import category-theory.maps-categories public -open import category-theory.maps-from-small-to-large-categories public -open import category-theory.maps-from-small-to-large-precategories public -open import category-theory.maps-precategories public -open import category-theory.maps-set-magmoids public -open import category-theory.monads-on-categories public -open import category-theory.monads-on-precategories public -open import category-theory.monomorphisms-in-large-precategories public -open import category-theory.natural-isomorphisms-functors-categories public -open import category-theory.natural-isomorphisms-functors-large-precategories public -open import category-theory.natural-isomorphisms-functors-precategories public -open import category-theory.natural-isomorphisms-maps-categories public -open import category-theory.natural-isomorphisms-maps-precategories public -open import category-theory.natural-numbers-object-precategories public -open import category-theory.natural-transformations-functors-categories public -open import category-theory.natural-transformations-functors-from-small-to-large-categories public -open import category-theory.natural-transformations-functors-from-small-to-large-precategories public -open import category-theory.natural-transformations-functors-large-categories public -open import category-theory.natural-transformations-functors-large-precategories public -open import category-theory.natural-transformations-functors-precategories public -open import category-theory.natural-transformations-maps-categories public -open import category-theory.natural-transformations-maps-from-small-to-large-precategories public -open import category-theory.natural-transformations-maps-precategories public -open import category-theory.nonunital-precategories public -open import category-theory.one-object-precategories public -open import category-theory.opposite-categories public -open import category-theory.opposite-large-precategories public -open import category-theory.opposite-precategories public -open import category-theory.opposite-preunivalent-categories public -open import category-theory.opposite-strongly-preunivalent-categories public -open import category-theory.pointed-endofunctors-categories public -open import category-theory.pointed-endofunctors-precategories public -open import category-theory.precategories public -open import category-theory.precategory-of-elements-of-a-presheaf public -open import category-theory.precategory-of-functors public -open import category-theory.precategory-of-functors-from-small-to-large-precategories public -open import category-theory.precategory-of-maps-from-small-to-large-precategories public -open import category-theory.precategory-of-maps-precategories public -open import category-theory.pregroupoids public -open import category-theory.presheaf-categories public -open import category-theory.preunivalent-categories public -open import category-theory.products-in-precategories public -open import category-theory.products-of-precategories public -open import category-theory.pseudomonic-functors-precategories public -open import category-theory.pullbacks-in-precategories public -open import category-theory.replete-subprecategories public -open import category-theory.representable-functors-categories public -open import category-theory.representable-functors-large-precategories public -open import category-theory.representable-functors-precategories public -open import category-theory.representing-arrow-category public -open import category-theory.restrictions-functors-cores-precategories public -open import category-theory.right-extensions-precategories public -open import category-theory.right-kan-extensions-precategories public -open import category-theory.rigid-objects-categories public -open import category-theory.rigid-objects-precategories public -open import category-theory.set-magmoids public -open import category-theory.sieves-in-categories public -open import category-theory.simplex-category public -open import category-theory.slice-precategories public -open import category-theory.split-essentially-surjective-functors-precategories public -open import category-theory.strict-categories public -open import category-theory.strongly-preunivalent-categories public -open import category-theory.structure-equivalences-set-magmoids public -open import category-theory.subcategories public -open import category-theory.subprecategories public -open import category-theory.subterminal-precategories public -open import category-theory.terminal-category public -open import category-theory.terminal-objects-precategories public -open import category-theory.wide-subcategories public -open import category-theory.wide-subprecategories public -open import category-theory.yoneda-lemma-categories public -open import category-theory.yoneda-lemma-precategories public +module category-theory + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where + +open import category-theory.adjunctions-large-categories funext univalence truncations public +open import category-theory.adjunctions-large-precategories funext univalence truncations public +open import category-theory.anafunctors-categories funext univalence truncations public +open import category-theory.anafunctors-precategories funext univalence truncations public +open import category-theory.augmented-simplex-category funext univalence truncations public +open import category-theory.categories funext univalence truncations public +open import category-theory.category-of-functors funext univalence truncations public +open import category-theory.category-of-functors-from-small-to-large-categories funext univalence truncations public +open import category-theory.category-of-maps-categories funext univalence truncations public +open import category-theory.category-of-maps-from-small-to-large-categories funext univalence truncations public +open import category-theory.commuting-squares-of-morphisms-in-large-precategories funext univalence truncations public +open import category-theory.commuting-squares-of-morphisms-in-precategories funext univalence truncations public +open import category-theory.commuting-squares-of-morphisms-in-set-magmoids funext univalence truncations public +open import category-theory.commuting-triangles-of-morphisms-in-precategories funext univalence truncations public +open import category-theory.commuting-triangles-of-morphisms-in-set-magmoids funext univalence truncations public +open import category-theory.complete-precategories funext univalence truncations public +open import category-theory.composition-operations-on-binary-families-of-sets funext univalence truncations public +open import category-theory.cones-precategories funext univalence truncations public +open import category-theory.conservative-functors-precategories funext univalence truncations public +open import category-theory.constant-functors funext univalence truncations public +open import category-theory.copresheaf-categories funext univalence truncations public +open import category-theory.coproducts-in-precategories funext univalence truncations public +open import category-theory.cores-categories funext univalence truncations public +open import category-theory.cores-precategories funext univalence truncations public +open import category-theory.coslice-precategories funext univalence truncations public +open import category-theory.dependent-composition-operations-over-precategories funext univalence truncations public +open import category-theory.dependent-products-of-categories funext univalence truncations public +open import category-theory.dependent-products-of-large-categories funext univalence truncations public +open import category-theory.dependent-products-of-large-precategories funext univalence truncations public +open import category-theory.dependent-products-of-precategories funext univalence truncations public +open import category-theory.discrete-categories funext univalence truncations public +open import category-theory.displayed-precategories funext univalence truncations public +open import category-theory.embedding-maps-precategories funext univalence truncations public +open import category-theory.embeddings-precategories funext univalence truncations public +open import category-theory.endomorphisms-in-categories funext univalence truncations public +open import category-theory.endomorphisms-in-precategories funext univalence truncations public +open import category-theory.epimorphisms-in-large-precategories funext univalence truncations public +open import category-theory.equivalences-of-categories funext univalence truncations public +open import category-theory.equivalences-of-large-precategories funext univalence truncations public +open import category-theory.equivalences-of-precategories funext univalence truncations public +open import category-theory.essential-fibers-of-functors-precategories funext univalence truncations public +open import category-theory.essentially-injective-functors-precategories funext univalence truncations public +open import category-theory.essentially-surjective-functors-precategories funext univalence truncations public +open import category-theory.exponential-objects-precategories funext univalence truncations public +open import category-theory.extensions-of-functors-precategories funext univalence truncations public +open import category-theory.faithful-functors-precategories funext univalence truncations public +open import category-theory.faithful-maps-precategories funext univalence truncations public +open import category-theory.full-functors-precategories funext univalence truncations public +open import category-theory.full-large-subcategories funext univalence truncations public +open import category-theory.full-large-subprecategories funext univalence truncations public +open import category-theory.full-maps-precategories funext univalence truncations public +open import category-theory.full-subcategories funext univalence truncations public +open import category-theory.full-subprecategories funext univalence truncations public +open import category-theory.fully-faithful-functors-precategories funext univalence truncations public +open import category-theory.fully-faithful-maps-precategories funext univalence truncations public +open import category-theory.function-categories funext univalence truncations public +open import category-theory.function-precategories funext univalence truncations public +open import category-theory.functors-categories funext univalence truncations public +open import category-theory.functors-from-small-to-large-categories funext univalence truncations public +open import category-theory.functors-from-small-to-large-precategories funext univalence truncations public +open import category-theory.functors-large-categories funext univalence truncations public +open import category-theory.functors-large-precategories funext univalence truncations public +open import category-theory.functors-nonunital-precategories funext univalence truncations public +open import category-theory.functors-precategories funext univalence truncations public +open import category-theory.functors-set-magmoids funext univalence truncations public +open import category-theory.gaunt-categories funext univalence truncations public +open import category-theory.groupoids funext univalence truncations public +open import category-theory.homotopies-natural-transformations-large-precategories funext univalence truncations public +open import category-theory.indiscrete-precategories funext univalence truncations public +open import category-theory.initial-category funext univalence truncations public +open import category-theory.initial-objects-large-categories funext univalence truncations public +open import category-theory.initial-objects-large-precategories funext univalence truncations public +open import category-theory.initial-objects-precategories funext univalence truncations public +open import category-theory.isomorphism-induction-categories funext univalence truncations public +open import category-theory.isomorphism-induction-precategories funext univalence truncations public +open import category-theory.isomorphisms-in-categories funext univalence truncations public +open import category-theory.isomorphisms-in-large-categories funext univalence truncations public +open import category-theory.isomorphisms-in-large-precategories funext univalence truncations public +open import category-theory.isomorphisms-in-precategories funext univalence truncations public +open import category-theory.isomorphisms-in-subprecategories funext univalence truncations public +open import category-theory.large-categories funext univalence truncations public +open import category-theory.large-function-categories funext univalence truncations public +open import category-theory.large-function-precategories funext univalence truncations public +open import category-theory.large-precategories funext univalence truncations public +open import category-theory.large-subcategories funext univalence truncations public +open import category-theory.large-subprecategories funext univalence truncations public +open import category-theory.limits-precategories funext univalence truncations public +open import category-theory.maps-categories funext univalence truncations public +open import category-theory.maps-from-small-to-large-categories funext univalence truncations public +open import category-theory.maps-from-small-to-large-precategories funext univalence truncations public +open import category-theory.maps-precategories funext univalence truncations public +open import category-theory.maps-set-magmoids funext univalence truncations public +open import category-theory.monads-on-categories funext univalence truncations public +open import category-theory.monads-on-precategories funext univalence truncations public +open import category-theory.monomorphisms-in-large-precategories funext univalence truncations public +open import category-theory.natural-isomorphisms-functors-categories funext univalence truncations public +open import category-theory.natural-isomorphisms-functors-large-precategories funext univalence truncations public +open import category-theory.natural-isomorphisms-functors-precategories funext univalence truncations public +open import category-theory.natural-isomorphisms-maps-categories funext univalence truncations public +open import category-theory.natural-isomorphisms-maps-precategories funext univalence truncations public +open import category-theory.natural-numbers-object-precategories funext univalence truncations public +open import category-theory.natural-transformations-functors-categories funext univalence truncations public +open import category-theory.natural-transformations-functors-from-small-to-large-categories funext univalence truncations public +open import category-theory.natural-transformations-functors-from-small-to-large-precategories funext univalence truncations public +open import category-theory.natural-transformations-functors-large-categories funext univalence truncations public +open import category-theory.natural-transformations-functors-large-precategories funext univalence truncations public +open import category-theory.natural-transformations-functors-precategories funext univalence truncations public +open import category-theory.natural-transformations-maps-categories funext univalence truncations public +open import category-theory.natural-transformations-maps-from-small-to-large-precategories funext univalence truncations public +open import category-theory.natural-transformations-maps-precategories funext univalence truncations public +open import category-theory.nonunital-precategories funext univalence truncations public +open import category-theory.one-object-precategories funext univalence truncations public +open import category-theory.opposite-categories funext univalence truncations public +open import category-theory.opposite-large-precategories funext univalence truncations public +open import category-theory.opposite-precategories funext univalence truncations public +open import category-theory.opposite-preunivalent-categories funext univalence truncations public +open import category-theory.opposite-strongly-preunivalent-categories funext univalence truncations public +open import category-theory.pointed-endofunctors-categories funext univalence truncations public +open import category-theory.pointed-endofunctors-precategories funext univalence truncations public +open import category-theory.precategories funext univalence truncations public +open import category-theory.precategory-of-elements-of-a-presheaf funext univalence truncations public +open import category-theory.precategory-of-functors funext univalence truncations public +open import category-theory.precategory-of-functors-from-small-to-large-precategories funext univalence truncations public +open import category-theory.precategory-of-maps-from-small-to-large-precategories funext univalence truncations public +open import category-theory.precategory-of-maps-precategories funext univalence truncations public +open import category-theory.pregroupoids funext univalence truncations public +open import category-theory.presheaf-categories funext univalence truncations public +open import category-theory.preunivalent-categories funext univalence truncations public +open import category-theory.products-in-precategories funext univalence truncations public +open import category-theory.products-of-precategories funext univalence truncations public +open import category-theory.pseudomonic-functors-precategories funext univalence truncations public +open import category-theory.pullbacks-in-precategories funext univalence truncations public +open import category-theory.replete-subprecategories funext univalence truncations public +open import category-theory.representable-functors-categories funext univalence truncations public +open import category-theory.representable-functors-large-precategories funext univalence truncations public +open import category-theory.representable-functors-precategories funext univalence truncations public +open import category-theory.representing-arrow-category funext univalence truncations public +open import category-theory.restrictions-functors-cores-precategories funext univalence truncations public +open import category-theory.right-extensions-precategories funext univalence truncations public +open import category-theory.right-kan-extensions-precategories funext univalence truncations public +open import category-theory.rigid-objects-categories funext univalence truncations public +open import category-theory.rigid-objects-precategories funext univalence truncations public +open import category-theory.set-magmoids funext univalence truncations public +open import category-theory.sieves-in-categories funext univalence truncations public +open import category-theory.simplex-category funext univalence truncations public +open import category-theory.slice-precategories funext univalence truncations public +open import category-theory.split-essentially-surjective-functors-precategories funext univalence truncations public +open import category-theory.strict-categories funext univalence truncations public +open import category-theory.strongly-preunivalent-categories funext univalence truncations public +open import category-theory.structure-equivalences-set-magmoids funext univalence truncations public +open import category-theory.subcategories funext univalence truncations public +open import category-theory.subprecategories funext univalence truncations public +open import category-theory.subterminal-precategories funext univalence truncations public +open import category-theory.terminal-category funext univalence truncations public +open import category-theory.terminal-objects-precategories funext univalence truncations public +open import category-theory.wide-subcategories funext univalence truncations public +open import category-theory.wide-subprecategories funext univalence truncations public +open import category-theory.yoneda-lemma-categories funext univalence truncations public +open import category-theory.yoneda-lemma-precategories funext univalence truncations public ``` diff --git a/src/category-theory/adjunctions-large-categories.lagda.md b/src/category-theory/adjunctions-large-categories.lagda.md index a8adbd3bcd..9f3251c0f4 100644 --- a/src/category-theory/adjunctions-large-categories.lagda.md +++ b/src/category-theory/adjunctions-large-categories.lagda.md @@ -1,20 +1,28 @@ # Adjunctions between large categories ```agda -module category-theory.adjunctions-large-categories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.adjunctions-large-categories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.adjunctions-large-precategories -open import category-theory.functors-large-categories -open import category-theory.large-categories -open import category-theory.natural-transformations-functors-large-categories - -open import foundation.commuting-squares-of-maps -open import foundation.equivalences -open import foundation.identity-types +open import category-theory.adjunctions-large-precategories funext univalence truncations +open import category-theory.functors-large-categories funext univalence truncations +open import category-theory.large-categories funext univalence truncations +open import category-theory.natural-transformations-functors-large-categories funext univalence truncations + +open import foundation.commuting-squares-of-maps funext univalence +open import foundation.equivalences funext +open import foundation.identity-types funext open import foundation.universe-levels ``` diff --git a/src/category-theory/adjunctions-large-precategories.lagda.md b/src/category-theory/adjunctions-large-precategories.lagda.md index ac473c743e..13aaaa79e1 100644 --- a/src/category-theory/adjunctions-large-precategories.lagda.md +++ b/src/category-theory/adjunctions-large-precategories.lagda.md @@ -1,20 +1,28 @@ # Adjunctions between large precategories ```agda -module category-theory.adjunctions-large-precategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.adjunctions-large-precategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.functors-large-precategories -open import category-theory.large-precategories -open import category-theory.natural-transformations-functors-large-precategories +open import category-theory.functors-large-precategories funext univalence truncations +open import category-theory.large-precategories funext univalence truncations +open import category-theory.natural-transformations-functors-large-precategories funext univalence truncations open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-maps -open import foundation.equivalences -open import foundation.identity-types +open import foundation.commuting-squares-of-maps funext univalence +open import foundation.equivalences funext +open import foundation.identity-types funext open import foundation.universe-levels ``` diff --git a/src/category-theory/anafunctors-categories.lagda.md b/src/category-theory/anafunctors-categories.lagda.md index 447086f3eb..dc7da699db 100644 --- a/src/category-theory/anafunctors-categories.lagda.md +++ b/src/category-theory/anafunctors-categories.lagda.md @@ -1,18 +1,26 @@ # Anafunctors between categories ```agda -module category-theory.anafunctors-categories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.anafunctors-categories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.anafunctors-precategories -open import category-theory.categories -open import category-theory.functors-categories +open import category-theory.anafunctors-precategories funext univalence truncations +open import category-theory.categories funext univalence truncations +open import category-theory.functors-categories funext univalence truncations open import foundation.dependent-pair-types -open import foundation.propositional-truncations +open import foundation.propositional-truncations funext univalence open import foundation.universe-levels ``` diff --git a/src/category-theory/anafunctors-precategories.lagda.md b/src/category-theory/anafunctors-precategories.lagda.md index 105714a8a5..277393097c 100644 --- a/src/category-theory/anafunctors-precategories.lagda.md +++ b/src/category-theory/anafunctors-precategories.lagda.md @@ -1,21 +1,29 @@ # Anafunctors between precategories ```agda -module category-theory.anafunctors-precategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.anafunctors-precategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.functors-precategories -open import category-theory.isomorphisms-in-precategories -open import category-theory.precategories +open import category-theory.functors-precategories funext univalence truncations +open import category-theory.isomorphisms-in-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.propositional-truncations +open import foundation.identity-types funext +open import foundation.propositional-truncations funext univalence open import foundation.universe-levels ``` diff --git a/src/category-theory/augmented-simplex-category.lagda.md b/src/category-theory/augmented-simplex-category.lagda.md index 9c59e0e7b2..3c2ada651f 100644 --- a/src/category-theory/augmented-simplex-category.lagda.md +++ b/src/category-theory/augmented-simplex-category.lagda.md @@ -1,25 +1,33 @@ # The augmented simplex category ```agda -module category-theory.augmented-simplex-category where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.augmented-simplex-category + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.composition-operations-on-binary-families-of-sets -open import category-theory.precategories +open import category-theory.composition-operations-on-binary-families-of-sets funext univalence truncations +open import category-theory.precategories funext univalence truncations -open import elementary-number-theory.inequality-standard-finite-types +open import elementary-number-theory.inequality-standard-finite-types funext univalence truncations open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.sets -open import foundation.strictly-involutive-identity-types +open import foundation.identity-types funext +open import foundation.sets funext univalence +open import foundation.strictly-involutive-identity-types funext univalence open import foundation.universe-levels -open import order-theory.order-preserving-maps-posets +open import order-theory.order-preserving-maps-posets funext univalence truncations ```
diff --git a/src/category-theory/categories.lagda.md b/src/category-theory/categories.lagda.md index 42f12c7076..7ef9630274 100644 --- a/src/category-theory/categories.lagda.md +++ b/src/category-theory/categories.lagda.md @@ -1,30 +1,39 @@ # Categories ```agda -module category-theory.categories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.categories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.composition-operations-on-binary-families-of-sets -open import category-theory.isomorphisms-in-precategories -open import category-theory.nonunital-precategories -open import category-theory.precategories -open import category-theory.preunivalent-categories -open import category-theory.strongly-preunivalent-categories - -open import foundation.1-types -open import foundation.cartesian-product-types +open import category-theory.composition-operations-on-binary-families-of-sets funext univalence truncations +open import category-theory.isomorphisms-in-precategories funext univalence truncations +open import category-theory.nonunital-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations +open import category-theory.preunivalent-categories funext univalence truncations +open import category-theory.strongly-preunivalent-categories funext univalence truncations + +open import foundation.1-types funext univalence +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.propositions -open import foundation.sets -open import foundation.strictly-involutive-identity-types -open import foundation.surjective-maps +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.strictly-involutive-identity-types funext univalence +open import foundation.surjective-maps funext univalence truncations open import foundation.universe-levels ``` diff --git a/src/category-theory/category-of-functors-from-small-to-large-categories.lagda.md b/src/category-theory/category-of-functors-from-small-to-large-categories.lagda.md index a79a1fe316..3227ea7ced 100644 --- a/src/category-theory/category-of-functors-from-small-to-large-categories.lagda.md +++ b/src/category-theory/category-of-functors-from-small-to-large-categories.lagda.md @@ -1,27 +1,35 @@ # The category of functors and natural transformations from small to large categories ```agda -module category-theory.category-of-functors-from-small-to-large-categories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.category-of-functors-from-small-to-large-categories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.category-of-functors -open import category-theory.functors-from-small-to-large-categories -open import category-theory.functors-from-small-to-large-precategories -open import category-theory.isomorphisms-in-large-precategories -open import category-theory.isomorphisms-in-precategories -open import category-theory.large-categories -open import category-theory.large-precategories -open import category-theory.natural-isomorphisms-functors-categories -open import category-theory.natural-isomorphisms-functors-precategories -open import category-theory.precategories -open import category-theory.precategory-of-functors-from-small-to-large-precategories - -open import foundation.equivalences -open import foundation.identity-types +open import category-theory.categories funext univalence truncations +open import category-theory.category-of-functors funext univalence truncations +open import category-theory.functors-from-small-to-large-categories funext univalence truncations +open import category-theory.functors-from-small-to-large-precategories funext univalence truncations +open import category-theory.isomorphisms-in-large-precategories funext univalence truncations +open import category-theory.isomorphisms-in-precategories funext univalence truncations +open import category-theory.large-categories funext univalence truncations +open import category-theory.large-precategories funext univalence truncations +open import category-theory.natural-isomorphisms-functors-categories funext univalence truncations +open import category-theory.natural-isomorphisms-functors-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations +open import category-theory.precategory-of-functors-from-small-to-large-precategories funext univalence truncations + +open import foundation.equivalences funext +open import foundation.identity-types funext open import foundation.universe-levels ``` diff --git a/src/category-theory/category-of-functors.lagda.md b/src/category-theory/category-of-functors.lagda.md index c2486d1ff0..56c1d90afa 100644 --- a/src/category-theory/category-of-functors.lagda.md +++ b/src/category-theory/category-of-functors.lagda.md @@ -1,25 +1,33 @@ # The category of functors and natural transformations between two categories ```agda -module category-theory.category-of-functors where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.category-of-functors + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.category-of-maps-categories -open import category-theory.functors-categories -open import category-theory.functors-precategories -open import category-theory.isomorphisms-in-categories -open import category-theory.natural-isomorphisms-functors-categories -open import category-theory.natural-isomorphisms-functors-precategories -open import category-theory.precategories -open import category-theory.precategory-of-functors +open import category-theory.categories funext univalence truncations +open import category-theory.category-of-maps-categories funext univalence truncations +open import category-theory.functors-categories funext univalence truncations +open import category-theory.functors-precategories funext univalence truncations +open import category-theory.isomorphisms-in-categories funext univalence truncations +open import category-theory.natural-isomorphisms-functors-categories funext univalence truncations +open import category-theory.natural-isomorphisms-functors-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations +open import category-theory.precategory-of-functors funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.identity-types +open import foundation.equivalences funext +open import foundation.identity-types funext open import foundation.universe-levels ``` diff --git a/src/category-theory/category-of-maps-categories.lagda.md b/src/category-theory/category-of-maps-categories.lagda.md index 1226b6f854..03d2b4aba1 100644 --- a/src/category-theory/category-of-maps-categories.lagda.md +++ b/src/category-theory/category-of-maps-categories.lagda.md @@ -1,34 +1,42 @@ # The category of maps and natural transformations between two categories ```agda -module category-theory.category-of-maps-categories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.category-of-maps-categories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.commuting-squares-of-morphisms-in-precategories -open import category-theory.isomorphisms-in-categories -open import category-theory.isomorphisms-in-precategories -open import category-theory.maps-categories -open import category-theory.maps-precategories -open import category-theory.natural-isomorphisms-maps-categories -open import category-theory.natural-isomorphisms-maps-precategories -open import category-theory.natural-transformations-maps-precategories -open import category-theory.precategories -open import category-theory.precategory-of-maps-precategories +open import category-theory.categories funext univalence truncations +open import category-theory.commuting-squares-of-morphisms-in-precategories funext univalence truncations +open import category-theory.isomorphisms-in-categories funext univalence truncations +open import category-theory.isomorphisms-in-precategories funext univalence truncations +open import category-theory.maps-categories funext univalence truncations +open import category-theory.maps-precategories funext univalence truncations +open import category-theory.natural-isomorphisms-maps-categories funext univalence truncations +open import category-theory.natural-isomorphisms-maps-precategories funext univalence truncations +open import category-theory.natural-transformations-maps-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations +open import category-theory.precategory-of-maps-precategories funext univalence truncations open import foundation.action-on-identifications-binary-functions open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.identity-types +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-function-types funext univalence +open import foundation.functoriality-dependent-pair-types funext +open import foundation.identity-types funext open import foundation.type-arithmetic-dependent-pair-types -open import foundation.type-theoretic-principle-of-choice -open import foundation.univalence +open import foundation.type-theoretic-principle-of-choice funext +open import foundation.univalence funext univalence open import foundation.universe-levels ``` diff --git a/src/category-theory/category-of-maps-from-small-to-large-categories.lagda.md b/src/category-theory/category-of-maps-from-small-to-large-categories.lagda.md index bf67d50b0e..7f30c1716a 100644 --- a/src/category-theory/category-of-maps-from-small-to-large-categories.lagda.md +++ b/src/category-theory/category-of-maps-from-small-to-large-categories.lagda.md @@ -1,27 +1,35 @@ # The category of maps and natural transformations from small to large categories ```agda -module category-theory.category-of-maps-from-small-to-large-categories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.category-of-maps-from-small-to-large-categories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.category-of-maps-categories -open import category-theory.isomorphisms-in-large-precategories -open import category-theory.isomorphisms-in-precategories -open import category-theory.large-categories -open import category-theory.large-precategories -open import category-theory.maps-from-small-to-large-categories -open import category-theory.maps-from-small-to-large-precategories -open import category-theory.natural-isomorphisms-maps-categories -open import category-theory.natural-isomorphisms-maps-precategories -open import category-theory.precategories -open import category-theory.precategory-of-maps-from-small-to-large-precategories - -open import foundation.equivalences -open import foundation.identity-types +open import category-theory.categories funext univalence truncations +open import category-theory.category-of-maps-categories funext univalence truncations +open import category-theory.isomorphisms-in-large-precategories funext univalence truncations +open import category-theory.isomorphisms-in-precategories funext univalence truncations +open import category-theory.large-categories funext univalence truncations +open import category-theory.large-precategories funext univalence truncations +open import category-theory.maps-from-small-to-large-categories funext univalence truncations +open import category-theory.maps-from-small-to-large-precategories funext univalence truncations +open import category-theory.natural-isomorphisms-maps-categories funext univalence truncations +open import category-theory.natural-isomorphisms-maps-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations +open import category-theory.precategory-of-maps-from-small-to-large-precategories funext univalence truncations + +open import foundation.equivalences funext +open import foundation.identity-types funext open import foundation.universe-levels ``` diff --git a/src/category-theory/commuting-squares-of-morphisms-in-large-precategories.lagda.md b/src/category-theory/commuting-squares-of-morphisms-in-large-precategories.lagda.md index 3e6f636e0b..c53ba8c67c 100644 --- a/src/category-theory/commuting-squares-of-morphisms-in-large-precategories.lagda.md +++ b/src/category-theory/commuting-squares-of-morphisms-in-large-precategories.lagda.md @@ -1,15 +1,23 @@ # Commuting squares of morphisms in large precategories ```agda -module category-theory.commuting-squares-of-morphisms-in-large-precategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.commuting-squares-of-morphisms-in-large-precategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.large-precategories +open import category-theory.large-precategories funext univalence truncations -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels ``` diff --git a/src/category-theory/commuting-squares-of-morphisms-in-precategories.lagda.md b/src/category-theory/commuting-squares-of-morphisms-in-precategories.lagda.md index 9fce14c311..27a3a0e907 100644 --- a/src/category-theory/commuting-squares-of-morphisms-in-precategories.lagda.md +++ b/src/category-theory/commuting-squares-of-morphisms-in-precategories.lagda.md @@ -1,14 +1,22 @@ # Commuting squares of morphisms in precategories ```agda -module category-theory.commuting-squares-of-morphisms-in-precategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.commuting-squares-of-morphisms-in-precategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.commuting-squares-of-morphisms-in-set-magmoids -open import category-theory.precategories +open import category-theory.commuting-squares-of-morphisms-in-set-magmoids funext univalence truncations +open import category-theory.precategories funext univalence truncations open import foundation.universe-levels ``` diff --git a/src/category-theory/commuting-squares-of-morphisms-in-set-magmoids.lagda.md b/src/category-theory/commuting-squares-of-morphisms-in-set-magmoids.lagda.md index 9bcce6ed57..ade3147c44 100644 --- a/src/category-theory/commuting-squares-of-morphisms-in-set-magmoids.lagda.md +++ b/src/category-theory/commuting-squares-of-morphisms-in-set-magmoids.lagda.md @@ -1,15 +1,23 @@ # Commuting squares of morphisms in set-magmoids ```agda -module category-theory.commuting-squares-of-morphisms-in-set-magmoids where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.commuting-squares-of-morphisms-in-set-magmoids + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.set-magmoids +open import category-theory.set-magmoids funext univalence truncations -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels ``` diff --git a/src/category-theory/commuting-triangles-of-morphisms-in-precategories.lagda.md b/src/category-theory/commuting-triangles-of-morphisms-in-precategories.lagda.md index 7ba7f47e35..b8c79b6f2c 100644 --- a/src/category-theory/commuting-triangles-of-morphisms-in-precategories.lagda.md +++ b/src/category-theory/commuting-triangles-of-morphisms-in-precategories.lagda.md @@ -1,16 +1,24 @@ # Commuting triangles of morphisms in precategories ```agda -module category-theory.commuting-triangles-of-morphisms-in-precategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.commuting-triangles-of-morphisms-in-precategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.commuting-triangles-of-morphisms-in-set-magmoids -open import category-theory.precategories +open import category-theory.commuting-triangles-of-morphisms-in-set-magmoids funext univalence truncations +open import category-theory.precategories funext univalence truncations -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels ``` diff --git a/src/category-theory/commuting-triangles-of-morphisms-in-set-magmoids.lagda.md b/src/category-theory/commuting-triangles-of-morphisms-in-set-magmoids.lagda.md index 3e43a6c09f..403d2fd79f 100644 --- a/src/category-theory/commuting-triangles-of-morphisms-in-set-magmoids.lagda.md +++ b/src/category-theory/commuting-triangles-of-morphisms-in-set-magmoids.lagda.md @@ -1,15 +1,23 @@ # Commuting triangles of morphisms in set-magmoids ```agda -module category-theory.commuting-triangles-of-morphisms-in-set-magmoids where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.commuting-triangles-of-morphisms-in-set-magmoids + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.set-magmoids +open import category-theory.set-magmoids funext univalence truncations -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels ``` diff --git a/src/category-theory/complete-precategories.lagda.md b/src/category-theory/complete-precategories.lagda.md index aed7151ba7..851243d3db 100644 --- a/src/category-theory/complete-precategories.lagda.md +++ b/src/category-theory/complete-precategories.lagda.md @@ -1,17 +1,25 @@ # Complete precategories ```agda -module category-theory.complete-precategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.complete-precategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.cones-precategories -open import category-theory.functors-precategories -open import category-theory.limits-precategories -open import category-theory.precategories -open import category-theory.terminal-objects-precategories +open import category-theory.cones-precategories funext univalence truncations +open import category-theory.functors-precategories funext univalence truncations +open import category-theory.limits-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations +open import category-theory.terminal-objects-precategories funext univalence truncations open import foundation.universe-levels ``` diff --git a/src/category-theory/composition-operations-on-binary-families-of-sets.lagda.md b/src/category-theory/composition-operations-on-binary-families-of-sets.lagda.md index d4e50dfdf4..c4cb5ca635 100644 --- a/src/category-theory/composition-operations-on-binary-families-of-sets.lagda.md +++ b/src/category-theory/composition-operations-on-binary-families-of-sets.lagda.md @@ -1,21 +1,31 @@ # Composition operations on binary families of sets ```agda -module category-theory.composition-operations-on-binary-families-of-sets where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.composition-operations-on-binary-families-of-sets + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.function-extensionality -open import foundation.identity-types -open import foundation.iterated-dependent-product-types -open import foundation.propositions -open import foundation.sets -open import foundation.strictly-involutive-identity-types -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.function-extensionality funext +open import foundation.identity-types funext +open import foundation.iterated-dependent-product-types funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.strictly-involutive-identity-types funext univalence +open import foundation.subtypes funext univalence truncations +open import foundation.telescopes open import foundation.universe-levels ``` diff --git a/src/category-theory/cones-precategories.lagda.md b/src/category-theory/cones-precategories.lagda.md index 12df81dc10..27c73c810d 100644 --- a/src/category-theory/cones-precategories.lagda.md +++ b/src/category-theory/cones-precategories.lagda.md @@ -1,45 +1,55 @@ # Cones in precategories ```agda -module category-theory.cones-precategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.cones-precategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.commuting-squares-of-morphisms-in-precategories -open import category-theory.commuting-triangles-of-morphisms-in-precategories -open import category-theory.constant-functors -open import category-theory.functors-precategories -open import category-theory.maps-precategories -open import category-theory.natural-transformations-functors-precategories -open import category-theory.precategories -open import category-theory.precategory-of-functors -open import category-theory.right-extensions-precategories -open import category-theory.terminal-category +open import category-theory.commuting-squares-of-morphisms-in-precategories funext univalence truncations +open import category-theory.commuting-triangles-of-morphisms-in-precategories funext univalence truncations +open import category-theory.constant-functors funext univalence truncations +open import category-theory.functors-precategories funext univalence truncations +open import category-theory.maps-precategories funext univalence truncations +open import category-theory.natural-transformations-functors-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations +open import category-theory.precategory-of-functors funext univalence truncations +open import category-theory.right-extensions-precategories funext univalence truncations +open import category-theory.terminal-category funext univalence truncations open import foundation.action-on-identifications-functions -open import foundation.contractible-types -open import foundation.dependent-identifications +open import foundation.contractible-types funext univalence +open import foundation.dependent-identifications funext open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types -open import foundation.equality-dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.functoriality-dependent-function-types -open import foundation.functoriality-dependent-pair-types +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.equality-dependent-function-types funext +open import foundation.equality-dependent-pair-types funext +open import foundation.equivalences funext +open import foundation.function-extensionality funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-function-types funext univalence +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types -open import foundation.multivariable-homotopies -open import foundation.propositions -open import foundation.retractions -open import foundation.sections -open import foundation.sets +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext +open import foundation.multivariable-homotopies funext +open import foundation.propositions funext univalence +open import foundation.retractions funext +open import foundation.sections funext +open import foundation.sets funext univalence open import foundation.structure-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext univalence truncations open import foundation.unit-type open import foundation.universe-levels ``` diff --git a/src/category-theory/conservative-functors-precategories.lagda.md b/src/category-theory/conservative-functors-precategories.lagda.md index bdbd787dcb..f9e4068ef2 100644 --- a/src/category-theory/conservative-functors-precategories.lagda.md +++ b/src/category-theory/conservative-functors-precategories.lagda.md @@ -1,19 +1,29 @@ # Conservative functors between precategories ```agda -module category-theory.conservative-functors-precategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.conservative-functors-precategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.functors-precategories -open import category-theory.isomorphisms-in-precategories -open import category-theory.precategories +open import category-theory.functors-precategories funext univalence truncations +open import category-theory.isomorphisms-in-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations open import foundation.dependent-pair-types -open import foundation.iterated-dependent-product-types -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.iterated-dependent-product-types funext +open import foundation.propositions funext univalence +open import foundation.telescopes open import foundation.universe-levels ``` diff --git a/src/category-theory/constant-functors.lagda.md b/src/category-theory/constant-functors.lagda.md index a07c37b14b..bc2c19c237 100644 --- a/src/category-theory/constant-functors.lagda.md +++ b/src/category-theory/constant-functors.lagda.md @@ -1,28 +1,37 @@ # Constant functors ```agda -module category-theory.constant-functors where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.constant-functors + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.functors-categories -open import category-theory.functors-large-categories -open import category-theory.functors-large-precategories -open import category-theory.functors-precategories -open import category-theory.large-categories -open import category-theory.large-precategories -open import category-theory.natural-transformations-functors-precategories -open import category-theory.precategories -open import category-theory.precategory-of-functors +open import category-theory.categories funext univalence truncations +open import category-theory.functors-categories funext univalence truncations +open import category-theory.functors-large-categories funext univalence truncations +open import category-theory.functors-large-precategories funext univalence truncations +open import category-theory.functors-precategories funext univalence truncations +open import category-theory.large-categories funext univalence truncations +open import category-theory.large-precategories funext univalence truncations +open import category-theory.natural-transformations-functors-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations +open import category-theory.precategory-of-functors funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.equality-dependent-pair-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence open import foundation.universe-levels ``` diff --git a/src/category-theory/copresheaf-categories.lagda.md b/src/category-theory/copresheaf-categories.lagda.md index 2916d3e0b2..609ef343e3 100644 --- a/src/category-theory/copresheaf-categories.lagda.md +++ b/src/category-theory/copresheaf-categories.lagda.md @@ -1,41 +1,52 @@ # Copresheaf categories ```agda -module category-theory.copresheaf-categories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.copresheaf-categories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.category-of-functors-from-small-to-large-categories -open import category-theory.constant-functors -open import category-theory.functors-from-small-to-large-precategories -open import category-theory.functors-precategories -open import category-theory.initial-objects-precategories -open import category-theory.large-categories -open import category-theory.large-precategories -open import category-theory.natural-transformations-functors-from-small-to-large-precategories -open import category-theory.natural-transformations-functors-precategories -open import category-theory.precategories -open import category-theory.precategory-of-functors-from-small-to-large-precategories -open import category-theory.terminal-objects-precategories - -open import foundation.category-of-sets -open import foundation.commuting-squares-of-maps +open import category-theory.categories funext univalence truncations +open import category-theory.category-of-functors-from-small-to-large-categories funext univalence truncations +open import category-theory.constant-functors funext univalence truncations +open import category-theory.functors-from-small-to-large-precategories funext univalence truncations +open import category-theory.functors-precategories funext univalence truncations +open import category-theory.initial-objects-precategories funext univalence truncations +open import category-theory.large-categories funext univalence truncations +open import category-theory.large-precategories funext univalence truncations +open import category-theory.natural-transformations-functors-from-small-to-large-precategories funext univalence truncations +open import category-theory.natural-transformations-functors-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations +open import category-theory.precategory-of-functors-from-small-to-large-precategories funext univalence truncations +open import category-theory.terminal-objects-precategories funext univalence truncations + +open import foundation.category-of-sets funext univalence truncations +open import foundation.commuting-squares-of-maps funext univalence open import foundation.dependent-pair-types -open import foundation.empty-types +open import foundation.dependent-products-propositions funext +open import foundation.empty-types funext univalence truncations open import foundation.equality-cartesian-product-types -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.functoriality-cartesian-product-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.propositions -open import foundation.raising-universe-levels -open import foundation.sets +open import foundation.function-extensionality funext +open import foundation.function-types funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.raising-universe-levels-unit-type +open import foundation.sets funext univalence open import foundation.unit-type open import foundation.universe-levels + +open import foundation-core.raising-universe-levels ```
diff --git a/src/category-theory/coproducts-in-precategories.lagda.md b/src/category-theory/coproducts-in-precategories.lagda.md index cc72f57907..0a2cfee937 100644 --- a/src/category-theory/coproducts-in-precategories.lagda.md +++ b/src/category-theory/coproducts-in-precategories.lagda.md @@ -1,22 +1,33 @@ # Coproducts in precategories ```agda -module category-theory.coproducts-in-precategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.coproducts-in-precategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.precategories +open import category-theory.precategories funext univalence truncations open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types -open import foundation.contractible-types +open import foundation.cartesian-product-types funext univalence +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.iterated-dependent-product-types -open import foundation.propositions -open import foundation.uniqueness-quantification +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.identity-types funext +open import foundation.iterated-dependent-product-types funext +open import foundation.propositions funext univalence +open import foundation.telescopes +open import foundation.uniqueness-quantification funext univalence truncations open import foundation.universe-levels ``` diff --git a/src/category-theory/cores-categories.lagda.md b/src/category-theory/cores-categories.lagda.md index d8577944ab..ccdb29c542 100644 --- a/src/category-theory/cores-categories.lagda.md +++ b/src/category-theory/cores-categories.lagda.md @@ -1,23 +1,31 @@ # Cores of categories ```agda -module category-theory.cores-categories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.cores-categories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.cores-precategories -open import category-theory.groupoids -open import category-theory.isomorphisms-in-categories -open import category-theory.precategories -open import category-theory.pregroupoids -open import category-theory.subcategories -open import category-theory.wide-subcategories +open import category-theory.categories funext univalence truncations +open import category-theory.cores-precategories funext univalence truncations +open import category-theory.groupoids funext univalence truncations +open import category-theory.isomorphisms-in-categories funext univalence truncations +open import category-theory.precategories funext univalence truncations +open import category-theory.pregroupoids funext univalence truncations +open import category-theory.subcategories funext univalence truncations +open import category-theory.wide-subcategories funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalences +open import foundation.equivalences funext open import foundation.universe-levels ``` diff --git a/src/category-theory/cores-precategories.lagda.md b/src/category-theory/cores-precategories.lagda.md index 210c08f99c..66a4660fcb 100644 --- a/src/category-theory/cores-precategories.lagda.md +++ b/src/category-theory/cores-precategories.lagda.md @@ -1,28 +1,37 @@ # Cores of precategories ```agda -module category-theory.cores-precategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.cores-precategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.isomorphisms-in-categories -open import category-theory.isomorphisms-in-precategories -open import category-theory.precategories -open import category-theory.pregroupoids -open import category-theory.replete-subprecategories -open import category-theory.subprecategories -open import category-theory.wide-subprecategories - -open import foundation.contractible-types +open import category-theory.categories funext univalence truncations +open import category-theory.isomorphisms-in-categories funext univalence truncations +open import category-theory.isomorphisms-in-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations +open import category-theory.pregroupoids funext univalence truncations +open import category-theory.replete-subprecategories funext univalence truncations +open import category-theory.subprecategories funext univalence truncations +open import category-theory.wide-subprecategories funext univalence truncations + +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.functoriality-dependent-pair-types +open import foundation.dependent-products-contractible-types funext +open import foundation.equivalences funext +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.subtypes -open import foundation.torsorial-type-families +open import foundation.subtypes funext univalence truncations +open import foundation.torsorial-type-families funext univalence truncations open import foundation.unit-type open import foundation.universe-levels ``` diff --git a/src/category-theory/coslice-precategories.lagda.md b/src/category-theory/coslice-precategories.lagda.md index b47a0de89f..4d05df3b5c 100644 --- a/src/category-theory/coslice-precategories.lagda.md +++ b/src/category-theory/coslice-precategories.lagda.md @@ -1,16 +1,24 @@ # Coslice precategories ```agda -module category-theory.coslice-precategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.coslice-precategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.functors-precategories -open import category-theory.opposite-precategories -open import category-theory.precategories -open import category-theory.slice-precategories +open import category-theory.functors-precategories funext univalence truncations +open import category-theory.opposite-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations +open import category-theory.slice-precategories funext univalence truncations open import foundation.universe-levels ``` diff --git a/src/category-theory/dependent-composition-operations-over-precategories.lagda.md b/src/category-theory/dependent-composition-operations-over-precategories.lagda.md index 8f663b706e..86017b5a51 100644 --- a/src/category-theory/dependent-composition-operations-over-precategories.lagda.md +++ b/src/category-theory/dependent-composition-operations-over-precategories.lagda.md @@ -1,27 +1,38 @@ # Dependent composition operations over precategories ```agda -module category-theory.dependent-composition-operations-over-precategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.dependent-composition-operations-over-precategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.composition-operations-on-binary-families-of-sets -open import category-theory.nonunital-precategories -open import category-theory.precategories -open import category-theory.set-magmoids +open import category-theory.composition-operations-on-binary-families-of-sets funext univalence truncations +open import category-theory.nonunital-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations +open import category-theory.set-magmoids funext univalence truncations -open import foundation.cartesian-product-types -open import foundation.dependent-identifications +open import foundation.cartesian-product-types funext univalence +open import foundation.dependent-identifications funext open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.identity-types -open import foundation.iterated-dependent-product-types -open import foundation.propositions -open import foundation.sets +open import foundation.dependent-products-propositions funext +open import foundation.dependent-products-truncated-types funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.iterated-dependent-product-types funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.telescopes open import foundation.transport-along-identifications -open import foundation.truncated-types +open import foundation.truncated-types funext univalence open import foundation.truncation-levels open import foundation.universe-levels ``` diff --git a/src/category-theory/dependent-products-of-categories.lagda.md b/src/category-theory/dependent-products-of-categories.lagda.md index 64742bf6c0..2853836d22 100644 --- a/src/category-theory/dependent-products-of-categories.lagda.md +++ b/src/category-theory/dependent-products-of-categories.lagda.md @@ -1,26 +1,34 @@ # Dependent products of categories ```agda -module category-theory.dependent-products-of-categories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.dependent-products-of-categories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.composition-operations-on-binary-families-of-sets -open import category-theory.dependent-products-of-precategories -open import category-theory.isomorphisms-in-categories -open import category-theory.precategories +open import category-theory.categories funext univalence truncations +open import category-theory.composition-operations-on-binary-families-of-sets funext univalence truncations +open import category-theory.dependent-products-of-precategories funext univalence truncations +open import category-theory.isomorphisms-in-categories funext univalence truncations +open import category-theory.precategories funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.functoriality-dependent-function-types -open import foundation.identity-types -open import foundation.sets -open import foundation.strictly-involutive-identity-types +open import foundation.equivalences funext +open import foundation.function-extensionality funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-function-types funext univalence +open import foundation.identity-types funext +open import foundation.sets funext univalence +open import foundation.strictly-involutive-identity-types funext univalence open import foundation.universe-levels ``` diff --git a/src/category-theory/dependent-products-of-large-categories.lagda.md b/src/category-theory/dependent-products-of-large-categories.lagda.md index d674d884ab..f2aa1e7be3 100644 --- a/src/category-theory/dependent-products-of-large-categories.lagda.md +++ b/src/category-theory/dependent-products-of-large-categories.lagda.md @@ -1,23 +1,31 @@ # Dependent products of large categories ```agda -module category-theory.dependent-products-of-large-categories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.dependent-products-of-large-categories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.dependent-products-of-large-precategories -open import category-theory.isomorphisms-in-large-categories -open import category-theory.large-categories -open import category-theory.large-precategories - -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.functoriality-dependent-function-types -open import foundation.identity-types -open import foundation.sets -open import foundation.strictly-involutive-identity-types +open import category-theory.dependent-products-of-large-precategories funext univalence truncations +open import category-theory.isomorphisms-in-large-categories funext univalence truncations +open import category-theory.large-categories funext univalence truncations +open import category-theory.large-precategories funext univalence truncations + +open import foundation.equivalences funext +open import foundation.function-extensionality funext +open import foundation.functoriality-dependent-function-types funext univalence +open import foundation.identity-types funext +open import foundation.sets funext univalence +open import foundation.strictly-involutive-identity-types funext univalence open import foundation.universe-levels ``` diff --git a/src/category-theory/dependent-products-of-large-precategories.lagda.md b/src/category-theory/dependent-products-of-large-precategories.lagda.md index eacb31a0b5..bde26f1067 100644 --- a/src/category-theory/dependent-products-of-large-precategories.lagda.md +++ b/src/category-theory/dependent-products-of-large-precategories.lagda.md @@ -1,24 +1,33 @@ # Dependent products of large precategories ```agda -module category-theory.dependent-products-of-large-precategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.dependent-products-of-large-precategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.isomorphisms-in-large-precategories -open import category-theory.large-precategories +open import category-theory.isomorphisms-in-large-precategories funext univalence truncations +open import category-theory.large-precategories funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.propositions -open import foundation.sets -open import foundation.strictly-involutive-identity-types -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.function-extensionality funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.strictly-involutive-identity-types funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels ``` diff --git a/src/category-theory/dependent-products-of-precategories.lagda.md b/src/category-theory/dependent-products-of-precategories.lagda.md index 4ee2a1858a..840f52216c 100644 --- a/src/category-theory/dependent-products-of-precategories.lagda.md +++ b/src/category-theory/dependent-products-of-precategories.lagda.md @@ -1,25 +1,34 @@ # Dependent products of precategories ```agda -module category-theory.dependent-products-of-precategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.dependent-products-of-precategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.composition-operations-on-binary-families-of-sets -open import category-theory.isomorphisms-in-precategories -open import category-theory.precategories +open import category-theory.composition-operations-on-binary-families-of-sets funext univalence truncations +open import category-theory.isomorphisms-in-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.propositions -open import foundation.sets -open import foundation.strictly-involutive-identity-types -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.function-extensionality funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.strictly-involutive-identity-types funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels ``` diff --git a/src/category-theory/discrete-categories.lagda.md b/src/category-theory/discrete-categories.lagda.md index f4a10cea33..87a2a89c8a 100644 --- a/src/category-theory/discrete-categories.lagda.md +++ b/src/category-theory/discrete-categories.lagda.md @@ -1,18 +1,26 @@ # Discrete categories ```agda -module category-theory.discrete-categories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.discrete-categories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.precategories +open import category-theory.precategories funext univalence truncations open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.sets -open import foundation.strictly-involutive-identity-types +open import foundation.identity-types funext +open import foundation.sets funext univalence +open import foundation.strictly-involutive-identity-types funext univalence open import foundation.universe-levels ``` diff --git a/src/category-theory/displayed-precategories.lagda.md b/src/category-theory/displayed-precategories.lagda.md index 959ce0871a..0c49646a4f 100644 --- a/src/category-theory/displayed-precategories.lagda.md +++ b/src/category-theory/displayed-precategories.lagda.md @@ -1,31 +1,41 @@ # Displayed precategories ```agda -module category-theory.displayed-precategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.displayed-precategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.composition-operations-on-binary-families-of-sets -open import category-theory.dependent-composition-operations-over-precategories -open import category-theory.nonunital-precategories -open import category-theory.precategories -open import category-theory.set-magmoids - -open import foundation.cartesian-product-types -open import foundation.dependent-identifications +open import category-theory.composition-operations-on-binary-families-of-sets funext univalence truncations +open import category-theory.dependent-composition-operations-over-precategories funext univalence truncations +open import category-theory.nonunital-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations +open import category-theory.set-magmoids funext univalence truncations + +open import foundation.cartesian-product-types funext univalence +open import foundation.dependent-identifications funext open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types -open import foundation.function-types -open import foundation.identity-types -open import foundation.iterated-dependent-product-types -open import foundation.propositions -open import foundation.sets -open import foundation.strictly-involutive-identity-types +open import foundation.dependent-products-propositions funext +open import foundation.dependent-products-truncated-types funext +open import foundation.equality-dependent-pair-types funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.iterated-dependent-product-types funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.strictly-involutive-identity-types funext univalence open import foundation.subsingleton-induction open import foundation.transport-along-identifications -open import foundation.truncated-types +open import foundation.truncated-types funext univalence open import foundation.truncation-levels open import foundation.universe-levels ``` diff --git a/src/category-theory/embedding-maps-precategories.lagda.md b/src/category-theory/embedding-maps-precategories.lagda.md index 469ee2913d..1cbcc44fad 100644 --- a/src/category-theory/embedding-maps-precategories.lagda.md +++ b/src/category-theory/embedding-maps-precategories.lagda.md @@ -1,19 +1,28 @@ # Embedding maps between precategories ```agda -module category-theory.embedding-maps-precategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.embedding-maps-precategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.fully-faithful-maps-precategories -open import category-theory.maps-precategories -open import category-theory.precategories +open import category-theory.fully-faithful-maps-precategories funext univalence truncations +open import category-theory.maps-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.embeddings funext +open import foundation.propositions funext univalence open import foundation.universe-levels ``` diff --git a/src/category-theory/embeddings-precategories.lagda.md b/src/category-theory/embeddings-precategories.lagda.md index 39ffe2e71f..9fa0a07bbb 100644 --- a/src/category-theory/embeddings-precategories.lagda.md +++ b/src/category-theory/embeddings-precategories.lagda.md @@ -1,19 +1,28 @@ # Embeddings between precategories ```agda -module category-theory.embeddings-precategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.embeddings-precategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.embedding-maps-precategories -open import category-theory.functors-precategories -open import category-theory.maps-precategories -open import category-theory.precategories +open import category-theory.embedding-maps-precategories funext univalence truncations +open import category-theory.functors-precategories funext univalence truncations +open import category-theory.maps-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations open import foundation.dependent-pair-types -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.propositions funext univalence open import foundation.universe-levels ``` diff --git a/src/category-theory/endomorphisms-in-categories.lagda.md b/src/category-theory/endomorphisms-in-categories.lagda.md index 91a32f4441..c85c105940 100644 --- a/src/category-theory/endomorphisms-in-categories.lagda.md +++ b/src/category-theory/endomorphisms-in-categories.lagda.md @@ -1,21 +1,29 @@ # Endomorphisms in categories ```agda -module category-theory.endomorphisms-in-categories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.endomorphisms-in-categories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.endomorphisms-in-precategories +open import category-theory.categories funext univalence truncations +open import category-theory.endomorphisms-in-precategories funext univalence truncations -open import foundation.identity-types -open import foundation.sets +open import foundation.identity-types funext +open import foundation.sets funext univalence open import foundation.universe-levels -open import group-theory.monoids -open import group-theory.semigroups +open import group-theory.monoids funext univalence truncations +open import group-theory.semigroups funext univalence ```
diff --git a/src/category-theory/endomorphisms-in-precategories.lagda.md b/src/category-theory/endomorphisms-in-precategories.lagda.md index 75cac02bde..1c6bcec832 100644 --- a/src/category-theory/endomorphisms-in-precategories.lagda.md +++ b/src/category-theory/endomorphisms-in-precategories.lagda.md @@ -1,21 +1,29 @@ # Endomorphisms in precategories ```agda -module category-theory.endomorphisms-in-precategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.endomorphisms-in-precategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.precategories +open import category-theory.precategories funext univalence truncations open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.sets +open import foundation.identity-types funext +open import foundation.sets funext univalence open import foundation.universe-levels -open import group-theory.monoids -open import group-theory.semigroups +open import group-theory.monoids funext univalence truncations +open import group-theory.semigroups funext univalence ```
diff --git a/src/category-theory/epimorphisms-in-large-precategories.lagda.md b/src/category-theory/epimorphisms-in-large-precategories.lagda.md index d03cd93b4a..38e6fe8a8a 100644 --- a/src/category-theory/epimorphisms-in-large-precategories.lagda.md +++ b/src/category-theory/epimorphisms-in-large-precategories.lagda.md @@ -1,18 +1,27 @@ # Epimorphism in large precategories ```agda -module category-theory.epimorphisms-in-large-precategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.epimorphisms-in-large-precategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.isomorphisms-in-large-precategories -open import category-theory.large-precategories +open import category-theory.isomorphisms-in-large-precategories funext univalence truncations +open import category-theory.large-precategories funext univalence truncations -open import foundation.embeddings -open import foundation.equivalences -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.propositions funext univalence open import foundation.universe-levels ``` diff --git a/src/category-theory/equivalences-of-categories.lagda.md b/src/category-theory/equivalences-of-categories.lagda.md index 3f49dba3f0..cb349159c7 100644 --- a/src/category-theory/equivalences-of-categories.lagda.md +++ b/src/category-theory/equivalences-of-categories.lagda.md @@ -1,15 +1,23 @@ # Equivalences between categories ```agda -module category-theory.equivalences-of-categories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.equivalences-of-categories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.equivalences-of-precategories -open import category-theory.functors-categories +open import category-theory.categories funext univalence truncations +open import category-theory.equivalences-of-precategories funext univalence truncations +open import category-theory.functors-categories funext univalence truncations open import foundation.universe-levels ``` diff --git a/src/category-theory/equivalences-of-large-precategories.lagda.md b/src/category-theory/equivalences-of-large-precategories.lagda.md index c6dd8e5fb5..3590202e80 100644 --- a/src/category-theory/equivalences-of-large-precategories.lagda.md +++ b/src/category-theory/equivalences-of-large-precategories.lagda.md @@ -1,15 +1,23 @@ # Equivalences between large precategories ```agda -module category-theory.equivalences-of-large-precategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.equivalences-of-large-precategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.functors-large-precategories -open import category-theory.large-precategories -open import category-theory.natural-isomorphisms-functors-large-precategories +open import category-theory.functors-large-precategories funext univalence truncations +open import category-theory.large-precategories funext univalence truncations +open import category-theory.natural-isomorphisms-functors-large-precategories funext univalence truncations open import foundation.universe-levels ``` diff --git a/src/category-theory/equivalences-of-precategories.lagda.md b/src/category-theory/equivalences-of-precategories.lagda.md index 5478d066df..b1826815ce 100644 --- a/src/category-theory/equivalences-of-precategories.lagda.md +++ b/src/category-theory/equivalences-of-precategories.lagda.md @@ -1,17 +1,25 @@ # Equivalences between precategories ```agda -module category-theory.equivalences-of-precategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.equivalences-of-precategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.functors-precategories -open import category-theory.natural-isomorphisms-functors-precategories -open import category-theory.precategories +open import category-theory.functors-precategories funext univalence truncations +open import category-theory.natural-isomorphisms-functors-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types open import foundation.universe-levels ``` diff --git a/src/category-theory/essential-fibers-of-functors-precategories.lagda.md b/src/category-theory/essential-fibers-of-functors-precategories.lagda.md index f0bdaf07fc..a03f04425d 100644 --- a/src/category-theory/essential-fibers-of-functors-precategories.lagda.md +++ b/src/category-theory/essential-fibers-of-functors-precategories.lagda.md @@ -1,15 +1,23 @@ # Essential fibers of functors between precategories ```agda -module category-theory.essential-fibers-of-functors-precategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.essential-fibers-of-functors-precategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.functors-precategories -open import category-theory.isomorphisms-in-precategories -open import category-theory.precategories +open import category-theory.functors-precategories funext univalence truncations +open import category-theory.isomorphisms-in-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations open import foundation.dependent-pair-types open import foundation.universe-levels diff --git a/src/category-theory/essentially-injective-functors-precategories.lagda.md b/src/category-theory/essentially-injective-functors-precategories.lagda.md index db632862bb..965d830085 100644 --- a/src/category-theory/essentially-injective-functors-precategories.lagda.md +++ b/src/category-theory/essentially-injective-functors-precategories.lagda.md @@ -1,15 +1,23 @@ # Essentially injective functors between precategories ```agda -module category-theory.essentially-injective-functors-precategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.essentially-injective-functors-precategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.functors-precategories -open import category-theory.isomorphisms-in-precategories -open import category-theory.precategories +open import category-theory.functors-precategories funext univalence truncations +open import category-theory.isomorphisms-in-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations open import foundation.dependent-pair-types open import foundation.universe-levels diff --git a/src/category-theory/essentially-surjective-functors-precategories.lagda.md b/src/category-theory/essentially-surjective-functors-precategories.lagda.md index da79c73d46..bb3debae6a 100644 --- a/src/category-theory/essentially-surjective-functors-precategories.lagda.md +++ b/src/category-theory/essentially-surjective-functors-precategories.lagda.md @@ -1,19 +1,28 @@ # Essentially surjective functors between precategories ```agda -module category-theory.essentially-surjective-functors-precategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.essentially-surjective-functors-precategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.functors-precategories -open import category-theory.isomorphisms-in-precategories -open import category-theory.precategories +open import category-theory.functors-precategories funext univalence truncations +open import category-theory.isomorphisms-in-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations open import foundation.dependent-pair-types -open import foundation.existential-quantification -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.existential-quantification funext univalence truncations +open import foundation.propositions funext univalence open import foundation.universe-levels ``` diff --git a/src/category-theory/exponential-objects-precategories.lagda.md b/src/category-theory/exponential-objects-precategories.lagda.md index e2fad05451..a4b8663a5c 100644 --- a/src/category-theory/exponential-objects-precategories.lagda.md +++ b/src/category-theory/exponential-objects-precategories.lagda.md @@ -1,19 +1,27 @@ # Exponential objects in precategories ```agda -module category-theory.exponential-objects-precategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.exponential-objects-precategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.precategories -open import category-theory.products-in-precategories +open import category-theory.precategories funext univalence truncations +open import category-theory.products-in-precategories funext univalence truncations open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.uniqueness-quantification +open import foundation.identity-types funext +open import foundation.uniqueness-quantification funext univalence truncations open import foundation.universe-levels ``` diff --git a/src/category-theory/extensions-of-functors-precategories.lagda.md b/src/category-theory/extensions-of-functors-precategories.lagda.md index bf91bbfdb8..1b8f180d1c 100644 --- a/src/category-theory/extensions-of-functors-precategories.lagda.md +++ b/src/category-theory/extensions-of-functors-precategories.lagda.md @@ -1,17 +1,25 @@ # Extensions of functors between precategories ```agda -module category-theory.extensions-of-functors-precategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.extensions-of-functors-precategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.functors-precategories -open import category-theory.precategories +open import category-theory.functors-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels ``` diff --git a/src/category-theory/faithful-functors-precategories.lagda.md b/src/category-theory/faithful-functors-precategories.lagda.md index 8c6ea55099..de686051ac 100644 --- a/src/category-theory/faithful-functors-precategories.lagda.md +++ b/src/category-theory/faithful-functors-precategories.lagda.md @@ -1,22 +1,31 @@ # Faithful functors between precategories ```agda -module category-theory.faithful-functors-precategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.faithful-functors-precategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.faithful-maps-precategories -open import category-theory.functors-precategories -open import category-theory.isomorphisms-in-precategories -open import category-theory.precategories +open import category-theory.faithful-maps-precategories funext univalence truncations +open import category-theory.functors-precategories funext univalence truncations +open import category-theory.isomorphisms-in-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalences -open import foundation.propositions -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.propositions funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels ``` diff --git a/src/category-theory/faithful-maps-precategories.lagda.md b/src/category-theory/faithful-maps-precategories.lagda.md index 69cc0cd483..b7b7327e16 100644 --- a/src/category-theory/faithful-maps-precategories.lagda.md +++ b/src/category-theory/faithful-maps-precategories.lagda.md @@ -1,24 +1,34 @@ # Faithful maps between precategories ```agda -module category-theory.faithful-maps-precategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.faithful-maps-precategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.maps-precategories -open import category-theory.precategories +open import category-theory.maps-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalences -open import foundation.function-types -open import foundation.injective-maps -open import foundation.iterated-dependent-product-types -open import foundation.logical-equivalences -open import foundation.propositions -open import foundation.sets +open import foundation.dependent-products-propositions funext +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.injective-maps funext +open import foundation.iterated-dependent-product-types funext +open import foundation.logical-equivalences funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.telescopes open import foundation.universe-levels ``` diff --git a/src/category-theory/full-functors-precategories.lagda.md b/src/category-theory/full-functors-precategories.lagda.md index 6fcd4a2690..bc35419769 100644 --- a/src/category-theory/full-functors-precategories.lagda.md +++ b/src/category-theory/full-functors-precategories.lagda.md @@ -1,19 +1,28 @@ # Full functors between precategories ```agda -module category-theory.full-functors-precategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.full-functors-precategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.full-maps-precategories -open import category-theory.functors-precategories -open import category-theory.precategories +open import category-theory.full-maps-precategories funext univalence truncations +open import category-theory.functors-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.function-types funext +open import foundation.propositions funext univalence open import foundation.universe-levels ``` diff --git a/src/category-theory/full-large-subcategories.lagda.md b/src/category-theory/full-large-subcategories.lagda.md index 4b96c679d6..b6febca1be 100644 --- a/src/category-theory/full-large-subcategories.lagda.md +++ b/src/category-theory/full-large-subcategories.lagda.md @@ -1,21 +1,30 @@ # Full large subcategories ```agda -module category-theory.full-large-subcategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.full-large-subcategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.full-large-subprecategories -open import category-theory.functors-large-categories -open import category-theory.large-categories -open import category-theory.large-precategories - -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets -open import foundation.strictly-involutive-identity-types +open import category-theory.full-large-subprecategories funext univalence truncations +open import category-theory.functors-large-categories funext univalence truncations +open import category-theory.large-categories funext univalence truncations +open import category-theory.large-precategories funext univalence truncations + +open import foundation.dependent-products-propositions funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.strictly-involutive-identity-types funext univalence open import foundation.universe-levels ``` diff --git a/src/category-theory/full-large-subprecategories.lagda.md b/src/category-theory/full-large-subprecategories.lagda.md index a3789dd83e..59fd8d97ca 100644 --- a/src/category-theory/full-large-subprecategories.lagda.md +++ b/src/category-theory/full-large-subprecategories.lagda.md @@ -1,26 +1,35 @@ # Full large subprecategories ```agda -module category-theory.full-large-subprecategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.full-large-subprecategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.functors-large-precategories -open import category-theory.isomorphisms-in-large-categories -open import category-theory.isomorphisms-in-large-precategories -open import category-theory.large-categories -open import category-theory.large-precategories - -open import foundation.function-types +open import category-theory.functors-large-precategories funext univalence truncations +open import category-theory.isomorphisms-in-large-categories funext univalence truncations +open import category-theory.isomorphisms-in-large-precategories funext univalence truncations +open import category-theory.large-categories funext univalence truncations +open import category-theory.large-precategories funext univalence truncations + +open import foundation.dependent-products-propositions funext +open import foundation.function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets -open import foundation.strictly-involutive-identity-types +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.strictly-involutive-identity-types funext univalence open import foundation.subtype-identity-principle -open import foundation.subtypes +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels ``` diff --git a/src/category-theory/full-maps-precategories.lagda.md b/src/category-theory/full-maps-precategories.lagda.md index 8b9755fe96..60c02c9aff 100644 --- a/src/category-theory/full-maps-precategories.lagda.md +++ b/src/category-theory/full-maps-precategories.lagda.md @@ -1,20 +1,30 @@ # Full maps between precategories ```agda -module category-theory.full-maps-precategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.full-maps-precategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.maps-precategories -open import category-theory.precategories +open import category-theory.maps-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.iterated-dependent-product-types -open import foundation.propositions -open import foundation.surjective-maps +open import foundation.dependent-products-propositions funext +open import foundation.function-types funext +open import foundation.iterated-dependent-product-types funext +open import foundation.propositions funext univalence +open import foundation.surjective-maps funext univalence truncations +open import foundation.telescopes open import foundation.universe-levels ``` diff --git a/src/category-theory/full-subcategories.lagda.md b/src/category-theory/full-subcategories.lagda.md index a1921d9182..1a239ed034 100644 --- a/src/category-theory/full-subcategories.lagda.md +++ b/src/category-theory/full-subcategories.lagda.md @@ -1,28 +1,37 @@ # Full subcategories ```agda -module category-theory.full-subcategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.full-subcategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.composition-operations-on-binary-families-of-sets -open import category-theory.embeddings-precategories -open import category-theory.full-subprecategories -open import category-theory.fully-faithful-functors-precategories -open import category-theory.functors-categories -open import category-theory.maps-categories -open import category-theory.precategories +open import category-theory.categories funext univalence truncations +open import category-theory.composition-operations-on-binary-families-of-sets funext univalence truncations +open import category-theory.embeddings-precategories funext univalence truncations +open import category-theory.full-subprecategories funext univalence truncations +open import category-theory.fully-faithful-functors-precategories funext univalence truncations +open import category-theory.functors-categories funext univalence truncations +open import category-theory.maps-categories funext univalence truncations +open import category-theory.precategories funext univalence truncations open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets -open import foundation.strictly-involutive-identity-types -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.embeddings funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.strictly-involutive-identity-types funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels ``` diff --git a/src/category-theory/full-subprecategories.lagda.md b/src/category-theory/full-subprecategories.lagda.md index 7d2faeebad..e7bd48a80b 100644 --- a/src/category-theory/full-subprecategories.lagda.md +++ b/src/category-theory/full-subprecategories.lagda.md @@ -1,33 +1,42 @@ # Full subprecategories ```agda -module category-theory.full-subprecategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.full-subprecategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.composition-operations-on-binary-families-of-sets -open import category-theory.embeddings-precategories -open import category-theory.fully-faithful-functors-precategories -open import category-theory.functors-precategories -open import category-theory.isomorphisms-in-categories -open import category-theory.isomorphisms-in-precategories -open import category-theory.maps-precategories -open import category-theory.precategories +open import category-theory.categories funext univalence truncations +open import category-theory.composition-operations-on-binary-families-of-sets funext univalence truncations +open import category-theory.embeddings-precategories funext univalence truncations +open import category-theory.fully-faithful-functors-precategories funext univalence truncations +open import category-theory.functors-precategories funext univalence truncations +open import category-theory.isomorphisms-in-categories funext univalence truncations +open import category-theory.isomorphisms-in-precategories funext univalence truncations +open import category-theory.maps-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalences -open import foundation.function-types +open import foundation.dependent-products-propositions funext +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets -open import foundation.strictly-involutive-identity-types +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.strictly-involutive-identity-types funext univalence open import foundation.subtype-identity-principle -open import foundation.subtypes +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels ``` diff --git a/src/category-theory/fully-faithful-functors-precategories.lagda.md b/src/category-theory/fully-faithful-functors-precategories.lagda.md index a0de4952c0..b9c86b7742 100644 --- a/src/category-theory/fully-faithful-functors-precategories.lagda.md +++ b/src/category-theory/fully-faithful-functors-precategories.lagda.md @@ -1,32 +1,41 @@ # Fully faithful functors between precategories ```agda -module category-theory.fully-faithful-functors-precategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.fully-faithful-functors-precategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.conservative-functors-precategories -open import category-theory.essentially-injective-functors-precategories -open import category-theory.faithful-functors-precategories -open import category-theory.full-functors-precategories -open import category-theory.fully-faithful-maps-precategories -open import category-theory.functors-precategories -open import category-theory.isomorphisms-in-precategories -open import category-theory.precategories -open import category-theory.pseudomonic-functors-precategories +open import category-theory.conservative-functors-precategories funext univalence truncations +open import category-theory.essentially-injective-functors-precategories funext univalence truncations +open import category-theory.faithful-functors-precategories funext univalence truncations +open import category-theory.full-functors-precategories funext univalence truncations +open import category-theory.fully-faithful-maps-precategories funext univalence truncations +open import category-theory.functors-precategories funext univalence truncations +open import category-theory.isomorphisms-in-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations +open import category-theory.pseudomonic-functors-precategories funext univalence truncations open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.identity-types -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.subtypes -open import foundation.surjective-maps +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence +open import foundation.subtypes funext univalence truncations +open import foundation.surjective-maps funext univalence truncations open import foundation.universe-levels ``` diff --git a/src/category-theory/fully-faithful-maps-precategories.lagda.md b/src/category-theory/fully-faithful-maps-precategories.lagda.md index 3716c27af4..493978034f 100644 --- a/src/category-theory/fully-faithful-maps-precategories.lagda.md +++ b/src/category-theory/fully-faithful-maps-precategories.lagda.md @@ -1,23 +1,33 @@ # Fully faithful maps between precategories ```agda -module category-theory.fully-faithful-maps-precategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.fully-faithful-maps-precategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.faithful-maps-precategories -open import category-theory.full-maps-precategories -open import category-theory.maps-precategories -open import category-theory.precategories +open import category-theory.faithful-maps-precategories funext univalence truncations +open import category-theory.full-maps-precategories funext univalence truncations +open import category-theory.maps-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.iterated-dependent-product-types -open import foundation.propositions -open import foundation.surjective-maps +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.iterated-dependent-product-types funext +open import foundation.propositions funext univalence +open import foundation.surjective-maps funext univalence truncations +open import foundation.telescopes open import foundation.universe-levels ``` diff --git a/src/category-theory/function-categories.lagda.md b/src/category-theory/function-categories.lagda.md index 2e86a66718..276fc8bf6a 100644 --- a/src/category-theory/function-categories.lagda.md +++ b/src/category-theory/function-categories.lagda.md @@ -1,22 +1,30 @@ # Function categories ```agda -module category-theory.function-categories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.function-categories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.composition-operations-on-binary-families-of-sets -open import category-theory.dependent-products-of-categories -open import category-theory.isomorphisms-in-categories -open import category-theory.precategories - -open import foundation.equivalences -open import foundation.identity-types -open import foundation.sets -open import foundation.strictly-involutive-identity-types +open import category-theory.categories funext univalence truncations +open import category-theory.composition-operations-on-binary-families-of-sets funext univalence truncations +open import category-theory.dependent-products-of-categories funext univalence truncations +open import category-theory.isomorphisms-in-categories funext univalence truncations +open import category-theory.precategories funext univalence truncations + +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.sets funext univalence +open import foundation.strictly-involutive-identity-types funext univalence open import foundation.universe-levels ``` diff --git a/src/category-theory/function-precategories.lagda.md b/src/category-theory/function-precategories.lagda.md index 64506a827d..db893fc3b4 100644 --- a/src/category-theory/function-precategories.lagda.md +++ b/src/category-theory/function-precategories.lagda.md @@ -1,21 +1,29 @@ # Function precategories ```agda -module category-theory.function-precategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.function-precategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.composition-operations-on-binary-families-of-sets -open import category-theory.dependent-products-of-precategories -open import category-theory.isomorphisms-in-precategories -open import category-theory.precategories - -open import foundation.equivalences -open import foundation.identity-types -open import foundation.sets -open import foundation.strictly-involutive-identity-types +open import category-theory.composition-operations-on-binary-families-of-sets funext univalence truncations +open import category-theory.dependent-products-of-precategories funext univalence truncations +open import category-theory.isomorphisms-in-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations + +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.sets funext univalence +open import foundation.strictly-involutive-identity-types funext univalence open import foundation.universe-levels ``` diff --git a/src/category-theory/functors-categories.lagda.md b/src/category-theory/functors-categories.lagda.md index 8b751210a5..cf32c2967f 100644 --- a/src/category-theory/functors-categories.lagda.md +++ b/src/category-theory/functors-categories.lagda.md @@ -1,22 +1,31 @@ # Functors between categories ```agda -module category-theory.functors-categories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.functors-categories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.functors-precategories -open import category-theory.isomorphisms-in-categories -open import category-theory.maps-categories - -open import foundation.equivalences -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.propositions +open import category-theory.categories funext univalence truncations +open import category-theory.functors-precategories funext univalence truncations +open import category-theory.isomorphisms-in-categories funext univalence truncations +open import category-theory.maps-categories funext univalence truncations + +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence open import foundation.universe-levels ``` diff --git a/src/category-theory/functors-from-small-to-large-categories.lagda.md b/src/category-theory/functors-from-small-to-large-categories.lagda.md index 0194f3b8dd..88dd50e2e5 100644 --- a/src/category-theory/functors-from-small-to-large-categories.lagda.md +++ b/src/category-theory/functors-from-small-to-large-categories.lagda.md @@ -1,21 +1,29 @@ # Functors from small to large categories ```agda -module category-theory.functors-from-small-to-large-categories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.functors-from-small-to-large-categories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.functors-from-small-to-large-precategories -open import category-theory.large-categories -open import category-theory.maps-from-small-to-large-categories - -open import foundation.equivalences -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types +open import category-theory.categories funext univalence truncations +open import category-theory.functors-from-small-to-large-precategories funext univalence truncations +open import category-theory.large-categories funext univalence truncations +open import category-theory.maps-from-small-to-large-categories funext univalence truncations + +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.universe-levels ``` diff --git a/src/category-theory/functors-from-small-to-large-precategories.lagda.md b/src/category-theory/functors-from-small-to-large-precategories.lagda.md index 0565ce0d40..30cb842a5a 100644 --- a/src/category-theory/functors-from-small-to-large-precategories.lagda.md +++ b/src/category-theory/functors-from-small-to-large-precategories.lagda.md @@ -1,23 +1,31 @@ # Functors from small to large precategories ```agda -module category-theory.functors-from-small-to-large-precategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.functors-from-small-to-large-precategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.functors-precategories -open import category-theory.large-precategories -open import category-theory.maps-from-small-to-large-precategories -open import category-theory.precategories +open import category-theory.functors-precategories funext univalence truncations +open import category-theory.large-precategories funext univalence truncations +open import category-theory.maps-from-small-to-large-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.universe-levels ``` diff --git a/src/category-theory/functors-large-categories.lagda.md b/src/category-theory/functors-large-categories.lagda.md index 450779039d..0683a5ef7e 100644 --- a/src/category-theory/functors-large-categories.lagda.md +++ b/src/category-theory/functors-large-categories.lagda.md @@ -1,16 +1,24 @@ # Functors between large categories ```agda -module category-theory.functors-large-categories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.functors-large-categories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.functors-large-precategories -open import category-theory.large-categories +open import category-theory.functors-large-precategories funext univalence truncations +open import category-theory.large-categories funext univalence truncations -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels ``` diff --git a/src/category-theory/functors-large-precategories.lagda.md b/src/category-theory/functors-large-precategories.lagda.md index 0c4d15795a..5874e544d2 100644 --- a/src/category-theory/functors-large-precategories.lagda.md +++ b/src/category-theory/functors-large-precategories.lagda.md @@ -1,17 +1,25 @@ # Functors between large precategories ```agda -module category-theory.functors-large-precategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.functors-large-precategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.large-precategories +open import category-theory.large-precategories funext univalence truncations open import foundation.action-on-identifications-functions -open import foundation.function-types -open import foundation.identity-types +open import foundation.function-types funext +open import foundation.identity-types funext open import foundation.universe-levels ``` diff --git a/src/category-theory/functors-nonunital-precategories.lagda.md b/src/category-theory/functors-nonunital-precategories.lagda.md index a0a49b2b51..2075cd35ae 100644 --- a/src/category-theory/functors-nonunital-precategories.lagda.md +++ b/src/category-theory/functors-nonunital-precategories.lagda.md @@ -1,21 +1,29 @@ # Functors between nonunital precategories ```agda -module category-theory.functors-nonunital-precategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.functors-nonunital-precategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.functors-set-magmoids -open import category-theory.maps-set-magmoids -open import category-theory.nonunital-precategories +open import category-theory.functors-set-magmoids funext univalence truncations +open import category-theory.maps-set-magmoids funext univalence truncations +open import category-theory.nonunital-precategories funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.universe-levels ``` diff --git a/src/category-theory/functors-precategories.lagda.md b/src/category-theory/functors-precategories.lagda.md index 0a9c7a225e..17f2c28c42 100644 --- a/src/category-theory/functors-precategories.lagda.md +++ b/src/category-theory/functors-precategories.lagda.md @@ -1,27 +1,36 @@ # Functors between precategories ```agda -module category-theory.functors-precategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.functors-precategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.functors-set-magmoids -open import category-theory.isomorphisms-in-precategories -open import category-theory.maps-precategories -open import category-theory.opposite-precategories -open import category-theory.precategories +open import category-theory.functors-set-magmoids funext univalence truncations +open import category-theory.isomorphisms-in-precategories funext univalence truncations +open import category-theory.maps-precategories funext univalence truncations +open import category-theory.opposite-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalences -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.propositions -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels ``` diff --git a/src/category-theory/functors-set-magmoids.lagda.md b/src/category-theory/functors-set-magmoids.lagda.md index e3fcc50185..55a683da17 100644 --- a/src/category-theory/functors-set-magmoids.lagda.md +++ b/src/category-theory/functors-set-magmoids.lagda.md @@ -1,25 +1,35 @@ # Functors between set-magmoids ```agda -module category-theory.functors-set-magmoids where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.functors-set-magmoids + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.maps-set-magmoids -open import category-theory.set-magmoids +open import category-theory.maps-set-magmoids funext univalence truncations +open import category-theory.set-magmoids funext univalence truncations open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalences -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.iterated-dependent-product-types -open import foundation.propositions -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.iterated-dependent-product-types funext +open import foundation.propositions funext univalence +open import foundation.subtypes funext univalence truncations +open import foundation.telescopes open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels ``` diff --git a/src/category-theory/gaunt-categories.lagda.md b/src/category-theory/gaunt-categories.lagda.md index 01853cf160..0fafe25748 100644 --- a/src/category-theory/gaunt-categories.lagda.md +++ b/src/category-theory/gaunt-categories.lagda.md @@ -1,30 +1,39 @@ # Gaunt categories ```agda -module category-theory.gaunt-categories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.gaunt-categories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.composition-operations-on-binary-families-of-sets -open import category-theory.isomorphism-induction-categories -open import category-theory.isomorphisms-in-categories -open import category-theory.isomorphisms-in-precategories -open import category-theory.nonunital-precategories -open import category-theory.precategories -open import category-theory.rigid-objects-categories -open import category-theory.strict-categories -open import category-theory.strongly-preunivalent-categories - -open import foundation.cartesian-product-types +open import category-theory.categories funext univalence truncations +open import category-theory.composition-operations-on-binary-families-of-sets funext univalence truncations +open import category-theory.isomorphism-induction-categories funext univalence truncations +open import category-theory.isomorphisms-in-categories funext univalence truncations +open import category-theory.isomorphisms-in-precategories funext univalence truncations +open import category-theory.nonunital-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations +open import category-theory.rigid-objects-categories funext univalence truncations +open import category-theory.strict-categories funext univalence truncations +open import category-theory.strongly-preunivalent-categories funext univalence truncations + +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets -open import foundation.strictly-involutive-identity-types -open import foundation.surjective-maps +open import foundation.dependent-products-propositions funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.strictly-involutive-identity-types funext univalence +open import foundation.surjective-maps funext univalence truncations open import foundation.universe-levels ``` diff --git a/src/category-theory/groupoids.lagda.md b/src/category-theory/groupoids.lagda.md index 2fb548ee06..ad6840e587 100644 --- a/src/category-theory/groupoids.lagda.md +++ b/src/category-theory/groupoids.lagda.md @@ -1,32 +1,43 @@ # Groupoids ```agda -module category-theory.groupoids where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.groupoids + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.functors-categories -open import category-theory.isomorphisms-in-categories -open import category-theory.isomorphisms-in-precategories -open import category-theory.precategories -open import category-theory.pregroupoids - -open import foundation.1-types -open import foundation.contractible-types +open import category-theory.categories funext univalence truncations +open import category-theory.functors-categories funext univalence truncations +open import category-theory.isomorphisms-in-categories funext univalence truncations +open import category-theory.isomorphisms-in-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations +open import category-theory.pregroupoids funext univalence truncations + +open import foundation.1-types funext univalence +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.iterated-dependent-pair-types -open import foundation.propositions -open import foundation.sets -open import foundation.strictly-involutive-identity-types -open import foundation.torsorial-type-families +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.strictly-involutive-identity-types funext univalence +open import foundation.telescopes +open import foundation.torsorial-type-families funext univalence truncations open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels ``` diff --git a/src/category-theory/homotopies-natural-transformations-large-precategories.lagda.md b/src/category-theory/homotopies-natural-transformations-large-precategories.lagda.md index 1359d2abd4..f25c44c38c 100644 --- a/src/category-theory/homotopies-natural-transformations-large-precategories.lagda.md +++ b/src/category-theory/homotopies-natural-transformations-large-precategories.lagda.md @@ -1,18 +1,26 @@ # Homotopies of natural transformations in large precategories ```agda -module category-theory.homotopies-natural-transformations-large-precategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.homotopies-natural-transformations-large-precategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.functors-large-precategories -open import category-theory.large-precategories -open import category-theory.natural-transformations-functors-large-precategories +open import category-theory.functors-large-precategories funext univalence truncations +open import category-theory.large-precategories funext univalence truncations +open import category-theory.natural-transformations-functors-large-precategories funext univalence truncations -open import foundation.homotopies -open import foundation.identity-types +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.universe-levels ``` diff --git a/src/category-theory/indiscrete-precategories.lagda.md b/src/category-theory/indiscrete-precategories.lagda.md index 68479adbd5..43658da3a5 100644 --- a/src/category-theory/indiscrete-precategories.lagda.md +++ b/src/category-theory/indiscrete-precategories.lagda.md @@ -1,28 +1,39 @@ # Indiscrete precategories ```agda -module category-theory.indiscrete-precategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.indiscrete-precategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.isomorphisms-in-precategories -open import category-theory.precategories -open import category-theory.pregroupoids -open import category-theory.preunivalent-categories -open import category-theory.strict-categories -open import category-theory.subterminal-precategories - -open import foundation.contractible-types +open import category-theory.isomorphisms-in-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations +open import category-theory.pregroupoids funext univalence truncations +open import category-theory.preunivalent-categories funext univalence truncations +open import category-theory.strict-categories funext univalence truncations +open import category-theory.subterminal-precategories funext univalence truncations + +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.iterated-dependent-product-types -open import foundation.propositions -open import foundation.sets +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.iterated-dependent-product-types funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.telescopes open import foundation.unit-type open import foundation.universe-levels ``` diff --git a/src/category-theory/initial-category.lagda.md b/src/category-theory/initial-category.lagda.md index c24a71c44d..7e980b0049 100644 --- a/src/category-theory/initial-category.lagda.md +++ b/src/category-theory/initial-category.lagda.md @@ -1,25 +1,34 @@ # The initial category ```agda -module category-theory.initial-category where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.initial-category + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.functors-precategories -open import category-theory.gaunt-categories -open import category-theory.indiscrete-precategories -open import category-theory.precategories -open import category-theory.strict-categories -open import category-theory.strongly-preunivalent-categories - -open import foundation.contractible-types +open import category-theory.categories funext univalence truncations +open import category-theory.functors-precategories funext univalence truncations +open import category-theory.gaunt-categories funext univalence truncations +open import category-theory.indiscrete-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations +open import category-theory.strict-categories funext univalence truncations +open import category-theory.strongly-preunivalent-categories funext univalence truncations + +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.identity-types -open import foundation.sets +open import foundation.dependent-products-contractible-types funext +open import foundation.empty-types funext univalence truncations +open import foundation.identity-types funext +open import foundation.sets funext univalence open import foundation.unit-type open import foundation.universe-levels ``` diff --git a/src/category-theory/initial-objects-large-categories.lagda.md b/src/category-theory/initial-objects-large-categories.lagda.md index 8dce8c764a..44726221b8 100644 --- a/src/category-theory/initial-objects-large-categories.lagda.md +++ b/src/category-theory/initial-objects-large-categories.lagda.md @@ -1,14 +1,22 @@ # Initial objects of large categories ```agda -module category-theory.initial-objects-large-categories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.initial-objects-large-categories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.initial-objects-large-precategories -open import category-theory.large-categories +open import category-theory.initial-objects-large-precategories funext univalence truncations +open import category-theory.large-categories funext univalence truncations open import foundation.universe-levels ``` diff --git a/src/category-theory/initial-objects-large-precategories.lagda.md b/src/category-theory/initial-objects-large-precategories.lagda.md index c49900291d..ac9b8c1782 100644 --- a/src/category-theory/initial-objects-large-precategories.lagda.md +++ b/src/category-theory/initial-objects-large-precategories.lagda.md @@ -1,15 +1,24 @@ # Initial objects of large precategories ```agda -module category-theory.initial-objects-large-precategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.initial-objects-large-precategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.large-precategories +open import category-theory.large-precategories funext univalence truncations -open import foundation.contractible-types +open import foundation.contractible-types funext univalence +open import foundation.dependent-products-contractible-types funext open import foundation.universe-levels ``` diff --git a/src/category-theory/initial-objects-precategories.lagda.md b/src/category-theory/initial-objects-precategories.lagda.md index dac1af8fa9..8444cdf80e 100644 --- a/src/category-theory/initial-objects-precategories.lagda.md +++ b/src/category-theory/initial-objects-precategories.lagda.md @@ -1,18 +1,28 @@ # Initial objects in a precategory ```agda -module category-theory.initial-objects-precategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.initial-objects-precategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.precategories +open import category-theory.precategories funext univalence truncations -open import foundation.contractible-types +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.propositions +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.function-types funext +open import foundation.propositions funext univalence open import foundation.universe-levels open import foundation-core.identity-types diff --git a/src/category-theory/isomorphism-induction-categories.lagda.md b/src/category-theory/isomorphism-induction-categories.lagda.md index a23461c24d..9fe2386b5b 100644 --- a/src/category-theory/isomorphism-induction-categories.lagda.md +++ b/src/category-theory/isomorphism-induction-categories.lagda.md @@ -1,24 +1,32 @@ # Isomorphism induction in categories ```agda -module category-theory.isomorphism-induction-categories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.isomorphism-induction-categories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.isomorphism-induction-precategories -open import category-theory.isomorphisms-in-categories +open import category-theory.categories funext univalence truncations +open import category-theory.isomorphism-induction-precategories funext univalence truncations +open import category-theory.isomorphisms-in-categories funext univalence truncations -open import foundation.commuting-triangles-of-maps -open import foundation.contractible-maps +open import foundation.commuting-triangles-of-maps funext univalence +open import foundation.contractible-maps funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.identity-types -open import foundation.sections -open import foundation.universal-property-identity-systems +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.sections funext +open import foundation.universal-property-identity-systems funext open import foundation.universe-levels ``` diff --git a/src/category-theory/isomorphism-induction-precategories.lagda.md b/src/category-theory/isomorphism-induction-precategories.lagda.md index 60acd05355..b3b510c715 100644 --- a/src/category-theory/isomorphism-induction-precategories.lagda.md +++ b/src/category-theory/isomorphism-induction-precategories.lagda.md @@ -1,22 +1,30 @@ # Isomorphism induction in precategories ```agda -module category-theory.isomorphism-induction-precategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.isomorphism-induction-precategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.isomorphisms-in-precategories -open import category-theory.precategories +open import category-theory.isomorphisms-in-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations -open import foundation.commuting-triangles-of-maps +open import foundation.commuting-triangles-of-maps funext univalence open import foundation.dependent-pair-types -open import foundation.function-types +open import foundation.function-types funext open import foundation.identity-systems -open import foundation.identity-types -open import foundation.sections -open import foundation.torsorial-type-families +open import foundation.identity-types funext +open import foundation.sections funext +open import foundation.torsorial-type-families funext univalence truncations open import foundation.universe-levels ``` diff --git a/src/category-theory/isomorphisms-in-categories.lagda.md b/src/category-theory/isomorphisms-in-categories.lagda.md index a0f12490f9..96573e93bf 100644 --- a/src/category-theory/isomorphisms-in-categories.lagda.md +++ b/src/category-theory/isomorphisms-in-categories.lagda.md @@ -1,25 +1,35 @@ # Isomorphisms in categories ```agda -module category-theory.isomorphisms-in-categories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.isomorphisms-in-categories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.isomorphisms-in-precategories +open import category-theory.categories funext univalence truncations +open import category-theory.isomorphisms-in-precategories funext univalence truncations open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.contractible-types +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.functoriality-dependent-pair-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets -open import foundation.torsorial-type-families +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.torsorial-type-families funext univalence truncations open import foundation.universe-levels ``` diff --git a/src/category-theory/isomorphisms-in-large-categories.lagda.md b/src/category-theory/isomorphisms-in-large-categories.lagda.md index e6f13cb68a..084a7128f7 100644 --- a/src/category-theory/isomorphisms-in-large-categories.lagda.md +++ b/src/category-theory/isomorphisms-in-large-categories.lagda.md @@ -1,25 +1,35 @@ # Isomorphisms in large categories ```agda -module category-theory.isomorphisms-in-large-categories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.isomorphisms-in-large-categories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.isomorphisms-in-categories -open import category-theory.isomorphisms-in-large-precategories -open import category-theory.large-categories +open import category-theory.isomorphisms-in-categories funext univalence truncations +open import category-theory.isomorphisms-in-large-precategories funext univalence truncations +open import category-theory.large-categories funext univalence truncations -open import foundation.contractible-types +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets -open import foundation.torsorial-type-families +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.torsorial-type-families funext univalence truncations open import foundation.universe-levels ``` diff --git a/src/category-theory/isomorphisms-in-large-precategories.lagda.md b/src/category-theory/isomorphisms-in-large-precategories.lagda.md index 065f4abe1e..088f5c8ab1 100644 --- a/src/category-theory/isomorphisms-in-large-precategories.lagda.md +++ b/src/category-theory/isomorphisms-in-large-precategories.lagda.md @@ -1,28 +1,37 @@ # Isomorphisms in large precategories ```agda -module category-theory.isomorphisms-in-large-precategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.isomorphisms-in-large-precategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.isomorphisms-in-precategories -open import category-theory.large-precategories +open import category-theory.isomorphisms-in-precategories funext univalence truncations +open import category-theory.large-precategories funext univalence truncations open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.propositions -open import foundation.retractions -open import foundation.sections -open import foundation.sets -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.propositions funext univalence +open import foundation.retractions funext +open import foundation.sections funext +open import foundation.sets funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels ``` diff --git a/src/category-theory/isomorphisms-in-precategories.lagda.md b/src/category-theory/isomorphisms-in-precategories.lagda.md index 31a63e5d4f..c210ea81a8 100644 --- a/src/category-theory/isomorphisms-in-precategories.lagda.md +++ b/src/category-theory/isomorphisms-in-precategories.lagda.md @@ -1,27 +1,36 @@ # Isomorphisms in precategories ```agda -module category-theory.isomorphisms-in-precategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.isomorphisms-in-precategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.precategories +open import category-theory.precategories funext univalence truncations open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.propositions -open import foundation.retractions -open import foundation.sections -open import foundation.sets -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.propositions funext univalence +open import foundation.retractions funext +open import foundation.sections funext +open import foundation.sets funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels ``` diff --git a/src/category-theory/isomorphisms-in-subprecategories.lagda.md b/src/category-theory/isomorphisms-in-subprecategories.lagda.md index e0d8560de0..6027ec59f4 100644 --- a/src/category-theory/isomorphisms-in-subprecategories.lagda.md +++ b/src/category-theory/isomorphisms-in-subprecategories.lagda.md @@ -1,21 +1,30 @@ # Isomorphisms in subprecategories ```agda -module category-theory.isomorphisms-in-subprecategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.isomorphisms-in-subprecategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.isomorphisms-in-precategories -open import category-theory.precategories -open import category-theory.subprecategories +open import category-theory.isomorphisms-in-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations +open import category-theory.subprecategories funext univalence truncations open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.propositions -open import foundation.sets -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels ``` diff --git a/src/category-theory/large-categories.lagda.md b/src/category-theory/large-categories.lagda.md index b798eee311..ff20410813 100644 --- a/src/category-theory/large-categories.lagda.md +++ b/src/category-theory/large-categories.lagda.md @@ -1,24 +1,32 @@ # Large categories ```agda -module category-theory.large-categories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.large-categories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.isomorphisms-in-large-precategories -open import category-theory.large-precategories -open import category-theory.precategories +open import category-theory.categories funext univalence truncations +open import category-theory.isomorphisms-in-large-precategories funext univalence truncations +open import category-theory.large-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations open import foundation.action-on-identifications-binary-functions open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.homotopies -open import foundation.identity-types -open import foundation.sets -open import foundation.strictly-involutive-identity-types +open import foundation.equivalences funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.sets funext univalence +open import foundation.strictly-involutive-identity-types funext univalence open import foundation.universe-levels ``` diff --git a/src/category-theory/large-function-categories.lagda.md b/src/category-theory/large-function-categories.lagda.md index dedadafc7f..d4e90c7335 100644 --- a/src/category-theory/large-function-categories.lagda.md +++ b/src/category-theory/large-function-categories.lagda.md @@ -1,20 +1,28 @@ # Large function categories ```agda -module category-theory.large-function-categories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.large-function-categories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.dependent-products-of-large-categories -open import category-theory.isomorphisms-in-large-categories -open import category-theory.large-categories - -open import foundation.equivalences -open import foundation.identity-types -open import foundation.sets -open import foundation.strictly-involutive-identity-types +open import category-theory.dependent-products-of-large-categories funext univalence truncations +open import category-theory.isomorphisms-in-large-categories funext univalence truncations +open import category-theory.large-categories funext univalence truncations + +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.sets funext univalence +open import foundation.strictly-involutive-identity-types funext univalence open import foundation.universe-levels ``` diff --git a/src/category-theory/large-function-precategories.lagda.md b/src/category-theory/large-function-precategories.lagda.md index e7b592b608..2069060936 100644 --- a/src/category-theory/large-function-precategories.lagda.md +++ b/src/category-theory/large-function-precategories.lagda.md @@ -1,20 +1,28 @@ # Large function precategories ```agda -module category-theory.large-function-precategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.large-function-precategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.dependent-products-of-large-precategories -open import category-theory.isomorphisms-in-large-precategories -open import category-theory.large-precategories - -open import foundation.equivalences -open import foundation.identity-types -open import foundation.sets -open import foundation.strictly-involutive-identity-types +open import category-theory.dependent-products-of-large-precategories funext univalence truncations +open import category-theory.isomorphisms-in-large-precategories funext univalence truncations +open import category-theory.large-precategories funext univalence truncations + +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.sets funext univalence +open import foundation.strictly-involutive-identity-types funext univalence open import foundation.universe-levels ``` diff --git a/src/category-theory/large-precategories.lagda.md b/src/category-theory/large-precategories.lagda.md index 4220dda23e..247916e19e 100644 --- a/src/category-theory/large-precategories.lagda.md +++ b/src/category-theory/large-precategories.lagda.md @@ -1,21 +1,29 @@ # Large precategories ```agda -module category-theory.large-precategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.large-precategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.precategories +open import category-theory.precategories funext univalence truncations open import foundation.action-on-identifications-binary-functions open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.sets -open import foundation.strictly-involutive-identity-types +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.sets funext univalence +open import foundation.strictly-involutive-identity-types funext univalence open import foundation.universe-levels ``` diff --git a/src/category-theory/large-subcategories.lagda.md b/src/category-theory/large-subcategories.lagda.md index 375f57780d..07d4c2d6c1 100644 --- a/src/category-theory/large-subcategories.lagda.md +++ b/src/category-theory/large-subcategories.lagda.md @@ -1,14 +1,22 @@ # Large subcategories ```agda -module category-theory.large-subcategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.large-subcategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.large-categories -open import category-theory.large-subprecategories +open import category-theory.large-categories funext univalence truncations +open import category-theory.large-subprecategories funext univalence truncations open import foundation.universe-levels ``` diff --git a/src/category-theory/large-subprecategories.lagda.md b/src/category-theory/large-subprecategories.lagda.md index 935a5ad81c..1fe1664d4e 100644 --- a/src/category-theory/large-subprecategories.lagda.md +++ b/src/category-theory/large-subprecategories.lagda.md @@ -1,19 +1,27 @@ # Large subprecategories ```agda -module category-theory.large-subprecategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.large-subprecategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.large-precategories +open import category-theory.large-precategories funext univalence truncations open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.sets -open import foundation.strictly-involutive-identity-types -open import foundation.subtypes +open import foundation.identity-types funext +open import foundation.sets funext univalence +open import foundation.strictly-involutive-identity-types funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels ``` diff --git a/src/category-theory/limits-precategories.lagda.md b/src/category-theory/limits-precategories.lagda.md index 60015d9a58..36c9b9c831 100644 --- a/src/category-theory/limits-precategories.lagda.md +++ b/src/category-theory/limits-precategories.lagda.md @@ -1,30 +1,39 @@ # Limits in precategories ```agda -module category-theory.limits-precategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.limits-precategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.cones-precategories -open import category-theory.constant-functors -open import category-theory.functors-precategories -open import category-theory.natural-transformations-functors-precategories -open import category-theory.precategories -open import category-theory.right-extensions-precategories -open import category-theory.right-kan-extensions-precategories -open import category-theory.terminal-category +open import category-theory.cones-precategories funext univalence truncations +open import category-theory.constant-functors funext univalence truncations +open import category-theory.functors-precategories funext univalence truncations +open import category-theory.natural-transformations-functors-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations +open import category-theory.right-extensions-precategories funext univalence truncations +open import category-theory.right-kan-extensions-precategories funext univalence truncations +open import category-theory.terminal-category funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.functoriality-dependent-function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.function-extensionality funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-function-types funext univalence +open import foundation.functoriality-dependent-pair-types funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.propositions funext univalence open import foundation.transport-along-identifications open import foundation.unit-type open import foundation.universe-levels diff --git a/src/category-theory/maps-categories.lagda.md b/src/category-theory/maps-categories.lagda.md index ac264b5160..e25bbb986e 100644 --- a/src/category-theory/maps-categories.lagda.md +++ b/src/category-theory/maps-categories.lagda.md @@ -1,19 +1,27 @@ # Maps between categories ```agda -module category-theory.maps-categories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.maps-categories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.maps-precategories +open import category-theory.categories funext univalence truncations +open import category-theory.maps-precategories funext univalence truncations -open import foundation.equivalences -open import foundation.homotopies -open import foundation.identity-types -open import foundation.torsorial-type-families +open import foundation.equivalences funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.torsorial-type-families funext univalence truncations open import foundation.universe-levels ``` diff --git a/src/category-theory/maps-from-small-to-large-categories.lagda.md b/src/category-theory/maps-from-small-to-large-categories.lagda.md index 9f96fbd611..58e557cfbc 100644 --- a/src/category-theory/maps-from-small-to-large-categories.lagda.md +++ b/src/category-theory/maps-from-small-to-large-categories.lagda.md @@ -1,19 +1,27 @@ # Maps from small to large categories ```agda -module category-theory.maps-from-small-to-large-categories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.maps-from-small-to-large-categories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.large-categories -open import category-theory.maps-from-small-to-large-precategories +open import category-theory.categories funext univalence truncations +open import category-theory.large-categories funext univalence truncations +open import category-theory.maps-from-small-to-large-precategories funext univalence truncations -open import foundation.equivalences -open import foundation.identity-types -open import foundation.torsorial-type-families +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.torsorial-type-families funext univalence truncations open import foundation.universe-levels ``` diff --git a/src/category-theory/maps-from-small-to-large-precategories.lagda.md b/src/category-theory/maps-from-small-to-large-precategories.lagda.md index e577f98972..4e77668be3 100644 --- a/src/category-theory/maps-from-small-to-large-precategories.lagda.md +++ b/src/category-theory/maps-from-small-to-large-precategories.lagda.md @@ -1,19 +1,27 @@ # Maps from small to large precategories ```agda -module category-theory.maps-from-small-to-large-precategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.maps-from-small-to-large-precategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.large-precategories -open import category-theory.maps-precategories -open import category-theory.precategories +open import category-theory.large-precategories funext univalence truncations +open import category-theory.maps-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations -open import foundation.equivalences -open import foundation.identity-types -open import foundation.torsorial-type-families +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.torsorial-type-families funext univalence truncations open import foundation.universe-levels ``` diff --git a/src/category-theory/maps-precategories.lagda.md b/src/category-theory/maps-precategories.lagda.md index ba08c41d5c..4a0bb3503b 100644 --- a/src/category-theory/maps-precategories.lagda.md +++ b/src/category-theory/maps-precategories.lagda.md @@ -1,29 +1,38 @@ # Maps between precategories ```agda -module category-theory.maps-precategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.maps-precategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.commuting-squares-of-morphisms-in-precategories -open import category-theory.maps-set-magmoids -open import category-theory.precategories +open import category-theory.commuting-squares-of-morphisms-in-precategories funext univalence truncations +open import category-theory.maps-set-magmoids funext univalence truncations +open import category-theory.precategories funext univalence truncations open import foundation.binary-transport -open import foundation.contractible-types +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types +open import foundation.dependent-products-contractible-types funext +open import foundation.equality-dependent-function-types funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext open import foundation.structure-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext univalence truncations open import foundation.universe-levels ``` diff --git a/src/category-theory/maps-set-magmoids.lagda.md b/src/category-theory/maps-set-magmoids.lagda.md index 33d9842d6b..73241733a6 100644 --- a/src/category-theory/maps-set-magmoids.lagda.md +++ b/src/category-theory/maps-set-magmoids.lagda.md @@ -1,19 +1,27 @@ # Maps between set-magmoids ```agda -module category-theory.maps-set-magmoids where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.maps-set-magmoids + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.set-magmoids +open import category-theory.set-magmoids funext univalence truncations open import foundation.action-on-identifications-functions open import foundation.commuting-pentagons-of-identifications open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.identity-types +open import foundation.function-types funext +open import foundation.identity-types funext open import foundation.universe-levels ``` diff --git a/src/category-theory/monads-on-categories.lagda.md b/src/category-theory/monads-on-categories.lagda.md index c09db9468b..b744150ec4 100644 --- a/src/category-theory/monads-on-categories.lagda.md +++ b/src/category-theory/monads-on-categories.lagda.md @@ -1,20 +1,28 @@ # Monads on categories ```agda -module category-theory.monads-on-categories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.monads-on-categories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.functors-categories -open import category-theory.monads-on-precategories -open import category-theory.natural-transformations-functors-categories -open import category-theory.pointed-endofunctors-categories +open import category-theory.categories funext univalence truncations +open import category-theory.functors-categories funext univalence truncations +open import category-theory.monads-on-precategories funext univalence truncations +open import category-theory.natural-transformations-functors-categories funext univalence truncations +open import category-theory.pointed-endofunctors-categories funext univalence truncations open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels open import foundation-core.cartesian-product-types diff --git a/src/category-theory/monads-on-precategories.lagda.md b/src/category-theory/monads-on-precategories.lagda.md index 63225d5d66..a6b4871df7 100644 --- a/src/category-theory/monads-on-precategories.lagda.md +++ b/src/category-theory/monads-on-precategories.lagda.md @@ -1,19 +1,27 @@ # Monads on precategories ```agda -module category-theory.monads-on-precategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.monads-on-precategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.functors-precategories -open import category-theory.natural-transformations-functors-precategories -open import category-theory.pointed-endofunctors-precategories -open import category-theory.precategories +open import category-theory.functors-precategories funext univalence truncations +open import category-theory.natural-transformations-functors-precategories funext univalence truncations +open import category-theory.pointed-endofunctors-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels open import foundation-core.cartesian-product-types diff --git a/src/category-theory/monomorphisms-in-large-precategories.lagda.md b/src/category-theory/monomorphisms-in-large-precategories.lagda.md index 73ce9e3886..30f17a770a 100644 --- a/src/category-theory/monomorphisms-in-large-precategories.lagda.md +++ b/src/category-theory/monomorphisms-in-large-precategories.lagda.md @@ -1,18 +1,27 @@ # Monomorphisms in large precategories ```agda -module category-theory.monomorphisms-in-large-precategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.monomorphisms-in-large-precategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.isomorphisms-in-large-precategories -open import category-theory.large-precategories +open import category-theory.isomorphisms-in-large-precategories funext univalence truncations +open import category-theory.large-precategories funext univalence truncations -open import foundation.embeddings -open import foundation.equivalences -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.propositions funext univalence open import foundation.universe-levels ``` diff --git a/src/category-theory/natural-isomorphisms-functors-categories.lagda.md b/src/category-theory/natural-isomorphisms-functors-categories.lagda.md index f8f8894aea..9741e81a25 100644 --- a/src/category-theory/natural-isomorphisms-functors-categories.lagda.md +++ b/src/category-theory/natural-isomorphisms-functors-categories.lagda.md @@ -1,26 +1,35 @@ # Natural isomorphisms between functors between categories ```agda -module category-theory.natural-isomorphisms-functors-categories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.natural-isomorphisms-functors-categories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.functors-categories -open import category-theory.isomorphisms-in-categories -open import category-theory.natural-isomorphisms-functors-precategories -open import category-theory.natural-transformations-functors-categories +open import category-theory.categories funext univalence truncations +open import category-theory.functors-categories funext univalence truncations +open import category-theory.isomorphisms-in-categories funext univalence truncations +open import category-theory.natural-isomorphisms-functors-precategories funext univalence truncations +open import category-theory.natural-transformations-functors-categories funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels ``` diff --git a/src/category-theory/natural-isomorphisms-functors-large-precategories.lagda.md b/src/category-theory/natural-isomorphisms-functors-large-precategories.lagda.md index edaf9fc991..e33782c436 100644 --- a/src/category-theory/natural-isomorphisms-functors-large-precategories.lagda.md +++ b/src/category-theory/natural-isomorphisms-functors-large-precategories.lagda.md @@ -1,17 +1,25 @@ # Natural isomorphisms between functors between large precategories ```agda -module category-theory.natural-isomorphisms-functors-large-precategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.natural-isomorphisms-functors-large-precategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.commuting-squares-of-morphisms-in-large-precategories -open import category-theory.functors-large-precategories -open import category-theory.isomorphisms-in-large-precategories -open import category-theory.large-precategories -open import category-theory.natural-transformations-functors-large-precategories +open import category-theory.commuting-squares-of-morphisms-in-large-precategories funext univalence truncations +open import category-theory.functors-large-precategories funext univalence truncations +open import category-theory.isomorphisms-in-large-precategories funext univalence truncations +open import category-theory.large-precategories funext univalence truncations +open import category-theory.natural-transformations-functors-large-precategories funext univalence truncations open import foundation.universe-levels ``` diff --git a/src/category-theory/natural-isomorphisms-functors-precategories.lagda.md b/src/category-theory/natural-isomorphisms-functors-precategories.lagda.md index 35a1b71552..40691f49c1 100644 --- a/src/category-theory/natural-isomorphisms-functors-precategories.lagda.md +++ b/src/category-theory/natural-isomorphisms-functors-precategories.lagda.md @@ -1,26 +1,35 @@ # Natural isomorphisms between functors between precategories ```agda -module category-theory.natural-isomorphisms-functors-precategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.natural-isomorphisms-functors-precategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.functors-precategories -open import category-theory.isomorphisms-in-precategories -open import category-theory.natural-isomorphisms-maps-precategories -open import category-theory.natural-transformations-functors-precategories -open import category-theory.precategories +open import category-theory.functors-precategories funext univalence truncations +open import category-theory.isomorphisms-in-precategories funext univalence truncations +open import category-theory.natural-isomorphisms-maps-precategories funext univalence truncations +open import category-theory.natural-transformations-functors-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels ``` diff --git a/src/category-theory/natural-isomorphisms-maps-categories.lagda.md b/src/category-theory/natural-isomorphisms-maps-categories.lagda.md index 571c2723dc..df507106fd 100644 --- a/src/category-theory/natural-isomorphisms-maps-categories.lagda.md +++ b/src/category-theory/natural-isomorphisms-maps-categories.lagda.md @@ -1,26 +1,35 @@ # Natural isomorphisms between maps between categories ```agda -module category-theory.natural-isomorphisms-maps-categories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.natural-isomorphisms-maps-categories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.isomorphisms-in-categories -open import category-theory.maps-categories -open import category-theory.natural-isomorphisms-maps-precategories -open import category-theory.natural-transformations-maps-categories +open import category-theory.categories funext univalence truncations +open import category-theory.isomorphisms-in-categories funext univalence truncations +open import category-theory.maps-categories funext univalence truncations +open import category-theory.natural-isomorphisms-maps-precategories funext univalence truncations +open import category-theory.natural-transformations-maps-categories funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels ``` diff --git a/src/category-theory/natural-isomorphisms-maps-precategories.lagda.md b/src/category-theory/natural-isomorphisms-maps-precategories.lagda.md index 1e2ff1ccc6..ae54270e73 100644 --- a/src/category-theory/natural-isomorphisms-maps-precategories.lagda.md +++ b/src/category-theory/natural-isomorphisms-maps-precategories.lagda.md @@ -1,27 +1,36 @@ # Natural isomorphisms between maps between precategories ```agda -module category-theory.natural-isomorphisms-maps-precategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.natural-isomorphisms-maps-precategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.isomorphisms-in-precategories -open import category-theory.maps-precategories -open import category-theory.natural-transformations-maps-precategories -open import category-theory.precategories +open import category-theory.isomorphisms-in-precategories funext univalence truncations +open import category-theory.maps-precategories funext univalence truncations +open import category-theory.natural-transformations-maps-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalences -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels ``` diff --git a/src/category-theory/natural-numbers-object-precategories.lagda.md b/src/category-theory/natural-numbers-object-precategories.lagda.md index 33cad6e351..12716a0bdd 100644 --- a/src/category-theory/natural-numbers-object-precategories.lagda.md +++ b/src/category-theory/natural-numbers-object-precategories.lagda.md @@ -1,20 +1,28 @@ # Natural numbers object in a precategory ```agda -module category-theory.natural-numbers-object-precategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.natural-numbers-object-precategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.precategories -open import category-theory.terminal-objects-precategories +open import category-theory.precategories funext univalence truncations +open import category-theory.terminal-objects-precategories funext univalence truncations open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.uniqueness-quantification +open import foundation.identity-types funext +open import foundation.uniqueness-quantification funext univalence truncations open import foundation.universe-levels ``` diff --git a/src/category-theory/natural-transformations-functors-categories.lagda.md b/src/category-theory/natural-transformations-functors-categories.lagda.md index 31ddf1de0b..c03654378b 100644 --- a/src/category-theory/natural-transformations-functors-categories.lagda.md +++ b/src/category-theory/natural-transformations-functors-categories.lagda.md @@ -1,22 +1,31 @@ # Natural transformations between functors between categories ```agda -module category-theory.natural-transformations-functors-categories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.natural-transformations-functors-categories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.functors-categories -open import category-theory.natural-transformations-functors-precategories - -open import foundation.embeddings -open import foundation.equivalences -open import foundation.homotopies -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets +open import category-theory.categories funext univalence truncations +open import category-theory.functors-categories funext univalence truncations +open import category-theory.natural-transformations-functors-precategories funext univalence truncations + +open import foundation.dependent-products-propositions funext +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence open import foundation.universe-levels ``` diff --git a/src/category-theory/natural-transformations-functors-from-small-to-large-categories.lagda.md b/src/category-theory/natural-transformations-functors-from-small-to-large-categories.lagda.md index 229103a8d2..2ddd58e765 100644 --- a/src/category-theory/natural-transformations-functors-from-small-to-large-categories.lagda.md +++ b/src/category-theory/natural-transformations-functors-from-small-to-large-categories.lagda.md @@ -1,24 +1,33 @@ # Natural transformations between functors from small to large categories ```agda -module category-theory.natural-transformations-functors-from-small-to-large-categories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.natural-transformations-functors-from-small-to-large-categories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.functors-from-small-to-large-categories -open import category-theory.large-categories -open import category-theory.natural-transformations-functors-from-small-to-large-precategories +open import category-theory.categories funext univalence truncations +open import category-theory.functors-from-small-to-large-categories funext univalence truncations +open import category-theory.large-categories funext univalence truncations +open import category-theory.natural-transformations-functors-from-small-to-large-precategories funext univalence truncations open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalences -open import foundation.homotopies -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets +open import foundation.dependent-products-propositions funext +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence open import foundation.universe-levels ``` diff --git a/src/category-theory/natural-transformations-functors-from-small-to-large-precategories.lagda.md b/src/category-theory/natural-transformations-functors-from-small-to-large-precategories.lagda.md index bde1b382d5..21df1d5a1b 100644 --- a/src/category-theory/natural-transformations-functors-from-small-to-large-precategories.lagda.md +++ b/src/category-theory/natural-transformations-functors-from-small-to-large-precategories.lagda.md @@ -1,25 +1,34 @@ # Natural transformations between functors from small to large precategories ```agda -module category-theory.natural-transformations-functors-from-small-to-large-precategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.natural-transformations-functors-from-small-to-large-precategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.functors-from-small-to-large-precategories -open import category-theory.large-precategories -open import category-theory.natural-transformations-maps-from-small-to-large-precategories -open import category-theory.precategories +open import category-theory.functors-from-small-to-large-precategories funext univalence truncations +open import category-theory.large-precategories funext univalence truncations +open import category-theory.natural-transformations-maps-from-small-to-large-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalences -open import foundation.homotopies -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets -open import foundation.strictly-involutive-identity-types +open import foundation.dependent-products-propositions funext +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.strictly-involutive-identity-types funext univalence open import foundation.universe-levels ``` diff --git a/src/category-theory/natural-transformations-functors-large-categories.lagda.md b/src/category-theory/natural-transformations-functors-large-categories.lagda.md index 756ae5d8b1..22fc774c8b 100644 --- a/src/category-theory/natural-transformations-functors-large-categories.lagda.md +++ b/src/category-theory/natural-transformations-functors-large-categories.lagda.md @@ -1,15 +1,23 @@ # Natural transformations between functors between large categories ```agda -module category-theory.natural-transformations-functors-large-categories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.natural-transformations-functors-large-categories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.functors-large-categories -open import category-theory.large-categories -open import category-theory.natural-transformations-functors-large-precategories +open import category-theory.functors-large-categories funext univalence truncations +open import category-theory.large-categories funext univalence truncations +open import category-theory.natural-transformations-functors-large-precategories funext univalence truncations open import foundation.universe-levels ``` diff --git a/src/category-theory/natural-transformations-functors-large-precategories.lagda.md b/src/category-theory/natural-transformations-functors-large-precategories.lagda.md index 40e89cd14c..1e2cfdb16f 100644 --- a/src/category-theory/natural-transformations-functors-large-precategories.lagda.md +++ b/src/category-theory/natural-transformations-functors-large-precategories.lagda.md @@ -1,18 +1,26 @@ # Natural transformations between functors between large precategories ```agda -module category-theory.natural-transformations-functors-large-precategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.natural-transformations-functors-large-precategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.commuting-squares-of-morphisms-in-large-precategories -open import category-theory.functors-large-precategories -open import category-theory.large-precategories +open import category-theory.commuting-squares-of-morphisms-in-large-precategories funext univalence truncations +open import category-theory.functors-large-precategories funext univalence truncations +open import category-theory.large-precategories funext univalence truncations open import foundation.action-on-identifications-functions -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels ``` diff --git a/src/category-theory/natural-transformations-functors-precategories.lagda.md b/src/category-theory/natural-transformations-functors-precategories.lagda.md index 7076ad1387..13fc593b37 100644 --- a/src/category-theory/natural-transformations-functors-precategories.lagda.md +++ b/src/category-theory/natural-transformations-functors-precategories.lagda.md @@ -1,26 +1,35 @@ # Natural transformations between functors between precategories ```agda -module category-theory.natural-transformations-functors-precategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.natural-transformations-functors-precategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.functors-precategories -open import category-theory.natural-transformations-maps-precategories -open import category-theory.precategories +open import category-theory.functors-precategories funext univalence truncations +open import category-theory.natural-transformations-maps-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalences -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets -open import foundation.strictly-involutive-identity-types +open import foundation.dependent-products-propositions funext +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.strictly-involutive-identity-types funext univalence open import foundation.universe-levels ``` diff --git a/src/category-theory/natural-transformations-maps-categories.lagda.md b/src/category-theory/natural-transformations-maps-categories.lagda.md index 04e78aa05e..17a4c720d1 100644 --- a/src/category-theory/natural-transformations-maps-categories.lagda.md +++ b/src/category-theory/natural-transformations-maps-categories.lagda.md @@ -1,22 +1,31 @@ # Natural transformations between maps between categories ```agda -module category-theory.natural-transformations-maps-categories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.natural-transformations-maps-categories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.maps-categories -open import category-theory.natural-transformations-maps-precategories - -open import foundation.embeddings -open import foundation.equivalences -open import foundation.homotopies -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets +open import category-theory.categories funext univalence truncations +open import category-theory.maps-categories funext univalence truncations +open import category-theory.natural-transformations-maps-precategories funext univalence truncations + +open import foundation.dependent-products-propositions funext +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence open import foundation.universe-levels ``` diff --git a/src/category-theory/natural-transformations-maps-from-small-to-large-precategories.lagda.md b/src/category-theory/natural-transformations-maps-from-small-to-large-precategories.lagda.md index 3158288d63..1f8fb51142 100644 --- a/src/category-theory/natural-transformations-maps-from-small-to-large-precategories.lagda.md +++ b/src/category-theory/natural-transformations-maps-from-small-to-large-precategories.lagda.md @@ -1,29 +1,38 @@ # Natural transformations between maps from small to large precategories ```agda -module category-theory.natural-transformations-maps-from-small-to-large-precategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.natural-transformations-maps-from-small-to-large-precategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.commuting-squares-of-morphisms-in-large-precategories -open import category-theory.large-precategories -open import category-theory.maps-from-small-to-large-precategories -open import category-theory.precategories +open import category-theory.commuting-squares-of-morphisms-in-large-precategories funext univalence truncations +open import category-theory.large-precategories funext univalence truncations +open import category-theory.maps-from-small-to-large-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets -open import foundation.strictly-involutive-identity-types -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.function-extensionality funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.strictly-involutive-identity-types funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels ``` diff --git a/src/category-theory/natural-transformations-maps-precategories.lagda.md b/src/category-theory/natural-transformations-maps-precategories.lagda.md index 57b61936ce..c52cf9cb22 100644 --- a/src/category-theory/natural-transformations-maps-precategories.lagda.md +++ b/src/category-theory/natural-transformations-maps-precategories.lagda.md @@ -1,28 +1,37 @@ # Natural transformations between maps between precategories ```agda -module category-theory.natural-transformations-maps-precategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.natural-transformations-maps-precategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.commuting-squares-of-morphisms-in-precategories -open import category-theory.maps-precategories -open import category-theory.precategories +open import category-theory.commuting-squares-of-morphisms-in-precategories funext univalence truncations +open import category-theory.maps-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets -open import foundation.strictly-involutive-identity-types -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.function-extensionality funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.strictly-involutive-identity-types funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels ``` diff --git a/src/category-theory/nonunital-precategories.lagda.md b/src/category-theory/nonunital-precategories.lagda.md index 32f4782eab..b07f76092b 100644 --- a/src/category-theory/nonunital-precategories.lagda.md +++ b/src/category-theory/nonunital-precategories.lagda.md @@ -1,22 +1,32 @@ # Nonunital precategories ```agda -module category-theory.nonunital-precategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.nonunital-precategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.composition-operations-on-binary-families-of-sets -open import category-theory.set-magmoids +open import category-theory.composition-operations-on-binary-families-of-sets funext univalence truncations +open import category-theory.set-magmoids funext univalence truncations -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets -open import foundation.strictly-involutive-identity-types -open import foundation.truncated-types +open import foundation.dependent-products-propositions funext +open import foundation.dependent-products-truncated-types funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.strictly-involutive-identity-types funext univalence +open import foundation.truncated-types funext univalence open import foundation.truncation-levels open import foundation.universe-levels ``` diff --git a/src/category-theory/one-object-precategories.lagda.md b/src/category-theory/one-object-precategories.lagda.md index 76dbd98741..3eba5fb0e9 100644 --- a/src/category-theory/one-object-precategories.lagda.md +++ b/src/category-theory/one-object-precategories.lagda.md @@ -1,24 +1,34 @@ # One object precategories ```agda -module category-theory.one-object-precategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.one-object-precategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.endomorphisms-in-precategories -open import category-theory.precategories +open import category-theory.endomorphisms-in-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations -open import foundation.contractible-types +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence open import foundation.unit-type open import foundation.universe-levels -open import group-theory.monoids +open import group-theory.monoids funext univalence truncations ```
diff --git a/src/category-theory/opposite-categories.lagda.md b/src/category-theory/opposite-categories.lagda.md index 8eefb6735c..3b39095d71 100644 --- a/src/category-theory/opposite-categories.lagda.md +++ b/src/category-theory/opposite-categories.lagda.md @@ -1,24 +1,32 @@ # Opposite categories ```agda -module category-theory.opposite-categories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.opposite-categories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.isomorphisms-in-precategories -open import category-theory.opposite-precategories -open import category-theory.precategories +open import category-theory.categories funext univalence truncations +open import category-theory.isomorphisms-in-precategories funext univalence truncations +open import category-theory.opposite-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.identity-types -open import foundation.involutions -open import foundation.sets -open import foundation.strictly-involutive-identity-types -open import foundation.subtypes +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.involutions funext univalence +open import foundation.sets funext univalence +open import foundation.strictly-involutive-identity-types funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels ``` diff --git a/src/category-theory/opposite-large-precategories.lagda.md b/src/category-theory/opposite-large-precategories.lagda.md index 99647dd2de..c8bee9c059 100644 --- a/src/category-theory/opposite-large-precategories.lagda.md +++ b/src/category-theory/opposite-large-precategories.lagda.md @@ -1,22 +1,30 @@ # Opposite large precategories ```agda -module category-theory.opposite-large-precategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.opposite-large-precategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.isomorphisms-in-large-precategories -open import category-theory.large-precategories +open import category-theory.isomorphisms-in-large-precategories funext univalence truncations +open import category-theory.large-precategories funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.homotopies -open import foundation.identity-types +open import foundation.equivalences funext +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.large-identity-types -open import foundation.sets -open import foundation.strictly-involutive-identity-types +open import foundation.sets funext univalence +open import foundation.strictly-involutive-identity-types funext univalence open import foundation.universe-levels ``` diff --git a/src/category-theory/opposite-precategories.lagda.md b/src/category-theory/opposite-precategories.lagda.md index d349bfe93e..9b511d74c1 100644 --- a/src/category-theory/opposite-precategories.lagda.md +++ b/src/category-theory/opposite-precategories.lagda.md @@ -1,22 +1,30 @@ # Opposite precategories ```agda -module category-theory.opposite-precategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.opposite-precategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.isomorphisms-in-precategories -open import category-theory.precategories +open import category-theory.isomorphisms-in-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.homotopies -open import foundation.identity-types -open import foundation.involutions -open import foundation.sets -open import foundation.strictly-involutive-identity-types +open import foundation.equivalences funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.involutions funext univalence +open import foundation.sets funext univalence +open import foundation.strictly-involutive-identity-types funext univalence open import foundation.universe-levels ``` diff --git a/src/category-theory/opposite-preunivalent-categories.lagda.md b/src/category-theory/opposite-preunivalent-categories.lagda.md index 4ea17ae265..097991c1e6 100644 --- a/src/category-theory/opposite-preunivalent-categories.lagda.md +++ b/src/category-theory/opposite-preunivalent-categories.lagda.md @@ -1,25 +1,33 @@ # Opposite preunivalent categories ```agda -module category-theory.opposite-preunivalent-categories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.opposite-preunivalent-categories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.isomorphisms-in-precategories -open import category-theory.opposite-precategories -open import category-theory.precategories -open import category-theory.preunivalent-categories +open import category-theory.isomorphisms-in-precategories funext univalence truncations +open import category-theory.opposite-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations +open import category-theory.preunivalent-categories funext univalence truncations open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalences -open import foundation.identity-types -open import foundation.involutions -open import foundation.sets -open import foundation.strictly-involutive-identity-types -open import foundation.subtypes +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.involutions funext univalence +open import foundation.sets funext univalence +open import foundation.strictly-involutive-identity-types funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels ``` diff --git a/src/category-theory/opposite-strongly-preunivalent-categories.lagda.md b/src/category-theory/opposite-strongly-preunivalent-categories.lagda.md index 131c39a411..bcd838bde4 100644 --- a/src/category-theory/opposite-strongly-preunivalent-categories.lagda.md +++ b/src/category-theory/opposite-strongly-preunivalent-categories.lagda.md @@ -1,26 +1,34 @@ # Opposite strongly preunivalent categories ```agda -module category-theory.opposite-strongly-preunivalent-categories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.opposite-strongly-preunivalent-categories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.isomorphisms-in-precategories -open import category-theory.opposite-precategories -open import category-theory.precategories -open import category-theory.strongly-preunivalent-categories +open import category-theory.isomorphisms-in-precategories funext univalence truncations +open import category-theory.opposite-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations +open import category-theory.strongly-preunivalent-categories funext univalence truncations open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalences -open import foundation.functoriality-dependent-pair-types -open import foundation.identity-types -open import foundation.involutions -open import foundation.sets -open import foundation.strictly-involutive-identity-types -open import foundation.subtypes +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.identity-types funext +open import foundation.involutions funext univalence +open import foundation.sets funext univalence +open import foundation.strictly-involutive-identity-types funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels ``` diff --git a/src/category-theory/pointed-endofunctors-categories.lagda.md b/src/category-theory/pointed-endofunctors-categories.lagda.md index f5d7468bb0..4d7f1dcce6 100644 --- a/src/category-theory/pointed-endofunctors-categories.lagda.md +++ b/src/category-theory/pointed-endofunctors-categories.lagda.md @@ -1,19 +1,27 @@ # Pointed endofunctors on categories ```agda -module category-theory.pointed-endofunctors-categories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.pointed-endofunctors-categories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.functors-categories -open import category-theory.natural-transformations-functors-categories -open import category-theory.pointed-endofunctors-precategories +open import category-theory.categories funext univalence truncations +open import category-theory.functors-categories funext univalence truncations +open import category-theory.natural-transformations-functors-categories funext univalence truncations +open import category-theory.pointed-endofunctors-precategories funext univalence truncations open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels ``` diff --git a/src/category-theory/pointed-endofunctors-precategories.lagda.md b/src/category-theory/pointed-endofunctors-precategories.lagda.md index 2472a4dab6..07f47c7f9e 100644 --- a/src/category-theory/pointed-endofunctors-precategories.lagda.md +++ b/src/category-theory/pointed-endofunctors-precategories.lagda.md @@ -1,18 +1,26 @@ # Pointed endofunctors ```agda -module category-theory.pointed-endofunctors-precategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.pointed-endofunctors-precategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.functors-precategories -open import category-theory.natural-transformations-functors-precategories -open import category-theory.precategories +open import category-theory.functors-precategories funext univalence truncations +open import category-theory.natural-transformations-functors-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels ``` diff --git a/src/category-theory/precategories.lagda.md b/src/category-theory/precategories.lagda.md index 1eb71cad75..1a7ef26208 100644 --- a/src/category-theory/precategories.lagda.md +++ b/src/category-theory/precategories.lagda.md @@ -1,25 +1,35 @@ # Precategories ```agda -module category-theory.precategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.precategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.composition-operations-on-binary-families-of-sets -open import category-theory.nonunital-precategories -open import category-theory.set-magmoids +open import category-theory.composition-operations-on-binary-families-of-sets funext univalence truncations +open import category-theory.nonunital-precategories funext univalence truncations +open import category-theory.set-magmoids funext univalence truncations open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets -open import foundation.strictly-involutive-identity-types -open import foundation.truncated-types +open import foundation.dependent-products-propositions funext +open import foundation.dependent-products-truncated-types funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.strictly-involutive-identity-types funext univalence +open import foundation.truncated-types funext univalence open import foundation.truncation-levels open import foundation.universe-levels ``` diff --git a/src/category-theory/precategory-of-elements-of-a-presheaf.lagda.md b/src/category-theory/precategory-of-elements-of-a-presheaf.lagda.md index 2e36074e3f..11161c24dc 100644 --- a/src/category-theory/precategory-of-elements-of-a-presheaf.lagda.md +++ b/src/category-theory/precategory-of-elements-of-a-presheaf.lagda.md @@ -1,23 +1,31 @@ # Precategory of elements of a presheaf ```agda -module category-theory.precategory-of-elements-of-a-presheaf where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.precategory-of-elements-of-a-presheaf + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.functors-precategories -open import category-theory.opposite-precategories -open import category-theory.precategories -open import category-theory.presheaf-categories +open import category-theory.functors-precategories funext univalence truncations +open import category-theory.opposite-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations +open import category-theory.presheaf-categories funext univalence truncations open import foundation.action-on-identifications-functions -open import foundation.category-of-sets +open import foundation.category-of-sets funext univalence truncations open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.sets -open import foundation.subtypes +open import foundation.identity-types funext +open import foundation.sets funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels ``` diff --git a/src/category-theory/precategory-of-functors-from-small-to-large-precategories.lagda.md b/src/category-theory/precategory-of-functors-from-small-to-large-precategories.lagda.md index 6494609f6b..ff9d7da585 100644 --- a/src/category-theory/precategory-of-functors-from-small-to-large-precategories.lagda.md +++ b/src/category-theory/precategory-of-functors-from-small-to-large-precategories.lagda.md @@ -1,19 +1,27 @@ # The precategory of functors and natural transformations from small to large precategories ```agda -module category-theory.precategory-of-functors-from-small-to-large-precategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.precategory-of-functors-from-small-to-large-precategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.functors-from-small-to-large-precategories -open import category-theory.large-precategories -open import category-theory.natural-transformations-functors-from-small-to-large-precategories -open import category-theory.precategories +open import category-theory.functors-from-small-to-large-precategories funext univalence truncations +open import category-theory.large-precategories funext univalence truncations +open import category-theory.natural-transformations-functors-from-small-to-large-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations -open import foundation.identity-types -open import foundation.strictly-involutive-identity-types +open import foundation.identity-types funext +open import foundation.strictly-involutive-identity-types funext univalence open import foundation.universe-levels ``` diff --git a/src/category-theory/precategory-of-functors.lagda.md b/src/category-theory/precategory-of-functors.lagda.md index 1797d461fa..d87ca60bf2 100644 --- a/src/category-theory/precategory-of-functors.lagda.md +++ b/src/category-theory/precategory-of-functors.lagda.md @@ -1,28 +1,34 @@ # The precategory of functors and natural transformations between two precategories ```agda -module category-theory.precategory-of-functors where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.precategory-of-functors + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.composition-operations-on-binary-families-of-sets -open import category-theory.functors-precategories -open import category-theory.isomorphisms-in-precategories -open import category-theory.natural-isomorphisms-functors-precategories -open import category-theory.natural-transformations-functors-precategories -open import category-theory.precategories +open import category-theory.composition-operations-on-binary-families-of-sets funext univalence truncations +open import category-theory.functors-precategories funext univalence truncations +open import category-theory.isomorphisms-in-precategories funext univalence truncations +open import category-theory.natural-isomorphisms-functors-precategories funext univalence truncations +open import category-theory.natural-transformations-functors-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.functoriality-dependent-pair-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.propositions -open import foundation.strictly-involutive-identity-types +open import foundation.equivalences funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.strictly-involutive-identity-types funext univalence open import foundation.universe-levels ``` diff --git a/src/category-theory/precategory-of-maps-from-small-to-large-precategories.lagda.md b/src/category-theory/precategory-of-maps-from-small-to-large-precategories.lagda.md index 7c755df183..c9330ca91a 100644 --- a/src/category-theory/precategory-of-maps-from-small-to-large-precategories.lagda.md +++ b/src/category-theory/precategory-of-maps-from-small-to-large-precategories.lagda.md @@ -1,19 +1,27 @@ # The precategory of maps and natural transformations from a small to a large precategory ```agda -module category-theory.precategory-of-maps-from-small-to-large-precategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.precategory-of-maps-from-small-to-large-precategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.large-precategories -open import category-theory.maps-from-small-to-large-precategories -open import category-theory.natural-transformations-maps-from-small-to-large-precategories -open import category-theory.precategories +open import category-theory.large-precategories funext univalence truncations +open import category-theory.maps-from-small-to-large-precategories funext univalence truncations +open import category-theory.natural-transformations-maps-from-small-to-large-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations -open import foundation.identity-types -open import foundation.strictly-involutive-identity-types +open import foundation.identity-types funext +open import foundation.strictly-involutive-identity-types funext univalence open import foundation.universe-levels ``` diff --git a/src/category-theory/precategory-of-maps-precategories.lagda.md b/src/category-theory/precategory-of-maps-precategories.lagda.md index 8fc3c449a5..b0e8ba85ba 100644 --- a/src/category-theory/precategory-of-maps-precategories.lagda.md +++ b/src/category-theory/precategory-of-maps-precategories.lagda.md @@ -1,28 +1,34 @@ # The precategory of maps and natural transformations between two precategories ```agda -module category-theory.precategory-of-maps-precategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.precategory-of-maps-precategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.composition-operations-on-binary-families-of-sets -open import category-theory.isomorphisms-in-precategories -open import category-theory.maps-precategories -open import category-theory.natural-isomorphisms-maps-precategories -open import category-theory.natural-transformations-maps-precategories -open import category-theory.precategories +open import category-theory.composition-operations-on-binary-families-of-sets funext univalence truncations +open import category-theory.isomorphisms-in-precategories funext univalence truncations +open import category-theory.maps-precategories funext univalence truncations +open import category-theory.natural-isomorphisms-maps-precategories funext univalence truncations +open import category-theory.natural-transformations-maps-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.functoriality-dependent-pair-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.propositions -open import foundation.strictly-involutive-identity-types +open import foundation.equivalences funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.strictly-involutive-identity-types funext univalence open import foundation.universe-levels ``` diff --git a/src/category-theory/pregroupoids.lagda.md b/src/category-theory/pregroupoids.lagda.md index e5cd73ad42..ff11c24fde 100644 --- a/src/category-theory/pregroupoids.lagda.md +++ b/src/category-theory/pregroupoids.lagda.md @@ -1,22 +1,32 @@ # Pregroupoids ```agda -module category-theory.pregroupoids where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.pregroupoids + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.isomorphisms-in-precategories -open import category-theory.precategories +open import category-theory.isomorphisms-in-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.identity-types -open import foundation.iterated-dependent-product-types -open import foundation.propositions -open import foundation.sets -open import foundation.strictly-involutive-identity-types +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.iterated-dependent-product-types funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.strictly-involutive-identity-types funext univalence +open import foundation.telescopes open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels ``` diff --git a/src/category-theory/presheaf-categories.lagda.md b/src/category-theory/presheaf-categories.lagda.md index 1e61775687..3a1b76fa02 100644 --- a/src/category-theory/presheaf-categories.lagda.md +++ b/src/category-theory/presheaf-categories.lagda.md @@ -1,29 +1,36 @@ # Presheaf categories ```agda -module category-theory.presheaf-categories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.presheaf-categories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.copresheaf-categories -open import category-theory.functors-from-small-to-large-precategories -open import category-theory.large-categories -open import category-theory.large-precategories -open import category-theory.natural-transformations-functors-from-small-to-large-precategories -open import category-theory.opposite-precategories -open import category-theory.precategories - -open import foundation.category-of-sets -open import foundation.commuting-squares-of-maps -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.sets -open import foundation.strictly-involutive-identity-types +open import category-theory.categories funext univalence truncations +open import category-theory.copresheaf-categories funext univalence truncations +open import category-theory.functors-from-small-to-large-precategories funext univalence truncations +open import category-theory.large-categories funext univalence truncations +open import category-theory.large-precategories funext univalence truncations +open import category-theory.natural-transformations-functors-from-small-to-large-precategories funext univalence truncations +open import category-theory.opposite-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations + +open import foundation.category-of-sets funext univalence truncations +open import foundation.commuting-squares-of-maps funext univalence +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.sets funext univalence +open import foundation.strictly-involutive-identity-types funext univalence open import foundation.universe-levels ``` diff --git a/src/category-theory/preunivalent-categories.lagda.md b/src/category-theory/preunivalent-categories.lagda.md index 15f683b862..c6e95978fe 100644 --- a/src/category-theory/preunivalent-categories.lagda.md +++ b/src/category-theory/preunivalent-categories.lagda.md @@ -1,24 +1,33 @@ # Preunivalent categories ```agda -module category-theory.preunivalent-categories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.preunivalent-categories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.composition-operations-on-binary-families-of-sets -open import category-theory.isomorphisms-in-precategories -open import category-theory.precategories +open import category-theory.composition-operations-on-binary-families-of-sets funext univalence truncations +open import category-theory.isomorphisms-in-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations -open import foundation.1-types -open import foundation.cartesian-product-types +open import foundation.1-types funext univalence +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets -open import foundation.strictly-involutive-identity-types +open import foundation.dependent-products-propositions funext +open import foundation.embeddings funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.strictly-involutive-identity-types funext univalence open import foundation.universe-levels ``` diff --git a/src/category-theory/products-in-precategories.lagda.md b/src/category-theory/products-in-precategories.lagda.md index 78e0668af4..08a7da49ab 100644 --- a/src/category-theory/products-in-precategories.lagda.md +++ b/src/category-theory/products-in-precategories.lagda.md @@ -1,22 +1,33 @@ # Products in precategories ```agda -module category-theory.products-in-precategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.products-in-precategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.precategories +open import category-theory.precategories funext univalence truncations open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types -open import foundation.contractible-types +open import foundation.cartesian-product-types funext univalence +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.iterated-dependent-product-types -open import foundation.propositions -open import foundation.uniqueness-quantification +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.identity-types funext +open import foundation.iterated-dependent-product-types funext +open import foundation.propositions funext univalence +open import foundation.telescopes +open import foundation.uniqueness-quantification funext univalence truncations open import foundation.universe-levels ``` diff --git a/src/category-theory/products-of-precategories.lagda.md b/src/category-theory/products-of-precategories.lagda.md index cb52fdd0e6..277b6b3cb8 100644 --- a/src/category-theory/products-of-precategories.lagda.md +++ b/src/category-theory/products-of-precategories.lagda.md @@ -1,19 +1,27 @@ # Products of precategories ```agda -module category-theory.products-of-precategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.products-of-precategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.precategories +open import category-theory.precategories funext univalence truncations -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types open import foundation.equality-cartesian-product-types -open import foundation.identity-types -open import foundation.sets +open import foundation.identity-types funext +open import foundation.sets funext univalence open import foundation.universe-levels ``` diff --git a/src/category-theory/pseudomonic-functors-precategories.lagda.md b/src/category-theory/pseudomonic-functors-precategories.lagda.md index 12821ec3b4..fac2c327e9 100644 --- a/src/category-theory/pseudomonic-functors-precategories.lagda.md +++ b/src/category-theory/pseudomonic-functors-precategories.lagda.md @@ -1,27 +1,37 @@ # Pseudomonic functors between precategories ```agda -module category-theory.pseudomonic-functors-precategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.pseudomonic-functors-precategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.conservative-functors-precategories -open import category-theory.faithful-functors-precategories -open import category-theory.functors-precategories -open import category-theory.isomorphisms-in-precategories -open import category-theory.precategories +open import category-theory.conservative-functors-precategories funext univalence truncations +open import category-theory.faithful-functors-precategories funext univalence truncations +open import category-theory.functors-precategories funext univalence truncations +open import category-theory.isomorphisms-in-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.iterated-dependent-product-types -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.surjective-maps +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.iterated-dependent-product-types funext +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence +open import foundation.surjective-maps funext univalence truncations +open import foundation.telescopes open import foundation.universe-levels ``` diff --git a/src/category-theory/pullbacks-in-precategories.lagda.md b/src/category-theory/pullbacks-in-precategories.lagda.md index aaefb61ec6..86ba4edcfe 100644 --- a/src/category-theory/pullbacks-in-precategories.lagda.md +++ b/src/category-theory/pullbacks-in-precategories.lagda.md @@ -1,22 +1,33 @@ # Pullbacks in precategories ```agda -module category-theory.pullbacks-in-precategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.pullbacks-in-precategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.precategories +open import category-theory.precategories funext univalence truncations open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types -open import foundation.contractible-types +open import foundation.cartesian-product-types funext univalence +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.iterated-dependent-product-types -open import foundation.propositions -open import foundation.uniqueness-quantification +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.identity-types funext +open import foundation.iterated-dependent-product-types funext +open import foundation.propositions funext univalence +open import foundation.telescopes +open import foundation.uniqueness-quantification funext univalence truncations open import foundation.universe-levels ``` diff --git a/src/category-theory/replete-subprecategories.lagda.md b/src/category-theory/replete-subprecategories.lagda.md index 50d39bd9b3..c62fdfc072 100644 --- a/src/category-theory/replete-subprecategories.lagda.md +++ b/src/category-theory/replete-subprecategories.lagda.md @@ -1,27 +1,37 @@ # Replete subprecategories ```agda -module category-theory.replete-subprecategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.replete-subprecategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.isomorphism-induction-categories -open import category-theory.isomorphisms-in-precategories -open import category-theory.isomorphisms-in-subprecategories -open import category-theory.precategories -open import category-theory.subprecategories +open import category-theory.categories funext univalence truncations +open import category-theory.isomorphism-induction-categories funext univalence truncations +open import category-theory.isomorphisms-in-precategories funext univalence truncations +open import category-theory.isomorphisms-in-subprecategories funext univalence truncations +open import category-theory.precategories funext univalence truncations +open import category-theory.subprecategories funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.functoriality-dependent-pair-types -open import foundation.iterated-dependent-product-types -open import foundation.logical-equivalences -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.iterated-dependent-product-types funext +open import foundation.logical-equivalences funext +open import foundation.propositions funext univalence open import foundation.subsingleton-induction -open import foundation.subtypes +open import foundation.subtypes funext univalence truncations +open import foundation.telescopes open import foundation.type-arithmetic-cartesian-product-types open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels diff --git a/src/category-theory/representable-functors-categories.lagda.md b/src/category-theory/representable-functors-categories.lagda.md index 22014d5f9d..e49b1a5fbd 100644 --- a/src/category-theory/representable-functors-categories.lagda.md +++ b/src/category-theory/representable-functors-categories.lagda.md @@ -1,18 +1,26 @@ # Representable functors between categories ```agda -module category-theory.representable-functors-categories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.representable-functors-categories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.functors-categories -open import category-theory.natural-transformations-functors-categories -open import category-theory.representable-functors-precategories +open import category-theory.categories funext univalence truncations +open import category-theory.functors-categories funext univalence truncations +open import category-theory.natural-transformations-functors-categories funext univalence truncations +open import category-theory.representable-functors-precategories funext univalence truncations -open import foundation.category-of-sets +open import foundation.category-of-sets funext univalence truncations open import foundation.universe-levels ``` diff --git a/src/category-theory/representable-functors-large-precategories.lagda.md b/src/category-theory/representable-functors-large-precategories.lagda.md index 6a88be63e6..cba1fde3a3 100644 --- a/src/category-theory/representable-functors-large-precategories.lagda.md +++ b/src/category-theory/representable-functors-large-precategories.lagda.md @@ -1,21 +1,29 @@ # Representable functors between large precategories ```agda -module category-theory.representable-functors-large-precategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.representable-functors-large-precategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.functors-large-precategories -open import category-theory.large-precategories -open import category-theory.natural-transformations-functors-large-precategories - -open import foundation.category-of-sets -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.identity-types -open import foundation.sets +open import category-theory.functors-large-precategories funext univalence truncations +open import category-theory.large-precategories funext univalence truncations +open import category-theory.natural-transformations-functors-large-precategories funext univalence truncations + +open import foundation.category-of-sets funext univalence truncations +open import foundation.function-extensionality funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.sets funext univalence open import foundation.universe-levels ``` diff --git a/src/category-theory/representable-functors-precategories.lagda.md b/src/category-theory/representable-functors-precategories.lagda.md index 64efc53409..a01fdd2e41 100644 --- a/src/category-theory/representable-functors-precategories.lagda.md +++ b/src/category-theory/representable-functors-precategories.lagda.md @@ -1,25 +1,33 @@ # Representable functors between precategories ```agda -module category-theory.representable-functors-precategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.representable-functors-precategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.copresheaf-categories -open import category-theory.functors-precategories -open import category-theory.maps-precategories -open import category-theory.natural-transformations-functors-precategories -open import category-theory.opposite-precategories -open import category-theory.precategories - -open import foundation.category-of-sets +open import category-theory.copresheaf-categories funext univalence truncations +open import category-theory.functors-precategories funext univalence truncations +open import category-theory.maps-precategories funext univalence truncations +open import category-theory.natural-transformations-functors-precategories funext univalence truncations +open import category-theory.opposite-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations + +open import foundation.category-of-sets funext univalence truncations open import foundation.dependent-pair-types -open import foundation.function-extensionality -open import foundation.homotopies -open import foundation.identity-types -open import foundation.sets +open import foundation.function-extensionality funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.sets funext univalence open import foundation.universe-levels ``` diff --git a/src/category-theory/representing-arrow-category.lagda.md b/src/category-theory/representing-arrow-category.lagda.md index dbdfec5962..d673e2ba4f 100644 --- a/src/category-theory/representing-arrow-category.lagda.md +++ b/src/category-theory/representing-arrow-category.lagda.md @@ -1,26 +1,36 @@ # The representing arrow category ```agda -module category-theory.representing-arrow-category where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.representing-arrow-category + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.isomorphisms-in-precategories -open import category-theory.precategories +open import category-theory.categories funext univalence truncations +open import category-theory.isomorphisms-in-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations -open import foundation.booleans open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.propositions -open import foundation.sets -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.empty-types funext univalence truncations +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.unit-type open import foundation.universe-levels + +open import foundation-core.booleans ```
@@ -30,7 +40,7 @@ open import foundation.universe-levels The **representing arrow** is the [category](category-theory.categories.md) that [represents](category-theory.representable-functors-categories.md) arrows in a ([pre-](category-theory.precategories.md))category. We model it after -implication on the [booleans](foundation.booleans.md). +implication on the [booleans](foundation-core.booleans.md). ## Definition diff --git a/src/category-theory/restrictions-functors-cores-precategories.lagda.md b/src/category-theory/restrictions-functors-cores-precategories.lagda.md index 1463265b07..8d67c388ba 100644 --- a/src/category-theory/restrictions-functors-cores-precategories.lagda.md +++ b/src/category-theory/restrictions-functors-cores-precategories.lagda.md @@ -1,23 +1,31 @@ # Restrictions of functors to cores of precategories ```agda -module category-theory.restrictions-functors-cores-precategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.restrictions-functors-cores-precategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.cores-precategories -open import category-theory.faithful-functors-precategories -open import category-theory.fully-faithful-functors-precategories -open import category-theory.functors-precategories -open import category-theory.isomorphisms-in-precategories -open import category-theory.maps-precategories -open import category-theory.precategories -open import category-theory.pseudomonic-functors-precategories +open import category-theory.cores-precategories funext univalence truncations +open import category-theory.faithful-functors-precategories funext univalence truncations +open import category-theory.fully-faithful-functors-precategories funext univalence truncations +open import category-theory.functors-precategories funext univalence truncations +open import category-theory.isomorphisms-in-precategories funext univalence truncations +open import category-theory.maps-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations +open import category-theory.pseudomonic-functors-precategories funext univalence truncations open import foundation.dependent-pair-types -open import foundation.subtypes +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels ``` diff --git a/src/category-theory/right-extensions-precategories.lagda.md b/src/category-theory/right-extensions-precategories.lagda.md index 4c3828347f..4906a54d18 100644 --- a/src/category-theory/right-extensions-precategories.lagda.md +++ b/src/category-theory/right-extensions-precategories.lagda.md @@ -1,42 +1,52 @@ # Right extensions in precategories ```agda -module category-theory.right-extensions-precategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.right-extensions-precategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.functors-precategories -open import category-theory.natural-transformations-functors-precategories -open import category-theory.precategories +open import category-theory.functors-precategories funext univalence truncations +open import category-theory.natural-transformations-functors-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations -open import foundation.action-on-equivalences-functions +open import foundation.action-on-equivalences-functions funext univalence open import foundation.action-on-identifications-functions -open import foundation.contractible-types -open import foundation.dependent-identifications +open import foundation.contractible-types funext univalence +open import foundation.dependent-identifications funext open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types -open import foundation.equality-dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.equality-dependent-function-types funext +open import foundation.equality-dependent-pair-types funext +open import foundation.equivalences funext +open import foundation.function-extensionality funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types -open import foundation.multivariable-homotopies -open import foundation.propositions -open import foundation.retractions -open import foundation.sections -open import foundation.sets +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext +open import foundation.multivariable-homotopies funext +open import foundation.propositions funext univalence +open import foundation.retractions funext +open import foundation.sections funext +open import foundation.sets funext univalence open import foundation.structure-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext univalence truncations open import foundation.unit-type open import foundation.universe-levels -open import foundation-core.functoriality-dependent-function-types +open import foundation-core.functoriality-dependent-function-types funext ```
diff --git a/src/category-theory/right-kan-extensions-precategories.lagda.md b/src/category-theory/right-kan-extensions-precategories.lagda.md index 1af7fd92a1..1c33c9b300 100644 --- a/src/category-theory/right-kan-extensions-precategories.lagda.md +++ b/src/category-theory/right-kan-extensions-precategories.lagda.md @@ -1,20 +1,28 @@ # Right Kan extensions in precategories ```agda -module category-theory.right-kan-extensions-precategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.right-kan-extensions-precategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.functors-precategories -open import category-theory.natural-transformations-functors-precategories -open import category-theory.precategories -open import category-theory.right-extensions-precategories +open import category-theory.functors-precategories funext univalence truncations +open import category-theory.natural-transformations-functors-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations +open import category-theory.right-extensions-precategories funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.identity-types +open import foundation.equivalences funext +open import foundation.identity-types funext open import foundation.universe-levels ``` diff --git a/src/category-theory/rigid-objects-categories.lagda.md b/src/category-theory/rigid-objects-categories.lagda.md index ed69843f56..f0b1d6b8b4 100644 --- a/src/category-theory/rigid-objects-categories.lagda.md +++ b/src/category-theory/rigid-objects-categories.lagda.md @@ -1,16 +1,25 @@ # Rigid objects in a category ```agda -module category-theory.rigid-objects-categories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.rigid-objects-categories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.rigid-objects-precategories +open import category-theory.categories funext univalence truncations +open import category-theory.rigid-objects-precategories funext univalence truncations -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.propositions funext univalence open import foundation.universe-levels ``` diff --git a/src/category-theory/rigid-objects-precategories.lagda.md b/src/category-theory/rigid-objects-precategories.lagda.md index 356a7f517a..5fcc91a7cf 100644 --- a/src/category-theory/rigid-objects-precategories.lagda.md +++ b/src/category-theory/rigid-objects-precategories.lagda.md @@ -1,18 +1,28 @@ # Rigid objects in a precategory ```agda -module category-theory.rigid-objects-precategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.rigid-objects-precategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.isomorphisms-in-precategories -open import category-theory.precategories +open import category-theory.isomorphisms-in-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations -open import foundation.contractible-types +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.propositions +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.propositions funext univalence open import foundation.universe-levels ``` diff --git a/src/category-theory/set-magmoids.lagda.md b/src/category-theory/set-magmoids.lagda.md index ec501dc223..4ebdf81567 100644 --- a/src/category-theory/set-magmoids.lagda.md +++ b/src/category-theory/set-magmoids.lagda.md @@ -1,19 +1,29 @@ # Set-magmoids ```agda -module category-theory.set-magmoids where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.set-magmoids + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.composition-operations-on-binary-families-of-sets +open import category-theory.composition-operations-on-binary-families-of-sets funext univalence truncations -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.propositions -open import foundation.sets -open import foundation.truncated-types +open import foundation.dependent-products-propositions funext +open import foundation.dependent-products-truncated-types funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.truncated-types funext univalence open import foundation.truncation-levels open import foundation.universe-levels ``` diff --git a/src/category-theory/sieves-in-categories.lagda.md b/src/category-theory/sieves-in-categories.lagda.md index 1bab198afa..ab2f4da7f1 100644 --- a/src/category-theory/sieves-in-categories.lagda.md +++ b/src/category-theory/sieves-in-categories.lagda.md @@ -1,16 +1,25 @@ # Sieves in categories ```agda -module category-theory.sieves-in-categories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.sieves-in-categories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.categories +open import category-theory.categories funext univalence truncations -open import foundation.propositions -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.propositions funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels ``` diff --git a/src/category-theory/simplex-category.lagda.md b/src/category-theory/simplex-category.lagda.md index aa311fa6b6..22ce9ed724 100644 --- a/src/category-theory/simplex-category.lagda.md +++ b/src/category-theory/simplex-category.lagda.md @@ -1,25 +1,33 @@ # The simplex category ```agda -module category-theory.simplex-category where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.simplex-category + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.composition-operations-on-binary-families-of-sets -open import category-theory.precategories +open import category-theory.composition-operations-on-binary-families-of-sets funext univalence truncations +open import category-theory.precategories funext univalence truncations -open import elementary-number-theory.inequality-standard-finite-types +open import elementary-number-theory.inequality-standard-finite-types funext univalence truncations open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.sets -open import foundation.strictly-involutive-identity-types +open import foundation.identity-types funext +open import foundation.sets funext univalence +open import foundation.strictly-involutive-identity-types funext univalence open import foundation.universe-levels -open import order-theory.order-preserving-maps-posets +open import order-theory.order-preserving-maps-posets funext univalence truncations ```
diff --git a/src/category-theory/slice-precategories.lagda.md b/src/category-theory/slice-precategories.lagda.md index 9443a721e1..d0cb899b35 100644 --- a/src/category-theory/slice-precategories.lagda.md +++ b/src/category-theory/slice-precategories.lagda.md @@ -1,34 +1,44 @@ # Slice precategories ```agda -module category-theory.slice-precategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.slice-precategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.functors-precategories -open import category-theory.precategories -open import category-theory.products-in-precategories -open import category-theory.pullbacks-in-precategories -open import category-theory.terminal-objects-precategories +open import category-theory.functors-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations +open import category-theory.products-in-precategories funext univalence truncations +open import category-theory.pullbacks-in-precategories funext univalence truncations +open import category-theory.terminal-objects-precategories funext univalence truncations open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types -open import foundation.contractible-types +open import foundation.cartesian-product-types funext univalence +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.propositions -open import foundation.sets -open import foundation.strictly-involutive-identity-types -open import foundation.subtypes -open import foundation.torsorial-type-families +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.equality-dependent-pair-types funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.strictly-involutive-identity-types funext univalence +open import foundation.subtypes funext univalence truncations +open import foundation.torsorial-type-families funext univalence truncations open import foundation.universe-levels ``` diff --git a/src/category-theory/split-essentially-surjective-functors-precategories.lagda.md b/src/category-theory/split-essentially-surjective-functors-precategories.lagda.md index d62ed8e8fe..239b2c2856 100644 --- a/src/category-theory/split-essentially-surjective-functors-precategories.lagda.md +++ b/src/category-theory/split-essentially-surjective-functors-precategories.lagda.md @@ -1,32 +1,42 @@ # Split essentially surjective functors between precategories ```agda -module category-theory.split-essentially-surjective-functors-precategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.split-essentially-surjective-functors-precategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.cores-precategories -open import category-theory.essential-fibers-of-functors-precategories -open import category-theory.essentially-surjective-functors-precategories -open import category-theory.fully-faithful-functors-precategories -open import category-theory.functors-precategories -open import category-theory.isomorphisms-in-categories -open import category-theory.isomorphisms-in-precategories -open import category-theory.precategories -open import category-theory.pseudomonic-functors-precategories - -open import foundation.contractible-types +open import category-theory.categories funext univalence truncations +open import category-theory.cores-precategories funext univalence truncations +open import category-theory.essential-fibers-of-functors-precategories funext univalence truncations +open import category-theory.essentially-surjective-functors-precategories funext univalence truncations +open import category-theory.fully-faithful-functors-precategories funext univalence truncations +open import category-theory.functors-precategories funext univalence truncations +open import category-theory.isomorphisms-in-categories funext univalence truncations +open import category-theory.isomorphisms-in-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations +open import category-theory.pseudomonic-functors-precategories funext univalence truncations + +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.retracts-of-types -open import foundation.sections +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence +open import foundation.retracts-of-types funext univalence +open import foundation.sections funext open import foundation.universe-levels ``` diff --git a/src/category-theory/strict-categories.lagda.md b/src/category-theory/strict-categories.lagda.md index 549eed68e0..5945d113bd 100644 --- a/src/category-theory/strict-categories.lagda.md +++ b/src/category-theory/strict-categories.lagda.md @@ -1,26 +1,35 @@ # Strict categories ```agda -module category-theory.strict-categories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.strict-categories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.composition-operations-on-binary-families-of-sets -open import category-theory.isomorphisms-in-precategories -open import category-theory.nonunital-precategories -open import category-theory.precategories -open import category-theory.strongly-preunivalent-categories - -open import foundation.cartesian-product-types +open import category-theory.categories funext univalence truncations +open import category-theory.composition-operations-on-binary-families-of-sets funext univalence truncations +open import category-theory.isomorphisms-in-precategories funext univalence truncations +open import category-theory.nonunital-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations +open import category-theory.strongly-preunivalent-categories funext univalence truncations + +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.propositions -open import foundation.sets -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels ``` diff --git a/src/category-theory/strongly-preunivalent-categories.lagda.md b/src/category-theory/strongly-preunivalent-categories.lagda.md index 8ba02ef3ba..30c4cf191b 100644 --- a/src/category-theory/strongly-preunivalent-categories.lagda.md +++ b/src/category-theory/strongly-preunivalent-categories.lagda.md @@ -1,28 +1,37 @@ # Strongly preunivalent categories ```agda -module category-theory.strongly-preunivalent-categories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.strongly-preunivalent-categories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.composition-operations-on-binary-families-of-sets -open import category-theory.isomorphisms-in-precategories -open import category-theory.precategories -open import category-theory.preunivalent-categories +open import category-theory.composition-operations-on-binary-families-of-sets funext univalence truncations +open import category-theory.isomorphisms-in-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations +open import category-theory.preunivalent-categories funext univalence truncations -open import foundation.1-types -open import foundation.cartesian-product-types +open import foundation.1-types funext univalence +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.functoriality-dependent-pair-types -open import foundation.identity-types -open import foundation.propositional-maps -open import foundation.propositions -open import foundation.sets -open import foundation.strictly-involutive-identity-types -open import foundation.structured-equality-duality +open import foundation.dependent-products-propositions funext +open import foundation.embeddings funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.identity-types funext +open import foundation.propositional-maps funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.strictly-involutive-identity-types funext univalence +open import foundation.structured-equality-duality funext univalence open import foundation.universe-levels ``` diff --git a/src/category-theory/structure-equivalences-set-magmoids.lagda.md b/src/category-theory/structure-equivalences-set-magmoids.lagda.md index 97006c2dcd..5f5f5b47f2 100644 --- a/src/category-theory/structure-equivalences-set-magmoids.lagda.md +++ b/src/category-theory/structure-equivalences-set-magmoids.lagda.md @@ -1,25 +1,35 @@ # Structure equivalences between set-magmoids ```agda -module category-theory.structure-equivalences-set-magmoids where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.structure-equivalences-set-magmoids + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.functors-set-magmoids -open import category-theory.set-magmoids +open import category-theory.functors-set-magmoids funext univalence truncations +open import category-theory.set-magmoids funext univalence truncations -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.functoriality-dependent-function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.identity-types -open import foundation.iterated-dependent-product-types -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.functoriality-dependent-function-types funext univalence +open import foundation.functoriality-dependent-pair-types funext +open import foundation.identity-types funext +open import foundation.iterated-dependent-product-types funext +open import foundation.propositions funext univalence +open import foundation.telescopes open import foundation.type-arithmetic-dependent-pair-types -open import foundation.type-theoretic-principle-of-choice +open import foundation.type-theoretic-principle-of-choice funext open import foundation.universe-levels ``` diff --git a/src/category-theory/subcategories.lagda.md b/src/category-theory/subcategories.lagda.md index cb8cf062cf..008e76e7d6 100644 --- a/src/category-theory/subcategories.lagda.md +++ b/src/category-theory/subcategories.lagda.md @@ -1,36 +1,46 @@ # Subcategories ```agda -module category-theory.subcategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.subcategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.composition-operations-on-binary-families-of-sets -open import category-theory.faithful-functors-precategories -open import category-theory.functors-precategories -open import category-theory.isomorphisms-in-categories -open import category-theory.isomorphisms-in-precategories -open import category-theory.isomorphisms-in-subprecategories -open import category-theory.maps-precategories -open import category-theory.precategories -open import category-theory.replete-subprecategories -open import category-theory.subprecategories - -open import foundation.contractible-types +open import category-theory.categories funext univalence truncations +open import category-theory.composition-operations-on-binary-families-of-sets funext univalence truncations +open import category-theory.faithful-functors-precategories funext univalence truncations +open import category-theory.functors-precategories funext univalence truncations +open import category-theory.isomorphisms-in-categories funext univalence truncations +open import category-theory.isomorphisms-in-precategories funext univalence truncations +open import category-theory.isomorphisms-in-subprecategories funext univalence truncations +open import category-theory.maps-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations +open import category-theory.replete-subprecategories funext univalence truncations +open import category-theory.subprecategories funext univalence truncations + +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalences -open import foundation.functoriality-dependent-pair-types +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets -open import foundation.strictly-involutive-identity-types +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.strictly-involutive-identity-types funext univalence open import foundation.subtype-identity-principle -open import foundation.subtypes +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels ``` diff --git a/src/category-theory/subprecategories.lagda.md b/src/category-theory/subprecategories.lagda.md index 684e900afc..1f0eec4d3b 100644 --- a/src/category-theory/subprecategories.lagda.md +++ b/src/category-theory/subprecategories.lagda.md @@ -1,26 +1,36 @@ # Subprecategories ```agda -module category-theory.subprecategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.subprecategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.composition-operations-on-binary-families-of-sets -open import category-theory.faithful-functors-precategories -open import category-theory.functors-precategories -open import category-theory.maps-precategories -open import category-theory.precategories +open import category-theory.composition-operations-on-binary-families-of-sets funext univalence truncations +open import category-theory.faithful-functors-precategories funext univalence truncations +open import category-theory.functors-precategories funext univalence truncations +open import category-theory.maps-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.identity-types -open import foundation.iterated-dependent-product-types -open import foundation.propositions -open import foundation.sets -open import foundation.strictly-involutive-identity-types -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.embeddings funext +open import foundation.identity-types funext +open import foundation.iterated-dependent-product-types funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.strictly-involutive-identity-types funext univalence +open import foundation.subtypes funext univalence truncations +open import foundation.telescopes open import foundation.universe-levels ``` diff --git a/src/category-theory/subterminal-precategories.lagda.md b/src/category-theory/subterminal-precategories.lagda.md index a85c94a746..195e41f79a 100644 --- a/src/category-theory/subterminal-precategories.lagda.md +++ b/src/category-theory/subterminal-precategories.lagda.md @@ -1,32 +1,42 @@ # Subterminal precategories ```agda -module category-theory.subterminal-precategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.subterminal-precategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.composition-operations-on-binary-families-of-sets -open import category-theory.fully-faithful-functors-precategories -open import category-theory.isomorphisms-in-precategories -open import category-theory.precategories -open import category-theory.pregroupoids -open import category-theory.strict-categories -open import category-theory.terminal-category +open import category-theory.composition-operations-on-binary-families-of-sets funext univalence truncations +open import category-theory.fully-faithful-functors-precategories funext univalence truncations +open import category-theory.isomorphisms-in-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations +open import category-theory.pregroupoids funext univalence truncations +open import category-theory.strict-categories funext univalence truncations +open import category-theory.terminal-category funext univalence truncations open import foundation.action-on-identifications-functions -open import foundation.contractible-types +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalences -open import foundation.function-types +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.iterated-dependent-product-types -open import foundation.propositions -open import foundation.sets +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.iterated-dependent-product-types funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence open import foundation.subtype-identity-principle open import foundation.unit-type open import foundation.universe-levels diff --git a/src/category-theory/terminal-category.lagda.md b/src/category-theory/terminal-category.lagda.md index a8a8284077..a52fb611c1 100644 --- a/src/category-theory/terminal-category.lagda.md +++ b/src/category-theory/terminal-category.lagda.md @@ -1,32 +1,42 @@ # The terminal category ```agda -module category-theory.terminal-category where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.terminal-category + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.constant-functors -open import category-theory.functors-categories -open import category-theory.functors-precategories -open import category-theory.gaunt-categories -open import category-theory.isomorphisms-in-categories -open import category-theory.isomorphisms-in-precategories -open import category-theory.natural-transformations-functors-precategories -open import category-theory.precategories -open import category-theory.strict-categories -open import category-theory.strongly-preunivalent-categories +open import category-theory.categories funext univalence truncations +open import category-theory.constant-functors funext univalence truncations +open import category-theory.functors-categories funext univalence truncations +open import category-theory.functors-precategories funext univalence truncations +open import category-theory.gaunt-categories funext univalence truncations +open import category-theory.isomorphisms-in-categories funext univalence truncations +open import category-theory.isomorphisms-in-precategories funext univalence truncations +open import category-theory.natural-transformations-functors-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations +open import category-theory.strict-categories funext univalence truncations +open import category-theory.strongly-preunivalent-categories funext univalence truncations open import foundation.action-on-identifications-functions -open import foundation.contractible-types +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.homotopies -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence open import foundation.unit-type open import foundation.universe-levels ``` diff --git a/src/category-theory/terminal-objects-precategories.lagda.md b/src/category-theory/terminal-objects-precategories.lagda.md index 5a1fcb7d9c..30cd162ba6 100644 --- a/src/category-theory/terminal-objects-precategories.lagda.md +++ b/src/category-theory/terminal-objects-precategories.lagda.md @@ -1,18 +1,27 @@ # Terminal objects in a precategory ```agda -module category-theory.terminal-objects-precategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.terminal-objects-precategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.precategories +open import category-theory.precategories funext univalence truncations -open import foundation.contractible-types +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.identity-types +open import foundation.dependent-products-contractible-types funext +open import foundation.function-types funext +open import foundation.identity-types funext open import foundation.universe-levels ``` diff --git a/src/category-theory/wide-subcategories.lagda.md b/src/category-theory/wide-subcategories.lagda.md index 8b3b4631fd..dcc4bbdb76 100644 --- a/src/category-theory/wide-subcategories.lagda.md +++ b/src/category-theory/wide-subcategories.lagda.md @@ -1,35 +1,46 @@ # Wide subcategories ```agda -module category-theory.wide-subcategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.wide-subcategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.composition-operations-on-binary-families-of-sets -open import category-theory.faithful-functors-precategories -open import category-theory.functors-categories -open import category-theory.isomorphisms-in-categories -open import category-theory.isomorphisms-in-precategories -open import category-theory.maps-categories -open import category-theory.precategories -open import category-theory.subcategories -open import category-theory.wide-subprecategories - -open import foundation.contractible-types +open import category-theory.categories funext univalence truncations +open import category-theory.composition-operations-on-binary-families-of-sets funext univalence truncations +open import category-theory.faithful-functors-precategories funext univalence truncations +open import category-theory.functors-categories funext univalence truncations +open import category-theory.isomorphisms-in-categories funext univalence truncations +open import category-theory.isomorphisms-in-precategories funext univalence truncations +open import category-theory.maps-categories funext univalence truncations +open import category-theory.precategories funext univalence truncations +open import category-theory.subcategories funext univalence truncations +open import category-theory.wide-subprecategories funext univalence truncations + +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types -open import foundation.iterated-dependent-product-types -open import foundation.propositions -open import foundation.sets -open import foundation.strictly-involutive-identity-types -open import foundation.subtypes +open import foundation.identity-types funext +open import foundation.iterated-dependent-product-types funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.strictly-involutive-identity-types funext univalence +open import foundation.subtypes funext univalence truncations +open import foundation.telescopes open import foundation.unit-type open import foundation.universe-levels ``` diff --git a/src/category-theory/wide-subprecategories.lagda.md b/src/category-theory/wide-subprecategories.lagda.md index 598da33856..bac383888e 100644 --- a/src/category-theory/wide-subprecategories.lagda.md +++ b/src/category-theory/wide-subprecategories.lagda.md @@ -1,28 +1,38 @@ # Wide subprecategories ```agda -module category-theory.wide-subprecategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.wide-subprecategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.composition-operations-on-binary-families-of-sets -open import category-theory.faithful-functors-precategories -open import category-theory.functors-precategories -open import category-theory.maps-precategories -open import category-theory.precategories -open import category-theory.subprecategories +open import category-theory.composition-operations-on-binary-families-of-sets funext univalence truncations +open import category-theory.faithful-functors-precategories funext univalence truncations +open import category-theory.functors-precategories funext univalence truncations +open import category-theory.maps-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations +open import category-theory.subprecategories funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.identity-types -open import foundation.iterated-dependent-product-types -open import foundation.propositions -open import foundation.sets -open import foundation.strictly-involutive-identity-types -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.iterated-dependent-product-types funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.strictly-involutive-identity-types funext univalence +open import foundation.subtypes funext univalence truncations +open import foundation.telescopes open import foundation.unit-type open import foundation.universe-levels ``` diff --git a/src/category-theory/yoneda-lemma-categories.lagda.md b/src/category-theory/yoneda-lemma-categories.lagda.md index 3548e0a58d..b4b63b6c1c 100644 --- a/src/category-theory/yoneda-lemma-categories.lagda.md +++ b/src/category-theory/yoneda-lemma-categories.lagda.md @@ -1,20 +1,28 @@ # The Yoneda lemma for categories ```agda -module category-theory.yoneda-lemma-categories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.yoneda-lemma-categories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.copresheaf-categories -open import category-theory.natural-transformations-functors-from-small-to-large-categories -open import category-theory.representable-functors-categories -open import category-theory.yoneda-lemma-precategories - -open import foundation.category-of-sets -open import foundation.equivalences +open import category-theory.categories funext univalence truncations +open import category-theory.copresheaf-categories funext univalence truncations +open import category-theory.natural-transformations-functors-from-small-to-large-categories funext univalence truncations +open import category-theory.representable-functors-categories funext univalence truncations +open import category-theory.yoneda-lemma-precategories funext univalence truncations + +open import foundation.category-of-sets funext univalence truncations +open import foundation.equivalences funext open import foundation.universe-levels ``` diff --git a/src/category-theory/yoneda-lemma-precategories.lagda.md b/src/category-theory/yoneda-lemma-precategories.lagda.md index 0820f19127..c34cd4ea51 100644 --- a/src/category-theory/yoneda-lemma-precategories.lagda.md +++ b/src/category-theory/yoneda-lemma-precategories.lagda.md @@ -1,27 +1,35 @@ # The Yoneda lemma for precategories ```agda -module category-theory.yoneda-lemma-precategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module category-theory.yoneda-lemma-precategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.copresheaf-categories -open import category-theory.functors-from-small-to-large-precategories -open import category-theory.natural-transformations-functors-from-small-to-large-precategories -open import category-theory.precategories -open import category-theory.representable-functors-precategories +open import category-theory.copresheaf-categories funext univalence truncations +open import category-theory.functors-from-small-to-large-precategories funext univalence truncations +open import category-theory.natural-transformations-functors-from-small-to-large-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations +open import category-theory.representable-functors-precategories funext univalence truncations open import foundation.action-on-identifications-functions -open import foundation.category-of-sets +open import foundation.category-of-sets funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.subtypes +open import foundation.equivalences funext +open import foundation.function-extensionality funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels ``` diff --git a/src/commutative-algebra.lagda.md b/src/commutative-algebra.lagda.md index 7719d0d4d2..227d982938 100644 --- a/src/commutative-algebra.lagda.md +++ b/src/commutative-algebra.lagda.md @@ -3,62 +3,70 @@ ## Modules in the commutative algebra namespace ```agda -module commutative-algebra where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom -open import commutative-algebra.binomial-theorem-commutative-rings public -open import commutative-algebra.binomial-theorem-commutative-semirings public -open import commutative-algebra.boolean-rings public -open import commutative-algebra.category-of-commutative-rings public -open import commutative-algebra.commutative-rings public -open import commutative-algebra.commutative-semirings public -open import commutative-algebra.dependent-products-commutative-rings public -open import commutative-algebra.dependent-products-commutative-semirings public -open import commutative-algebra.discrete-fields public -open import commutative-algebra.eisenstein-integers public -open import commutative-algebra.euclidean-domains public -open import commutative-algebra.full-ideals-commutative-rings public -open import commutative-algebra.function-commutative-rings public -open import commutative-algebra.function-commutative-semirings public -open import commutative-algebra.gaussian-integers public -open import commutative-algebra.groups-of-units-commutative-rings public -open import commutative-algebra.homomorphisms-commutative-rings public -open import commutative-algebra.homomorphisms-commutative-semirings public -open import commutative-algebra.ideals-commutative-rings public -open import commutative-algebra.ideals-commutative-semirings public -open import commutative-algebra.ideals-generated-by-subsets-commutative-rings public -open import commutative-algebra.integer-multiples-of-elements-commutative-rings public -open import commutative-algebra.integral-domains public -open import commutative-algebra.intersections-ideals-commutative-rings public -open import commutative-algebra.intersections-radical-ideals-commutative-rings public -open import commutative-algebra.invertible-elements-commutative-rings public -open import commutative-algebra.isomorphisms-commutative-rings public -open import commutative-algebra.joins-ideals-commutative-rings public -open import commutative-algebra.joins-radical-ideals-commutative-rings public -open import commutative-algebra.local-commutative-rings public +module commutative-algebra + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where + +open import commutative-algebra.binomial-theorem-commutative-rings funext univalence truncations public +open import commutative-algebra.binomial-theorem-commutative-semirings funext univalence truncations public +open import commutative-algebra.boolean-rings funext univalence truncations public +open import commutative-algebra.category-of-commutative-rings funext univalence truncations public +open import commutative-algebra.commutative-rings funext univalence truncations public +open import commutative-algebra.commutative-semirings funext univalence truncations public +open import commutative-algebra.dependent-products-commutative-rings funext univalence truncations public +open import commutative-algebra.dependent-products-commutative-semirings funext univalence truncations public +open import commutative-algebra.discrete-fields funext univalence truncations public +open import commutative-algebra.eisenstein-integers funext univalence truncations public +open import commutative-algebra.euclidean-domains funext univalence truncations public +open import commutative-algebra.full-ideals-commutative-rings funext univalence truncations public +open import commutative-algebra.function-commutative-rings funext univalence truncations public +open import commutative-algebra.function-commutative-semirings funext univalence truncations public +open import commutative-algebra.gaussian-integers funext univalence truncations public +open import commutative-algebra.groups-of-units-commutative-rings funext univalence truncations public +open import commutative-algebra.homomorphisms-commutative-rings funext univalence truncations public +open import commutative-algebra.homomorphisms-commutative-semirings funext univalence truncations public +open import commutative-algebra.ideals-commutative-rings funext univalence truncations public +open import commutative-algebra.ideals-commutative-semirings funext univalence truncations public +open import commutative-algebra.ideals-generated-by-subsets-commutative-rings funext univalence truncations public +open import commutative-algebra.integer-multiples-of-elements-commutative-rings funext univalence truncations public +open import commutative-algebra.integral-domains funext univalence truncations public +open import commutative-algebra.intersections-ideals-commutative-rings funext univalence truncations public +open import commutative-algebra.intersections-radical-ideals-commutative-rings funext univalence truncations public +open import commutative-algebra.invertible-elements-commutative-rings funext univalence truncations public +open import commutative-algebra.isomorphisms-commutative-rings funext univalence truncations public +open import commutative-algebra.joins-ideals-commutative-rings funext univalence truncations public +open import commutative-algebra.joins-radical-ideals-commutative-rings funext univalence truncations public +open import commutative-algebra.local-commutative-rings funext univalence truncations public open import commutative-algebra.maximal-ideals-commutative-rings public -open import commutative-algebra.multiples-of-elements-commutative-rings public -open import commutative-algebra.nilradical-commutative-rings public -open import commutative-algebra.nilradicals-commutative-semirings public -open import commutative-algebra.poset-of-ideals-commutative-rings public -open import commutative-algebra.poset-of-radical-ideals-commutative-rings public -open import commutative-algebra.powers-of-elements-commutative-rings public -open import commutative-algebra.powers-of-elements-commutative-semirings public -open import commutative-algebra.precategory-of-commutative-rings public -open import commutative-algebra.precategory-of-commutative-semirings public -open import commutative-algebra.prime-ideals-commutative-rings public -open import commutative-algebra.products-commutative-rings public -open import commutative-algebra.products-ideals-commutative-rings public -open import commutative-algebra.products-radical-ideals-commutative-rings public -open import commutative-algebra.products-subsets-commutative-rings public -open import commutative-algebra.radical-ideals-commutative-rings public -open import commutative-algebra.radical-ideals-generated-by-subsets-commutative-rings public -open import commutative-algebra.radicals-of-ideals-commutative-rings public -open import commutative-algebra.subsets-commutative-rings public -open import commutative-algebra.subsets-commutative-semirings public -open import commutative-algebra.sums-commutative-rings public -open import commutative-algebra.sums-commutative-semirings public -open import commutative-algebra.transporting-commutative-ring-structure-isomorphisms-abelian-groups public -open import commutative-algebra.trivial-commutative-rings public -open import commutative-algebra.zariski-locale public -open import commutative-algebra.zariski-topology public +open import commutative-algebra.multiples-of-elements-commutative-rings funext univalence truncations public +open import commutative-algebra.nilradical-commutative-rings funext univalence truncations public +open import commutative-algebra.nilradicals-commutative-semirings funext univalence truncations public +open import commutative-algebra.poset-of-ideals-commutative-rings funext univalence truncations public +open import commutative-algebra.poset-of-radical-ideals-commutative-rings funext univalence truncations public +open import commutative-algebra.powers-of-elements-commutative-rings funext univalence truncations public +open import commutative-algebra.powers-of-elements-commutative-semirings funext univalence truncations public +open import commutative-algebra.precategory-of-commutative-rings funext univalence truncations public +open import commutative-algebra.precategory-of-commutative-semirings funext univalence truncations public +open import commutative-algebra.prime-ideals-commutative-rings funext univalence truncations public +open import commutative-algebra.products-commutative-rings funext univalence truncations public +open import commutative-algebra.products-ideals-commutative-rings funext univalence truncations public +open import commutative-algebra.products-radical-ideals-commutative-rings funext univalence truncations public +open import commutative-algebra.products-subsets-commutative-rings funext univalence truncations public +open import commutative-algebra.radical-ideals-commutative-rings funext univalence truncations public +open import commutative-algebra.radical-ideals-generated-by-subsets-commutative-rings funext univalence truncations public +open import commutative-algebra.radicals-of-ideals-commutative-rings funext univalence truncations public +open import commutative-algebra.subsets-commutative-rings funext univalence truncations public +open import commutative-algebra.subsets-commutative-semirings funext univalence truncations public +open import commutative-algebra.sums-commutative-rings funext univalence truncations public +open import commutative-algebra.sums-commutative-semirings funext univalence truncations public +open import commutative-algebra.transporting-commutative-ring-structure-isomorphisms-abelian-groups funext univalence truncations public +open import commutative-algebra.trivial-commutative-rings funext univalence truncations public +open import commutative-algebra.zariski-locale funext univalence truncations public +open import commutative-algebra.zariski-topology funext univalence truncations public ``` diff --git a/src/commutative-algebra/binomial-theorem-commutative-rings.lagda.md b/src/commutative-algebra/binomial-theorem-commutative-rings.lagda.md index 2e3e0a4f5e..2e429934e3 100644 --- a/src/commutative-algebra/binomial-theorem-commutative-rings.lagda.md +++ b/src/commutative-algebra/binomial-theorem-commutative-rings.lagda.md @@ -1,31 +1,39 @@ # The binomial theorem in commutative rings ```agda -module commutative-algebra.binomial-theorem-commutative-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module commutative-algebra.binomial-theorem-commutative-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import commutative-algebra.binomial-theorem-commutative-semirings -open import commutative-algebra.commutative-rings -open import commutative-algebra.powers-of-elements-commutative-rings -open import commutative-algebra.sums-commutative-rings +open import commutative-algebra.binomial-theorem-commutative-semirings funext univalence truncations +open import commutative-algebra.commutative-rings funext univalence truncations +open import commutative-algebra.powers-of-elements-commutative-rings funext univalence truncations +open import commutative-algebra.sums-commutative-rings funext univalence truncations open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.binomial-coefficients -open import elementary-number-theory.distance-natural-numbers +open import elementary-number-theory.binomial-coefficients funext univalence truncations +open import elementary-number-theory.distance-natural-numbers funext univalence truncations open import elementary-number-theory.natural-numbers -open import foundation.homotopies -open import foundation.identity-types +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.universe-levels -open import linear-algebra.vectors-on-commutative-rings +open import linear-algebra.vectors-on-commutative-rings funext univalence truncations -open import ring-theory.binomial-theorem-rings +open import ring-theory.binomial-theorem-rings funext univalence truncations -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/commutative-algebra/binomial-theorem-commutative-semirings.lagda.md b/src/commutative-algebra/binomial-theorem-commutative-semirings.lagda.md index 3bbda32f19..a52d54f9e0 100644 --- a/src/commutative-algebra/binomial-theorem-commutative-semirings.lagda.md +++ b/src/commutative-algebra/binomial-theorem-commutative-semirings.lagda.md @@ -1,30 +1,38 @@ # The binomial theorem in commutative semirings ```agda -module commutative-algebra.binomial-theorem-commutative-semirings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module commutative-algebra.binomial-theorem-commutative-semirings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import commutative-algebra.commutative-semirings -open import commutative-algebra.powers-of-elements-commutative-semirings -open import commutative-algebra.sums-commutative-semirings +open import commutative-algebra.commutative-semirings funext univalence truncations +open import commutative-algebra.powers-of-elements-commutative-semirings funext univalence truncations +open import commutative-algebra.sums-commutative-semirings funext univalence truncations open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.binomial-coefficients -open import elementary-number-theory.distance-natural-numbers +open import elementary-number-theory.binomial-coefficients funext univalence truncations +open import elementary-number-theory.distance-natural-numbers funext univalence truncations open import elementary-number-theory.natural-numbers -open import foundation.homotopies -open import foundation.identity-types +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.universe-levels -open import linear-algebra.vectors-on-commutative-semirings +open import linear-algebra.vectors-on-commutative-semirings funext univalence truncations -open import ring-theory.binomial-theorem-semirings +open import ring-theory.binomial-theorem-semirings funext univalence truncations -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/commutative-algebra/boolean-rings.lagda.md b/src/commutative-algebra/boolean-rings.lagda.md index 6ae1075b5d..0db42ca629 100644 --- a/src/commutative-algebra/boolean-rings.lagda.md +++ b/src/commutative-algebra/boolean-rings.lagda.md @@ -1,18 +1,26 @@ # Boolean rings ```agda -module commutative-algebra.boolean-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module commutative-algebra.boolean-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import commutative-algebra.commutative-rings +open import commutative-algebra.commutative-rings funext univalence truncations open import foundation.dependent-pair-types open import foundation.universe-levels -open import ring-theory.idempotent-elements-rings +open import ring-theory.idempotent-elements-rings funext univalence truncations ```
diff --git a/src/commutative-algebra/category-of-commutative-rings.lagda.md b/src/commutative-algebra/category-of-commutative-rings.lagda.md index c3fd89fa48..8373a45338 100644 --- a/src/commutative-algebra/category-of-commutative-rings.lagda.md +++ b/src/commutative-algebra/category-of-commutative-rings.lagda.md @@ -1,17 +1,25 @@ # The category of commutative rings ```agda -module commutative-algebra.category-of-commutative-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module commutative-algebra.category-of-commutative-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.large-categories +open import category-theory.categories funext univalence truncations +open import category-theory.large-categories funext univalence truncations -open import commutative-algebra.isomorphisms-commutative-rings -open import commutative-algebra.precategory-of-commutative-rings +open import commutative-algebra.isomorphisms-commutative-rings funext univalence truncations +open import commutative-algebra.precategory-of-commutative-rings funext univalence truncations open import foundation.universe-levels ``` diff --git a/src/commutative-algebra/commutative-rings.lagda.md b/src/commutative-algebra/commutative-rings.lagda.md index 06b3e5d600..c2aebf88e0 100644 --- a/src/commutative-algebra/commutative-rings.lagda.md +++ b/src/commutative-algebra/commutative-rings.lagda.md @@ -1,47 +1,56 @@ # Commutative rings ```agda -module commutative-algebra.commutative-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module commutative-algebra.commutative-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import commutative-algebra.commutative-semirings +open import commutative-algebra.commutative-semirings funext univalence truncations open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.binary-embeddings +open import foundation.binary-embeddings funext open import foundation.binary-equivalences open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalences -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.injective-maps +open import foundation.dependent-products-propositions funext +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.injective-maps funext open import foundation.interchange-law -open import foundation.involutions -open import foundation.negation -open import foundation.propositions -open import foundation.sets +open import foundation.involutions funext univalence +open import foundation.negation funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence open import foundation.unital-binary-operations open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.commutative-monoids -open import group-theory.groups -open import group-theory.monoids -open import group-theory.semigroups +open import group-theory.abelian-groups funext univalence truncations +open import group-theory.commutative-monoids funext univalence truncations +open import group-theory.groups funext univalence truncations +open import group-theory.monoids funext univalence truncations +open import group-theory.semigroups funext univalence -open import lists.concatenation-lists +open import lists.concatenation-lists funext univalence truncations open import lists.lists -open import ring-theory.rings -open import ring-theory.semirings +open import ring-theory.rings funext univalence truncations +open import ring-theory.semirings funext univalence truncations ```
diff --git a/src/commutative-algebra/commutative-semirings.lagda.md b/src/commutative-algebra/commutative-semirings.lagda.md index 78e21f5b30..32ff08187e 100644 --- a/src/commutative-algebra/commutative-semirings.lagda.md +++ b/src/commutative-algebra/commutative-semirings.lagda.md @@ -1,7 +1,15 @@ # Commutative semirings ```agda -module commutative-algebra.commutative-semirings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module commutative-algebra.commutative-semirings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -11,16 +19,18 @@ open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.iterated-dependent-product-types -open import foundation.propositions -open import foundation.sets +open import foundation.dependent-products-propositions funext +open import foundation.identity-types funext +open import foundation.iterated-dependent-product-types funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.telescopes open import foundation.universe-levels -open import group-theory.commutative-monoids -open import group-theory.monoids +open import group-theory.commutative-monoids funext univalence truncations +open import group-theory.monoids funext univalence truncations -open import ring-theory.semirings +open import ring-theory.semirings funext univalence truncations ```
diff --git a/src/commutative-algebra/dependent-products-commutative-rings.lagda.md b/src/commutative-algebra/dependent-products-commutative-rings.lagda.md index 45881aecf1..4454a4db1d 100644 --- a/src/commutative-algebra/dependent-products-commutative-rings.lagda.md +++ b/src/commutative-algebra/dependent-products-commutative-rings.lagda.md @@ -1,25 +1,33 @@ # Dependent products of commutative rings ```agda -module commutative-algebra.dependent-products-commutative-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module commutative-algebra.dependent-products-commutative-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import commutative-algebra.commutative-rings +open import commutative-algebra.commutative-rings funext univalence truncations open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.sets +open import foundation.identity-types funext +open import foundation.sets funext univalence open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.commutative-monoids -open import group-theory.dependent-products-commutative-monoids +open import group-theory.abelian-groups funext univalence truncations +open import group-theory.commutative-monoids funext univalence truncations +open import group-theory.dependent-products-commutative-monoids funext univalence truncations -open import ring-theory.dependent-products-rings -open import ring-theory.rings +open import ring-theory.dependent-products-rings funext univalence truncations +open import ring-theory.rings funext univalence truncations ```
diff --git a/src/commutative-algebra/dependent-products-commutative-semirings.lagda.md b/src/commutative-algebra/dependent-products-commutative-semirings.lagda.md index abcf6a837e..e96906513e 100644 --- a/src/commutative-algebra/dependent-products-commutative-semirings.lagda.md +++ b/src/commutative-algebra/dependent-products-commutative-semirings.lagda.md @@ -1,24 +1,32 @@ # Dependent products of commutative semirings ```agda -module commutative-algebra.dependent-products-commutative-semirings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module commutative-algebra.dependent-products-commutative-semirings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import commutative-algebra.commutative-semirings +open import commutative-algebra.commutative-semirings funext univalence truncations open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.sets +open import foundation.identity-types funext +open import foundation.sets funext univalence open import foundation.universe-levels -open import group-theory.commutative-monoids -open import group-theory.dependent-products-commutative-monoids +open import group-theory.commutative-monoids funext univalence truncations +open import group-theory.dependent-products-commutative-monoids funext univalence truncations -open import ring-theory.dependent-products-semirings -open import ring-theory.semirings +open import ring-theory.dependent-products-semirings funext univalence truncations +open import ring-theory.semirings funext univalence truncations ```
diff --git a/src/commutative-algebra/discrete-fields.lagda.md b/src/commutative-algebra/discrete-fields.lagda.md index 6943d29b4b..1a5c8e6878 100644 --- a/src/commutative-algebra/discrete-fields.lagda.md +++ b/src/commutative-algebra/discrete-fields.lagda.md @@ -1,17 +1,25 @@ # Discrete fields ```agda -module commutative-algebra.discrete-fields where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module commutative-algebra.discrete-fields + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import commutative-algebra.commutative-rings +open import commutative-algebra.commutative-rings funext univalence truncations open import foundation.universe-levels -open import ring-theory.division-rings +open import ring-theory.division-rings funext univalence truncations ```
diff --git a/src/commutative-algebra/eisenstein-integers.lagda.md b/src/commutative-algebra/eisenstein-integers.lagda.md index e7bdaf0e62..c5e49351cf 100644 --- a/src/commutative-algebra/eisenstein-integers.lagda.md +++ b/src/commutative-algebra/eisenstein-integers.lagda.md @@ -1,31 +1,40 @@ # The Eisenstein integers ```agda -module commutative-algebra.eisenstein-integers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module commutative-algebra.eisenstein-integers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import commutative-algebra.commutative-rings +open import commutative-algebra.commutative-rings funext univalence truncations -open import elementary-number-theory.addition-integers +open import elementary-number-theory.addition-integers funext univalence truncations +open import elementary-number-theory.equality-integers funext univalence truncations open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-integers +open import elementary-number-theory.multiplication-integers funext univalence truncations open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.sets +open import foundation.identity-types funext +open import foundation.sets funext univalence open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.groups -open import group-theory.semigroups +open import group-theory.abelian-groups funext univalence truncations +open import group-theory.groups funext univalence truncations +open import group-theory.semigroups funext univalence -open import ring-theory.rings +open import ring-theory.rings funext univalence truncations ```
diff --git a/src/commutative-algebra/euclidean-domains.lagda.md b/src/commutative-algebra/euclidean-domains.lagda.md index abd586d5ef..34c0642b4f 100644 --- a/src/commutative-algebra/euclidean-domains.lagda.md +++ b/src/commutative-algebra/euclidean-domains.lagda.md @@ -1,51 +1,60 @@ # Euclidean domains ```agda -module commutative-algebra.euclidean-domains where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module commutative-algebra.euclidean-domains + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import commutative-algebra.commutative-rings -open import commutative-algebra.commutative-semirings -open import commutative-algebra.integral-domains -open import commutative-algebra.trivial-commutative-rings +open import commutative-algebra.commutative-rings funext univalence truncations +open import commutative-algebra.commutative-semirings funext univalence truncations +open import commutative-algebra.integral-domains funext univalence truncations +open import commutative-algebra.trivial-commutative-rings funext univalence truncations open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.strict-inequality-natural-numbers +open import elementary-number-theory.strict-inequality-natural-numbers funext univalence truncations open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.binary-embeddings +open import foundation.binary-embeddings funext open import foundation.binary-equivalences -open import foundation.cartesian-product-types -open import foundation.coproduct-types +open import foundation.cartesian-product-types funext univalence +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalences -open import foundation.identity-types -open import foundation.injective-maps +open import foundation.dependent-products-propositions funext +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.injective-maps funext open import foundation.interchange-law -open import foundation.involutions -open import foundation.negation -open import foundation.propositions -open import foundation.sets +open import foundation.involutions funext univalence +open import foundation.negation funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence open import foundation.unital-binary-operations open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.commutative-monoids -open import group-theory.groups -open import group-theory.monoids -open import group-theory.semigroups +open import group-theory.abelian-groups funext univalence truncations +open import group-theory.commutative-monoids funext univalence truncations +open import group-theory.groups funext univalence truncations +open import group-theory.monoids funext univalence truncations +open import group-theory.semigroups funext univalence -open import lists.concatenation-lists +open import lists.concatenation-lists funext univalence truncations open import lists.lists -open import ring-theory.rings -open import ring-theory.semirings +open import ring-theory.rings funext univalence truncations +open import ring-theory.semirings funext univalence truncations ```
diff --git a/src/commutative-algebra/full-ideals-commutative-rings.lagda.md b/src/commutative-algebra/full-ideals-commutative-rings.lagda.md index 74e4efd94e..f930c4594a 100644 --- a/src/commutative-algebra/full-ideals-commutative-rings.lagda.md +++ b/src/commutative-algebra/full-ideals-commutative-rings.lagda.md @@ -1,27 +1,37 @@ # Full ideals of commutative rings ```agda -module commutative-algebra.full-ideals-commutative-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module commutative-algebra.full-ideals-commutative-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import commutative-algebra.commutative-rings -open import commutative-algebra.ideals-commutative-rings -open import commutative-algebra.poset-of-ideals-commutative-rings -open import commutative-algebra.poset-of-radical-ideals-commutative-rings -open import commutative-algebra.radical-ideals-commutative-rings -open import commutative-algebra.subsets-commutative-rings +open import commutative-algebra.commutative-rings funext univalence truncations +open import commutative-algebra.ideals-commutative-rings funext univalence truncations +open import commutative-algebra.poset-of-ideals-commutative-rings funext univalence truncations +open import commutative-algebra.poset-of-radical-ideals-commutative-rings funext univalence truncations +open import commutative-algebra.radical-ideals-commutative-rings funext univalence truncations +open import commutative-algebra.subsets-commutative-rings funext univalence truncations open import foundation.dependent-pair-types -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.propositions funext univalence +open import foundation.raising-universe-levels-unit-type open import foundation.unit-type open import foundation.universe-levels -open import order-theory.top-elements-large-posets +open import order-theory.top-elements-large-posets funext univalence truncations -open import ring-theory.full-ideals-rings +open import ring-theory.full-ideals-rings funext univalence truncations ```
diff --git a/src/commutative-algebra/function-commutative-rings.lagda.md b/src/commutative-algebra/function-commutative-rings.lagda.md index fb7920277a..0dafb9d473 100644 --- a/src/commutative-algebra/function-commutative-rings.lagda.md +++ b/src/commutative-algebra/function-commutative-rings.lagda.md @@ -1,23 +1,31 @@ # Function commutative rings ```agda -module commutative-algebra.function-commutative-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module commutative-algebra.function-commutative-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import commutative-algebra.commutative-rings -open import commutative-algebra.dependent-products-commutative-rings +open import commutative-algebra.commutative-rings funext univalence truncations +open import commutative-algebra.dependent-products-commutative-rings funext univalence truncations -open import foundation.identity-types -open import foundation.sets +open import foundation.identity-types funext +open import foundation.sets funext univalence open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.commutative-monoids +open import group-theory.abelian-groups funext univalence truncations +open import group-theory.commutative-monoids funext univalence truncations -open import ring-theory.rings +open import ring-theory.rings funext univalence truncations ```
diff --git a/src/commutative-algebra/function-commutative-semirings.lagda.md b/src/commutative-algebra/function-commutative-semirings.lagda.md index 186bc1dbc1..b55b1fdf31 100644 --- a/src/commutative-algebra/function-commutative-semirings.lagda.md +++ b/src/commutative-algebra/function-commutative-semirings.lagda.md @@ -1,22 +1,30 @@ # Function commutative semirings ```agda -module commutative-algebra.function-commutative-semirings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module commutative-algebra.function-commutative-semirings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import commutative-algebra.commutative-semirings -open import commutative-algebra.dependent-products-commutative-semirings +open import commutative-algebra.commutative-semirings funext univalence truncations +open import commutative-algebra.dependent-products-commutative-semirings funext univalence truncations -open import foundation.identity-types -open import foundation.sets +open import foundation.identity-types funext +open import foundation.sets funext univalence open import foundation.universe-levels -open import group-theory.commutative-monoids +open import group-theory.commutative-monoids funext univalence truncations -open import ring-theory.semirings +open import ring-theory.semirings funext univalence truncations ```
diff --git a/src/commutative-algebra/gaussian-integers.lagda.md b/src/commutative-algebra/gaussian-integers.lagda.md index c4b999395d..8b552ec55f 100644 --- a/src/commutative-algebra/gaussian-integers.lagda.md +++ b/src/commutative-algebra/gaussian-integers.lagda.md @@ -1,32 +1,41 @@ # The Gaussian integers ```agda -module commutative-algebra.gaussian-integers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module commutative-algebra.gaussian-integers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import commutative-algebra.commutative-rings +open import commutative-algebra.commutative-rings funext univalence truncations -open import elementary-number-theory.addition-integers -open import elementary-number-theory.difference-integers +open import elementary-number-theory.addition-integers funext univalence truncations +open import elementary-number-theory.difference-integers funext univalence truncations +open import elementary-number-theory.equality-integers funext univalence truncations open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-integers +open import elementary-number-theory.multiplication-integers funext univalence truncations open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.sets +open import foundation.identity-types funext +open import foundation.sets funext univalence open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.groups -open import group-theory.semigroups +open import group-theory.abelian-groups funext univalence truncations +open import group-theory.groups funext univalence truncations +open import group-theory.semigroups funext univalence -open import ring-theory.rings +open import ring-theory.rings funext univalence truncations ```
diff --git a/src/commutative-algebra/groups-of-units-commutative-rings.lagda.md b/src/commutative-algebra/groups-of-units-commutative-rings.lagda.md index f3fcd5aac1..ff52d06c9f 100644 --- a/src/commutative-algebra/groups-of-units-commutative-rings.lagda.md +++ b/src/commutative-algebra/groups-of-units-commutative-rings.lagda.md @@ -1,34 +1,43 @@ # The group of multiplicative units of a commutative ring ```agda -module commutative-algebra.groups-of-units-commutative-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module commutative-algebra.groups-of-units-commutative-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.functors-large-precategories +open import category-theory.functors-large-precategories funext univalence truncations -open import commutative-algebra.commutative-rings -open import commutative-algebra.homomorphisms-commutative-rings -open import commutative-algebra.precategory-of-commutative-rings +open import commutative-algebra.commutative-rings funext univalence truncations +open import commutative-algebra.homomorphisms-commutative-rings funext univalence truncations +open import commutative-algebra.precategory-of-commutative-rings funext univalence truncations open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.category-of-abelian-groups -open import group-theory.groups -open import group-theory.homomorphisms-groups -open import group-theory.homomorphisms-monoids -open import group-theory.monoids -open import group-theory.semigroups -open import group-theory.submonoids +open import group-theory.abelian-groups funext univalence truncations +open import group-theory.category-of-abelian-groups funext univalence truncations +open import group-theory.groups funext univalence truncations +open import group-theory.homomorphisms-groups funext univalence truncations +open import group-theory.homomorphisms-monoids funext univalence truncations +open import group-theory.monoids funext univalence truncations +open import group-theory.semigroups funext univalence +open import group-theory.submonoids funext univalence truncations -open import ring-theory.groups-of-units-rings +open import ring-theory.groups-of-units-rings funext univalence truncations ```
diff --git a/src/commutative-algebra/homomorphisms-commutative-rings.lagda.md b/src/commutative-algebra/homomorphisms-commutative-rings.lagda.md index 284d752ce5..d4b8aa5f6e 100644 --- a/src/commutative-algebra/homomorphisms-commutative-rings.lagda.md +++ b/src/commutative-algebra/homomorphisms-commutative-rings.lagda.md @@ -1,27 +1,36 @@ # Homomorphisms of commutative rings ```agda -module commutative-algebra.homomorphisms-commutative-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module commutative-algebra.homomorphisms-commutative-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import commutative-algebra.commutative-rings -open import commutative-algebra.homomorphisms-commutative-semirings -open import commutative-algebra.invertible-elements-commutative-rings - -open import foundation.equivalences -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets -open import foundation.torsorial-type-families +open import commutative-algebra.commutative-rings funext univalence truncations +open import commutative-algebra.homomorphisms-commutative-semirings funext univalence truncations +open import commutative-algebra.invertible-elements-commutative-rings funext univalence truncations + +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.torsorial-type-families funext univalence truncations open import foundation.universe-levels -open import group-theory.homomorphisms-abelian-groups -open import group-theory.homomorphisms-monoids +open import group-theory.homomorphisms-abelian-groups funext univalence truncations +open import group-theory.homomorphisms-monoids funext univalence truncations -open import ring-theory.homomorphisms-rings +open import ring-theory.homomorphisms-rings funext univalence truncations ```
diff --git a/src/commutative-algebra/homomorphisms-commutative-semirings.lagda.md b/src/commutative-algebra/homomorphisms-commutative-semirings.lagda.md index c5ee3254af..8cbc726905 100644 --- a/src/commutative-algebra/homomorphisms-commutative-semirings.lagda.md +++ b/src/commutative-algebra/homomorphisms-commutative-semirings.lagda.md @@ -1,24 +1,32 @@ # Homomorphisms of commutative semirings ```agda -module commutative-algebra.homomorphisms-commutative-semirings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module commutative-algebra.homomorphisms-commutative-semirings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import commutative-algebra.commutative-semirings +open import commutative-algebra.commutative-semirings funext univalence truncations -open import foundation.equivalences -open import foundation.identity-types -open import foundation.sets -open import foundation.torsorial-type-families +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.sets funext univalence +open import foundation.torsorial-type-families funext univalence truncations open import foundation.universe-levels -open import group-theory.homomorphisms-commutative-monoids -open import group-theory.homomorphisms-monoids +open import group-theory.homomorphisms-commutative-monoids funext univalence truncations +open import group-theory.homomorphisms-monoids funext univalence truncations -open import ring-theory.homomorphisms-semirings +open import ring-theory.homomorphisms-semirings funext univalence truncations ```
diff --git a/src/commutative-algebra/ideals-commutative-rings.lagda.md b/src/commutative-algebra/ideals-commutative-rings.lagda.md index 90f082cc86..2e07bf0adb 100644 --- a/src/commutative-algebra/ideals-commutative-rings.lagda.md +++ b/src/commutative-algebra/ideals-commutative-rings.lagda.md @@ -1,29 +1,38 @@ # Ideals of commutative rings ```agda -module commutative-algebra.ideals-commutative-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module commutative-algebra.ideals-commutative-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import commutative-algebra.commutative-rings -open import commutative-algebra.powers-of-elements-commutative-rings -open import commutative-algebra.subsets-commutative-rings +open import commutative-algebra.commutative-rings funext univalence truncations +open import commutative-algebra.powers-of-elements-commutative-rings funext univalence truncations +open import commutative-algebra.subsets-commutative-rings funext univalence truncations open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.identity-types -open import foundation.propositions -open import foundation.torsorial-type-families +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.torsorial-type-families funext univalence truncations open import foundation.universe-levels -open import ring-theory.ideals-rings -open import ring-theory.left-ideals-rings -open import ring-theory.right-ideals-rings -open import ring-theory.subsets-rings +open import ring-theory.ideals-rings funext univalence truncations +open import ring-theory.left-ideals-rings funext univalence truncations +open import ring-theory.right-ideals-rings funext univalence truncations +open import ring-theory.subsets-rings funext univalence truncations ```
diff --git a/src/commutative-algebra/ideals-commutative-semirings.lagda.md b/src/commutative-algebra/ideals-commutative-semirings.lagda.md index 8fb7d4a127..4c365b5610 100644 --- a/src/commutative-algebra/ideals-commutative-semirings.lagda.md +++ b/src/commutative-algebra/ideals-commutative-semirings.lagda.md @@ -1,21 +1,30 @@ # Ideals of commutative semirings ```agda -module commutative-algebra.ideals-commutative-semirings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module commutative-algebra.ideals-commutative-semirings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import commutative-algebra.commutative-semirings -open import commutative-algebra.subsets-commutative-semirings +open import commutative-algebra.commutative-semirings funext univalence truncations +open import commutative-algebra.subsets-commutative-semirings funext univalence truncations open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence open import foundation.universe-levels -open import ring-theory.ideals-semirings +open import ring-theory.ideals-semirings funext univalence truncations ```
diff --git a/src/commutative-algebra/ideals-generated-by-subsets-commutative-rings.lagda.md b/src/commutative-algebra/ideals-generated-by-subsets-commutative-rings.lagda.md index c057c98271..6c5a9375a3 100644 --- a/src/commutative-algebra/ideals-generated-by-subsets-commutative-rings.lagda.md +++ b/src/commutative-algebra/ideals-generated-by-subsets-commutative-rings.lagda.md @@ -1,24 +1,32 @@ # Ideals generated by subsets of commutative rings ```agda -module commutative-algebra.ideals-generated-by-subsets-commutative-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module commutative-algebra.ideals-generated-by-subsets-commutative-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import commutative-algebra.commutative-rings -open import commutative-algebra.ideals-commutative-rings -open import commutative-algebra.poset-of-ideals-commutative-rings -open import commutative-algebra.subsets-commutative-rings +open import commutative-algebra.commutative-rings funext univalence truncations +open import commutative-algebra.ideals-commutative-rings funext univalence truncations +open import commutative-algebra.poset-of-ideals-commutative-rings funext univalence truncations +open import commutative-algebra.subsets-commutative-rings funext univalence truncations -open import foundation.identity-types -open import foundation.subtypes +open import foundation.identity-types funext +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels -open import lists.concatenation-lists +open import lists.concatenation-lists funext univalence truncations -open import ring-theory.ideals-generated-by-subsets-rings +open import ring-theory.ideals-generated-by-subsets-rings funext univalence truncations ```
diff --git a/src/commutative-algebra/integer-multiples-of-elements-commutative-rings.lagda.md b/src/commutative-algebra/integer-multiples-of-elements-commutative-rings.lagda.md index ea8f228c18..5d6f037fa8 100644 --- a/src/commutative-algebra/integer-multiples-of-elements-commutative-rings.lagda.md +++ b/src/commutative-algebra/integer-multiples-of-elements-commutative-rings.lagda.md @@ -1,27 +1,35 @@ # Integer multiples of elements of commutative rings ```agda -module commutative-algebra.integer-multiples-of-elements-commutative-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module commutative-algebra.integer-multiples-of-elements-commutative-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import commutative-algebra.commutative-rings -open import commutative-algebra.homomorphisms-commutative-rings -open import commutative-algebra.multiples-of-elements-commutative-rings +open import commutative-algebra.commutative-rings funext univalence truncations +open import commutative-algebra.homomorphisms-commutative-rings funext univalence truncations +open import commutative-algebra.multiples-of-elements-commutative-rings funext univalence truncations -open import elementary-number-theory.addition-integers +open import elementary-number-theory.addition-integers funext univalence truncations open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-integers +open import elementary-number-theory.multiplication-integers funext univalence truncations open import elementary-number-theory.natural-numbers -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import group-theory.homomorphisms-abelian-groups +open import group-theory.homomorphisms-abelian-groups funext univalence truncations -open import ring-theory.integer-multiples-of-elements-rings +open import ring-theory.integer-multiples-of-elements-rings funext univalence truncations ```
diff --git a/src/commutative-algebra/integral-domains.lagda.md b/src/commutative-algebra/integral-domains.lagda.md index d960d94053..b37452ba24 100644 --- a/src/commutative-algebra/integral-domains.lagda.md +++ b/src/commutative-algebra/integral-domains.lagda.md @@ -1,48 +1,57 @@ # Integral domains ```agda -module commutative-algebra.integral-domains where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module commutative-algebra.integral-domains + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import commutative-algebra.commutative-rings -open import commutative-algebra.commutative-semirings -open import commutative-algebra.trivial-commutative-rings +open import commutative-algebra.commutative-rings funext univalence truncations +open import commutative-algebra.commutative-semirings funext univalence truncations +open import commutative-algebra.trivial-commutative-rings funext univalence truncations open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.binary-embeddings +open import foundation.binary-embeddings funext open import foundation.binary-equivalences -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalences -open import foundation.identity-types -open import foundation.injective-maps +open import foundation.dependent-products-propositions funext +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.injective-maps funext open import foundation.interchange-law -open import foundation.involutions -open import foundation.negation -open import foundation.propositions -open import foundation.sets +open import foundation.involutions funext univalence +open import foundation.negation funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence open import foundation.unital-binary-operations open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.commutative-monoids -open import group-theory.groups -open import group-theory.monoids -open import group-theory.semigroups +open import group-theory.abelian-groups funext univalence truncations +open import group-theory.commutative-monoids funext univalence truncations +open import group-theory.groups funext univalence truncations +open import group-theory.monoids funext univalence truncations +open import group-theory.semigroups funext univalence -open import lists.concatenation-lists +open import lists.concatenation-lists funext univalence truncations open import lists.lists -open import ring-theory.rings -open import ring-theory.semirings +open import ring-theory.rings funext univalence truncations +open import ring-theory.semirings funext univalence truncations ```
diff --git a/src/commutative-algebra/intersections-ideals-commutative-rings.lagda.md b/src/commutative-algebra/intersections-ideals-commutative-rings.lagda.md index 6846baf280..7c9afc5218 100644 --- a/src/commutative-algebra/intersections-ideals-commutative-rings.lagda.md +++ b/src/commutative-algebra/intersections-ideals-commutative-rings.lagda.md @@ -1,25 +1,33 @@ # Intersections of ideals of commutative rings ```agda -module commutative-algebra.intersections-ideals-commutative-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module commutative-algebra.intersections-ideals-commutative-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import commutative-algebra.commutative-rings -open import commutative-algebra.ideals-commutative-rings -open import commutative-algebra.poset-of-ideals-commutative-rings -open import commutative-algebra.subsets-commutative-rings +open import commutative-algebra.commutative-rings funext univalence truncations +open import commutative-algebra.ideals-commutative-rings funext univalence truncations +open import commutative-algebra.poset-of-ideals-commutative-rings funext univalence truncations +open import commutative-algebra.subsets-commutative-rings funext univalence truncations open import foundation.dependent-pair-types -open import foundation.intersections-subtypes -open import foundation.subtypes +open import foundation.intersections-subtypes funext univalence truncations +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels -open import order-theory.greatest-lower-bounds-large-posets +open import order-theory.greatest-lower-bounds-large-posets funext univalence truncations -open import ring-theory.intersections-ideals-rings +open import ring-theory.intersections-ideals-rings funext univalence truncations ```
diff --git a/src/commutative-algebra/intersections-radical-ideals-commutative-rings.lagda.md b/src/commutative-algebra/intersections-radical-ideals-commutative-rings.lagda.md index 1bf031cb1c..1f57876655 100644 --- a/src/commutative-algebra/intersections-radical-ideals-commutative-rings.lagda.md +++ b/src/commutative-algebra/intersections-radical-ideals-commutative-rings.lagda.md @@ -1,34 +1,42 @@ # Intersections of radical ideals of commutative rings ```agda -module commutative-algebra.intersections-radical-ideals-commutative-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module commutative-algebra.intersections-radical-ideals-commutative-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import commutative-algebra.commutative-rings -open import commutative-algebra.full-ideals-commutative-rings -open import commutative-algebra.ideals-commutative-rings -open import commutative-algebra.intersections-ideals-commutative-rings -open import commutative-algebra.poset-of-ideals-commutative-rings -open import commutative-algebra.poset-of-radical-ideals-commutative-rings -open import commutative-algebra.powers-of-elements-commutative-rings -open import commutative-algebra.products-ideals-commutative-rings -open import commutative-algebra.products-radical-ideals-commutative-rings -open import commutative-algebra.radical-ideals-commutative-rings -open import commutative-algebra.radicals-of-ideals-commutative-rings +open import commutative-algebra.commutative-rings funext univalence truncations +open import commutative-algebra.full-ideals-commutative-rings funext univalence truncations +open import commutative-algebra.ideals-commutative-rings funext univalence truncations +open import commutative-algebra.intersections-ideals-commutative-rings funext univalence truncations +open import commutative-algebra.poset-of-ideals-commutative-rings funext univalence truncations +open import commutative-algebra.poset-of-radical-ideals-commutative-rings funext univalence truncations +open import commutative-algebra.powers-of-elements-commutative-rings funext univalence truncations +open import commutative-algebra.products-ideals-commutative-rings funext univalence truncations +open import commutative-algebra.products-radical-ideals-commutative-rings funext univalence truncations +open import commutative-algebra.radical-ideals-commutative-rings funext univalence truncations +open import commutative-algebra.radicals-of-ideals-commutative-rings funext univalence truncations open import elementary-number-theory.addition-natural-numbers open import foundation.dependent-pair-types -open import foundation.existential-quantification -open import foundation.identity-types -open import foundation.propositional-truncations +open import foundation.existential-quantification funext univalence truncations +open import foundation.identity-types funext +open import foundation.propositional-truncations funext univalence open import foundation.universe-levels -open import order-theory.greatest-lower-bounds-large-posets -open import order-theory.large-meet-semilattices +open import order-theory.greatest-lower-bounds-large-posets funext univalence truncations +open import order-theory.large-meet-semilattices funext univalence truncations ```
diff --git a/src/commutative-algebra/invertible-elements-commutative-rings.lagda.md b/src/commutative-algebra/invertible-elements-commutative-rings.lagda.md index ebc4116027..57f727d27e 100644 --- a/src/commutative-algebra/invertible-elements-commutative-rings.lagda.md +++ b/src/commutative-algebra/invertible-elements-commutative-rings.lagda.md @@ -1,21 +1,31 @@ # Invertible elements in commutative rings ```agda -module commutative-algebra.invertible-elements-commutative-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module commutative-algebra.invertible-elements-commutative-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import commutative-algebra.commutative-rings +open import commutative-algebra.commutative-rings funext univalence truncations -open import foundation.contractible-types +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.propositions +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence open import foundation.universe-levels -open import ring-theory.invertible-elements-rings +open import ring-theory.invertible-elements-rings funext univalence truncations ```
diff --git a/src/commutative-algebra/isomorphisms-commutative-rings.lagda.md b/src/commutative-algebra/isomorphisms-commutative-rings.lagda.md index 663583921f..ff924e77b5 100644 --- a/src/commutative-algebra/isomorphisms-commutative-rings.lagda.md +++ b/src/commutative-algebra/isomorphisms-commutative-rings.lagda.md @@ -1,33 +1,42 @@ # Isomorphisms of commutative rings ```agda -module commutative-algebra.isomorphisms-commutative-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module commutative-algebra.isomorphisms-commutative-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.isomorphisms-in-large-precategories +open import category-theory.isomorphisms-in-large-precategories funext univalence truncations -open import commutative-algebra.commutative-rings -open import commutative-algebra.homomorphisms-commutative-rings -open import commutative-algebra.invertible-elements-commutative-rings -open import commutative-algebra.precategory-of-commutative-rings +open import commutative-algebra.commutative-rings funext univalence truncations +open import commutative-algebra.homomorphisms-commutative-rings funext univalence truncations +open import commutative-algebra.invertible-elements-commutative-rings funext univalence truncations +open import commutative-algebra.precategory-of-commutative-rings funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.propositions +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence open import foundation.subtype-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext univalence truncations open import foundation.universe-levels -open import group-theory.isomorphisms-abelian-groups +open import group-theory.isomorphisms-abelian-groups funext univalence truncations -open import ring-theory.isomorphisms-rings +open import ring-theory.isomorphisms-rings funext univalence truncations ```
diff --git a/src/commutative-algebra/joins-ideals-commutative-rings.lagda.md b/src/commutative-algebra/joins-ideals-commutative-rings.lagda.md index 52deaa9ff9..b48bc93102 100644 --- a/src/commutative-algebra/joins-ideals-commutative-rings.lagda.md +++ b/src/commutative-algebra/joins-ideals-commutative-rings.lagda.md @@ -1,28 +1,36 @@ # Joins of ideals of commutative rings ```agda -module commutative-algebra.joins-ideals-commutative-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module commutative-algebra.joins-ideals-commutative-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import commutative-algebra.commutative-rings -open import commutative-algebra.ideals-commutative-rings -open import commutative-algebra.ideals-generated-by-subsets-commutative-rings -open import commutative-algebra.poset-of-ideals-commutative-rings -open import commutative-algebra.products-ideals-commutative-rings -open import commutative-algebra.products-subsets-commutative-rings -open import commutative-algebra.subsets-commutative-rings +open import commutative-algebra.commutative-rings funext univalence truncations +open import commutative-algebra.ideals-commutative-rings funext univalence truncations +open import commutative-algebra.ideals-generated-by-subsets-commutative-rings funext univalence truncations +open import commutative-algebra.poset-of-ideals-commutative-rings funext univalence truncations +open import commutative-algebra.products-ideals-commutative-rings funext univalence truncations +open import commutative-algebra.products-subsets-commutative-rings funext univalence truncations +open import commutative-algebra.subsets-commutative-rings funext univalence truncations open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.subtypes -open import foundation.unions-subtypes +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.subtypes funext univalence truncations +open import foundation.unions-subtypes funext univalence truncations open import foundation.universe-levels -open import ring-theory.joins-ideals-rings +open import ring-theory.joins-ideals-rings funext univalence truncations ```
diff --git a/src/commutative-algebra/joins-radical-ideals-commutative-rings.lagda.md b/src/commutative-algebra/joins-radical-ideals-commutative-rings.lagda.md index 3cd6e927ed..872a583b0f 100644 --- a/src/commutative-algebra/joins-radical-ideals-commutative-rings.lagda.md +++ b/src/commutative-algebra/joins-radical-ideals-commutative-rings.lagda.md @@ -1,31 +1,39 @@ # Joins of radical ideals of commutative rings ```agda -module commutative-algebra.joins-radical-ideals-commutative-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module commutative-algebra.joins-radical-ideals-commutative-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import commutative-algebra.commutative-rings -open import commutative-algebra.ideals-commutative-rings -open import commutative-algebra.intersections-radical-ideals-commutative-rings -open import commutative-algebra.joins-ideals-commutative-rings -open import commutative-algebra.poset-of-radical-ideals-commutative-rings -open import commutative-algebra.products-ideals-commutative-rings -open import commutative-algebra.products-radical-ideals-commutative-rings -open import commutative-algebra.radical-ideals-commutative-rings -open import commutative-algebra.radical-ideals-generated-by-subsets-commutative-rings -open import commutative-algebra.radicals-of-ideals-commutative-rings -open import commutative-algebra.subsets-commutative-rings +open import commutative-algebra.commutative-rings funext univalence truncations +open import commutative-algebra.ideals-commutative-rings funext univalence truncations +open import commutative-algebra.intersections-radical-ideals-commutative-rings funext univalence truncations +open import commutative-algebra.joins-ideals-commutative-rings funext univalence truncations +open import commutative-algebra.poset-of-radical-ideals-commutative-rings funext univalence truncations +open import commutative-algebra.products-ideals-commutative-rings funext univalence truncations +open import commutative-algebra.products-radical-ideals-commutative-rings funext univalence truncations +open import commutative-algebra.radical-ideals-commutative-rings funext univalence truncations +open import commutative-algebra.radical-ideals-generated-by-subsets-commutative-rings funext univalence truncations +open import commutative-algebra.radicals-of-ideals-commutative-rings funext univalence truncations +open import commutative-algebra.subsets-commutative-rings funext univalence truncations open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.identity-types +open import foundation.function-types funext +open import foundation.identity-types funext open import foundation.universe-levels -open import order-theory.large-suplattices -open import order-theory.least-upper-bounds-large-posets +open import order-theory.large-suplattices funext univalence truncations +open import order-theory.least-upper-bounds-large-posets funext univalence truncations ```
diff --git a/src/commutative-algebra/local-commutative-rings.lagda.md b/src/commutative-algebra/local-commutative-rings.lagda.md index 9de71b60fc..530f71dc9a 100644 --- a/src/commutative-algebra/local-commutative-rings.lagda.md +++ b/src/commutative-algebra/local-commutative-rings.lagda.md @@ -1,21 +1,30 @@ # Local commutative rings ```agda -module commutative-algebra.local-commutative-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module commutative-algebra.local-commutative-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import commutative-algebra.commutative-rings +open import commutative-algebra.commutative-rings funext univalence truncations open import foundation.dependent-pair-types -open import foundation.propositions -open import foundation.sets +open import foundation.dependent-products-propositions funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence open import foundation.universe-levels -open import ring-theory.local-rings -open import ring-theory.rings +open import ring-theory.local-rings funext univalence truncations +open import ring-theory.rings funext univalence truncations ```
diff --git a/src/commutative-algebra/multiples-of-elements-commutative-rings.lagda.md b/src/commutative-algebra/multiples-of-elements-commutative-rings.lagda.md index 9121d62200..e62edd4c47 100644 --- a/src/commutative-algebra/multiples-of-elements-commutative-rings.lagda.md +++ b/src/commutative-algebra/multiples-of-elements-commutative-rings.lagda.md @@ -1,22 +1,30 @@ # Multiples of elements in commutative rings ```agda -module commutative-algebra.multiples-of-elements-commutative-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module commutative-algebra.multiples-of-elements-commutative-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import commutative-algebra.commutative-rings +open import commutative-algebra.commutative-rings funext univalence truncations open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import ring-theory.multiples-of-elements-rings +open import ring-theory.multiples-of-elements-rings funext univalence truncations ```
diff --git a/src/commutative-algebra/nilradical-commutative-rings.lagda.md b/src/commutative-algebra/nilradical-commutative-rings.lagda.md index e8cae03fe9..20500b6efe 100644 --- a/src/commutative-algebra/nilradical-commutative-rings.lagda.md +++ b/src/commutative-algebra/nilradical-commutative-rings.lagda.md @@ -1,25 +1,33 @@ # Nilradical of a commutative ring ```agda -module commutative-algebra.nilradical-commutative-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module commutative-algebra.nilradical-commutative-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import commutative-algebra.commutative-rings -open import commutative-algebra.ideals-commutative-rings -open import commutative-algebra.prime-ideals-commutative-rings -open import commutative-algebra.radical-ideals-commutative-rings -open import commutative-algebra.subsets-commutative-rings +open import commutative-algebra.commutative-rings funext univalence truncations +open import commutative-algebra.ideals-commutative-rings funext univalence truncations +open import commutative-algebra.prime-ideals-commutative-rings funext univalence truncations +open import commutative-algebra.radical-ideals-commutative-rings funext univalence truncations +open import commutative-algebra.subsets-commutative-rings funext univalence truncations open import foundation.dependent-pair-types -open import foundation.existential-quantification -open import foundation.identity-types -open import foundation.propositional-truncations +open import foundation.existential-quantification funext univalence truncations +open import foundation.identity-types funext +open import foundation.propositional-truncations funext univalence open import foundation.universe-levels -open import ring-theory.nilpotent-elements-rings +open import ring-theory.nilpotent-elements-rings funext univalence truncations ```
diff --git a/src/commutative-algebra/nilradicals-commutative-semirings.lagda.md b/src/commutative-algebra/nilradicals-commutative-semirings.lagda.md index 994c83bc29..35714916f6 100644 --- a/src/commutative-algebra/nilradicals-commutative-semirings.lagda.md +++ b/src/commutative-algebra/nilradicals-commutative-semirings.lagda.md @@ -1,20 +1,28 @@ # The nilradical of a commutative semiring ```agda -module commutative-algebra.nilradicals-commutative-semirings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module commutative-algebra.nilradicals-commutative-semirings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import commutative-algebra.commutative-semirings -open import commutative-algebra.subsets-commutative-semirings +open import commutative-algebra.commutative-semirings funext univalence truncations +open import commutative-algebra.subsets-commutative-semirings funext univalence truncations -open import foundation.existential-quantification -open import foundation.identity-types +open import foundation.existential-quantification funext univalence truncations +open import foundation.identity-types funext open import foundation.universe-levels -open import ring-theory.nilpotent-elements-semirings +open import ring-theory.nilpotent-elements-semirings funext univalence truncations ```
diff --git a/src/commutative-algebra/poset-of-ideals-commutative-rings.lagda.md b/src/commutative-algebra/poset-of-ideals-commutative-rings.lagda.md index 4b5b4c589f..d3e55cdb6d 100644 --- a/src/commutative-algebra/poset-of-ideals-commutative-rings.lagda.md +++ b/src/commutative-algebra/poset-of-ideals-commutative-rings.lagda.md @@ -1,23 +1,32 @@ # The poset of ideals of a commutative ring ```agda -module commutative-algebra.poset-of-ideals-commutative-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module commutative-algebra.poset-of-ideals-commutative-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import commutative-algebra.commutative-rings -open import commutative-algebra.ideals-commutative-rings +open import commutative-algebra.commutative-rings funext univalence truncations +open import commutative-algebra.ideals-commutative-rings funext univalence truncations -open import foundation.identity-types -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence open import foundation.universe-levels -open import order-theory.large-posets -open import order-theory.large-preorders +open import order-theory.large-posets funext univalence truncations +open import order-theory.large-preorders funext univalence truncations -open import ring-theory.poset-of-ideals-rings +open import ring-theory.poset-of-ideals-rings funext univalence truncations ```
diff --git a/src/commutative-algebra/poset-of-radical-ideals-commutative-rings.lagda.md b/src/commutative-algebra/poset-of-radical-ideals-commutative-rings.lagda.md index 79e6803732..5b20806170 100644 --- a/src/commutative-algebra/poset-of-radical-ideals-commutative-rings.lagda.md +++ b/src/commutative-algebra/poset-of-radical-ideals-commutative-rings.lagda.md @@ -1,26 +1,35 @@ # The poset of radical ideals of a commutative ring ```agda -module commutative-algebra.poset-of-radical-ideals-commutative-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module commutative-algebra.poset-of-radical-ideals-commutative-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import commutative-algebra.commutative-rings -open import commutative-algebra.poset-of-ideals-commutative-rings -open import commutative-algebra.radical-ideals-commutative-rings - -open import foundation.identity-types -open import foundation.propositions -open import foundation.subtypes +open import commutative-algebra.commutative-rings funext univalence truncations +open import commutative-algebra.poset-of-ideals-commutative-rings funext univalence truncations +open import commutative-algebra.radical-ideals-commutative-rings funext univalence truncations + +open import foundation.dependent-products-propositions funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels -open import order-theory.large-posets -open import order-theory.large-preorders -open import order-theory.order-preserving-maps-large-posets -open import order-theory.order-preserving-maps-large-preorders -open import order-theory.similarity-of-elements-large-posets +open import order-theory.large-posets funext univalence truncations +open import order-theory.large-preorders funext univalence truncations +open import order-theory.order-preserving-maps-large-posets funext univalence truncations +open import order-theory.order-preserving-maps-large-preorders funext univalence truncations +open import order-theory.similarity-of-elements-large-posets funext univalence truncations ```
diff --git a/src/commutative-algebra/powers-of-elements-commutative-rings.lagda.md b/src/commutative-algebra/powers-of-elements-commutative-rings.lagda.md index 9cd508163f..0edf2fea00 100644 --- a/src/commutative-algebra/powers-of-elements-commutative-rings.lagda.md +++ b/src/commutative-algebra/powers-of-elements-commutative-rings.lagda.md @@ -1,23 +1,31 @@ # Powers of elements in commutative rings ```agda -module commutative-algebra.powers-of-elements-commutative-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module commutative-algebra.powers-of-elements-commutative-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import commutative-algebra.commutative-rings +open import commutative-algebra.commutative-rings funext univalence truncations open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.parity-natural-numbers +open import elementary-number-theory.parity-natural-numbers funext univalence truncations -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import ring-theory.powers-of-elements-rings +open import ring-theory.powers-of-elements-rings funext univalence truncations ```
diff --git a/src/commutative-algebra/powers-of-elements-commutative-semirings.lagda.md b/src/commutative-algebra/powers-of-elements-commutative-semirings.lagda.md index 0bda772d1a..e22368de65 100644 --- a/src/commutative-algebra/powers-of-elements-commutative-semirings.lagda.md +++ b/src/commutative-algebra/powers-of-elements-commutative-semirings.lagda.md @@ -1,21 +1,29 @@ # Powers of elements in commutative semirings ```agda -module commutative-algebra.powers-of-elements-commutative-semirings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module commutative-algebra.powers-of-elements-commutative-semirings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import commutative-algebra.commutative-semirings +open import commutative-algebra.commutative-semirings funext univalence truncations open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.natural-numbers -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import ring-theory.powers-of-elements-semirings +open import ring-theory.powers-of-elements-semirings funext univalence truncations ```
diff --git a/src/commutative-algebra/precategory-of-commutative-rings.lagda.md b/src/commutative-algebra/precategory-of-commutative-rings.lagda.md index 51c54f1c3f..b0b7e63607 100644 --- a/src/commutative-algebra/precategory-of-commutative-rings.lagda.md +++ b/src/commutative-algebra/precategory-of-commutative-rings.lagda.md @@ -1,21 +1,29 @@ # The precategory of commutative rings ```agda -module commutative-algebra.precategory-of-commutative-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module commutative-algebra.precategory-of-commutative-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.full-large-subprecategories -open import category-theory.large-precategories -open import category-theory.precategories +open import category-theory.full-large-subprecategories funext univalence truncations +open import category-theory.large-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations -open import commutative-algebra.commutative-rings +open import commutative-algebra.commutative-rings funext univalence truncations open import foundation.universe-levels -open import ring-theory.precategory-of-rings +open import ring-theory.precategory-of-rings funext univalence truncations ```
diff --git a/src/commutative-algebra/precategory-of-commutative-semirings.lagda.md b/src/commutative-algebra/precategory-of-commutative-semirings.lagda.md index e0239a074f..627f5b0567 100644 --- a/src/commutative-algebra/precategory-of-commutative-semirings.lagda.md +++ b/src/commutative-algebra/precategory-of-commutative-semirings.lagda.md @@ -1,21 +1,29 @@ # The precategory of commutative semirings ```agda -module commutative-algebra.precategory-of-commutative-semirings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module commutative-algebra.precategory-of-commutative-semirings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.full-large-subprecategories -open import category-theory.large-precategories -open import category-theory.precategories +open import category-theory.full-large-subprecategories funext univalence truncations +open import category-theory.large-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations -open import commutative-algebra.commutative-semirings +open import commutative-algebra.commutative-semirings funext univalence truncations open import foundation.universe-levels -open import ring-theory.precategory-of-semirings +open import ring-theory.precategory-of-semirings funext univalence truncations ```
diff --git a/src/commutative-algebra/prime-ideals-commutative-rings.lagda.md b/src/commutative-algebra/prime-ideals-commutative-rings.lagda.md index de9a327c13..2d3f57a0cf 100644 --- a/src/commutative-algebra/prime-ideals-commutative-rings.lagda.md +++ b/src/commutative-algebra/prime-ideals-commutative-rings.lagda.md @@ -1,29 +1,38 @@ # Prime ideals of commutative rings ```agda -module commutative-algebra.prime-ideals-commutative-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module commutative-algebra.prime-ideals-commutative-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import commutative-algebra.commutative-rings -open import commutative-algebra.full-ideals-commutative-rings -open import commutative-algebra.ideals-commutative-rings -open import commutative-algebra.powers-of-elements-commutative-rings -open import commutative-algebra.radical-ideals-commutative-rings -open import commutative-algebra.subsets-commutative-rings +open import commutative-algebra.commutative-rings funext univalence truncations +open import commutative-algebra.full-ideals-commutative-rings funext univalence truncations +open import commutative-algebra.ideals-commutative-rings funext univalence truncations +open import commutative-algebra.powers-of-elements-commutative-rings funext univalence truncations +open import commutative-algebra.radical-ideals-commutative-rings funext univalence truncations +open import commutative-algebra.subsets-commutative-rings funext univalence truncations open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.disjunction -open import foundation.function-types -open import foundation.identity-types -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.disjunction funext univalence truncations +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence open import foundation.universe-levels -open import ring-theory.subsets-rings +open import ring-theory.subsets-rings funext univalence truncations ```
diff --git a/src/commutative-algebra/products-commutative-rings.lagda.md b/src/commutative-algebra/products-commutative-rings.lagda.md index dee1a7ee38..b6f619b097 100644 --- a/src/commutative-algebra/products-commutative-rings.lagda.md +++ b/src/commutative-algebra/products-commutative-rings.lagda.md @@ -1,26 +1,34 @@ # Products of commutative rings ```agda -module commutative-algebra.products-commutative-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module commutative-algebra.products-commutative-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import commutative-algebra.commutative-rings +open import commutative-algebra.commutative-rings funext univalence truncations open import foundation.dependent-pair-types open import foundation.equality-cartesian-product-types -open import foundation.identity-types -open import foundation.sets +open import foundation.identity-types funext +open import foundation.sets funext univalence open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.groups -open import group-theory.semigroups +open import group-theory.abelian-groups funext univalence truncations +open import group-theory.groups funext univalence truncations +open import group-theory.semigroups funext univalence -open import ring-theory.products-rings -open import ring-theory.rings +open import ring-theory.products-rings funext univalence truncations +open import ring-theory.rings funext univalence truncations ```
diff --git a/src/commutative-algebra/products-ideals-commutative-rings.lagda.md b/src/commutative-algebra/products-ideals-commutative-rings.lagda.md index 9e1a2d1173..f7a419a370 100644 --- a/src/commutative-algebra/products-ideals-commutative-rings.lagda.md +++ b/src/commutative-algebra/products-ideals-commutative-rings.lagda.md @@ -1,28 +1,36 @@ # Products of ideals of commutative rings ```agda -module commutative-algebra.products-ideals-commutative-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module commutative-algebra.products-ideals-commutative-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import commutative-algebra.commutative-rings -open import commutative-algebra.ideals-commutative-rings -open import commutative-algebra.ideals-generated-by-subsets-commutative-rings -open import commutative-algebra.poset-of-ideals-commutative-rings -open import commutative-algebra.products-subsets-commutative-rings -open import commutative-algebra.subsets-commutative-rings +open import commutative-algebra.commutative-rings funext univalence truncations +open import commutative-algebra.ideals-commutative-rings funext univalence truncations +open import commutative-algebra.ideals-generated-by-subsets-commutative-rings funext univalence truncations +open import commutative-algebra.poset-of-ideals-commutative-rings funext univalence truncations +open import commutative-algebra.products-subsets-commutative-rings funext univalence truncations +open import commutative-algebra.subsets-commutative-rings funext univalence truncations open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.propositional-truncations +open import foundation.identity-types funext +open import foundation.propositional-truncations funext univalence open import foundation.universe-levels open import lists.lists -open import ring-theory.products-ideals-rings +open import ring-theory.products-ideals-rings funext univalence truncations ```
diff --git a/src/commutative-algebra/products-radical-ideals-commutative-rings.lagda.md b/src/commutative-algebra/products-radical-ideals-commutative-rings.lagda.md index f112058f6d..36a596f5e6 100644 --- a/src/commutative-algebra/products-radical-ideals-commutative-rings.lagda.md +++ b/src/commutative-algebra/products-radical-ideals-commutative-rings.lagda.md @@ -1,27 +1,35 @@ # Products of radical ideals of a commutative ring ```agda -module commutative-algebra.products-radical-ideals-commutative-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module commutative-algebra.products-radical-ideals-commutative-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import commutative-algebra.commutative-rings -open import commutative-algebra.ideals-commutative-rings -open import commutative-algebra.poset-of-radical-ideals-commutative-rings -open import commutative-algebra.powers-of-elements-commutative-rings -open import commutative-algebra.products-ideals-commutative-rings -open import commutative-algebra.radical-ideals-commutative-rings -open import commutative-algebra.radicals-of-ideals-commutative-rings -open import commutative-algebra.subsets-commutative-rings +open import commutative-algebra.commutative-rings funext univalence truncations +open import commutative-algebra.ideals-commutative-rings funext univalence truncations +open import commutative-algebra.poset-of-radical-ideals-commutative-rings funext univalence truncations +open import commutative-algebra.powers-of-elements-commutative-rings funext univalence truncations +open import commutative-algebra.products-ideals-commutative-rings funext univalence truncations +open import commutative-algebra.radical-ideals-commutative-rings funext univalence truncations +open import commutative-algebra.radicals-of-ideals-commutative-rings funext univalence truncations +open import commutative-algebra.subsets-commutative-rings funext univalence truncations open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.existential-quantification -open import foundation.identity-types -open import foundation.propositional-truncations +open import foundation.existential-quantification funext univalence truncations +open import foundation.identity-types funext +open import foundation.propositional-truncations funext univalence open import foundation.universe-levels ``` diff --git a/src/commutative-algebra/products-subsets-commutative-rings.lagda.md b/src/commutative-algebra/products-subsets-commutative-rings.lagda.md index 9bad16cb22..a9799e1556 100644 --- a/src/commutative-algebra/products-subsets-commutative-rings.lagda.md +++ b/src/commutative-algebra/products-subsets-commutative-rings.lagda.md @@ -1,21 +1,29 @@ # Products of subsets of commutative rings ```agda -module commutative-algebra.products-subsets-commutative-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module commutative-algebra.products-subsets-commutative-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import commutative-algebra.commutative-rings -open import commutative-algebra.subsets-commutative-rings +open import commutative-algebra.commutative-rings funext univalence truncations +open import commutative-algebra.subsets-commutative-rings funext univalence truncations -open import foundation.identity-types -open import foundation.subtypes -open import foundation.unions-subtypes +open import foundation.identity-types funext +open import foundation.subtypes funext univalence truncations +open import foundation.unions-subtypes funext univalence truncations open import foundation.universe-levels -open import ring-theory.products-subsets-rings +open import ring-theory.products-subsets-rings funext univalence truncations ```
diff --git a/src/commutative-algebra/radical-ideals-commutative-rings.lagda.md b/src/commutative-algebra/radical-ideals-commutative-rings.lagda.md index f087226bc9..3068c12261 100644 --- a/src/commutative-algebra/radical-ideals-commutative-rings.lagda.md +++ b/src/commutative-algebra/radical-ideals-commutative-rings.lagda.md @@ -1,26 +1,35 @@ # Radical ideals of commutative rings ```agda -module commutative-algebra.radical-ideals-commutative-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module commutative-algebra.radical-ideals-commutative-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import commutative-algebra.commutative-rings -open import commutative-algebra.ideals-commutative-rings -open import commutative-algebra.powers-of-elements-commutative-rings -open import commutative-algebra.subsets-commutative-rings +open import commutative-algebra.commutative-rings funext univalence truncations +open import commutative-algebra.ideals-commutative-rings funext univalence truncations +open import commutative-algebra.powers-of-elements-commutative-rings funext univalence truncations +open import commutative-algebra.subsets-commutative-rings funext univalence truncations open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.equivalences +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types -open import foundation.propositions +open import foundation.identity-types funext +open import foundation.propositions funext univalence open import foundation.subtype-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext univalence truncations open import foundation.universe-levels ``` diff --git a/src/commutative-algebra/radical-ideals-generated-by-subsets-commutative-rings.lagda.md b/src/commutative-algebra/radical-ideals-generated-by-subsets-commutative-rings.lagda.md index 9c09b474bf..ecde3b6b36 100644 --- a/src/commutative-algebra/radical-ideals-generated-by-subsets-commutative-rings.lagda.md +++ b/src/commutative-algebra/radical-ideals-generated-by-subsets-commutative-rings.lagda.md @@ -9,14 +9,14 @@ module
Imports ```agda -open import commutative-algebra.commutative-rings -open import commutative-algebra.ideals-commutative-rings -open import commutative-algebra.ideals-generated-by-subsets-commutative-rings -open import commutative-algebra.radical-ideals-commutative-rings -open import commutative-algebra.radicals-of-ideals-commutative-rings -open import commutative-algebra.subsets-commutative-rings - -open import foundation.subtypes +open import commutative-algebra.commutative-rings funext univalence truncations +open import commutative-algebra.ideals-commutative-rings funext univalence truncations +open import commutative-algebra.ideals-generated-by-subsets-commutative-rings funext univalence truncations +open import commutative-algebra.radical-ideals-commutative-rings funext univalence truncations +open import commutative-algebra.radicals-of-ideals-commutative-rings funext univalence truncations +open import commutative-algebra.subsets-commutative-rings funext univalence truncations + +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels ``` @@ -34,7 +34,14 @@ containing `S`. ### The universal property of the radical ideal generated by a subset ```agda +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + module _ + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) {l1 l2 l3 : Level} (A : Commutative-Ring l1) (S : subset-Commutative-Ring l2 A) (I : radical-ideal-Commutative-Ring l3 A) diff --git a/src/commutative-algebra/radicals-of-ideals-commutative-rings.lagda.md b/src/commutative-algebra/radicals-of-ideals-commutative-rings.lagda.md index 13a2f12ae2..e0e74826ee 100644 --- a/src/commutative-algebra/radicals-of-ideals-commutative-rings.lagda.md +++ b/src/commutative-algebra/radicals-of-ideals-commutative-rings.lagda.md @@ -1,37 +1,46 @@ # Radicals of ideals of commutative rings ```agda -module commutative-algebra.radicals-of-ideals-commutative-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module commutative-algebra.radicals-of-ideals-commutative-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import commutative-algebra.binomial-theorem-commutative-rings -open import commutative-algebra.commutative-rings -open import commutative-algebra.ideals-commutative-rings -open import commutative-algebra.poset-of-ideals-commutative-rings -open import commutative-algebra.poset-of-radical-ideals-commutative-rings -open import commutative-algebra.powers-of-elements-commutative-rings -open import commutative-algebra.radical-ideals-commutative-rings -open import commutative-algebra.subsets-commutative-rings +open import commutative-algebra.binomial-theorem-commutative-rings funext univalence truncations +open import commutative-algebra.commutative-rings funext univalence truncations +open import commutative-algebra.ideals-commutative-rings funext univalence truncations +open import commutative-algebra.poset-of-ideals-commutative-rings funext univalence truncations +open import commutative-algebra.poset-of-radical-ideals-commutative-rings funext univalence truncations +open import commutative-algebra.powers-of-elements-commutative-rings funext univalence truncations +open import commutative-algebra.radical-ideals-commutative-rings funext univalence truncations +open import commutative-algebra.subsets-commutative-rings funext univalence truncations open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.existential-quantification -open import foundation.logical-equivalences -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.existential-quantification funext univalence truncations +open import foundation.logical-equivalences funext +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels -open import order-theory.galois-connections-large-posets -open import order-theory.order-preserving-maps-large-posets -open import order-theory.order-preserving-maps-large-preorders -open import order-theory.reflective-galois-connections-large-posets +open import order-theory.galois-connections-large-posets funext univalence truncations +open import order-theory.order-preserving-maps-large-posets funext univalence truncations +open import order-theory.order-preserving-maps-large-preorders funext univalence truncations +open import order-theory.reflective-galois-connections-large-posets funext univalence truncations ```
diff --git a/src/commutative-algebra/subsets-commutative-rings.lagda.md b/src/commutative-algebra/subsets-commutative-rings.lagda.md index fd7c2d204e..2d72432055 100644 --- a/src/commutative-algebra/subsets-commutative-rings.lagda.md +++ b/src/commutative-algebra/subsets-commutative-rings.lagda.md @@ -1,24 +1,33 @@ # Subsets of commutative rings ```agda -module commutative-algebra.subsets-commutative-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module commutative-algebra.subsets-commutative-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import commutative-algebra.commutative-rings - -open import foundation.identity-types -open import foundation.propositional-extensionality -open import foundation.propositions -open import foundation.sets -open import foundation.subtypes +open import commutative-algebra.commutative-rings funext univalence truncations + +open import foundation.dependent-products-propositions funext +open import foundation.identity-types funext +open import foundation.propositional-extensionality funext univalence truncations +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels -open import group-theory.subgroups-abelian-groups +open import group-theory.subgroups-abelian-groups funext univalence truncations -open import ring-theory.subsets-rings +open import ring-theory.subsets-rings funext univalence truncations ```
diff --git a/src/commutative-algebra/subsets-commutative-semirings.lagda.md b/src/commutative-algebra/subsets-commutative-semirings.lagda.md index 73f9932341..fabc46ffda 100644 --- a/src/commutative-algebra/subsets-commutative-semirings.lagda.md +++ b/src/commutative-algebra/subsets-commutative-semirings.lagda.md @@ -1,21 +1,30 @@ # Subsets of commutative semirings ```agda -module commutative-algebra.subsets-commutative-semirings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module commutative-algebra.subsets-commutative-semirings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import commutative-algebra.commutative-semirings +open import commutative-algebra.commutative-semirings funext univalence truncations -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels -open import ring-theory.subsets-semirings +open import ring-theory.subsets-semirings funext univalence truncations ```
diff --git a/src/commutative-algebra/sums-commutative-rings.lagda.md b/src/commutative-algebra/sums-commutative-rings.lagda.md index f26a86e6db..fb01b5eddf 100644 --- a/src/commutative-algebra/sums-commutative-rings.lagda.md +++ b/src/commutative-algebra/sums-commutative-rings.lagda.md @@ -1,32 +1,40 @@ # Sums in commutative rings ```agda -module commutative-algebra.sums-commutative-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module commutative-algebra.sums-commutative-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import commutative-algebra.commutative-rings +open import commutative-algebra.commutative-rings funext univalence truncations open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.coproduct-types -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types +open import foundation.coproduct-types funext univalence truncations +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.unit-type open import foundation.universe-levels -open import linear-algebra.vectors -open import linear-algebra.vectors-on-commutative-rings +open import linear-algebra.vectors funext univalence truncations +open import linear-algebra.vectors-on-commutative-rings funext univalence truncations -open import ring-theory.sums-rings +open import ring-theory.sums-rings funext univalence truncations -open import univalent-combinatorics.coproduct-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.coproduct-types funext univalence truncations +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/commutative-algebra/sums-commutative-semirings.lagda.md b/src/commutative-algebra/sums-commutative-semirings.lagda.md index 16eaf02de8..da64cbb079 100644 --- a/src/commutative-algebra/sums-commutative-semirings.lagda.md +++ b/src/commutative-algebra/sums-commutative-semirings.lagda.md @@ -1,29 +1,37 @@ # Sums in commutative semirings ```agda -module commutative-algebra.sums-commutative-semirings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module commutative-algebra.sums-commutative-semirings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import commutative-algebra.commutative-semirings +open import commutative-algebra.commutative-semirings funext univalence truncations open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.natural-numbers -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.universe-levels -open import linear-algebra.vectors -open import linear-algebra.vectors-on-commutative-semirings +open import linear-algebra.vectors funext univalence truncations +open import linear-algebra.vectors-on-commutative-semirings funext univalence truncations -open import ring-theory.sums-semirings +open import ring-theory.sums-semirings funext univalence truncations -open import univalent-combinatorics.coproduct-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.coproduct-types funext univalence truncations +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/commutative-algebra/transporting-commutative-ring-structure-isomorphisms-abelian-groups.lagda.md b/src/commutative-algebra/transporting-commutative-ring-structure-isomorphisms-abelian-groups.lagda.md index d504ae3dbc..e23ef5bf4c 100644 --- a/src/commutative-algebra/transporting-commutative-ring-structure-isomorphisms-abelian-groups.lagda.md +++ b/src/commutative-algebra/transporting-commutative-ring-structure-isomorphisms-abelian-groups.lagda.md @@ -9,23 +9,23 @@ module
Imports ```agda -open import commutative-algebra.commutative-rings -open import commutative-algebra.homomorphisms-commutative-rings -open import commutative-algebra.isomorphisms-commutative-rings +open import commutative-algebra.commutative-rings funext univalence truncations +open import commutative-algebra.homomorphisms-commutative-rings funext univalence truncations +open import commutative-algebra.isomorphisms-commutative-rings funext univalence truncations open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.unital-binary-operations open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.isomorphisms-abelian-groups -open import group-theory.semigroups +open import group-theory.abelian-groups funext univalence truncations +open import group-theory.isomorphisms-abelian-groups funext univalence truncations +open import group-theory.semigroups funext univalence -open import ring-theory.homomorphisms-rings -open import ring-theory.rings -open import ring-theory.transporting-ring-structure-along-isomorphisms-abelian-groups +open import ring-theory.homomorphisms-rings funext univalence truncations +open import ring-theory.rings funext univalence truncations +open import ring-theory.transporting-ring-structure-along-isomorphisms-abelian-groups funext univalence truncations ```
@@ -48,7 +48,14 @@ transported ring structure. ### Transporting the multiplicative structure of a commutative ring along an isomorphism of abelian groups ```agda +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + module _ + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) {l1 l2 : Level} (A : Commutative-Ring l1) (B : Ab l2) (f : iso-Ab (ab-Commutative-Ring A) B) where diff --git a/src/commutative-algebra/trivial-commutative-rings.lagda.md b/src/commutative-algebra/trivial-commutative-rings.lagda.md index 8aa4781e63..5c6a5260d6 100644 --- a/src/commutative-algebra/trivial-commutative-rings.lagda.md +++ b/src/commutative-algebra/trivial-commutative-rings.lagda.md @@ -1,31 +1,41 @@ # Trivial commutative rings ```agda -module commutative-algebra.trivial-commutative-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module commutative-algebra.trivial-commutative-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import commutative-algebra.commutative-rings -open import commutative-algebra.isomorphisms-commutative-rings +open import commutative-algebra.commutative-rings funext univalence truncations +open import commutative-algebra.isomorphisms-commutative-rings funext univalence truncations -open import foundation.contractible-types +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.negation -open import foundation.propositions -open import foundation.sets +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.negation funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence open import foundation.structure-identity-principle open import foundation.unit-type open import foundation.universe-levels open import foundation-core.identity-types -open import group-theory.abelian-groups -open import group-theory.trivial-groups +open import group-theory.abelian-groups funext univalence truncations +open import group-theory.trivial-groups funext univalence truncations -open import ring-theory.rings -open import ring-theory.trivial-rings +open import ring-theory.rings funext univalence truncations +open import ring-theory.trivial-rings funext univalence truncations ```
diff --git a/src/commutative-algebra/zariski-locale.lagda.md b/src/commutative-algebra/zariski-locale.lagda.md index 512b67f821..526bc7b308 100644 --- a/src/commutative-algebra/zariski-locale.lagda.md +++ b/src/commutative-algebra/zariski-locale.lagda.md @@ -1,21 +1,29 @@ # The Zariski locale ```agda -module commutative-algebra.zariski-locale where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module commutative-algebra.zariski-locale + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import commutative-algebra.commutative-rings -open import commutative-algebra.intersections-radical-ideals-commutative-rings -open import commutative-algebra.joins-radical-ideals-commutative-rings -open import commutative-algebra.poset-of-radical-ideals-commutative-rings +open import commutative-algebra.commutative-rings funext univalence truncations +open import commutative-algebra.intersections-radical-ideals-commutative-rings funext univalence truncations +open import commutative-algebra.joins-radical-ideals-commutative-rings funext univalence truncations +open import commutative-algebra.poset-of-radical-ideals-commutative-rings funext univalence truncations open import foundation.universe-levels -open import order-theory.large-frames -open import order-theory.large-locales +open import order-theory.large-frames funext univalence truncations +open import order-theory.large-locales funext univalence truncations ```
diff --git a/src/commutative-algebra/zariski-topology.lagda.md b/src/commutative-algebra/zariski-topology.lagda.md index b3bbbec25c..d6f10828bb 100644 --- a/src/commutative-algebra/zariski-topology.lagda.md +++ b/src/commutative-algebra/zariski-topology.lagda.md @@ -1,19 +1,28 @@ # The Zariski topology on the set of prime ideals of a commutative ring ```agda -module commutative-algebra.zariski-topology where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module commutative-algebra.zariski-topology + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import commutative-algebra.commutative-rings -open import commutative-algebra.prime-ideals-commutative-rings +open import commutative-algebra.commutative-rings funext univalence truncations +open import commutative-algebra.prime-ideals-commutative-rings funext univalence truncations -open import foundation.existential-quantification -open import foundation.identity-types -open import foundation.propositions -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.existential-quantification funext univalence truncations +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels ``` diff --git a/src/domain-theory.lagda.md b/src/domain-theory.lagda.md index 5e1cb84b7f..33446e9122 100644 --- a/src/domain-theory.lagda.md +++ b/src/domain-theory.lagda.md @@ -3,15 +3,23 @@ ## Modules in the domain theory namespace ```agda -module domain-theory where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom -open import domain-theory.directed-complete-posets public -open import domain-theory.directed-families-posets public -open import domain-theory.kleenes-fixed-point-theorem-omega-complete-posets public -open import domain-theory.kleenes-fixed-point-theorem-posets public -open import domain-theory.omega-complete-posets public -open import domain-theory.omega-continuous-maps-omega-complete-posets public -open import domain-theory.omega-continuous-maps-posets public -open import domain-theory.reindexing-directed-families-posets public -open import domain-theory.scott-continuous-maps-posets public +module domain-theory + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where + +open import domain-theory.directed-complete-posets funext univalence truncations public +open import domain-theory.directed-families-posets funext univalence truncations public +open import domain-theory.kleenes-fixed-point-theorem-omega-complete-posets funext univalence truncations public +open import domain-theory.kleenes-fixed-point-theorem-posets funext univalence truncations public +open import domain-theory.omega-complete-posets funext univalence truncations public +open import domain-theory.omega-continuous-maps-omega-complete-posets funext univalence truncations public +open import domain-theory.omega-continuous-maps-posets funext univalence truncations public +open import domain-theory.reindexing-directed-families-posets funext univalence truncations public +open import domain-theory.scott-continuous-maps-posets funext univalence truncations public ``` diff --git a/src/domain-theory/directed-complete-posets.lagda.md b/src/domain-theory/directed-complete-posets.lagda.md index 2225aeff51..50d7af2a18 100644 --- a/src/domain-theory/directed-complete-posets.lagda.md +++ b/src/domain-theory/directed-complete-posets.lagda.md @@ -1,25 +1,34 @@ # Directed complete posets ```agda -module domain-theory.directed-complete-posets where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module domain-theory.directed-complete-posets + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import domain-theory.directed-families-posets +open import domain-theory.directed-families-posets funext univalence truncations -open import foundation.binary-relations +open import foundation.binary-relations funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.logical-equivalences -open import foundation.propositions -open import foundation.sets +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.logical-equivalences funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence open import foundation.universe-levels -open import order-theory.least-upper-bounds-posets -open import order-theory.posets +open import order-theory.least-upper-bounds-posets funext univalence truncations +open import order-theory.posets funext univalence truncations ```
diff --git a/src/domain-theory/directed-families-posets.lagda.md b/src/domain-theory/directed-families-posets.lagda.md index 0b192c1b84..22f72965b2 100644 --- a/src/domain-theory/directed-families-posets.lagda.md +++ b/src/domain-theory/directed-families-posets.lagda.md @@ -1,29 +1,38 @@ # Directed families in posets ```agda -module domain-theory.directed-families-posets where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module domain-theory.directed-families-posets + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types -open import foundation.conjunction +open import foundation.cartesian-product-types funext univalence +open import foundation.conjunction funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.existential-quantification -open import foundation.function-types -open import foundation.identity-types -open import foundation.inhabited-types -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.surjective-maps -open import foundation.universal-quantification +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.existential-quantification funext univalence truncations +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.inhabited-types funext univalence truncations +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence +open import foundation.surjective-maps funext univalence truncations +open import foundation.universal-quantification funext univalence truncations open import foundation.universe-levels -open import order-theory.order-preserving-maps-posets -open import order-theory.posets +open import order-theory.order-preserving-maps-posets funext univalence truncations +open import order-theory.posets funext univalence truncations ```
diff --git a/src/domain-theory/kleenes-fixed-point-theorem-omega-complete-posets.lagda.md b/src/domain-theory/kleenes-fixed-point-theorem-omega-complete-posets.lagda.md index 0e760554ec..0c074b2d25 100644 --- a/src/domain-theory/kleenes-fixed-point-theorem-omega-complete-posets.lagda.md +++ b/src/domain-theory/kleenes-fixed-point-theorem-omega-complete-posets.lagda.md @@ -1,41 +1,49 @@ # Kleene's fixed point theorem for ω-complete posets ```agda -module domain-theory.kleenes-fixed-point-theorem-omega-complete-posets where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module domain-theory.kleenes-fixed-point-theorem-omega-complete-posets + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import domain-theory.directed-families-posets -open import domain-theory.kleenes-fixed-point-theorem-posets -open import domain-theory.omega-complete-posets -open import domain-theory.omega-continuous-maps-omega-complete-posets -open import domain-theory.omega-continuous-maps-posets - -open import elementary-number-theory.decidable-total-order-natural-numbers -open import elementary-number-theory.inequality-natural-numbers +open import domain-theory.directed-families-posets funext univalence truncations +open import domain-theory.kleenes-fixed-point-theorem-posets funext univalence truncations +open import domain-theory.omega-complete-posets funext univalence truncations +open import domain-theory.omega-continuous-maps-omega-complete-posets funext univalence truncations +open import domain-theory.omega-continuous-maps-posets funext univalence truncations + +open import elementary-number-theory.decidable-total-order-natural-numbers funext univalence truncations +open import elementary-number-theory.inequality-natural-numbers funext univalence truncations open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types open import foundation.fixed-points-endofunctions -open import foundation.function-types -open import foundation.identity-types -open import foundation.inhabited-types -open import foundation.iterating-functions -open import foundation.logical-equivalences -open import foundation.propositional-truncations +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.inhabited-types funext univalence truncations +open import foundation.iterating-functions funext univalence truncations +open import foundation.logical-equivalences funext +open import foundation.propositional-truncations funext univalence open import foundation.universe-levels -open import order-theory.bottom-elements-posets -open import order-theory.chains-posets -open import order-theory.inflattices -open import order-theory.inhabited-chains-posets -open import order-theory.least-upper-bounds-posets -open import order-theory.order-preserving-maps-posets -open import order-theory.posets -open import order-theory.suplattices -open import order-theory.upper-bounds-posets +open import order-theory.bottom-elements-posets funext univalence truncations +open import order-theory.chains-posets funext univalence truncations +open import order-theory.inflattices funext univalence truncations +open import order-theory.inhabited-chains-posets funext univalence truncations +open import order-theory.least-upper-bounds-posets funext univalence truncations +open import order-theory.order-preserving-maps-posets funext univalence truncations +open import order-theory.posets funext univalence truncations +open import order-theory.suplattices funext univalence truncations +open import order-theory.upper-bounds-posets funext univalence truncations ```
diff --git a/src/domain-theory/kleenes-fixed-point-theorem-posets.lagda.md b/src/domain-theory/kleenes-fixed-point-theorem-posets.lagda.md index 8a3518c188..daac9e88f4 100644 --- a/src/domain-theory/kleenes-fixed-point-theorem-posets.lagda.md +++ b/src/domain-theory/kleenes-fixed-point-theorem-posets.lagda.md @@ -1,38 +1,46 @@ # Kleene's fixed point theorem for posets ```agda -module domain-theory.kleenes-fixed-point-theorem-posets where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module domain-theory.kleenes-fixed-point-theorem-posets + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import domain-theory.directed-families-posets -open import domain-theory.omega-continuous-maps-posets +open import domain-theory.directed-families-posets funext univalence truncations +open import domain-theory.omega-continuous-maps-posets funext univalence truncations -open import elementary-number-theory.decidable-total-order-natural-numbers -open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.decidable-total-order-natural-numbers funext univalence truncations +open import elementary-number-theory.inequality-natural-numbers funext univalence truncations open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types open import foundation.fixed-points-endofunctions -open import foundation.function-types -open import foundation.identity-types -open import foundation.inhabited-types -open import foundation.iterating-functions -open import foundation.logical-equivalences -open import foundation.propositional-truncations +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.inhabited-types funext univalence truncations +open import foundation.iterating-functions funext univalence truncations +open import foundation.logical-equivalences funext +open import foundation.propositional-truncations funext univalence open import foundation.universe-levels -open import order-theory.bottom-elements-posets -open import order-theory.chains-posets -open import order-theory.inflattices -open import order-theory.inhabited-chains-posets -open import order-theory.least-upper-bounds-posets -open import order-theory.order-preserving-maps-posets -open import order-theory.posets -open import order-theory.suplattices -open import order-theory.upper-bounds-posets +open import order-theory.bottom-elements-posets funext univalence truncations +open import order-theory.chains-posets funext univalence truncations +open import order-theory.inflattices funext univalence truncations +open import order-theory.inhabited-chains-posets funext univalence truncations +open import order-theory.least-upper-bounds-posets funext univalence truncations +open import order-theory.order-preserving-maps-posets funext univalence truncations +open import order-theory.posets funext univalence truncations +open import order-theory.suplattices funext univalence truncations +open import order-theory.upper-bounds-posets funext univalence truncations ```
diff --git a/src/domain-theory/omega-complete-posets.lagda.md b/src/domain-theory/omega-complete-posets.lagda.md index 612e60affb..64507c8f91 100644 --- a/src/domain-theory/omega-complete-posets.lagda.md +++ b/src/domain-theory/omega-complete-posets.lagda.md @@ -1,29 +1,38 @@ # ω-Complete posets ```agda -module domain-theory.omega-complete-posets where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module domain-theory.omega-complete-posets + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.decidable-total-order-natural-numbers -open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.decidable-total-order-natural-numbers funext univalence truncations +open import elementary-number-theory.inequality-natural-numbers funext univalence truncations open import elementary-number-theory.natural-numbers -open import foundation.binary-relations +open import foundation.binary-relations funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.logical-equivalences -open import foundation.propositions -open import foundation.sets +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.logical-equivalences funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence open import foundation.universe-levels -open import order-theory.least-upper-bounds-posets -open import order-theory.order-preserving-maps-posets -open import order-theory.posets -open import order-theory.upper-bounds-posets +open import order-theory.least-upper-bounds-posets funext univalence truncations +open import order-theory.order-preserving-maps-posets funext univalence truncations +open import order-theory.posets funext univalence truncations +open import order-theory.upper-bounds-posets funext univalence truncations ```
diff --git a/src/domain-theory/omega-continuous-maps-omega-complete-posets.lagda.md b/src/domain-theory/omega-continuous-maps-omega-complete-posets.lagda.md index 60ce16827f..14e05529bc 100644 --- a/src/domain-theory/omega-continuous-maps-omega-complete-posets.lagda.md +++ b/src/domain-theory/omega-continuous-maps-omega-complete-posets.lagda.md @@ -1,43 +1,53 @@ # ω-Continuous maps between ω-complete posets ```agda -module domain-theory.omega-continuous-maps-omega-complete-posets where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module domain-theory.omega-continuous-maps-omega-complete-posets + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import domain-theory.directed-families-posets -open import domain-theory.omega-complete-posets -open import domain-theory.omega-continuous-maps-posets +open import domain-theory.directed-families-posets funext univalence truncations +open import domain-theory.omega-complete-posets funext univalence truncations +open import domain-theory.omega-continuous-maps-posets funext univalence truncations -open import elementary-number-theory.decidable-total-order-natural-numbers -open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.decidable-total-order-natural-numbers funext univalence truncations +open import elementary-number-theory.inequality-natural-numbers funext univalence truncations open import elementary-number-theory.natural-numbers -open import foundation.booleans +open import foundation.booleans funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalences +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext open import foundation.evaluation-functions -open import foundation.existential-quantification -open import foundation.function-types +open import foundation.existential-quantification funext univalence truncations +open import foundation.function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.raising-universe-levels -open import foundation.strictly-involutive-identity-types +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence +open import foundation.strictly-involutive-identity-types funext univalence open import foundation.subtype-identity-principle -open import foundation.surjective-maps -open import foundation.torsorial-type-families +open import foundation.surjective-maps funext univalence truncations +open import foundation.torsorial-type-families funext univalence truncations open import foundation.universe-levels -open import order-theory.join-preserving-maps-posets -open import order-theory.least-upper-bounds-posets -open import order-theory.order-preserving-maps-posets -open import order-theory.posets +open import foundation-core.raising-universe-levels + +open import order-theory.join-preserving-maps-posets funext univalence truncations +open import order-theory.least-upper-bounds-posets funext univalence truncations +open import order-theory.order-preserving-maps-posets funext univalence truncations +open import order-theory.posets funext univalence truncations ```
diff --git a/src/domain-theory/omega-continuous-maps-posets.lagda.md b/src/domain-theory/omega-continuous-maps-posets.lagda.md index 3781ac426b..511328e7ab 100644 --- a/src/domain-theory/omega-continuous-maps-posets.lagda.md +++ b/src/domain-theory/omega-continuous-maps-posets.lagda.md @@ -1,41 +1,51 @@ # ω-Continuous maps between posets ```agda -module domain-theory.omega-continuous-maps-posets where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module domain-theory.omega-continuous-maps-posets + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import domain-theory.directed-families-posets +open import domain-theory.directed-families-posets funext univalence truncations -open import elementary-number-theory.decidable-total-order-natural-numbers -open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.decidable-total-order-natural-numbers funext univalence truncations +open import elementary-number-theory.inequality-natural-numbers funext univalence truncations open import elementary-number-theory.natural-numbers -open import foundation.booleans +open import foundation.booleans funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalences +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext open import foundation.evaluation-functions -open import foundation.existential-quantification -open import foundation.function-types +open import foundation.existential-quantification funext univalence truncations +open import foundation.function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.raising-universe-levels -open import foundation.strictly-involutive-identity-types +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence +open import foundation.strictly-involutive-identity-types funext univalence open import foundation.subtype-identity-principle -open import foundation.surjective-maps -open import foundation.torsorial-type-families +open import foundation.surjective-maps funext univalence truncations +open import foundation.torsorial-type-families funext univalence truncations open import foundation.universe-levels -open import order-theory.join-preserving-maps-posets -open import order-theory.least-upper-bounds-posets -open import order-theory.order-preserving-maps-posets -open import order-theory.posets +open import foundation-core.raising-universe-levels + +open import order-theory.join-preserving-maps-posets funext univalence truncations +open import order-theory.least-upper-bounds-posets funext univalence truncations +open import order-theory.order-preserving-maps-posets funext univalence truncations +open import order-theory.posets funext univalence truncations ```
diff --git a/src/domain-theory/reindexing-directed-families-posets.lagda.md b/src/domain-theory/reindexing-directed-families-posets.lagda.md index 28396bf30a..a6d80e30f4 100644 --- a/src/domain-theory/reindexing-directed-families-posets.lagda.md +++ b/src/domain-theory/reindexing-directed-families-posets.lagda.md @@ -1,31 +1,40 @@ # Reindexing directed families in posets ```agda -module domain-theory.reindexing-directed-families-posets where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module domain-theory.reindexing-directed-families-posets + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import domain-theory.directed-families-posets +open import domain-theory.directed-families-posets funext univalence truncations open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types -open import foundation.conjunction +open import foundation.cartesian-product-types funext univalence +open import foundation.conjunction funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.existential-quantification -open import foundation.function-types -open import foundation.identity-types -open import foundation.inhabited-types -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.surjective-maps -open import foundation.universal-quantification +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.existential-quantification funext univalence truncations +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.inhabited-types funext univalence truncations +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence +open import foundation.surjective-maps funext univalence truncations +open import foundation.universal-quantification funext univalence truncations open import foundation.universe-levels -open import order-theory.order-preserving-maps-posets -open import order-theory.posets +open import order-theory.order-preserving-maps-posets funext univalence truncations +open import order-theory.posets funext univalence truncations ```
diff --git a/src/domain-theory/scott-continuous-maps-posets.lagda.md b/src/domain-theory/scott-continuous-maps-posets.lagda.md index bd50ff479e..cf1f88a233 100644 --- a/src/domain-theory/scott-continuous-maps-posets.lagda.md +++ b/src/domain-theory/scott-continuous-maps-posets.lagda.md @@ -1,38 +1,48 @@ # Scott-continuous maps between posets ```agda -module domain-theory.scott-continuous-maps-posets where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module domain-theory.scott-continuous-maps-posets + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import domain-theory.directed-families-posets -open import domain-theory.reindexing-directed-families-posets +open import domain-theory.directed-families-posets funext univalence truncations +open import domain-theory.reindexing-directed-families-posets funext univalence truncations -open import foundation.booleans +open import foundation.booleans funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalences +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext open import foundation.evaluation-functions -open import foundation.existential-quantification -open import foundation.function-types +open import foundation.existential-quantification funext univalence truncations +open import foundation.function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.raising-universe-levels -open import foundation.small-types -open import foundation.strictly-involutive-identity-types +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence +open import foundation.small-types funext univalence truncations +open import foundation.strictly-involutive-identity-types funext univalence open import foundation.subtype-identity-principle -open import foundation.surjective-maps -open import foundation.torsorial-type-families +open import foundation.surjective-maps funext univalence truncations +open import foundation.torsorial-type-families funext univalence truncations open import foundation.universe-levels -open import order-theory.least-upper-bounds-posets -open import order-theory.order-preserving-maps-posets -open import order-theory.posets +open import foundation-core.raising-universe-levels + +open import order-theory.least-upper-bounds-posets funext univalence truncations +open import order-theory.order-preserving-maps-posets funext univalence truncations +open import order-theory.posets funext univalence truncations ```
diff --git a/src/elementary-number-theory.lagda.md b/src/elementary-number-theory.lagda.md index aecd69e5ec..4c28fffe20 100644 --- a/src/elementary-number-theory.lagda.md +++ b/src/elementary-number-theory.lagda.md @@ -7,182 +7,190 @@ ## Modules in the elementary number theory namespace ```agda -module elementary-number-theory where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom -open import elementary-number-theory.absolute-value-integers public +module elementary-number-theory + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where + +open import elementary-number-theory.absolute-value-integers funext univalence truncations public open import elementary-number-theory.ackermann-function public -open import elementary-number-theory.addition-integer-fractions public -open import elementary-number-theory.addition-integers public +open import elementary-number-theory.addition-integer-fractions funext univalence truncations public +open import elementary-number-theory.addition-integers funext univalence truncations public open import elementary-number-theory.addition-natural-numbers public -open import elementary-number-theory.addition-positive-and-negative-integers public -open import elementary-number-theory.addition-rational-numbers public -open import elementary-number-theory.additive-group-of-rational-numbers public -open import elementary-number-theory.archimedean-property-integer-fractions public -open import elementary-number-theory.archimedean-property-integers public -open import elementary-number-theory.archimedean-property-natural-numbers public -open import elementary-number-theory.archimedean-property-positive-rational-numbers public -open import elementary-number-theory.archimedean-property-rational-numbers public -open import elementary-number-theory.arithmetic-functions public -open import elementary-number-theory.based-induction-natural-numbers public -open import elementary-number-theory.based-strong-induction-natural-numbers public -open import elementary-number-theory.bell-numbers public -open import elementary-number-theory.bezouts-lemma-integers public -open import elementary-number-theory.bezouts-lemma-natural-numbers public -open import elementary-number-theory.binomial-coefficients public -open import elementary-number-theory.binomial-theorem-integers public -open import elementary-number-theory.binomial-theorem-natural-numbers public -open import elementary-number-theory.bounded-sums-arithmetic-functions public -open import elementary-number-theory.catalan-numbers public -open import elementary-number-theory.cofibonacci public -open import elementary-number-theory.collatz-bijection public -open import elementary-number-theory.collatz-conjecture public -open import elementary-number-theory.commutative-semiring-of-natural-numbers public -open import elementary-number-theory.conatural-numbers public -open import elementary-number-theory.congruence-integers public -open import elementary-number-theory.congruence-natural-numbers public -open import elementary-number-theory.cross-multiplication-difference-integer-fractions public -open import elementary-number-theory.cubes-natural-numbers public -open import elementary-number-theory.decidable-dependent-function-types public -open import elementary-number-theory.decidable-total-order-integers public -open import elementary-number-theory.decidable-total-order-natural-numbers public -open import elementary-number-theory.decidable-total-order-rational-numbers public -open import elementary-number-theory.decidable-total-order-standard-finite-types public -open import elementary-number-theory.decidable-types public -open import elementary-number-theory.difference-integers public -open import elementary-number-theory.difference-rational-numbers public -open import elementary-number-theory.dirichlet-convolution public -open import elementary-number-theory.distance-integers public -open import elementary-number-theory.distance-natural-numbers public -open import elementary-number-theory.divisibility-integers public -open import elementary-number-theory.divisibility-modular-arithmetic public -open import elementary-number-theory.divisibility-natural-numbers public -open import elementary-number-theory.divisibility-standard-finite-types public -open import elementary-number-theory.equality-conatural-numbers public -open import elementary-number-theory.equality-integers public -open import elementary-number-theory.equality-natural-numbers public -open import elementary-number-theory.equality-rational-numbers public -open import elementary-number-theory.euclid-mullin-sequence public -open import elementary-number-theory.euclidean-division-natural-numbers public -open import elementary-number-theory.eulers-totient-function public -open import elementary-number-theory.exponentiation-natural-numbers public -open import elementary-number-theory.factorials public +open import elementary-number-theory.addition-positive-and-negative-integers funext univalence truncations public +open import elementary-number-theory.addition-rational-numbers funext univalence truncations public +open import elementary-number-theory.additive-group-of-rational-numbers funext univalence truncations public +open import elementary-number-theory.archimedean-property-integer-fractions funext univalence truncations public +open import elementary-number-theory.archimedean-property-integers funext univalence truncations public +open import elementary-number-theory.archimedean-property-natural-numbers funext univalence truncations public +open import elementary-number-theory.archimedean-property-positive-rational-numbers funext univalence truncations public +open import elementary-number-theory.archimedean-property-rational-numbers funext univalence truncations public +open import elementary-number-theory.arithmetic-functions funext univalence truncations public +open import elementary-number-theory.based-induction-natural-numbers funext univalence truncations public +open import elementary-number-theory.based-strong-induction-natural-numbers funext univalence truncations public +open import elementary-number-theory.bell-numbers funext univalence truncations public +open import elementary-number-theory.bezouts-lemma-integers funext univalence truncations public +open import elementary-number-theory.bezouts-lemma-natural-numbers funext univalence truncations public +open import elementary-number-theory.binomial-coefficients funext univalence truncations public +open import elementary-number-theory.binomial-theorem-integers funext univalence truncations public +open import elementary-number-theory.binomial-theorem-natural-numbers funext univalence truncations public +open import elementary-number-theory.bounded-sums-arithmetic-functions funext univalence truncations public +open import elementary-number-theory.catalan-numbers funext univalence truncations public +open import elementary-number-theory.cofibonacci funext univalence truncations public +open import elementary-number-theory.collatz-bijection funext univalence truncations public +open import elementary-number-theory.collatz-conjecture funext univalence truncations public +open import elementary-number-theory.commutative-semiring-of-natural-numbers funext univalence truncations public +open import elementary-number-theory.conatural-numbers funext univalence truncations public +open import elementary-number-theory.congruence-integers funext univalence truncations public +open import elementary-number-theory.congruence-natural-numbers funext univalence truncations public +open import elementary-number-theory.cross-multiplication-difference-integer-fractions funext univalence truncations public +open import elementary-number-theory.cubes-natural-numbers funext univalence truncations public +open import elementary-number-theory.decidable-dependent-function-types funext univalence truncations public +open import elementary-number-theory.decidable-total-order-integers funext univalence truncations public +open import elementary-number-theory.decidable-total-order-natural-numbers funext univalence truncations public +open import elementary-number-theory.decidable-total-order-rational-numbers funext univalence truncations public +open import elementary-number-theory.decidable-total-order-standard-finite-types funext univalence truncations public +open import elementary-number-theory.decidable-types funext univalence truncations public +open import elementary-number-theory.difference-integers funext univalence truncations public +open import elementary-number-theory.difference-rational-numbers funext univalence truncations public +open import elementary-number-theory.dirichlet-convolution funext univalence truncations public +open import elementary-number-theory.distance-integers funext univalence truncations public +open import elementary-number-theory.distance-natural-numbers funext univalence truncations public +open import elementary-number-theory.divisibility-integers funext univalence truncations public +open import elementary-number-theory.divisibility-modular-arithmetic funext univalence truncations public +open import elementary-number-theory.divisibility-natural-numbers funext univalence truncations public +open import elementary-number-theory.divisibility-standard-finite-types funext univalence truncations public +open import elementary-number-theory.equality-conatural-numbers funext univalence truncations public +open import elementary-number-theory.equality-integers funext univalence truncations public +open import elementary-number-theory.equality-natural-numbers funext univalence truncations public +open import elementary-number-theory.equality-rational-numbers funext univalence truncations public +open import elementary-number-theory.euclid-mullin-sequence funext univalence truncations public +open import elementary-number-theory.euclidean-division-natural-numbers funext univalence truncations public +open import elementary-number-theory.eulers-totient-function funext univalence truncations public +open import elementary-number-theory.exponentiation-natural-numbers funext univalence truncations public +open import elementary-number-theory.factorials funext univalence truncations public open import elementary-number-theory.falling-factorials public -open import elementary-number-theory.fermat-numbers public -open import elementary-number-theory.fibonacci-sequence public -open import elementary-number-theory.field-of-rational-numbers public -open import elementary-number-theory.finitary-natural-numbers public -open import elementary-number-theory.finitely-cyclic-maps public -open import elementary-number-theory.fundamental-theorem-of-arithmetic public -open import elementary-number-theory.goldbach-conjecture public -open import elementary-number-theory.greatest-common-divisor-integers public -open import elementary-number-theory.greatest-common-divisor-natural-numbers public -open import elementary-number-theory.group-of-integers public -open import elementary-number-theory.half-integers public -open import elementary-number-theory.hardy-ramanujan-number public -open import elementary-number-theory.inclusion-natural-numbers-conatural-numbers public -open import elementary-number-theory.inequality-conatural-numbers public -open import elementary-number-theory.inequality-integer-fractions public -open import elementary-number-theory.inequality-integers public -open import elementary-number-theory.inequality-natural-numbers public -open import elementary-number-theory.inequality-rational-numbers public -open import elementary-number-theory.inequality-standard-finite-types public -open import elementary-number-theory.infinite-conatural-numbers public -open import elementary-number-theory.infinitude-of-primes public -open import elementary-number-theory.initial-segments-natural-numbers public -open import elementary-number-theory.integer-fractions public +open import elementary-number-theory.fermat-numbers funext univalence truncations public +open import elementary-number-theory.fibonacci-sequence funext univalence truncations public +open import elementary-number-theory.field-of-rational-numbers funext univalence truncations public +open import elementary-number-theory.finitary-natural-numbers funext univalence truncations public +open import elementary-number-theory.finitely-cyclic-maps funext univalence truncations public +open import elementary-number-theory.fundamental-theorem-of-arithmetic funext univalence truncations public +open import elementary-number-theory.goldbach-conjecture funext univalence truncations public +open import elementary-number-theory.greatest-common-divisor-integers funext univalence truncations public +open import elementary-number-theory.greatest-common-divisor-natural-numbers funext univalence truncations public +open import elementary-number-theory.group-of-integers funext univalence truncations public +open import elementary-number-theory.half-integers funext univalence truncations public +open import elementary-number-theory.hardy-ramanujan-number funext univalence truncations public +open import elementary-number-theory.inclusion-natural-numbers-conatural-numbers funext univalence truncations public +open import elementary-number-theory.inequality-conatural-numbers funext univalence truncations public +open import elementary-number-theory.inequality-integer-fractions funext univalence truncations public +open import elementary-number-theory.inequality-integers funext univalence truncations public +open import elementary-number-theory.inequality-natural-numbers funext univalence truncations public +open import elementary-number-theory.inequality-rational-numbers funext univalence truncations public +open import elementary-number-theory.inequality-standard-finite-types funext univalence truncations public +open import elementary-number-theory.infinite-conatural-numbers funext univalence truncations public +open import elementary-number-theory.infinitude-of-primes funext univalence truncations public +open import elementary-number-theory.initial-segments-natural-numbers funext univalence truncations public +open import elementary-number-theory.integer-fractions funext univalence truncations public open import elementary-number-theory.integer-partitions public open import elementary-number-theory.integers public -open import elementary-number-theory.jacobi-symbol public -open import elementary-number-theory.kolakoski-sequence public -open import elementary-number-theory.legendre-symbol public -open import elementary-number-theory.lower-bounds-natural-numbers public -open import elementary-number-theory.maximum-natural-numbers public -open import elementary-number-theory.maximum-rational-numbers public -open import elementary-number-theory.maximum-standard-finite-types public -open import elementary-number-theory.mediant-integer-fractions public -open import elementary-number-theory.mersenne-primes public -open import elementary-number-theory.minimum-natural-numbers public -open import elementary-number-theory.minimum-rational-numbers public -open import elementary-number-theory.minimum-standard-finite-types public -open import elementary-number-theory.modular-arithmetic public -open import elementary-number-theory.modular-arithmetic-standard-finite-types public -open import elementary-number-theory.monoid-of-natural-numbers-with-addition public -open import elementary-number-theory.monoid-of-natural-numbers-with-maximum public -open import elementary-number-theory.multiplication-integer-fractions public -open import elementary-number-theory.multiplication-integers public -open import elementary-number-theory.multiplication-lists-of-natural-numbers public +open import elementary-number-theory.jacobi-symbol funext univalence truncations public +open import elementary-number-theory.kolakoski-sequence funext univalence truncations public +open import elementary-number-theory.legendre-symbol funext univalence truncations public +open import elementary-number-theory.lower-bounds-natural-numbers funext univalence truncations public +open import elementary-number-theory.maximum-natural-numbers funext univalence truncations public +open import elementary-number-theory.maximum-rational-numbers funext univalence truncations public +open import elementary-number-theory.maximum-standard-finite-types funext univalence truncations public +open import elementary-number-theory.mediant-integer-fractions funext univalence truncations public +open import elementary-number-theory.mersenne-primes funext univalence truncations public +open import elementary-number-theory.minimum-natural-numbers funext univalence truncations public +open import elementary-number-theory.minimum-rational-numbers funext univalence truncations public +open import elementary-number-theory.minimum-standard-finite-types funext univalence truncations public +open import elementary-number-theory.modular-arithmetic funext univalence truncations public +open import elementary-number-theory.modular-arithmetic-standard-finite-types funext univalence truncations public +open import elementary-number-theory.monoid-of-natural-numbers-with-addition funext univalence truncations public +open import elementary-number-theory.monoid-of-natural-numbers-with-maximum funext univalence truncations public +open import elementary-number-theory.multiplication-integer-fractions funext univalence truncations public +open import elementary-number-theory.multiplication-integers funext univalence truncations public +open import elementary-number-theory.multiplication-lists-of-natural-numbers funext univalence truncations public open import elementary-number-theory.multiplication-natural-numbers public -open import elementary-number-theory.multiplication-positive-and-negative-integers public -open import elementary-number-theory.multiplication-rational-numbers public -open import elementary-number-theory.multiplicative-group-of-positive-rational-numbers public -open import elementary-number-theory.multiplicative-group-of-rational-numbers public -open import elementary-number-theory.multiplicative-inverses-positive-integer-fractions public -open import elementary-number-theory.multiplicative-monoid-of-natural-numbers public -open import elementary-number-theory.multiplicative-monoid-of-rational-numbers public +open import elementary-number-theory.multiplication-positive-and-negative-integers funext univalence truncations public +open import elementary-number-theory.multiplication-rational-numbers funext univalence truncations public +open import elementary-number-theory.multiplicative-group-of-positive-rational-numbers funext univalence truncations public +open import elementary-number-theory.multiplicative-group-of-rational-numbers funext univalence truncations public +open import elementary-number-theory.multiplicative-inverses-positive-integer-fractions funext univalence truncations public +open import elementary-number-theory.multiplicative-monoid-of-natural-numbers funext univalence truncations public +open import elementary-number-theory.multiplicative-monoid-of-rational-numbers funext univalence truncations public open import elementary-number-theory.multiplicative-units-integers public open import elementary-number-theory.multiplicative-units-standard-cyclic-rings public open import elementary-number-theory.multiset-coefficients public open import elementary-number-theory.natural-numbers public -open import elementary-number-theory.negative-integers public -open import elementary-number-theory.nonnegative-integers public -open import elementary-number-theory.nonpositive-integers public -open import elementary-number-theory.nonzero-integers public -open import elementary-number-theory.nonzero-natural-numbers public -open import elementary-number-theory.nonzero-rational-numbers public -open import elementary-number-theory.ordinal-induction-natural-numbers public -open import elementary-number-theory.parity-natural-numbers public -open import elementary-number-theory.peano-arithmetic public -open import elementary-number-theory.pisano-periods public -open import elementary-number-theory.poset-of-natural-numbers-ordered-by-divisibility public -open import elementary-number-theory.positive-and-negative-integers public -open import elementary-number-theory.positive-conatural-numbers public -open import elementary-number-theory.positive-integer-fractions public -open import elementary-number-theory.positive-integers public -open import elementary-number-theory.positive-rational-numbers public -open import elementary-number-theory.powers-integers public -open import elementary-number-theory.powers-of-two public -open import elementary-number-theory.prime-numbers public -open import elementary-number-theory.products-of-natural-numbers public -open import elementary-number-theory.proper-divisors-natural-numbers public -open import elementary-number-theory.pythagorean-triples public -open import elementary-number-theory.rational-numbers public -open import elementary-number-theory.reduced-integer-fractions public -open import elementary-number-theory.relatively-prime-integers public -open import elementary-number-theory.relatively-prime-natural-numbers public -open import elementary-number-theory.repeating-element-standard-finite-type public -open import elementary-number-theory.retracts-of-natural-numbers public -open import elementary-number-theory.ring-of-integers public -open import elementary-number-theory.ring-of-rational-numbers public -open import elementary-number-theory.sieve-of-eratosthenes public -open import elementary-number-theory.square-free-natural-numbers public -open import elementary-number-theory.squares-integers public -open import elementary-number-theory.squares-modular-arithmetic public -open import elementary-number-theory.squares-natural-numbers public -open import elementary-number-theory.standard-cyclic-groups public -open import elementary-number-theory.standard-cyclic-rings public +open import elementary-number-theory.negative-integers funext univalence truncations public +open import elementary-number-theory.nonnegative-integers funext univalence truncations public +open import elementary-number-theory.nonpositive-integers funext univalence truncations public +open import elementary-number-theory.nonzero-integers funext univalence truncations public +open import elementary-number-theory.nonzero-natural-numbers funext univalence truncations public +open import elementary-number-theory.nonzero-rational-numbers funext univalence truncations public +open import elementary-number-theory.ordinal-induction-natural-numbers funext univalence truncations public +open import elementary-number-theory.parity-natural-numbers funext univalence truncations public +open import elementary-number-theory.peano-arithmetic funext univalence truncations public +open import elementary-number-theory.pisano-periods funext univalence truncations public +open import elementary-number-theory.poset-of-natural-numbers-ordered-by-divisibility funext univalence truncations public +open import elementary-number-theory.positive-and-negative-integers funext univalence truncations public +open import elementary-number-theory.positive-conatural-numbers funext univalence truncations public +open import elementary-number-theory.positive-integer-fractions funext univalence truncations public +open import elementary-number-theory.positive-integers funext univalence truncations public +open import elementary-number-theory.positive-rational-numbers funext univalence truncations public +open import elementary-number-theory.powers-integers funext univalence truncations public +open import elementary-number-theory.powers-of-two funext univalence truncations public +open import elementary-number-theory.prime-numbers funext univalence truncations public +open import elementary-number-theory.products-of-natural-numbers funext univalence truncations public +open import elementary-number-theory.proper-divisors-natural-numbers funext univalence truncations public +open import elementary-number-theory.pythagorean-triples funext univalence truncations public +open import elementary-number-theory.rational-numbers funext univalence truncations public +open import elementary-number-theory.reduced-integer-fractions funext univalence truncations public +open import elementary-number-theory.relatively-prime-integers funext univalence truncations public +open import elementary-number-theory.relatively-prime-natural-numbers funext univalence truncations public +open import elementary-number-theory.repeating-element-standard-finite-type funext univalence truncations public +open import elementary-number-theory.retracts-of-natural-numbers funext univalence truncations public +open import elementary-number-theory.ring-of-integers funext univalence truncations public +open import elementary-number-theory.ring-of-rational-numbers funext univalence truncations public +open import elementary-number-theory.sieve-of-eratosthenes funext univalence truncations public +open import elementary-number-theory.square-free-natural-numbers funext univalence truncations public +open import elementary-number-theory.squares-integers funext univalence truncations public +open import elementary-number-theory.squares-modular-arithmetic funext univalence truncations public +open import elementary-number-theory.squares-natural-numbers funext univalence truncations public +open import elementary-number-theory.standard-cyclic-groups funext univalence truncations public +open import elementary-number-theory.standard-cyclic-rings funext univalence truncations public open import elementary-number-theory.stirling-numbers-of-the-second-kind public -open import elementary-number-theory.strict-inequality-integer-fractions public -open import elementary-number-theory.strict-inequality-integers public -open import elementary-number-theory.strict-inequality-natural-numbers public -open import elementary-number-theory.strict-inequality-rational-numbers public -open import elementary-number-theory.strict-inequality-standard-finite-types public -open import elementary-number-theory.strictly-ordered-pairs-of-natural-numbers public -open import elementary-number-theory.strong-induction-natural-numbers public -open import elementary-number-theory.sums-of-natural-numbers public -open import elementary-number-theory.sylvesters-sequence public -open import elementary-number-theory.taxicab-numbers public +open import elementary-number-theory.strict-inequality-integer-fractions funext univalence truncations public +open import elementary-number-theory.strict-inequality-integers funext univalence truncations public +open import elementary-number-theory.strict-inequality-natural-numbers funext univalence truncations public +open import elementary-number-theory.strict-inequality-rational-numbers funext univalence truncations public +open import elementary-number-theory.strict-inequality-standard-finite-types funext univalence truncations public +open import elementary-number-theory.strictly-ordered-pairs-of-natural-numbers funext univalence truncations public +open import elementary-number-theory.strong-induction-natural-numbers funext univalence truncations public +open import elementary-number-theory.sums-of-natural-numbers funext univalence truncations public +open import elementary-number-theory.sylvesters-sequence funext univalence truncations public +open import elementary-number-theory.taxicab-numbers funext univalence truncations public open import elementary-number-theory.telephone-numbers public open import elementary-number-theory.triangular-numbers public -open import elementary-number-theory.twin-prime-conjecture public -open import elementary-number-theory.type-arithmetic-natural-numbers public -open import elementary-number-theory.unit-elements-standard-finite-types public -open import elementary-number-theory.unit-fractions-rational-numbers public -open import elementary-number-theory.unit-similarity-standard-finite-types public -open import elementary-number-theory.universal-property-conatural-numbers public -open import elementary-number-theory.universal-property-integers public -open import elementary-number-theory.universal-property-natural-numbers public -open import elementary-number-theory.upper-bounds-natural-numbers public -open import elementary-number-theory.well-ordering-principle-natural-numbers public -open import elementary-number-theory.well-ordering-principle-standard-finite-types public -open import elementary-number-theory.zero-conatural-numbers public +open import elementary-number-theory.twin-prime-conjecture funext univalence truncations public +open import elementary-number-theory.type-arithmetic-natural-numbers funext univalence truncations public +open import elementary-number-theory.unit-elements-standard-finite-types funext univalence truncations public +open import elementary-number-theory.unit-fractions-rational-numbers funext univalence truncations public +open import elementary-number-theory.unit-similarity-standard-finite-types funext univalence truncations public +open import elementary-number-theory.universal-property-conatural-numbers funext univalence public +open import elementary-number-theory.universal-property-integers funext univalence truncations public +open import elementary-number-theory.universal-property-natural-numbers funext univalence truncations public +open import elementary-number-theory.upper-bounds-natural-numbers funext univalence truncations public +open import elementary-number-theory.well-ordering-principle-natural-numbers funext univalence truncations public +open import elementary-number-theory.well-ordering-principle-standard-finite-types funext univalence truncations public +open import elementary-number-theory.zero-conatural-numbers funext univalence truncations public ``` diff --git a/src/elementary-number-theory/absolute-value-integers.lagda.md b/src/elementary-number-theory/absolute-value-integers.lagda.md index 59455c73a5..65bf613983 100644 --- a/src/elementary-number-theory/absolute-value-integers.lagda.md +++ b/src/elementary-number-theory/absolute-value-integers.lagda.md @@ -1,26 +1,34 @@ # The absolute value function on the integers ```agda -module elementary-number-theory.absolute-value-integers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.absolute-value-integers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.addition-integers +open import elementary-number-theory.addition-integers funext univalence truncations open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.inequality-natural-numbers funext univalence truncations open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-integers +open import elementary-number-theory.multiplication-integers funext univalence truncations open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.nonnegative-integers -open import elementary-number-theory.positive-integers +open import elementary-number-theory.nonnegative-integers funext univalence truncations +open import elementary-number-theory.positive-integers funext univalence truncations open import foundation.action-on-identifications-functions -open import foundation.coproduct-types -open import foundation.function-types -open import foundation.identity-types +open import foundation.coproduct-types funext univalence truncations +open import foundation.function-types funext +open import foundation.identity-types funext open import foundation.unit-type ``` diff --git a/src/elementary-number-theory/addition-integer-fractions.lagda.md b/src/elementary-number-theory/addition-integer-fractions.lagda.md index 2ae01f48aa..c2c501ace3 100644 --- a/src/elementary-number-theory/addition-integer-fractions.lagda.md +++ b/src/elementary-number-theory/addition-integer-fractions.lagda.md @@ -1,22 +1,30 @@ # Addition on integer fractions ```agda -module elementary-number-theory.addition-integer-fractions where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.addition-integer-fractions + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.addition-integers -open import elementary-number-theory.integer-fractions +open import elementary-number-theory.addition-integers funext univalence truncations +open import elementary-number-theory.integer-fractions funext univalence truncations open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-integers -open import elementary-number-theory.multiplication-positive-and-negative-integers +open import elementary-number-theory.multiplication-integers funext univalence truncations +open import elementary-number-theory.multiplication-positive-and-negative-integers funext univalence truncations open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext ```
diff --git a/src/elementary-number-theory/addition-integers.lagda.md b/src/elementary-number-theory/addition-integers.lagda.md index 0074401613..31c7f34b0c 100644 --- a/src/elementary-number-theory/addition-integers.lagda.md +++ b/src/elementary-number-theory/addition-integers.lagda.md @@ -1,7 +1,15 @@ # Addition on the integers ```agda -module elementary-number-theory.addition-integers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.addition-integers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,23 +18,23 @@ module elementary-number-theory.addition-integers where open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.integers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.nonnegative-integers -open import elementary-number-theory.positive-and-negative-integers -open import elementary-number-theory.positive-integers +open import elementary-number-theory.nonnegative-integers funext univalence truncations +open import elementary-number-theory.positive-and-negative-integers funext univalence truncations +open import elementary-number-theory.positive-integers funext univalence truncations open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.binary-embeddings +open import foundation.binary-embeddings funext open import foundation.binary-equivalences -open import foundation.coproduct-types +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalences -open import foundation.function-types -open import foundation.identity-types -open import foundation.injective-maps +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.injective-maps funext open import foundation.interchange-law -open import foundation.sets +open import foundation.sets funext univalence open import foundation.unit-type ``` diff --git a/src/elementary-number-theory/addition-natural-numbers.lagda.md b/src/elementary-number-theory/addition-natural-numbers.lagda.md index 2bb395a863..cbb2406c1b 100644 --- a/src/elementary-number-theory/addition-natural-numbers.lagda.md +++ b/src/elementary-number-theory/addition-natural-numbers.lagda.md @@ -7,21 +7,19 @@ module elementary-number-theory.addition-natural-numbers where
Imports ```agda -open import elementary-number-theory.equality-natural-numbers open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.empty-types -open import foundation.function-types -open import foundation.identity-types -open import foundation.injective-maps open import foundation.interchange-law -open import foundation.negated-equality -open import foundation.sets + +open import foundation-core.cartesian-product-types +open import foundation-core.empty-types +open import foundation-core.function-types +open import foundation-core.identity-types +open import foundation-core.injective-maps +open import foundation-core.negation ```
@@ -154,19 +152,6 @@ abstract ( commutative-add-ℕ x k ∙ (p ∙ commutative-add-ℕ k y)) ``` -### Addition by a fixed element on either side is an embedding - -```agda -abstract - is-emb-left-add-ℕ : (x : ℕ) → is-emb (x +ℕ_) - is-emb-left-add-ℕ x = - is-emb-is-injective is-set-ℕ (is-injective-left-add-ℕ x) - - is-emb-right-add-ℕ : (x : ℕ) → is-emb (_+ℕ x) - is-emb-right-add-ℕ x = - is-emb-is-injective is-set-ℕ (is-injective-right-add-ℕ x) -``` - ### `x + y ＝ 0` if and only if both `x` and `y` are `0` ```agda @@ -197,7 +182,7 @@ abstract ```agda abstract neq-add-ℕ : - (m n : ℕ) → m ≠ m +ℕ (succ-ℕ n) + (m n : ℕ) → ¬ (m ＝ m +ℕ (succ-ℕ n)) neq-add-ℕ (succ-ℕ m) n p = neq-add-ℕ m n ( ( is-injective-succ-ℕ p) ∙ diff --git a/src/elementary-number-theory/addition-positive-and-negative-integers.lagda.md b/src/elementary-number-theory/addition-positive-and-negative-integers.lagda.md index cc38778380..10765a7b7c 100644 --- a/src/elementary-number-theory/addition-positive-and-negative-integers.lagda.md +++ b/src/elementary-number-theory/addition-positive-and-negative-integers.lagda.md @@ -1,26 +1,34 @@ # Addition of positive, negative, nonnegative and nonpositive integers ```agda -module elementary-number-theory.addition-positive-and-negative-integers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.addition-positive-and-negative-integers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.addition-integers +open import elementary-number-theory.addition-integers funext univalence truncations open import elementary-number-theory.integers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.negative-integers -open import elementary-number-theory.nonnegative-integers -open import elementary-number-theory.nonpositive-integers -open import elementary-number-theory.positive-and-negative-integers -open import elementary-number-theory.positive-integers +open import elementary-number-theory.negative-integers funext univalence truncations +open import elementary-number-theory.nonnegative-integers funext univalence truncations +open import elementary-number-theory.nonpositive-integers funext univalence truncations +open import elementary-number-theory.positive-and-negative-integers funext univalence truncations +open import elementary-number-theory.positive-integers funext univalence truncations -open import foundation.coproduct-types +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.identity-types -open import foundation.injective-maps +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.injective-maps funext open import foundation.unit-type ``` diff --git a/src/elementary-number-theory/addition-rational-numbers.lagda.md b/src/elementary-number-theory/addition-rational-numbers.lagda.md index 4bd4afc3d5..0158baf337 100644 --- a/src/elementary-number-theory/addition-rational-numbers.lagda.md +++ b/src/elementary-number-theory/addition-rational-numbers.lagda.md @@ -2,29 +2,36 @@ ```agda {-# OPTIONS --lossy-unification #-} - -module elementary-number-theory.addition-rational-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.addition-rational-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.addition-integer-fractions -open import elementary-number-theory.addition-integers -open import elementary-number-theory.integer-fractions +open import elementary-number-theory.addition-integer-fractions funext univalence truncations +open import elementary-number-theory.addition-integers funext univalence truncations +open import elementary-number-theory.integer-fractions funext univalence truncations open import elementary-number-theory.integers -open import elementary-number-theory.rational-numbers -open import elementary-number-theory.reduced-integer-fractions +open import elementary-number-theory.rational-numbers funext univalence truncations +open import elementary-number-theory.reduced-integer-fractions funext univalence truncations open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.identity-types -open import foundation.injective-maps +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.injective-maps funext open import foundation.interchange-law -open import foundation.retractions -open import foundation.sections +open import foundation.retractions funext +open import foundation.sections funext ```
diff --git a/src/elementary-number-theory/additive-group-of-rational-numbers.lagda.md b/src/elementary-number-theory/additive-group-of-rational-numbers.lagda.md index fa18d01e16..91a26a79b6 100644 --- a/src/elementary-number-theory/additive-group-of-rational-numbers.lagda.md +++ b/src/elementary-number-theory/additive-group-of-rational-numbers.lagda.md @@ -2,27 +2,34 @@ ```agda {-# OPTIONS --lossy-unification #-} - -module elementary-number-theory.additive-group-of-rational-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.additive-group-of-rational-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.addition-rational-numbers -open import elementary-number-theory.difference-rational-numbers -open import elementary-number-theory.rational-numbers +open import elementary-number-theory.addition-rational-numbers funext univalence truncations +open import elementary-number-theory.difference-rational-numbers funext univalence truncations +open import elementary-number-theory.rational-numbers funext univalence truncations open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.unital-binary-operations open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.commutative-monoids -open import group-theory.groups -open import group-theory.monoids -open import group-theory.semigroups +open import group-theory.abelian-groups funext univalence truncations +open import group-theory.commutative-monoids funext univalence truncations +open import group-theory.groups funext univalence truncations +open import group-theory.monoids funext univalence truncations +open import group-theory.semigroups funext univalence ```
diff --git a/src/elementary-number-theory/archimedean-property-integer-fractions.lagda.md b/src/elementary-number-theory/archimedean-property-integer-fractions.lagda.md index c28ab250d1..5dd085f04b 100644 --- a/src/elementary-number-theory/archimedean-property-integer-fractions.lagda.md +++ b/src/elementary-number-theory/archimedean-property-integer-fractions.lagda.md @@ -2,28 +2,35 @@ ```agda {-# OPTIONS --lossy-unification #-} +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom -module elementary-number-theory.archimedean-property-integer-fractions where +module elementary-number-theory.archimedean-property-integer-fractions + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.archimedean-property-integers -open import elementary-number-theory.integer-fractions +open import elementary-number-theory.archimedean-property-integers funext univalence truncations +open import elementary-number-theory.integer-fractions funext univalence truncations open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-integer-fractions -open import elementary-number-theory.multiplication-integers -open import elementary-number-theory.multiplication-positive-and-negative-integers +open import elementary-number-theory.multiplication-integer-fractions funext univalence truncations +open import elementary-number-theory.multiplication-integers funext univalence truncations +open import elementary-number-theory.multiplication-positive-and-negative-integers funext univalence truncations open import elementary-number-theory.natural-numbers -open import elementary-number-theory.positive-integer-fractions -open import elementary-number-theory.strict-inequality-integer-fractions -open import elementary-number-theory.strict-inequality-integers +open import elementary-number-theory.positive-integer-fractions funext univalence truncations +open import elementary-number-theory.strict-inequality-integer-fractions funext univalence truncations +open import elementary-number-theory.strict-inequality-integers funext univalence truncations open import foundation.dependent-pair-types -open import foundation.existential-quantification -open import foundation.identity-types -open import foundation.propositional-truncations +open import foundation.existential-quantification funext univalence truncations +open import foundation.identity-types funext +open import foundation.propositional-truncations funext univalence open import foundation.transport-along-identifications ``` diff --git a/src/elementary-number-theory/archimedean-property-integers.lagda.md b/src/elementary-number-theory/archimedean-property-integers.lagda.md index c96fb799cf..20886dca55 100644 --- a/src/elementary-number-theory/archimedean-property-integers.lagda.md +++ b/src/elementary-number-theory/archimedean-property-integers.lagda.md @@ -1,31 +1,38 @@ # The Archimedean property of the integers ```agda -module elementary-number-theory.archimedean-property-integers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.archimedean-property-integers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.archimedean-property-natural-numbers +open import elementary-number-theory.archimedean-property-natural-numbers funext univalence truncations open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-integers +open import elementary-number-theory.multiplication-integers funext univalence truncations open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.nonnegative-integers -open import elementary-number-theory.positive-and-negative-integers -open import elementary-number-theory.positive-integers -open import elementary-number-theory.strict-inequality-integers +open import elementary-number-theory.nonnegative-integers funext univalence truncations +open import elementary-number-theory.positive-and-negative-integers funext univalence truncations +open import elementary-number-theory.positive-integers funext univalence truncations +open import elementary-number-theory.strict-inequality-integers funext univalence truncations open import foundation.action-on-identifications-functions open import foundation.binary-transport -open import foundation.cartesian-product-types -open import foundation.coproduct-types +open import foundation.cartesian-product-types funext univalence +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.existential-quantification -open import foundation.identity-types -open import foundation.propositional-truncations -open import foundation.transport-along-identifications +open import foundation.existential-quantification funext univalence truncations +open import foundation.identity-types funext +open import foundation.propositional-truncations funext univalence ```
diff --git a/src/elementary-number-theory/archimedean-property-natural-numbers.lagda.md b/src/elementary-number-theory/archimedean-property-natural-numbers.lagda.md index d9f0edd2bd..7112f92352 100644 --- a/src/elementary-number-theory/archimedean-property-natural-numbers.lagda.md +++ b/src/elementary-number-theory/archimedean-property-natural-numbers.lagda.md @@ -1,21 +1,28 @@ # The Archimedean property of the natural numbers ```agda -module elementary-number-theory.archimedean-property-natural-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.archimedean-property-natural-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.euclidean-division-natural-numbers +open import elementary-number-theory.euclidean-division-natural-numbers funext univalence truncations open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.nonzero-natural-numbers -open import elementary-number-theory.strict-inequality-natural-numbers +open import elementary-number-theory.strict-inequality-natural-numbers funext univalence truncations open import foundation.dependent-pair-types -open import foundation.existential-quantification -open import foundation.propositional-truncations +open import foundation.existential-quantification funext univalence truncations +open import foundation.propositional-truncations funext univalence open import foundation.transport-along-identifications ``` diff --git a/src/elementary-number-theory/archimedean-property-positive-rational-numbers.lagda.md b/src/elementary-number-theory/archimedean-property-positive-rational-numbers.lagda.md index 532e026317..6e9ecf28fb 100644 --- a/src/elementary-number-theory/archimedean-property-positive-rational-numbers.lagda.md +++ b/src/elementary-number-theory/archimedean-property-positive-rational-numbers.lagda.md @@ -2,29 +2,34 @@ ```agda {-# OPTIONS --lossy-unification #-} +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom -module elementary-number-theory.archimedean-property-positive-rational-numbers where +module elementary-number-theory.archimedean-property-positive-rational-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.archimedean-property-rational-numbers +open import elementary-number-theory.archimedean-property-rational-numbers funext univalence truncations open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-rational-numbers -open import elementary-number-theory.multiplicative-group-of-positive-rational-numbers +open import elementary-number-theory.multiplication-rational-numbers funext univalence truncations open import elementary-number-theory.natural-numbers -open import elementary-number-theory.nonzero-natural-numbers -open import elementary-number-theory.positive-rational-numbers -open import elementary-number-theory.rational-numbers -open import elementary-number-theory.strict-inequality-rational-numbers +open import elementary-number-theory.nonzero-natural-numbers funext univalence truncations +open import elementary-number-theory.positive-rational-numbers funext univalence truncations +open import elementary-number-theory.rational-numbers funext univalence truncations +open import elementary-number-theory.strict-inequality-rational-numbers funext univalence truncations open import foundation.action-on-identifications-functions -open import foundation.binary-transport open import foundation.dependent-pair-types -open import foundation.existential-quantification -open import foundation.identity-types -open import foundation.propositional-truncations +open import foundation.existential-quantification funext univalence truncations +open import foundation.identity-types funext +open import foundation.propositional-truncations funext univalence open import foundation.transport-along-identifications ``` diff --git a/src/elementary-number-theory/archimedean-property-rational-numbers.lagda.md b/src/elementary-number-theory/archimedean-property-rational-numbers.lagda.md index dc4fd7b441..13661c0926 100644 --- a/src/elementary-number-theory/archimedean-property-rational-numbers.lagda.md +++ b/src/elementary-number-theory/archimedean-property-rational-numbers.lagda.md @@ -2,29 +2,36 @@ ```agda {-# OPTIONS --lossy-unification #-} +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom -module elementary-number-theory.archimedean-property-rational-numbers where +module elementary-number-theory.archimedean-property-rational-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.archimedean-property-integer-fractions -open import elementary-number-theory.integer-fractions +open import elementary-number-theory.archimedean-property-integer-fractions funext univalence truncations +open import elementary-number-theory.integer-fractions funext univalence truncations open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-integer-fractions -open import elementary-number-theory.multiplication-rational-numbers +open import elementary-number-theory.multiplication-integer-fractions funext univalence truncations +open import elementary-number-theory.multiplication-rational-numbers funext univalence truncations open import elementary-number-theory.natural-numbers -open import elementary-number-theory.positive-rational-numbers -open import elementary-number-theory.rational-numbers -open import elementary-number-theory.strict-inequality-rational-numbers +open import elementary-number-theory.positive-rational-numbers funext univalence truncations +open import elementary-number-theory.rational-numbers funext univalence truncations +open import elementary-number-theory.strict-inequality-rational-numbers funext univalence truncations open import foundation.action-on-identifications-binary-functions open import foundation.binary-transport open import foundation.dependent-pair-types -open import foundation.existential-quantification -open import foundation.identity-types -open import foundation.propositional-truncations +open import foundation.existential-quantification funext univalence truncations +open import foundation.identity-types funext +open import foundation.propositional-truncations funext univalence ```
diff --git a/src/elementary-number-theory/arithmetic-functions.lagda.md b/src/elementary-number-theory/arithmetic-functions.lagda.md index 291d7d48e5..7b017ee65a 100644 --- a/src/elementary-number-theory/arithmetic-functions.lagda.md +++ b/src/elementary-number-theory/arithmetic-functions.lagda.md @@ -1,17 +1,25 @@ # Arithmetic functions ```agda -module elementary-number-theory.arithmetic-functions where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.arithmetic-functions + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.nonzero-natural-numbers +open import elementary-number-theory.nonzero-natural-numbers funext univalence truncations open import foundation.universe-levels -open import ring-theory.rings +open import ring-theory.rings funext univalence truncations ```
diff --git a/src/elementary-number-theory/based-induction-natural-numbers.lagda.md b/src/elementary-number-theory/based-induction-natural-numbers.lagda.md index 04b3c569a4..566d488dac 100644 --- a/src/elementary-number-theory/based-induction-natural-numbers.lagda.md +++ b/src/elementary-number-theory/based-induction-natural-numbers.lagda.md @@ -1,17 +1,25 @@ # The based induction principle of the natural numbers ```agda -module elementary-number-theory.based-induction-natural-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.based-induction-natural-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.inequality-natural-numbers funext univalence truncations open import elementary-number-theory.natural-numbers -open import foundation.function-types -open import foundation.identity-types +open import foundation.function-types funext +open import foundation.identity-types funext open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/based-strong-induction-natural-numbers.lagda.md b/src/elementary-number-theory/based-strong-induction-natural-numbers.lagda.md index 52541dc0ab..d4ed15593e 100644 --- a/src/elementary-number-theory/based-strong-induction-natural-numbers.lagda.md +++ b/src/elementary-number-theory/based-strong-induction-natural-numbers.lagda.md @@ -1,26 +1,35 @@ # Based strong induction for the natural numbers ```agda -module elementary-number-theory.based-strong-induction-natural-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.based-strong-induction-natural-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.based-induction-natural-numbers -open import elementary-number-theory.equality-natural-numbers -open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.based-induction-natural-numbers funext univalence truncations +open import elementary-number-theory.equality-natural-numbers funext univalence truncations +open import elementary-number-theory.inequality-natural-numbers funext univalence truncations open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.coproduct-types -open import foundation.empty-types -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.universal-property-contractible-types +open import foundation.coproduct-types funext univalence truncations +open import foundation.dependent-products-propositions funext +open import foundation.empty-types funext univalence truncations +open import foundation.function-extensionality funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.universal-property-contractible-types funext open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/bell-numbers.lagda.md b/src/elementary-number-theory/bell-numbers.lagda.md index d824cdd82b..c0b4df5746 100644 --- a/src/elementary-number-theory/bell-numbers.lagda.md +++ b/src/elementary-number-theory/bell-numbers.lagda.md @@ -1,18 +1,26 @@ # The Bell numbers ```agda -module elementary-number-theory.bell-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.bell-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.binomial-coefficients +open import elementary-number-theory.binomial-coefficients funext univalence truncations open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.strict-inequality-natural-numbers -open import elementary-number-theory.strong-induction-natural-numbers -open import elementary-number-theory.sums-of-natural-numbers +open import elementary-number-theory.strict-inequality-natural-numbers funext univalence truncations +open import elementary-number-theory.strong-induction-natural-numbers funext univalence truncations +open import elementary-number-theory.sums-of-natural-numbers funext univalence truncations ```
diff --git a/src/elementary-number-theory/bezouts-lemma-integers.lagda.md b/src/elementary-number-theory/bezouts-lemma-integers.lagda.md index 1b169fb860..ad7819e1a5 100644 --- a/src/elementary-number-theory/bezouts-lemma-integers.lagda.md +++ b/src/elementary-number-theory/bezouts-lemma-integers.lagda.md @@ -1,37 +1,45 @@ # Bezout's lemma in the integers ```agda -module elementary-number-theory.bezouts-lemma-integers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.bezouts-lemma-integers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.absolute-value-integers -open import elementary-number-theory.addition-integers +open import elementary-number-theory.absolute-value-integers funext univalence truncations +open import elementary-number-theory.addition-integers funext univalence truncations open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.bezouts-lemma-natural-numbers -open import elementary-number-theory.difference-integers -open import elementary-number-theory.distance-integers -open import elementary-number-theory.distance-natural-numbers -open import elementary-number-theory.divisibility-integers -open import elementary-number-theory.divisibility-natural-numbers -open import elementary-number-theory.greatest-common-divisor-integers -open import elementary-number-theory.greatest-common-divisor-natural-numbers +open import elementary-number-theory.bezouts-lemma-natural-numbers funext univalence truncations +open import elementary-number-theory.difference-integers funext univalence truncations +open import elementary-number-theory.distance-integers funext univalence truncations +open import elementary-number-theory.distance-natural-numbers funext univalence truncations +open import elementary-number-theory.divisibility-integers funext univalence truncations +open import elementary-number-theory.divisibility-natural-numbers funext univalence truncations +open import elementary-number-theory.greatest-common-divisor-integers funext univalence truncations +open import elementary-number-theory.greatest-common-divisor-natural-numbers funext univalence truncations open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-integers +open import elementary-number-theory.multiplication-integers funext univalence truncations open import elementary-number-theory.multiplication-natural-numbers -open import elementary-number-theory.multiplication-positive-and-negative-integers +open import elementary-number-theory.multiplication-positive-and-negative-integers funext univalence truncations open import elementary-number-theory.natural-numbers -open import elementary-number-theory.nonnegative-integers -open import elementary-number-theory.positive-and-negative-integers -open import elementary-number-theory.positive-integers +open import elementary-number-theory.nonnegative-integers funext univalence truncations +open import elementary-number-theory.positive-and-negative-integers funext univalence truncations +open import elementary-number-theory.positive-integers funext univalence truncations open import foundation.action-on-identifications-functions -open import foundation.coproduct-types +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.identity-types +open import foundation.function-types funext +open import foundation.identity-types funext open import foundation.transport-along-identifications open import foundation.unit-type ``` diff --git a/src/elementary-number-theory/bezouts-lemma-natural-numbers.lagda.md b/src/elementary-number-theory/bezouts-lemma-natural-numbers.lagda.md index 681142d4bb..75ac0a8464 100755 --- a/src/elementary-number-theory/bezouts-lemma-natural-numbers.lagda.md +++ b/src/elementary-number-theory/bezouts-lemma-natural-numbers.lagda.md @@ -1,49 +1,57 @@ # Bezout's lemma on the natural numbers ```agda -module elementary-number-theory.bezouts-lemma-natural-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.bezouts-lemma-natural-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.absolute-value-integers -open import elementary-number-theory.addition-integers +open import elementary-number-theory.absolute-value-integers funext univalence truncations +open import elementary-number-theory.addition-integers funext univalence truncations open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.congruence-integers -open import elementary-number-theory.distance-integers -open import elementary-number-theory.distance-natural-numbers -open import elementary-number-theory.divisibility-modular-arithmetic -open import elementary-number-theory.divisibility-natural-numbers -open import elementary-number-theory.equality-natural-numbers -open import elementary-number-theory.euclidean-division-natural-numbers -open import elementary-number-theory.greatest-common-divisor-natural-numbers -open import elementary-number-theory.inequality-integers -open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.congruence-integers funext univalence truncations +open import elementary-number-theory.distance-integers funext univalence truncations +open import elementary-number-theory.distance-natural-numbers funext univalence truncations +open import elementary-number-theory.divisibility-modular-arithmetic funext univalence truncations +open import elementary-number-theory.divisibility-natural-numbers funext univalence truncations +open import elementary-number-theory.equality-natural-numbers funext univalence truncations +open import elementary-number-theory.euclidean-division-natural-numbers funext univalence truncations +open import elementary-number-theory.greatest-common-divisor-natural-numbers funext univalence truncations +open import elementary-number-theory.inequality-integers funext univalence truncations +open import elementary-number-theory.inequality-natural-numbers funext univalence truncations open import elementary-number-theory.integers -open import elementary-number-theory.lower-bounds-natural-numbers -open import elementary-number-theory.modular-arithmetic -open import elementary-number-theory.multiplication-integers +open import elementary-number-theory.lower-bounds-natural-numbers funext univalence truncations +open import elementary-number-theory.modular-arithmetic funext univalence truncations +open import elementary-number-theory.multiplication-integers funext univalence truncations open import elementary-number-theory.multiplication-natural-numbers -open import elementary-number-theory.multiplication-positive-and-negative-integers +open import elementary-number-theory.multiplication-positive-and-negative-integers funext univalence truncations open import elementary-number-theory.natural-numbers -open import elementary-number-theory.nonnegative-integers -open import elementary-number-theory.positive-and-negative-integers -open import elementary-number-theory.strict-inequality-natural-numbers -open import elementary-number-theory.well-ordering-principle-natural-numbers +open import elementary-number-theory.nonnegative-integers funext univalence truncations +open import elementary-number-theory.positive-and-negative-integers funext univalence truncations +open import elementary-number-theory.strict-inequality-natural-numbers funext univalence truncations +open import elementary-number-theory.well-ordering-principle-natural-numbers funext univalence truncations open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types -open import foundation.coproduct-types -open import foundation.decidable-types +open import foundation.cartesian-product-types funext univalence +open import foundation.coproduct-types funext univalence truncations +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.identity-types -open import foundation.negation +open import foundation.empty-types funext univalence truncations +open import foundation.identity-types funext +open import foundation.negation funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/elementary-number-theory/binomial-coefficients.lagda.md b/src/elementary-number-theory/binomial-coefficients.lagda.md index 655ad9e203..254d45b262 100644 --- a/src/elementary-number-theory/binomial-coefficients.lagda.md +++ b/src/elementary-number-theory/binomial-coefficients.lagda.md @@ -1,30 +1,38 @@ # The binomial coefficients ```agda -module elementary-number-theory.binomial-coefficients where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.binomial-coefficients + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import commutative-algebra.commutative-semirings +open import commutative-algebra.commutative-semirings funext univalence truncations open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.commutative-semiring-of-natural-numbers -open import elementary-number-theory.factorials -open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.commutative-semiring-of-natural-numbers funext univalence truncations +open import elementary-number-theory.factorials funext univalence truncations +open import elementary-number-theory.inequality-natural-numbers funext univalence truncations open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.strict-inequality-natural-numbers +open import elementary-number-theory.strict-inequality-natural-numbers funext univalence truncations open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.coproduct-types +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.identity-types +open import foundation.empty-types funext univalence truncations +open import foundation.identity-types funext -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/elementary-number-theory/binomial-theorem-integers.lagda.md b/src/elementary-number-theory/binomial-theorem-integers.lagda.md index ec01e91220..4728e322b6 100644 --- a/src/elementary-number-theory/binomial-theorem-integers.lagda.md +++ b/src/elementary-number-theory/binomial-theorem-integers.lagda.md @@ -1,28 +1,36 @@ # The binomial theorem for the integers ```agda -module elementary-number-theory.binomial-theorem-integers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.binomial-theorem-integers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import commutative-algebra.binomial-theorem-commutative-rings +open import commutative-algebra.binomial-theorem-commutative-rings funext univalence truncations -open import elementary-number-theory.addition-integers -open import elementary-number-theory.distance-natural-numbers +open import elementary-number-theory.addition-integers funext univalence truncations +open import elementary-number-theory.distance-natural-numbers funext univalence truncations open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-integers +open import elementary-number-theory.multiplication-integers funext univalence truncations open import elementary-number-theory.natural-numbers -open import elementary-number-theory.powers-integers -open import elementary-number-theory.ring-of-integers +open import elementary-number-theory.powers-integers funext univalence truncations +open import elementary-number-theory.ring-of-integers funext univalence truncations -open import foundation.homotopies -open import foundation.identity-types +open import foundation.homotopies funext +open import foundation.identity-types funext -open import linear-algebra.vectors +open import linear-algebra.vectors funext univalence truncations -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/elementary-number-theory/binomial-theorem-natural-numbers.lagda.md b/src/elementary-number-theory/binomial-theorem-natural-numbers.lagda.md index 08f650294f..616e5c2015 100644 --- a/src/elementary-number-theory/binomial-theorem-natural-numbers.lagda.md +++ b/src/elementary-number-theory/binomial-theorem-natural-numbers.lagda.md @@ -1,27 +1,35 @@ # The binomial theorem for the natural numbers ```agda -module elementary-number-theory.binomial-theorem-natural-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.binomial-theorem-natural-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import commutative-algebra.binomial-theorem-commutative-semirings +open import commutative-algebra.binomial-theorem-commutative-semirings funext univalence truncations open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.commutative-semiring-of-natural-numbers -open import elementary-number-theory.distance-natural-numbers -open import elementary-number-theory.exponentiation-natural-numbers +open import elementary-number-theory.commutative-semiring-of-natural-numbers funext univalence truncations +open import elementary-number-theory.distance-natural-numbers funext univalence truncations +open import elementary-number-theory.exponentiation-natural-numbers funext univalence truncations open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import foundation.homotopies -open import foundation.identity-types +open import foundation.homotopies funext +open import foundation.identity-types funext -open import linear-algebra.vectors +open import linear-algebra.vectors funext univalence truncations -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/elementary-number-theory/bounded-sums-arithmetic-functions.lagda.md b/src/elementary-number-theory/bounded-sums-arithmetic-functions.lagda.md index 7e513fd97a..78f4e4bf1d 100644 --- a/src/elementary-number-theory/bounded-sums-arithmetic-functions.lagda.md +++ b/src/elementary-number-theory/bounded-sums-arithmetic-functions.lagda.md @@ -1,23 +1,31 @@ # Bounded sums of arithmetic functions ```agda -module elementary-number-theory.bounded-sums-arithmetic-functions where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.bounded-sums-arithmetic-functions + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.arithmetic-functions +open import elementary-number-theory.arithmetic-functions funext univalence truncations open import elementary-number-theory.natural-numbers -open import elementary-number-theory.nonzero-natural-numbers +open import elementary-number-theory.nonzero-natural-numbers funext univalence truncations -open import foundation.coproduct-types -open import foundation.decidable-propositions -open import foundation.decidable-types -open import foundation.function-types +open import foundation.coproduct-types funext univalence truncations +open import foundation.decidable-propositions funext univalence truncations +open import foundation.decidable-types funext univalence truncations +open import foundation.function-types funext open import foundation.universe-levels -open import ring-theory.rings +open import ring-theory.rings funext univalence truncations ```
diff --git a/src/elementary-number-theory/catalan-numbers.lagda.md b/src/elementary-number-theory/catalan-numbers.lagda.md index 55257b4c79..fafb7c34a5 100644 --- a/src/elementary-number-theory/catalan-numbers.lagda.md +++ b/src/elementary-number-theory/catalan-numbers.lagda.md @@ -1,21 +1,29 @@ # Catalan numbers ```agda -module elementary-number-theory.catalan-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.catalan-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.binomial-coefficients -open import elementary-number-theory.distance-natural-numbers +open import elementary-number-theory.binomial-coefficients funext univalence truncations +open import elementary-number-theory.distance-natural-numbers funext univalence truncations open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.strict-inequality-natural-numbers -open import elementary-number-theory.strong-induction-natural-numbers -open import elementary-number-theory.sums-of-natural-numbers +open import elementary-number-theory.strict-inequality-natural-numbers funext univalence truncations +open import elementary-number-theory.strong-induction-natural-numbers funext univalence truncations +open import elementary-number-theory.sums-of-natural-numbers funext univalence truncations -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/elementary-number-theory/cofibonacci.lagda.md b/src/elementary-number-theory/cofibonacci.lagda.md index e2a6f001ba..9709cf6c62 100644 --- a/src/elementary-number-theory/cofibonacci.lagda.md +++ b/src/elementary-number-theory/cofibonacci.lagda.md @@ -1,27 +1,35 @@ # The cofibonacci sequence ```agda -module elementary-number-theory.cofibonacci where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.cofibonacci + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.divisibility-natural-numbers -open import elementary-number-theory.equality-natural-numbers -open import elementary-number-theory.fibonacci-sequence -open import elementary-number-theory.inequality-natural-numbers -open import elementary-number-theory.modular-arithmetic-standard-finite-types +open import elementary-number-theory.divisibility-natural-numbers funext univalence truncations +open import elementary-number-theory.equality-natural-numbers funext univalence truncations +open import elementary-number-theory.fibonacci-sequence funext univalence truncations +open import elementary-number-theory.inequality-natural-numbers funext univalence truncations +open import elementary-number-theory.modular-arithmetic-standard-finite-types funext univalence truncations open import elementary-number-theory.natural-numbers -open import elementary-number-theory.pisano-periods -open import elementary-number-theory.well-ordering-principle-natural-numbers +open import elementary-number-theory.pisano-periods funext univalence truncations +open import elementary-number-theory.well-ordering-principle-natural-numbers funext univalence truncations open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types -open import foundation.decidable-types +open import foundation.cartesian-product-types funext univalence +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.identity-types +open import foundation.empty-types funext univalence truncations +open import foundation.identity-types funext open import foundation.transport-along-identifications open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/collatz-bijection.lagda.md b/src/elementary-number-theory/collatz-bijection.lagda.md index 8e734174e5..2eef96ae0c 100644 --- a/src/elementary-number-theory/collatz-bijection.lagda.md +++ b/src/elementary-number-theory/collatz-bijection.lagda.md @@ -1,20 +1,28 @@ # The Collatz bijection ```agda -module elementary-number-theory.collatz-bijection where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.collatz-bijection + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.distance-natural-numbers -open import elementary-number-theory.euclidean-division-natural-numbers -open import elementary-number-theory.modular-arithmetic +open import elementary-number-theory.distance-natural-numbers funext univalence truncations +open import elementary-number-theory.euclidean-division-natural-numbers funext univalence truncations +open import elementary-number-theory.modular-arithmetic funext univalence truncations open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import foundation.coproduct-types -open import foundation.identity-types +open import foundation.coproduct-types funext univalence truncations +open import foundation.identity-types funext ```
diff --git a/src/elementary-number-theory/collatz-conjecture.lagda.md b/src/elementary-number-theory/collatz-conjecture.lagda.md index 9c44a48d71..e5d2aeae87 100644 --- a/src/elementary-number-theory/collatz-conjecture.lagda.md +++ b/src/elementary-number-theory/collatz-conjecture.lagda.md @@ -1,17 +1,25 @@ # The Collatz conjecture ```agda -module elementary-number-theory.collatz-conjecture where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.collatz-conjecture + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.modular-arithmetic-standard-finite-types +open import elementary-number-theory.modular-arithmetic-standard-finite-types funext univalence truncations open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import foundation.coproduct-types +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/commutative-semiring-of-natural-numbers.lagda.md b/src/elementary-number-theory/commutative-semiring-of-natural-numbers.lagda.md index 45f3324d10..ef5da1acc3 100644 --- a/src/elementary-number-theory/commutative-semiring-of-natural-numbers.lagda.md +++ b/src/elementary-number-theory/commutative-semiring-of-natural-numbers.lagda.md @@ -1,21 +1,29 @@ # The commutative semiring of natural numbers ```agda -module elementary-number-theory.commutative-semiring-of-natural-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.commutative-semiring-of-natural-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import commutative-algebra.commutative-semirings +open import commutative-algebra.commutative-semirings funext univalence truncations -open import elementary-number-theory.monoid-of-natural-numbers-with-addition +open import elementary-number-theory.monoid-of-natural-numbers-with-addition funext univalence truncations open import elementary-number-theory.multiplication-natural-numbers open import foundation.dependent-pair-types open import foundation.universe-levels -open import ring-theory.semirings +open import ring-theory.semirings funext univalence truncations ```
diff --git a/src/elementary-number-theory/conatural-numbers.lagda.md b/src/elementary-number-theory/conatural-numbers.lagda.md index 3a263db97d..26207e91eb 100644 --- a/src/elementary-number-theory/conatural-numbers.lagda.md +++ b/src/elementary-number-theory/conatural-numbers.lagda.md @@ -2,26 +2,33 @@ ```agda {-# OPTIONS --guardedness #-} - -module elementary-number-theory.conatural-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.conatural-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.coproduct-types +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.homotopies -open import foundation.injective-maps -open import foundation.maybe -open import foundation.negated-equality -open import foundation.retractions -open import foundation.sections +open import foundation.homotopies funext +open import foundation.injective-maps funext +open import foundation.negated-equality funext univalence truncations +open import foundation.retractions funext +open import foundation.sections funext open import foundation.unit-type open import foundation.universe-levels open import foundation-core.identity-types +open import foundation-core.maybe ```
diff --git a/src/elementary-number-theory/congruence-integers.lagda.md b/src/elementary-number-theory/congruence-integers.lagda.md index 9844348d01..a0b102d401 100644 --- a/src/elementary-number-theory/congruence-integers.lagda.md +++ b/src/elementary-number-theory/congruence-integers.lagda.md @@ -1,27 +1,35 @@ # The congruence relations on the integers ```agda -module elementary-number-theory.congruence-integers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.congruence-integers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.absolute-value-integers -open import elementary-number-theory.addition-integers -open import elementary-number-theory.congruence-natural-numbers -open import elementary-number-theory.difference-integers -open import elementary-number-theory.distance-integers -open import elementary-number-theory.divisibility-integers +open import elementary-number-theory.absolute-value-integers funext univalence truncations +open import elementary-number-theory.addition-integers funext univalence truncations +open import elementary-number-theory.congruence-natural-numbers funext univalence truncations +open import elementary-number-theory.difference-integers funext univalence truncations +open import elementary-number-theory.distance-integers funext univalence truncations +open import elementary-number-theory.divisibility-integers funext univalence truncations open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-integers +open import elementary-number-theory.multiplication-integers funext univalence truncations open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.binary-relations +open import foundation.binary-relations funext univalence truncations open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.identity-types +open import foundation.function-types funext +open import foundation.identity-types funext open import foundation.transport-along-identifications open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/congruence-natural-numbers.lagda.md b/src/elementary-number-theory/congruence-natural-numbers.lagda.md index d4c0ff60a4..880583f0cd 100644 --- a/src/elementary-number-theory/congruence-natural-numbers.lagda.md +++ b/src/elementary-number-theory/congruence-natural-numbers.lagda.md @@ -1,28 +1,36 @@ # The congruence relations on the natural numbers ```agda -module elementary-number-theory.congruence-natural-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.congruence-natural-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.distance-natural-numbers -open import elementary-number-theory.divisibility-natural-numbers +open import elementary-number-theory.distance-natural-numbers funext univalence truncations +open import elementary-number-theory.divisibility-natural-numbers funext univalence truncations open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.strict-inequality-natural-numbers +open import elementary-number-theory.strict-inequality-natural-numbers funext univalence truncations open import foundation.action-on-identifications-functions -open import foundation.binary-relations -open import foundation.coproduct-types +open import foundation.binary-relations funext univalence truncations +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/elementary-number-theory/cross-multiplication-difference-integer-fractions.lagda.md b/src/elementary-number-theory/cross-multiplication-difference-integer-fractions.lagda.md index 38bca51942..cd8c94c2fc 100644 --- a/src/elementary-number-theory/cross-multiplication-difference-integer-fractions.lagda.md +++ b/src/elementary-number-theory/cross-multiplication-difference-integer-fractions.lagda.md @@ -1,23 +1,32 @@ # The cross-multiplication difference of two integer fractions ```agda -module elementary-number-theory.cross-multiplication-difference-integer-fractions where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.cross-multiplication-difference-integer-fractions + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.addition-integers -open import elementary-number-theory.difference-integers -open import elementary-number-theory.integer-fractions +open import elementary-number-theory.addition-integers funext univalence truncations +open import elementary-number-theory.difference-integers funext univalence truncations +open import elementary-number-theory.integer-fractions funext univalence truncations open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-integers +open import elementary-number-theory.multiplication-integers funext univalence truncations open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.negation -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.identity-types funext +open import foundation.negation funext +open import foundation.propositions funext univalence ```
diff --git a/src/elementary-number-theory/cubes-natural-numbers.lagda.md b/src/elementary-number-theory/cubes-natural-numbers.lagda.md index 491369a597..ece62276b8 100644 --- a/src/elementary-number-theory/cubes-natural-numbers.lagda.md +++ b/src/elementary-number-theory/cubes-natural-numbers.lagda.md @@ -1,7 +1,15 @@ # Cubes of natural numbers ```agda -module elementary-number-theory.cubes-natural-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.cubes-natural-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,10 +17,10 @@ module elementary-number-theory.cubes-natural-numbers where ```agda open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.squares-natural-numbers +open import elementary-number-theory.squares-natural-numbers funext univalence truncations open import foundation.dependent-pair-types -open import foundation.fibers-of-maps +open import foundation.fibers-of-maps funext open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/decidable-dependent-function-types.lagda.md b/src/elementary-number-theory/decidable-dependent-function-types.lagda.md index ca2d7fd780..e4e484f4d5 100644 --- a/src/elementary-number-theory/decidable-dependent-function-types.lagda.md +++ b/src/elementary-number-theory/decidable-dependent-function-types.lagda.md @@ -1,9 +1,17 @@ # Decidable dependent function types ```agda -module elementary-number-theory.decidable-dependent-function-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom -open import foundation.decidable-dependent-function-types public +module elementary-number-theory.decidable-dependent-function-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where + +open import foundation.decidable-dependent-function-types funext univalence truncations public ```
Imports diff --git a/src/elementary-number-theory/decidable-total-order-integers.lagda.md b/src/elementary-number-theory/decidable-total-order-integers.lagda.md index f4e2772ec7..cd4abb3971 100644 --- a/src/elementary-number-theory/decidable-total-order-integers.lagda.md +++ b/src/elementary-number-theory/decidable-total-order-integers.lagda.md @@ -1,20 +1,28 @@ # The decidable total order of integers ```agda -module elementary-number-theory.decidable-total-order-integers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.decidable-total-order-integers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.inequality-integers +open import elementary-number-theory.inequality-integers funext univalence truncations open import foundation.dependent-pair-types -open import foundation.propositional-truncations +open import foundation.propositional-truncations funext univalence open import foundation.universe-levels -open import order-theory.decidable-total-orders -open import order-theory.total-orders +open import order-theory.decidable-total-orders funext univalence truncations +open import order-theory.total-orders funext univalence truncations ```
diff --git a/src/elementary-number-theory/decidable-total-order-natural-numbers.lagda.md b/src/elementary-number-theory/decidable-total-order-natural-numbers.lagda.md index ba6c9d2db7..f0b49410dd 100644 --- a/src/elementary-number-theory/decidable-total-order-natural-numbers.lagda.md +++ b/src/elementary-number-theory/decidable-total-order-natural-numbers.lagda.md @@ -1,27 +1,35 @@ # The decidable total order of natural numbers ```agda -module elementary-number-theory.decidable-total-order-natural-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.decidable-total-order-natural-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.inequality-natural-numbers funext univalence truncations open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.propositional-truncations +open import foundation.function-types funext +open import foundation.propositional-truncations funext univalence open import foundation.unit-type open import foundation.universe-levels -open import order-theory.decidable-total-orders -open import order-theory.order-preserving-maps-posets -open import order-theory.order-preserving-maps-preorders -open import order-theory.posets -open import order-theory.preorders -open import order-theory.total-orders +open import order-theory.decidable-total-orders funext univalence truncations +open import order-theory.order-preserving-maps-posets funext univalence truncations +open import order-theory.order-preserving-maps-preorders funext univalence truncations +open import order-theory.posets funext univalence truncations +open import order-theory.preorders funext univalence truncations +open import order-theory.total-orders funext univalence truncations ```
diff --git a/src/elementary-number-theory/decidable-total-order-rational-numbers.lagda.md b/src/elementary-number-theory/decidable-total-order-rational-numbers.lagda.md index 3a1b901c63..2f86f274fe 100644 --- a/src/elementary-number-theory/decidable-total-order-rational-numbers.lagda.md +++ b/src/elementary-number-theory/decidable-total-order-rational-numbers.lagda.md @@ -1,20 +1,28 @@ # The decidable total order of rational numbers ```agda -module elementary-number-theory.decidable-total-order-rational-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.decidable-total-order-rational-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.inequality-rational-numbers +open import elementary-number-theory.inequality-rational-numbers funext univalence truncations open import foundation.dependent-pair-types -open import foundation.propositional-truncations +open import foundation.propositional-truncations funext univalence open import foundation.universe-levels -open import order-theory.decidable-total-orders -open import order-theory.total-orders +open import order-theory.decidable-total-orders funext univalence truncations +open import order-theory.total-orders funext univalence truncations ```
diff --git a/src/elementary-number-theory/decidable-total-order-standard-finite-types.lagda.md b/src/elementary-number-theory/decidable-total-order-standard-finite-types.lagda.md index a33da4e7bb..ff15acff7d 100644 --- a/src/elementary-number-theory/decidable-total-order-standard-finite-types.lagda.md +++ b/src/elementary-number-theory/decidable-total-order-standard-finite-types.lagda.md @@ -1,21 +1,29 @@ # The decidable total order of a standard finite type ```agda -module elementary-number-theory.decidable-total-order-standard-finite-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.decidable-total-order-standard-finite-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.inequality-standard-finite-types +open import elementary-number-theory.inequality-standard-finite-types funext univalence truncations open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.propositional-truncations +open import foundation.propositional-truncations funext univalence open import foundation.universe-levels -open import order-theory.decidable-total-orders -open import order-theory.total-orders +open import order-theory.decidable-total-orders funext univalence truncations +open import order-theory.total-orders funext univalence truncations ```
diff --git a/src/elementary-number-theory/decidable-types.lagda.md b/src/elementary-number-theory/decidable-types.lagda.md index 047ada9a91..f28a92442b 100644 --- a/src/elementary-number-theory/decidable-types.lagda.md +++ b/src/elementary-number-theory/decidable-types.lagda.md @@ -1,23 +1,31 @@ # Decidable types in elementary number theory ```agda -module elementary-number-theory.decidable-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.decidable-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.inequality-natural-numbers funext univalence truncations open import elementary-number-theory.natural-numbers -open import elementary-number-theory.strict-inequality-natural-numbers -open import elementary-number-theory.upper-bounds-natural-numbers +open import elementary-number-theory.strict-inequality-natural-numbers funext univalence truncations +open import elementary-number-theory.upper-bounds-natural-numbers funext univalence truncations -open import foundation.cartesian-product-types -open import foundation.coproduct-types -open import foundation.decidable-types +open import foundation.cartesian-product-types funext univalence +open import foundation.coproduct-types funext univalence truncations +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.function-types +open import foundation.empty-types funext univalence truncations +open import foundation.function-types funext open import foundation.unit-type open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/difference-integers.lagda.md b/src/elementary-number-theory/difference-integers.lagda.md index 6cd796526c..ef4ec20a52 100644 --- a/src/elementary-number-theory/difference-integers.lagda.md +++ b/src/elementary-number-theory/difference-integers.lagda.md @@ -1,18 +1,26 @@ # The difference between integers ```agda -module elementary-number-theory.difference-integers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.difference-integers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.addition-integers +open import elementary-number-theory.addition-integers funext univalence truncations open import elementary-number-theory.integers open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.interchange-law ``` diff --git a/src/elementary-number-theory/difference-rational-numbers.lagda.md b/src/elementary-number-theory/difference-rational-numbers.lagda.md index 7dbe0779c1..badf5ddd12 100644 --- a/src/elementary-number-theory/difference-rational-numbers.lagda.md +++ b/src/elementary-number-theory/difference-rational-numbers.lagda.md @@ -2,19 +2,26 @@ ```agda {-# OPTIONS --lossy-unification #-} - -module elementary-number-theory.difference-rational-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.difference-rational-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.addition-rational-numbers -open import elementary-number-theory.rational-numbers +open import elementary-number-theory.addition-rational-numbers funext univalence truncations +open import elementary-number-theory.rational-numbers funext univalence truncations open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.interchange-law ``` diff --git a/src/elementary-number-theory/dirichlet-convolution.lagda.md b/src/elementary-number-theory/dirichlet-convolution.lagda.md index 0745ebdfe9..a23de1ba30 100644 --- a/src/elementary-number-theory/dirichlet-convolution.lagda.md +++ b/src/elementary-number-theory/dirichlet-convolution.lagda.md @@ -1,24 +1,32 @@ # Dirichlet convolution ```agda -module elementary-number-theory.dirichlet-convolution where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.dirichlet-convolution + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.arithmetic-functions -open import elementary-number-theory.bounded-sums-arithmetic-functions -open import elementary-number-theory.modular-arithmetic-standard-finite-types +open import elementary-number-theory.arithmetic-functions funext univalence truncations +open import elementary-number-theory.bounded-sums-arithmetic-functions funext univalence truncations +open import elementary-number-theory.modular-arithmetic-standard-finite-types funext univalence truncations open import elementary-number-theory.natural-numbers -open import elementary-number-theory.nonzero-natural-numbers +open import elementary-number-theory.nonzero-natural-numbers funext univalence truncations open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.identity-types +open import foundation.empty-types funext univalence truncations +open import foundation.identity-types funext open import foundation.universe-levels -open import ring-theory.rings +open import ring-theory.rings funext univalence truncations ```
diff --git a/src/elementary-number-theory/distance-integers.lagda.md b/src/elementary-number-theory/distance-integers.lagda.md index ee659aed25..b364759192 100644 --- a/src/elementary-number-theory/distance-integers.lagda.md +++ b/src/elementary-number-theory/distance-integers.lagda.md @@ -1,25 +1,33 @@ # The distance between integers ```agda -module elementary-number-theory.distance-integers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.distance-integers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.absolute-value-integers -open import elementary-number-theory.difference-integers -open import elementary-number-theory.distance-natural-numbers +open import elementary-number-theory.absolute-value-integers funext univalence truncations +open import elementary-number-theory.difference-integers funext univalence truncations +open import elementary-number-theory.distance-natural-numbers funext univalence truncations open import elementary-number-theory.integers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.nonnegative-integers -open import elementary-number-theory.positive-and-negative-integers -open import elementary-number-theory.positive-integers +open import elementary-number-theory.nonnegative-integers funext univalence truncations +open import elementary-number-theory.positive-and-negative-integers funext univalence truncations +open import elementary-number-theory.positive-integers funext univalence truncations open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.coproduct-types -open import foundation.identity-types +open import foundation.coproduct-types funext univalence truncations +open import foundation.identity-types funext ```
diff --git a/src/elementary-number-theory/distance-natural-numbers.lagda.md b/src/elementary-number-theory/distance-natural-numbers.lagda.md index 6026c735da..5ed79591a4 100644 --- a/src/elementary-number-theory/distance-natural-numbers.lagda.md +++ b/src/elementary-number-theory/distance-natural-numbers.lagda.md @@ -1,24 +1,32 @@ # The distance between natural numbers ```agda -module elementary-number-theory.distance-natural-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.distance-natural-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.inequality-natural-numbers funext univalence truncations open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.strict-inequality-natural-numbers +open import elementary-number-theory.strict-inequality-natural-numbers funext univalence truncations open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.coproduct-types +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.identity-types +open import foundation.function-types funext +open import foundation.identity-types funext open import foundation.transport-along-identifications open import foundation.unit-type open import foundation.universe-levels diff --git a/src/elementary-number-theory/divisibility-integers.lagda.md b/src/elementary-number-theory/divisibility-integers.lagda.md index bed59408c3..02267e4ee8 100644 --- a/src/elementary-number-theory/divisibility-integers.lagda.md +++ b/src/elementary-number-theory/divisibility-integers.lagda.md @@ -1,37 +1,46 @@ # Divisibility of integers ```agda -module elementary-number-theory.divisibility-integers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.divisibility-integers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.absolute-value-integers -open import elementary-number-theory.addition-integers -open import elementary-number-theory.divisibility-natural-numbers -open import elementary-number-theory.equality-integers +open import elementary-number-theory.absolute-value-integers funext univalence truncations +open import elementary-number-theory.addition-integers funext univalence truncations +open import elementary-number-theory.divisibility-natural-numbers funext univalence truncations +open import elementary-number-theory.equality-integers funext univalence truncations open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-integers -open import elementary-number-theory.multiplication-positive-and-negative-integers +open import elementary-number-theory.multiplication-integers funext univalence truncations +open import elementary-number-theory.multiplication-positive-and-negative-integers funext univalence truncations open import elementary-number-theory.natural-numbers -open import elementary-number-theory.nonnegative-integers -open import elementary-number-theory.nonpositive-integers -open import elementary-number-theory.nonzero-integers -open import elementary-number-theory.positive-and-negative-integers +open import elementary-number-theory.nonnegative-integers funext univalence truncations +open import elementary-number-theory.nonpositive-integers funext univalence truncations +open import elementary-number-theory.nonzero-integers funext univalence truncations +open import elementary-number-theory.positive-and-negative-integers funext univalence truncations open import foundation.action-on-identifications-functions -open import foundation.binary-relations -open import foundation.cartesian-product-types -open import foundation.coproduct-types -open import foundation.decidable-types +open import foundation.binary-relations funext univalence truncations +open import foundation.cartesian-product-types funext univalence +open import foundation.coproduct-types funext univalence truncations +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.function-types -open import foundation.identity-types -open import foundation.negation -open import foundation.propositional-maps -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.empty-types funext univalence truncations +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.negation funext +open import foundation.propositional-maps funext +open import foundation.propositions funext univalence open import foundation.transport-along-identifications open import foundation.unit-type open import foundation.universe-levels diff --git a/src/elementary-number-theory/divisibility-modular-arithmetic.lagda.md b/src/elementary-number-theory/divisibility-modular-arithmetic.lagda.md index 6d2a85ab6f..de8a0c2516 100644 --- a/src/elementary-number-theory/divisibility-modular-arithmetic.lagda.md +++ b/src/elementary-number-theory/divisibility-modular-arithmetic.lagda.md @@ -1,24 +1,32 @@ # Divisibility in modular arithmetic ```agda -module elementary-number-theory.divisibility-modular-arithmetic where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.divisibility-modular-arithmetic + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.divisibility-integers -open import elementary-number-theory.divisibility-standard-finite-types -open import elementary-number-theory.modular-arithmetic +open import elementary-number-theory.divisibility-integers funext univalence truncations +open import elementary-number-theory.divisibility-standard-finite-types funext univalence truncations +open import elementary-number-theory.modular-arithmetic funext univalence truncations open import elementary-number-theory.natural-numbers -open import foundation.binary-relations -open import foundation.decidable-types +open import foundation.binary-relations funext univalence truncations +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import univalent-combinatorics.fibers-of-maps +open import univalent-combinatorics.fibers-of-maps funext univalence truncations ```
diff --git a/src/elementary-number-theory/divisibility-natural-numbers.lagda.md b/src/elementary-number-theory/divisibility-natural-numbers.lagda.md index 9bf81abc22..8f269b3d50 100644 --- a/src/elementary-number-theory/divisibility-natural-numbers.lagda.md +++ b/src/elementary-number-theory/divisibility-natural-numbers.lagda.md @@ -1,31 +1,42 @@ # Divisibility of natural numbers ```agda -module elementary-number-theory.divisibility-natural-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.divisibility-natural-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.distance-natural-numbers -open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.distance-natural-numbers funext univalence truncations +open import elementary-number-theory.equality-natural-numbers funext univalence truncations +open import elementary-number-theory.inequality-natural-numbers funext univalence truncations open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.strict-inequality-natural-numbers +open import elementary-number-theory.strict-inequality-natural-numbers funext univalence truncations open import foundation.action-on-identifications-functions -open import foundation.binary-relations +open import foundation.binary-relations funext univalence truncations open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.negated-equality -open import foundation.negation -open import foundation.propositional-maps -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.empty-types funext univalence truncations +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.logical-equivalences funext +open import foundation.negated-equality funext univalence truncations +open import foundation.negation funext +open import foundation.propositional-maps funext +open import foundation.propositions funext univalence open import foundation.transport-along-identifications -open import foundation.type-arithmetic-empty-type +open import foundation.type-arithmetic-empty-type funext univalence truncations open import foundation.unit-type open import foundation.universe-levels ``` @@ -114,7 +125,10 @@ eq-quotient-div-eq-div-ℕ x y z n e H I = ```agda is-prop-div-ℕ : (k x : ℕ) → is-nonzero-ℕ k → is-prop (div-ℕ k x) -is-prop-div-ℕ k x f = is-prop-map-is-emb (is-emb-right-mul-ℕ k f) x +is-prop-div-ℕ k x f = + is-prop-map-is-emb + ( is-emb-is-injective is-set-ℕ (is-injective-right-mul-ℕ k f)) + ( x) ``` ### The divisibility relation is a partial order on the natural numbers diff --git a/src/elementary-number-theory/divisibility-standard-finite-types.lagda.md b/src/elementary-number-theory/divisibility-standard-finite-types.lagda.md index 0e659d21ac..d84be8246e 100644 --- a/src/elementary-number-theory/divisibility-standard-finite-types.lagda.md +++ b/src/elementary-number-theory/divisibility-standard-finite-types.lagda.md @@ -1,25 +1,33 @@ # The divisibility relation on the standard finite types ```agda -module elementary-number-theory.divisibility-standard-finite-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.divisibility-standard-finite-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.modular-arithmetic-standard-finite-types +open import elementary-number-theory.modular-arithmetic-standard-finite-types funext univalence truncations open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.binary-relations -open import foundation.decidable-types +open import foundation.binary-relations funext univalence truncations +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import univalent-combinatorics.decidable-dependent-pair-types -open import univalent-combinatorics.equality-standard-finite-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.decidable-dependent-pair-types funext univalence truncations +open import univalent-combinatorics.equality-standard-finite-types funext univalence truncations +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/elementary-number-theory/equality-conatural-numbers.lagda.md b/src/elementary-number-theory/equality-conatural-numbers.lagda.md index 9231d89474..09f1bffea7 100644 --- a/src/elementary-number-theory/equality-conatural-numbers.lagda.md +++ b/src/elementary-number-theory/equality-conatural-numbers.lagda.md @@ -2,41 +2,49 @@ ```agda {-# OPTIONS --guardedness #-} - -module elementary-number-theory.equality-conatural-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.equality-conatural-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.conatural-numbers +open import elementary-number-theory.conatural-numbers funext univalence truncations open import foundation.action-on-identifications-functions -open import foundation.coherently-invertible-maps -open import foundation.coproduct-types +open import foundation.coherently-invertible-maps funext +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.double-negation -open import foundation.double-negation-stable-equality -open import foundation.empty-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-coproduct-types +open import foundation.double-negation funext univalence truncations +open import foundation.double-negation-stable-equality funext univalence truncations +open import foundation.empty-types funext univalence truncations +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-coproduct-types funext univalence truncations open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.maybe -open import foundation.negation -open import foundation.retractions -open import foundation.retracts-of-types -open import foundation.sections -open import foundation.sets -open import foundation.tight-apartness-relations -open import foundation.torsorial-type-families +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.negation funext +open import foundation.retractions funext +open import foundation.retracts-of-types funext univalence +open import foundation.sections funext +open import foundation.sets funext univalence +open import foundation.tight-apartness-relations funext univalence truncations +open import foundation.torsorial-type-families funext univalence truncations open import foundation.unit-type open import foundation.universe-levels -open import logic.double-negation-elimination +open import foundation-core.maybe + +open import logic.double-negation-elimination funext univalence truncations ```
diff --git a/src/elementary-number-theory/equality-integers.lagda.md b/src/elementary-number-theory/equality-integers.lagda.md index 0638b0bb24..c43d084fd4 100644 --- a/src/elementary-number-theory/equality-integers.lagda.md +++ b/src/elementary-number-theory/equality-integers.lagda.md @@ -1,30 +1,41 @@ # Equality of integers ```agda -module elementary-number-theory.equality-integers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.equality-integers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.equality-natural-numbers +open import elementary-number-theory.equality-natural-numbers funext univalence truncations open import elementary-number-theory.integers open import foundation.action-on-identifications-functions -open import foundation.coproduct-types -open import foundation.decidable-equality -open import foundation.decidable-types +open import foundation.coproduct-types funext univalence truncations +open import foundation.decidable-equality funext univalence truncations +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.discrete-types -open import foundation.empty-types -open import foundation.equality-dependent-pair-types -open import foundation.equivalences -open import foundation.function-types +open import foundation.dependent-products-propositions funext +open import foundation.discrete-types funext univalence truncations +open import foundation.empty-types funext univalence truncations +open import foundation.equality-coproduct-types funext univalence truncations +open import foundation.equality-dependent-pair-types funext +open import foundation.equivalences funext +open import foundation.function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.set-truncations -open import foundation.torsorial-type-families +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.set-truncations funext univalence +open import foundation.sets funext univalence +open import foundation.torsorial-type-families funext univalence truncations open import foundation.unit-type open import foundation.universe-levels ``` @@ -92,6 +103,18 @@ pr1 ℤ-Discrete-Type = ℤ pr2 ℤ-Discrete-Type = has-decidable-equality-ℤ ``` +### The type of integers is a set + +```agda +abstract + is-set-ℤ : is-set ℤ + is-set-ℤ = is-set-coproduct is-set-ℕ (is-set-coproduct is-set-unit is-set-ℕ) + +ℤ-Set : Set lzero +pr1 ℤ-Set = ℤ +pr2 ℤ-Set = is-set-ℤ +``` + ### The type of integers is its own set truncation ```agda diff --git a/src/elementary-number-theory/equality-natural-numbers.lagda.md b/src/elementary-number-theory/equality-natural-numbers.lagda.md index bb335e5e58..c42100471e 100644 --- a/src/elementary-number-theory/equality-natural-numbers.lagda.md +++ b/src/elementary-number-theory/equality-natural-numbers.lagda.md @@ -1,7 +1,15 @@ # Equality of natural numbers ```agda -module elementary-number-theory.equality-natural-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.equality-natural-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,23 +18,24 @@ module elementary-number-theory.equality-natural-numbers where open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.coproduct-types -open import foundation.decidable-equality -open import foundation.decidable-types +open import foundation.coproduct-types funext univalence truncations +open import foundation.decidable-equality funext univalence truncations +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.equivalences -open import foundation.function-types +open import foundation.dependent-products-propositions funext +open import foundation.empty-types funext univalence truncations +open import foundation.equivalences funext +open import foundation.function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.set-truncations -open import foundation.sets +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.set-truncations funext univalence +open import foundation.sets funext univalence open import foundation.unit-type open import foundation.universe-levels -open import foundation-core.decidable-propositions -open import foundation-core.discrete-types +open import foundation-core.decidable-propositions funext univalence truncations +open import foundation-core.discrete-types funext univalence truncations open import foundation-core.torsorial-type-families ``` diff --git a/src/elementary-number-theory/equality-rational-numbers.lagda.md b/src/elementary-number-theory/equality-rational-numbers.lagda.md index 6aa0e27499..a23f125b85 100644 --- a/src/elementary-number-theory/equality-rational-numbers.lagda.md +++ b/src/elementary-number-theory/equality-rational-numbers.lagda.md @@ -1,26 +1,33 @@ # Equality of rational numbers ```agda -module elementary-number-theory.equality-rational-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.equality-rational-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.equality-integers -open import elementary-number-theory.integer-fractions -open import elementary-number-theory.positive-integers -open import elementary-number-theory.rational-numbers -open import elementary-number-theory.reduced-integer-fractions +open import elementary-number-theory.integer-fractions funext univalence truncations +open import elementary-number-theory.rational-numbers funext univalence truncations +open import elementary-number-theory.reduced-integer-fractions funext univalence truncations -open import foundation.decidable-equality +open import foundation.decidable-equality funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types -open import foundation.equivalences +open import foundation.dependent-products-propositions funext +open import foundation.equality-dependent-pair-types funext +open import foundation.equivalences funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.torsorial-type-families +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.torsorial-type-families funext univalence truncations open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/euclid-mullin-sequence.lagda.md b/src/elementary-number-theory/euclid-mullin-sequence.lagda.md index be53df7a65..c2dbb1211d 100644 --- a/src/elementary-number-theory/euclid-mullin-sequence.lagda.md +++ b/src/elementary-number-theory/euclid-mullin-sequence.lagda.md @@ -1,23 +1,31 @@ # The Euclid–Mullin sequence ```agda -module elementary-number-theory.euclid-mullin-sequence where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.euclid-mullin-sequence + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.fundamental-theorem-of-arithmetic +open import elementary-number-theory.fundamental-theorem-of-arithmetic funext univalence truncations open import elementary-number-theory.natural-numbers -open import elementary-number-theory.products-of-natural-numbers -open import elementary-number-theory.strict-inequality-natural-numbers -open import elementary-number-theory.strong-induction-natural-numbers +open import elementary-number-theory.products-of-natural-numbers funext univalence truncations +open import elementary-number-theory.strict-inequality-natural-numbers funext univalence truncations +open import elementary-number-theory.strong-induction-natural-numbers funext univalence truncations open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.unit-type -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/elementary-number-theory/euclidean-division-natural-numbers.lagda.md b/src/elementary-number-theory/euclidean-division-natural-numbers.lagda.md index 1ef17f8247..03dba28422 100644 --- a/src/elementary-number-theory/euclidean-division-natural-numbers.lagda.md +++ b/src/elementary-number-theory/euclidean-division-natural-numbers.lagda.md @@ -1,27 +1,35 @@ # Euclidean division on the natural numbers ```agda -module elementary-number-theory.euclidean-division-natural-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.euclidean-division-natural-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.congruence-natural-numbers -open import elementary-number-theory.distance-natural-numbers -open import elementary-number-theory.modular-arithmetic-standard-finite-types +open import elementary-number-theory.congruence-natural-numbers funext univalence truncations +open import elementary-number-theory.distance-natural-numbers funext univalence truncations +open import elementary-number-theory.modular-arithmetic-standard-finite-types funext univalence truncations open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.strict-inequality-natural-numbers +open import elementary-number-theory.strict-inequality-natural-numbers funext univalence truncations open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.identity-types +open import foundation.empty-types funext univalence truncations +open import foundation.identity-types funext -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/elementary-number-theory/eulers-totient-function.lagda.md b/src/elementary-number-theory/eulers-totient-function.lagda.md index 83f8c0970d..cb6710edeb 100644 --- a/src/elementary-number-theory/eulers-totient-function.lagda.md +++ b/src/elementary-number-theory/eulers-totient-function.lagda.md @@ -1,18 +1,26 @@ # Euler's totient function ```agda -module elementary-number-theory.eulers-totient-function where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.eulers-totient-function + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import elementary-number-theory.natural-numbers -open import elementary-number-theory.relatively-prime-natural-numbers +open import elementary-number-theory.relatively-prime-natural-numbers funext univalence truncations -open import univalent-combinatorics.decidable-subtypes -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.decidable-subtypes funext univalence truncations +open import univalent-combinatorics.finite-types funext univalence truncations +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/elementary-number-theory/exponentiation-natural-numbers.lagda.md b/src/elementary-number-theory/exponentiation-natural-numbers.lagda.md index abbf1734ae..cf44e91319 100644 --- a/src/elementary-number-theory/exponentiation-natural-numbers.lagda.md +++ b/src/elementary-number-theory/exponentiation-natural-numbers.lagda.md @@ -1,22 +1,30 @@ # Exponentiation of natural numbers ```agda -module elementary-number-theory.exponentiation-natural-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.exponentiation-natural-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import commutative-algebra.powers-of-elements-commutative-semirings +open import commutative-algebra.powers-of-elements-commutative-semirings funext univalence truncations open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.commutative-semiring-of-natural-numbers +open import elementary-number-theory.commutative-semiring-of-natural-numbers funext univalence truncations open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.products-of-natural-numbers +open import elementary-number-theory.products-of-natural-numbers funext univalence truncations open import foundation.action-on-identifications-functions -open import foundation.identity-types +open import foundation.identity-types funext ```
diff --git a/src/elementary-number-theory/factorials.lagda.md b/src/elementary-number-theory/factorials.lagda.md index 05851e426e..a1d7be0f25 100644 --- a/src/elementary-number-theory/factorials.lagda.md +++ b/src/elementary-number-theory/factorials.lagda.md @@ -1,22 +1,30 @@ # Factorials of natural numbers ```agda -module elementary-number-theory.factorials where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.factorials + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.divisibility-natural-numbers -open import elementary-number-theory.equality-natural-numbers -open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.divisibility-natural-numbers funext univalence truncations +open import elementary-number-theory.equality-natural-numbers funext univalence truncations +open import elementary-number-theory.inequality-natural-numbers funext univalence truncations open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import foundation.coproduct-types +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.identity-types +open import foundation.empty-types funext univalence truncations +open import foundation.identity-types funext ```
diff --git a/src/elementary-number-theory/fermat-numbers.lagda.md b/src/elementary-number-theory/fermat-numbers.lagda.md index 8a76e9fc21..79c2089725 100644 --- a/src/elementary-number-theory/fermat-numbers.lagda.md +++ b/src/elementary-number-theory/fermat-numbers.lagda.md @@ -1,19 +1,27 @@ # Fermat numbers ```agda -module elementary-number-theory.fermat-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.fermat-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.exponentiation-natural-numbers +open import elementary-number-theory.exponentiation-natural-numbers funext univalence truncations open import elementary-number-theory.natural-numbers -open import elementary-number-theory.products-of-natural-numbers -open import elementary-number-theory.strong-induction-natural-numbers +open import elementary-number-theory.products-of-natural-numbers funext univalence truncations +open import elementary-number-theory.strong-induction-natural-numbers funext univalence truncations -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/elementary-number-theory/fibonacci-sequence.lagda.md b/src/elementary-number-theory/fibonacci-sequence.lagda.md index 89af95e039..609285f2d9 100644 --- a/src/elementary-number-theory/fibonacci-sequence.lagda.md +++ b/src/elementary-number-theory/fibonacci-sequence.lagda.md @@ -1,22 +1,30 @@ # The Fibonacci sequence ```agda -module elementary-number-theory.fibonacci-sequence where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.fibonacci-sequence + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.divisibility-natural-numbers -open import elementary-number-theory.greatest-common-divisor-natural-numbers +open import elementary-number-theory.divisibility-natural-numbers funext univalence truncations +open import elementary-number-theory.greatest-common-divisor-natural-numbers funext univalence truncations open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.relatively-prime-natural-numbers +open import elementary-number-theory.relatively-prime-natural-numbers funext univalence truncations open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.transport-along-identifications ``` diff --git a/src/elementary-number-theory/field-of-rational-numbers.lagda.md b/src/elementary-number-theory/field-of-rational-numbers.lagda.md index 88e4a88422..b1dc5ed2f7 100644 --- a/src/elementary-number-theory/field-of-rational-numbers.lagda.md +++ b/src/elementary-number-theory/field-of-rational-numbers.lagda.md @@ -1,23 +1,31 @@ # The field of rational numbers ```agda -module elementary-number-theory.field-of-rational-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.field-of-rational-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import commutative-algebra.discrete-fields +open import commutative-algebra.discrete-fields funext univalence truncations -open import elementary-number-theory.multiplicative-group-of-rational-numbers -open import elementary-number-theory.nonzero-rational-numbers -open import elementary-number-theory.ring-of-rational-numbers +open import elementary-number-theory.multiplicative-group-of-rational-numbers funext univalence truncations +open import elementary-number-theory.nonzero-rational-numbers funext univalence truncations +open import elementary-number-theory.ring-of-rational-numbers funext univalence truncations open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.identity-types +open import foundation.function-types funext +open import foundation.identity-types funext -open import ring-theory.division-rings +open import ring-theory.division-rings funext univalence truncations ```
diff --git a/src/elementary-number-theory/finitary-natural-numbers.lagda.md b/src/elementary-number-theory/finitary-natural-numbers.lagda.md index 57acf9d9c0..35ed3cd202 100644 --- a/src/elementary-number-theory/finitary-natural-numbers.lagda.md +++ b/src/elementary-number-theory/finitary-natural-numbers.lagda.md @@ -1,30 +1,38 @@ # The natural numbers base `k` ```agda -module elementary-number-theory.finitary-natural-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.finitary-natural-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.congruence-natural-numbers -open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.congruence-natural-numbers funext univalence truncations +open import elementary-number-theory.inequality-natural-numbers funext univalence truncations open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.strict-inequality-natural-numbers +open import elementary-number-theory.strict-inequality-natural-numbers funext univalence truncations open import foundation.action-on-identifications-functions -open import foundation.coproduct-types +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.function-types -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.sets +open import foundation.empty-types funext univalence truncations +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.sets funext univalence open import foundation.universe-levels -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/elementary-number-theory/finitely-cyclic-maps.lagda.md b/src/elementary-number-theory/finitely-cyclic-maps.lagda.md index d70daec324..2bc4c45b8f 100644 --- a/src/elementary-number-theory/finitely-cyclic-maps.lagda.md +++ b/src/elementary-number-theory/finitely-cyclic-maps.lagda.md @@ -1,25 +1,33 @@ # Finitely cyclic maps ```agda -module elementary-number-theory.finitely-cyclic-maps where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.finitely-cyclic-maps + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.modular-arithmetic-standard-finite-types +open import elementary-number-theory.modular-arithmetic-standard-finite-types funext univalence truncations open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.iterating-functions +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.iterating-functions funext univalence truncations open import foundation.universe-levels -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/elementary-number-theory/fundamental-theorem-of-arithmetic.lagda.md b/src/elementary-number-theory/fundamental-theorem-of-arithmetic.lagda.md index 6badd26e4b..ca6e308c22 100644 --- a/src/elementary-number-theory/fundamental-theorem-of-arithmetic.lagda.md +++ b/src/elementary-number-theory/fundamental-theorem-of-arithmetic.lagda.md @@ -1,52 +1,64 @@ # The fundamental theorem of arithmetic ```agda -module elementary-number-theory.fundamental-theorem-of-arithmetic where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.fundamental-theorem-of-arithmetic + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.based-strong-induction-natural-numbers -open import elementary-number-theory.bezouts-lemma-integers -open import elementary-number-theory.decidable-total-order-natural-numbers -open import elementary-number-theory.divisibility-natural-numbers -open import elementary-number-theory.equality-natural-numbers -open import elementary-number-theory.inequality-natural-numbers -open import elementary-number-theory.lower-bounds-natural-numbers -open import elementary-number-theory.modular-arithmetic-standard-finite-types -open import elementary-number-theory.multiplication-lists-of-natural-numbers +open import elementary-number-theory.based-strong-induction-natural-numbers funext univalence truncations +open import elementary-number-theory.bezouts-lemma-integers funext univalence truncations +open import elementary-number-theory.decidable-total-order-natural-numbers funext univalence truncations +open import elementary-number-theory.divisibility-natural-numbers funext univalence truncations +open import elementary-number-theory.equality-natural-numbers funext univalence truncations +open import elementary-number-theory.inequality-natural-numbers funext univalence truncations +open import elementary-number-theory.lower-bounds-natural-numbers funext univalence truncations +open import elementary-number-theory.modular-arithmetic-standard-finite-types funext univalence truncations +open import elementary-number-theory.multiplication-lists-of-natural-numbers funext univalence truncations open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.prime-numbers -open import elementary-number-theory.relatively-prime-natural-numbers -open import elementary-number-theory.strict-inequality-natural-numbers -open import elementary-number-theory.well-ordering-principle-natural-numbers +open import elementary-number-theory.prime-numbers funext univalence truncations +open import elementary-number-theory.relatively-prime-natural-numbers funext univalence truncations +open import elementary-number-theory.strict-inequality-natural-numbers funext univalence truncations +open import elementary-number-theory.well-ordering-principle-natural-numbers funext univalence truncations -open import finite-group-theory.permutations-standard-finite-types +open import finite-group-theory.permutations-standard-finite-types funext univalence truncations open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types -open import foundation.contractible-types -open import foundation.coproduct-types -open import foundation.decidable-types +open import foundation.cartesian-product-types funext univalence +open import foundation.contractible-types funext univalence +open import foundation.coproduct-types funext univalence truncations +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.subtypes +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.empty-types funext univalence truncations +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.raising-universe-levels-unit-type +open import foundation.subtypes funext univalence truncations open import foundation.transport-along-identifications -open import foundation.type-arithmetic-empty-type +open import foundation.type-arithmetic-empty-type funext univalence truncations open import foundation.unit-type open import foundation.universe-levels -open import lists.concatenation-lists -open import lists.functoriality-lists +open import lists.concatenation-lists funext univalence truncations +open import lists.equality-lists funext univalence truncations +open import lists.functoriality-lists funext univalence truncations open import lists.lists -open import lists.permutation-lists -open import lists.predicates-on-lists -open import lists.sort-by-insertion-lists -open import lists.sorted-lists +open import lists.permutation-lists funext univalence truncations +open import lists.predicates-on-lists funext univalence +open import lists.sort-by-insertion-lists funext univalence truncations +open import lists.sorted-lists funext univalence truncations ```
diff --git a/src/elementary-number-theory/goldbach-conjecture.lagda.md b/src/elementary-number-theory/goldbach-conjecture.lagda.md index ab096dfab1..91d49cc6f2 100644 --- a/src/elementary-number-theory/goldbach-conjecture.lagda.md +++ b/src/elementary-number-theory/goldbach-conjecture.lagda.md @@ -1,7 +1,15 @@ # The Goldbach conjecture ```agda -module elementary-number-theory.goldbach-conjecture where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.goldbach-conjecture + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,13 +17,13 @@ module elementary-number-theory.goldbach-conjecture where ```agda open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.parity-natural-numbers -open import elementary-number-theory.prime-numbers -open import elementary-number-theory.strict-inequality-natural-numbers +open import elementary-number-theory.parity-natural-numbers funext univalence truncations +open import elementary-number-theory.prime-numbers funext univalence truncations +open import elementary-number-theory.strict-inequality-natural-numbers funext univalence truncations -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/greatest-common-divisor-integers.lagda.md b/src/elementary-number-theory/greatest-common-divisor-integers.lagda.md index fc8abf413d..c03e9542b2 100644 --- a/src/elementary-number-theory/greatest-common-divisor-integers.lagda.md +++ b/src/elementary-number-theory/greatest-common-divisor-integers.lagda.md @@ -1,32 +1,40 @@ # The greatest common divisor of integers ```agda -module elementary-number-theory.greatest-common-divisor-integers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.greatest-common-divisor-integers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.absolute-value-integers +open import elementary-number-theory.absolute-value-integers funext univalence truncations open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.divisibility-integers -open import elementary-number-theory.equality-integers -open import elementary-number-theory.greatest-common-divisor-natural-numbers +open import elementary-number-theory.divisibility-integers funext univalence truncations +open import elementary-number-theory.equality-integers funext univalence truncations +open import elementary-number-theory.greatest-common-divisor-natural-numbers funext univalence truncations open import elementary-number-theory.integers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.nonnegative-integers -open import elementary-number-theory.positive-and-negative-integers -open import elementary-number-theory.positive-integers +open import elementary-number-theory.nonnegative-integers funext univalence truncations +open import elementary-number-theory.positive-and-negative-integers funext univalence truncations +open import elementary-number-theory.positive-integers funext univalence truncations open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types -open import foundation.coproduct-types +open import foundation.cartesian-product-types funext univalence +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.function-types -open import foundation.functoriality-cartesian-product-types -open import foundation.identity-types -open import foundation.logical-equivalences +open import foundation.empty-types funext univalence truncations +open import foundation.function-types funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext open import foundation.transport-along-identifications open import foundation.unit-type open import foundation.universe-levels diff --git a/src/elementary-number-theory/greatest-common-divisor-natural-numbers.lagda.md b/src/elementary-number-theory/greatest-common-divisor-natural-numbers.lagda.md index 13347d69ac..743d732bd7 100644 --- a/src/elementary-number-theory/greatest-common-divisor-natural-numbers.lagda.md +++ b/src/elementary-number-theory/greatest-common-divisor-natural-numbers.lagda.md @@ -1,35 +1,43 @@ # The greatest common divisor of natural numbers ```agda -module elementary-number-theory.greatest-common-divisor-natural-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.greatest-common-divisor-natural-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.decidable-types -open import elementary-number-theory.distance-natural-numbers -open import elementary-number-theory.divisibility-natural-numbers -open import elementary-number-theory.equality-natural-numbers -open import elementary-number-theory.euclidean-division-natural-numbers -open import elementary-number-theory.inequality-natural-numbers -open import elementary-number-theory.lower-bounds-natural-numbers -open import elementary-number-theory.modular-arithmetic-standard-finite-types +open import elementary-number-theory.decidable-types funext univalence truncations +open import elementary-number-theory.distance-natural-numbers funext univalence truncations +open import elementary-number-theory.divisibility-natural-numbers funext univalence truncations +open import elementary-number-theory.equality-natural-numbers funext univalence truncations +open import elementary-number-theory.euclidean-division-natural-numbers funext univalence truncations +open import elementary-number-theory.inequality-natural-numbers funext univalence truncations +open import elementary-number-theory.lower-bounds-natural-numbers funext univalence truncations +open import elementary-number-theory.modular-arithmetic-standard-finite-types funext univalence truncations open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.strict-inequality-natural-numbers -open import elementary-number-theory.well-ordering-principle-natural-numbers +open import elementary-number-theory.strict-inequality-natural-numbers funext univalence truncations +open import elementary-number-theory.well-ordering-principle-natural-numbers funext univalence truncations open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types -open import foundation.coproduct-types -open import foundation.decidable-types +open import foundation.cartesian-product-types funext univalence +open import foundation.coproduct-types funext univalence truncations +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.functoriality-cartesian-product-types -open import foundation.identity-types -open import foundation.logical-equivalences +open import foundation.empty-types funext univalence truncations +open import foundation.functoriality-cartesian-product-types funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext open import foundation.transport-along-identifications open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/group-of-integers.lagda.md b/src/elementary-number-theory/group-of-integers.lagda.md index 358f281d2d..792856645b 100644 --- a/src/elementary-number-theory/group-of-integers.lagda.md +++ b/src/elementary-number-theory/group-of-integers.lagda.md @@ -1,21 +1,32 @@ # The group of integers ```agda -module elementary-number-theory.group-of-integers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.group-of-integers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.addition-integers +open import elementary-number-theory.addition-integers funext univalence truncations +open import elementary-number-theory.equality-integers funext univalence truncations open import elementary-number-theory.integers open import foundation.dependent-pair-types open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.groups -open import group-theory.semigroups +open import group-theory.abelian-groups funext univalence truncations +open import group-theory.groups funext univalence truncations +open import group-theory.semigroups funext univalence + +open import structured-types.types-equipped-with-endomorphisms funext univalence ```
@@ -28,6 +39,10 @@ forms a group. ## Definition ```agda +ℤ-Type-With-Endomorphism : Type-With-Endomorphism lzero +pr1 ℤ-Type-With-Endomorphism = ℤ +pr2 ℤ-Type-With-Endomorphism = succ-ℤ + ℤ-Semigroup : Semigroup lzero pr1 ℤ-Semigroup = ℤ-Set pr1 (pr2 ℤ-Semigroup) = add-ℤ diff --git a/src/elementary-number-theory/half-integers.lagda.md b/src/elementary-number-theory/half-integers.lagda.md index b62b4ae496..169c2d2d5a 100644 --- a/src/elementary-number-theory/half-integers.lagda.md +++ b/src/elementary-number-theory/half-integers.lagda.md @@ -1,16 +1,24 @@ # The half-integers ```agda -module elementary-number-theory.half-integers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.half-integers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.addition-integers +open import elementary-number-theory.addition-integers funext univalence truncations open import elementary-number-theory.integers -open import foundation.coproduct-types +open import foundation.coproduct-types funext univalence truncations open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/hardy-ramanujan-number.lagda.md b/src/elementary-number-theory/hardy-ramanujan-number.lagda.md index 9ecffa68bf..67f0e32ec4 100644 --- a/src/elementary-number-theory/hardy-ramanujan-number.lagda.md +++ b/src/elementary-number-theory/hardy-ramanujan-number.lagda.md @@ -1,17 +1,25 @@ # The Hardy-Ramanujan number ```agda -module elementary-number-theory.hardy-ramanujan-number where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.hardy-ramanujan-number + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import elementary-number-theory.natural-numbers -open import elementary-number-theory.taxicab-numbers +open import elementary-number-theory.taxicab-numbers funext univalence truncations open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.unit-type ``` diff --git a/src/elementary-number-theory/inclusion-natural-numbers-conatural-numbers.lagda.md b/src/elementary-number-theory/inclusion-natural-numbers-conatural-numbers.lagda.md index ea3f148c51..2f9fb1823e 100644 --- a/src/elementary-number-theory/inclusion-natural-numbers-conatural-numbers.lagda.md +++ b/src/elementary-number-theory/inclusion-natural-numbers-conatural-numbers.lagda.md @@ -2,23 +2,30 @@ ```agda {-# OPTIONS --guardedness #-} - -module elementary-number-theory.inclusion-natural-numbers-conatural-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.inclusion-natural-numbers-conatural-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.conatural-numbers -open import elementary-number-theory.infinite-conatural-numbers +open import elementary-number-theory.conatural-numbers funext univalence truncations +open import elementary-number-theory.infinite-conatural-numbers funext univalence truncations open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.existential-quantification -open import foundation.injective-maps -open import foundation.negated-equality -open import foundation.negation -open import foundation.surjective-maps +open import foundation.existential-quantification funext univalence truncations +open import foundation.injective-maps funext +open import foundation.negated-equality funext univalence truncations +open import foundation.negation funext +open import foundation.surjective-maps funext univalence truncations open import foundation-core.empty-types open import foundation-core.identity-types diff --git a/src/elementary-number-theory/inequality-conatural-numbers.lagda.md b/src/elementary-number-theory/inequality-conatural-numbers.lagda.md index a3aa5e7a0f..12933948af 100644 --- a/src/elementary-number-theory/inequality-conatural-numbers.lagda.md +++ b/src/elementary-number-theory/inequality-conatural-numbers.lagda.md @@ -2,33 +2,42 @@ ```agda {-# OPTIONS --guardedness #-} +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom -module elementary-number-theory.inequality-conatural-numbers where +module elementary-number-theory.inequality-conatural-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.conatural-numbers +open import elementary-number-theory.conatural-numbers funext univalence truncations open import foundation.action-on-identifications-functions -open import foundation.binary-relations -open import foundation.cartesian-product-types -open import foundation.coproduct-types -open import foundation.decidable-types +open import foundation.binary-relations funext univalence truncations +open import foundation.cartesian-product-types funext univalence +open import foundation.coproduct-types funext univalence truncations +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.function-types -open import foundation.functoriality-coproduct-types -open import foundation.identity-types -open import foundation.maybe -open import foundation.negation -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.empty-types funext univalence truncations +open import foundation.function-types funext +open import foundation.functoriality-coproduct-types funext univalence truncations +open import foundation.identity-types funext +open import foundation.negation funext +open import foundation.propositions funext univalence open import foundation.unit-type open import foundation.universe-levels -open import order-theory.posets -open import order-theory.preorders +open import foundation-core.maybe + +open import order-theory.posets funext univalence truncations +open import order-theory.preorders funext univalence truncations ```
diff --git a/src/elementary-number-theory/inequality-integer-fractions.lagda.md b/src/elementary-number-theory/inequality-integer-fractions.lagda.md index e87b85c1c3..2964c21c09 100644 --- a/src/elementary-number-theory/inequality-integer-fractions.lagda.md +++ b/src/elementary-number-theory/inequality-integer-fractions.lagda.md @@ -1,37 +1,46 @@ # Inequality on integer fractions ```agda -module elementary-number-theory.inequality-integer-fractions where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.inequality-integer-fractions + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.addition-integer-fractions -open import elementary-number-theory.addition-integers -open import elementary-number-theory.addition-positive-and-negative-integers -open import elementary-number-theory.cross-multiplication-difference-integer-fractions -open import elementary-number-theory.difference-integers -open import elementary-number-theory.inequality-integers -open import elementary-number-theory.integer-fractions +open import elementary-number-theory.addition-integer-fractions funext univalence truncations +open import elementary-number-theory.addition-integers funext univalence truncations +open import elementary-number-theory.addition-positive-and-negative-integers funext univalence truncations +open import elementary-number-theory.cross-multiplication-difference-integer-fractions funext univalence truncations +open import elementary-number-theory.difference-integers funext univalence truncations +open import elementary-number-theory.inequality-integers funext univalence truncations +open import elementary-number-theory.integer-fractions funext univalence truncations open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-integers -open import elementary-number-theory.multiplication-positive-and-negative-integers -open import elementary-number-theory.nonnegative-integers -open import elementary-number-theory.nonpositive-integers -open import elementary-number-theory.positive-and-negative-integers -open import elementary-number-theory.positive-integers -open import elementary-number-theory.strict-inequality-integers +open import elementary-number-theory.multiplication-integers funext univalence truncations +open import elementary-number-theory.multiplication-positive-and-negative-integers funext univalence truncations +open import elementary-number-theory.nonnegative-integers funext univalence truncations +open import elementary-number-theory.nonpositive-integers funext univalence truncations +open import elementary-number-theory.positive-and-negative-integers funext univalence truncations +open import elementary-number-theory.positive-integers funext univalence truncations +open import elementary-number-theory.strict-inequality-integers funext univalence truncations open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types -open import foundation.coproduct-types -open import foundation.decidable-propositions +open import foundation.cartesian-product-types funext univalence +open import foundation.coproduct-types funext univalence truncations +open import foundation.decidable-propositions funext univalence truncations open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.identity-types -open import foundation.negation -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.negation funext +open import foundation.propositions funext univalence open import foundation.transport-along-identifications open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/inequality-integers.lagda.md b/src/elementary-number-theory/inequality-integers.lagda.md index 1e9c9063f6..1def4fe255 100644 --- a/src/elementary-number-theory/inequality-integers.lagda.md +++ b/src/elementary-number-theory/inequality-integers.lagda.md @@ -1,40 +1,49 @@ # Inequality on the integers ```agda -module elementary-number-theory.inequality-integers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.inequality-integers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.addition-integers -open import elementary-number-theory.addition-positive-and-negative-integers -open import elementary-number-theory.difference-integers -open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.addition-integers funext univalence truncations +open import elementary-number-theory.addition-positive-and-negative-integers funext univalence truncations +open import elementary-number-theory.difference-integers funext univalence truncations +open import elementary-number-theory.inequality-natural-numbers funext univalence truncations open import elementary-number-theory.integers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.negative-integers -open import elementary-number-theory.nonnegative-integers -open import elementary-number-theory.nonpositive-integers -open import elementary-number-theory.positive-and-negative-integers -open import elementary-number-theory.positive-integers +open import elementary-number-theory.negative-integers funext univalence truncations +open import elementary-number-theory.nonnegative-integers funext univalence truncations +open import elementary-number-theory.nonpositive-integers funext univalence truncations +open import elementary-number-theory.positive-and-negative-integers funext univalence truncations +open import elementary-number-theory.positive-integers funext univalence truncations open import foundation.action-on-identifications-functions -open import foundation.coproduct-types -open import foundation.decidable-propositions +open import foundation.coproduct-types funext univalence truncations +open import foundation.decidable-propositions funext univalence truncations open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.functoriality-coproduct-types -open import foundation.identity-types -open import foundation.negated-equality -open import foundation.negation -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.function-types funext +open import foundation.functoriality-coproduct-types funext univalence truncations +open import foundation.identity-types funext +open import foundation.negated-equality funext univalence truncations +open import foundation.negation funext +open import foundation.propositions funext univalence open import foundation.transport-along-identifications open import foundation.unit-type open import foundation.universe-levels -open import order-theory.posets -open import order-theory.preorders +open import order-theory.posets funext univalence truncations +open import order-theory.preorders funext univalence truncations ```
diff --git a/src/elementary-number-theory/inequality-natural-numbers.lagda.md b/src/elementary-number-theory/inequality-natural-numbers.lagda.md index a31c50691d..582c0a094f 100644 --- a/src/elementary-number-theory/inequality-natural-numbers.lagda.md +++ b/src/elementary-number-theory/inequality-natural-numbers.lagda.md @@ -1,35 +1,44 @@ # Inequality of natural numbers ```agda -module elementary-number-theory.inequality-natural-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.inequality-natural-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.precategories +open import category-theory.precategories funext univalence truncations open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.binary-relations -open import foundation.cartesian-product-types -open import foundation.coproduct-types -open import foundation.decidable-types +open import foundation.binary-relations funext univalence truncations +open import foundation.cartesian-product-types funext univalence +open import foundation.coproduct-types funext univalence truncations +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.function-types -open import foundation.functoriality-coproduct-types -open import foundation.identity-types -open import foundation.negation -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.empty-types funext univalence truncations +open import foundation.function-types funext +open import foundation.functoriality-coproduct-types funext univalence truncations +open import foundation.identity-types funext +open import foundation.negation funext +open import foundation.propositions funext univalence open import foundation.unit-type open import foundation.universe-levels -open import order-theory.posets -open import order-theory.preorders +open import order-theory.posets funext univalence truncations +open import order-theory.preorders funext univalence truncations ```
diff --git a/src/elementary-number-theory/inequality-rational-numbers.lagda.md b/src/elementary-number-theory/inequality-rational-numbers.lagda.md index e602ea684a..268ecbe2f3 100644 --- a/src/elementary-number-theory/inequality-rational-numbers.lagda.md +++ b/src/elementary-number-theory/inequality-rational-numbers.lagda.md @@ -2,51 +2,54 @@ ```agda {-# OPTIONS --lossy-unification #-} - -module elementary-number-theory.inequality-rational-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.inequality-rational-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.addition-integer-fractions -open import elementary-number-theory.addition-rational-numbers -open import elementary-number-theory.additive-group-of-rational-numbers -open import elementary-number-theory.cross-multiplication-difference-integer-fractions -open import elementary-number-theory.difference-integers -open import elementary-number-theory.difference-rational-numbers -open import elementary-number-theory.inequality-integer-fractions -open import elementary-number-theory.inequality-integers -open import elementary-number-theory.integer-fractions -open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-integers -open import elementary-number-theory.nonnegative-integers -open import elementary-number-theory.nonpositive-integers -open import elementary-number-theory.positive-and-negative-integers -open import elementary-number-theory.positive-integers -open import elementary-number-theory.rational-numbers -open import elementary-number-theory.reduced-integer-fractions +open import elementary-number-theory.addition-integer-fractions funext univalence truncations +open import elementary-number-theory.addition-rational-numbers funext univalence truncations +open import elementary-number-theory.additive-group-of-rational-numbers funext univalence truncations +open import elementary-number-theory.cross-multiplication-difference-integer-fractions funext univalence truncations +open import elementary-number-theory.difference-integers funext univalence truncations +open import elementary-number-theory.difference-rational-numbers funext univalence truncations +open import elementary-number-theory.inequality-integer-fractions funext univalence truncations +open import elementary-number-theory.inequality-integers funext univalence truncations +open import elementary-number-theory.integer-fractions funext univalence truncations +open import elementary-number-theory.multiplication-integers funext univalence truncations +open import elementary-number-theory.nonnegative-integers funext univalence truncations +open import elementary-number-theory.positive-and-negative-integers funext univalence truncations +open import elementary-number-theory.rational-numbers funext univalence truncations +open import elementary-number-theory.reduced-integer-fractions funext univalence truncations open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types -open import foundation.conjunction -open import foundation.coproduct-types -open import foundation.decidable-propositions +open import foundation.coproduct-types funext univalence truncations +open import foundation.decidable-propositions funext univalence truncations open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.functoriality-coproduct-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.negation -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.function-types funext +open import foundation.functoriality-coproduct-types funext univalence truncations +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.negation funext +open import foundation.propositions funext univalence open import foundation.transport-along-identifications open import foundation.universe-levels -open import order-theory.order-preserving-maps-posets -open import order-theory.posets -open import order-theory.preorders -open import order-theory.transposition-inequalities-along-order-preserving-retractions-posets -open import order-theory.transposition-inequalities-along-sections-of-order-preserving-maps-posets +open import order-theory.order-preserving-maps-posets funext univalence truncations +open import order-theory.posets funext univalence truncations +open import order-theory.preorders funext univalence truncations +open import order-theory.transposition-inequalities-along-order-preserving-retractions-posets funext univalence truncations +open import order-theory.transposition-inequalities-along-sections-of-order-preserving-maps-posets funext univalence truncations ```
diff --git a/src/elementary-number-theory/inequality-standard-finite-types.lagda.md b/src/elementary-number-theory/inequality-standard-finite-types.lagda.md index d21985ad6f..4214d51f8b 100644 --- a/src/elementary-number-theory/inequality-standard-finite-types.lagda.md +++ b/src/elementary-number-theory/inequality-standard-finite-types.lagda.md @@ -1,32 +1,41 @@ # Inequality on the standard finite types ```agda -module elementary-number-theory.inequality-standard-finite-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.inequality-standard-finite-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.inequality-natural-numbers funext univalence truncations open import elementary-number-theory.natural-numbers -open import elementary-number-theory.strict-inequality-natural-numbers +open import elementary-number-theory.strict-inequality-natural-numbers funext univalence truncations open import foundation.action-on-identifications-functions -open import foundation.binary-relations -open import foundation.coproduct-types -open import foundation.decidable-propositions -open import foundation.decidable-types +open import foundation.binary-relations funext univalence truncations +open import foundation.coproduct-types funext univalence truncations +open import foundation.decidable-propositions funext univalence truncations +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.identity-types -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.empty-types funext univalence truncations +open import foundation.identity-types funext +open import foundation.propositions funext univalence open import foundation.unit-type open import foundation.universe-levels -open import order-theory.posets -open import order-theory.preorders +open import order-theory.posets funext univalence truncations +open import order-theory.preorders funext univalence truncations -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/elementary-number-theory/infinite-conatural-numbers.lagda.md b/src/elementary-number-theory/infinite-conatural-numbers.lagda.md index 4b5d718a19..7769591787 100644 --- a/src/elementary-number-theory/infinite-conatural-numbers.lagda.md +++ b/src/elementary-number-theory/infinite-conatural-numbers.lagda.md @@ -2,18 +2,25 @@ ```agda {-# OPTIONS --guardedness #-} - -module elementary-number-theory.infinite-conatural-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.infinite-conatural-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.conatural-numbers -open import elementary-number-theory.equality-conatural-numbers +open import elementary-number-theory.conatural-numbers funext univalence truncations +open import elementary-number-theory.equality-conatural-numbers funext univalence truncations open import foundation.action-on-identifications-functions -open import foundation.coproduct-types +open import foundation.coproduct-types funext univalence truncations open import foundation.universe-levels open import foundation-core.identity-types diff --git a/src/elementary-number-theory/infinitude-of-primes.lagda.md b/src/elementary-number-theory/infinitude-of-primes.lagda.md index 2da5b37a90..b4a5d21a5c 100644 --- a/src/elementary-number-theory/infinitude-of-primes.lagda.md +++ b/src/elementary-number-theory/infinitude-of-primes.lagda.md @@ -1,32 +1,40 @@ # The infinitude of primes ```agda -module elementary-number-theory.infinitude-of-primes where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.infinitude-of-primes + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.divisibility-natural-numbers -open import elementary-number-theory.equality-natural-numbers -open import elementary-number-theory.factorials -open import elementary-number-theory.lower-bounds-natural-numbers +open import elementary-number-theory.divisibility-natural-numbers funext univalence truncations +open import elementary-number-theory.equality-natural-numbers funext univalence truncations +open import elementary-number-theory.factorials funext univalence truncations +open import elementary-number-theory.lower-bounds-natural-numbers funext univalence truncations open import elementary-number-theory.natural-numbers -open import elementary-number-theory.prime-numbers -open import elementary-number-theory.proper-divisors-natural-numbers -open import elementary-number-theory.sieve-of-eratosthenes -open import elementary-number-theory.strict-inequality-natural-numbers -open import elementary-number-theory.well-ordering-principle-natural-numbers - -open import foundation.cartesian-product-types -open import foundation.coproduct-types -open import foundation.decidable-types +open import elementary-number-theory.prime-numbers funext univalence truncations +open import elementary-number-theory.proper-divisors-natural-numbers funext univalence truncations +open import elementary-number-theory.sieve-of-eratosthenes funext univalence truncations +open import elementary-number-theory.strict-inequality-natural-numbers funext univalence truncations +open import elementary-number-theory.well-ordering-principle-natural-numbers funext univalence truncations + +open import foundation.cartesian-product-types funext univalence +open import foundation.coproduct-types funext univalence truncations +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.identity-types -open import foundation.iterating-functions -open import foundation.negation -open import foundation.type-arithmetic-empty-type +open import foundation.empty-types funext univalence truncations +open import foundation.identity-types funext +open import foundation.iterating-functions funext univalence truncations +open import foundation.negation funext +open import foundation.type-arithmetic-empty-type funext univalence truncations open import foundation.unit-type open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/initial-segments-natural-numbers.lagda.md b/src/elementary-number-theory/initial-segments-natural-numbers.lagda.md index 9823b2c9a1..466d44a44d 100644 --- a/src/elementary-number-theory/initial-segments-natural-numbers.lagda.md +++ b/src/elementary-number-theory/initial-segments-natural-numbers.lagda.md @@ -1,20 +1,29 @@ # Initial segments of the natural numbers ```agda -module elementary-number-theory.initial-segments-natural-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.initial-segments-natural-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.maximum-natural-numbers +open import elementary-number-theory.maximum-natural-numbers funext univalence truncations open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/integer-fractions.lagda.md b/src/elementary-number-theory/integer-fractions.lagda.md index 246ccf0e7c..8a0a15d11a 100644 --- a/src/elementary-number-theory/integer-fractions.lagda.md +++ b/src/elementary-number-theory/integer-fractions.lagda.md @@ -1,33 +1,41 @@ # Integer fractions ```agda -module elementary-number-theory.integer-fractions where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.integer-fractions + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.equality-integers -open import elementary-number-theory.greatest-common-divisor-integers +open import elementary-number-theory.equality-integers funext univalence truncations +open import elementary-number-theory.greatest-common-divisor-integers funext univalence truncations open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-integers -open import elementary-number-theory.nonzero-integers -open import elementary-number-theory.positive-and-negative-integers -open import elementary-number-theory.positive-integers +open import elementary-number-theory.multiplication-integers funext univalence truncations +open import elementary-number-theory.nonzero-integers funext univalence truncations +open import elementary-number-theory.positive-integers funext univalence truncations open import foundation.action-on-identifications-functions -open import foundation.binary-relations -open import foundation.cartesian-product-types -open import foundation.decidable-equality +open import foundation.binary-relations funext univalence truncations +open import foundation.cartesian-product-types funext univalence +open import foundation.decidable-equality funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalence-relations -open import foundation.identity-types -open import foundation.negation -open import foundation.propositions -open import foundation.sets +open import foundation.dependent-products-propositions funext +open import foundation.equivalence-relations funext univalence truncations +open import foundation.identity-types funext +open import foundation.negation funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence open import foundation.universe-levels -open import set-theory.countable-sets +open import set-theory.countable-sets funext univalence truncations ```
diff --git a/src/elementary-number-theory/integers.lagda.md b/src/elementary-number-theory/integers.lagda.md index 2c1ea175d6..6b801f4787 100644 --- a/src/elementary-number-theory/integers.lagda.md +++ b/src/elementary-number-theory/integers.lagda.md @@ -7,30 +7,26 @@ module elementary-number-theory.integers where
Imports ```agda -open import elementary-number-theory.equality-natural-numbers open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.empty-types -open import foundation.equality-coproduct-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.negated-equality -open import foundation.negation -open import foundation.propositions -open import foundation.retractions -open import foundation.sections -open import foundation.sets open import foundation.unit-type open import foundation.universe-levels -open import structured-types.types-equipped-with-endomorphisms +open import foundation-core.coproduct-types +open import foundation-core.embeddings +open import foundation-core.empty-types +open import foundation-core.equivalences +open import foundation-core.function-types +open import foundation-core.homotopies +open import foundation-core.identity-types +open import foundation-core.injective-maps +open import foundation-core.negation +open import foundation-core.propositions +open import foundation-core.retractions +open import foundation-core.sections +open import foundation-core.sets ```
@@ -136,10 +132,6 @@ pred-ℤ (inl x) = inl (succ-ℕ x) pred-ℤ (inr (inl star)) = inl zero-ℕ pred-ℤ (inr (inr zero-ℕ)) = inr (inl star) pred-ℤ (inr (inr (succ-ℕ x))) = inr (inr x) - -ℤ-Type-With-Endomorphism : Type-With-Endomorphism lzero -pr1 ℤ-Type-With-Endomorphism = ℤ -pr2 ℤ-Type-With-Endomorphism = succ-ℤ ``` ### The negative of an integer @@ -153,18 +145,6 @@ neg-ℤ (inr (inr x)) = inl x ## Properties -### The type of integers is a set - -```agda -abstract - is-set-ℤ : is-set ℤ - is-set-ℤ = is-set-coproduct is-set-ℕ (is-set-coproduct is-set-unit is-set-ℕ) - -ℤ-Set : Set lzero -pr1 ℤ-Set = ℤ -pr2 ℤ-Set = is-set-ℤ -``` - ### The successor and predecessor functions on ℤ are mutual inverses ```agda @@ -214,7 +194,7 @@ abstract is-injective-succ-ℤ {x} {y} p = inv (is-retraction-pred-ℤ x) ∙ ap pred-ℤ p ∙ is-retraction-pred-ℤ y - has-no-fixed-points-succ-ℤ : (x : ℤ) → succ-ℤ x ≠ x + has-no-fixed-points-succ-ℤ : (x : ℤ) → ¬ (succ-ℤ x ＝ x) has-no-fixed-points-succ-ℤ (inl zero-ℕ) () has-no-fixed-points-succ-ℤ (inl (succ-ℕ x)) () has-no-fixed-points-succ-ℤ (inr (inl star)) () diff --git a/src/elementary-number-theory/jacobi-symbol.lagda.md b/src/elementary-number-theory/jacobi-symbol.lagda.md index b7c291a319..8dae1ed855 100644 --- a/src/elementary-number-theory/jacobi-symbol.lagda.md +++ b/src/elementary-number-theory/jacobi-symbol.lagda.md @@ -1,22 +1,30 @@ # The Jacobi symbol ```agda -module elementary-number-theory.jacobi-symbol where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.jacobi-symbol + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.fundamental-theorem-of-arithmetic +open import elementary-number-theory.fundamental-theorem-of-arithmetic funext univalence truncations open import elementary-number-theory.integers -open import elementary-number-theory.legendre-symbol -open import elementary-number-theory.multiplication-integers +open import elementary-number-theory.legendre-symbol funext univalence truncations +open import elementary-number-theory.multiplication-integers funext univalence truncations open import elementary-number-theory.natural-numbers -open import foundation.type-arithmetic-dependent-function-types +open import foundation.type-arithmetic-dependent-function-types funext univalence open import foundation.unit-type -open import lists.functoriality-lists +open import lists.functoriality-lists funext univalence truncations open import lists.lists ``` diff --git a/src/elementary-number-theory/kolakoski-sequence.lagda.md b/src/elementary-number-theory/kolakoski-sequence.lagda.md index 602bc2597a..d508f0c1af 100644 --- a/src/elementary-number-theory/kolakoski-sequence.lagda.md +++ b/src/elementary-number-theory/kolakoski-sequence.lagda.md @@ -1,18 +1,26 @@ # The Kolakoski sequence ```agda -module elementary-number-theory.kolakoski-sequence where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.kolakoski-sequence + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.inequality-natural-numbers funext univalence truncations open import elementary-number-theory.natural-numbers -open import elementary-number-theory.strong-induction-natural-numbers +open import elementary-number-theory.strong-induction-natural-numbers funext univalence truncations -open import foundation.booleans -open import foundation.cartesian-product-types +open import foundation.booleans funext univalence truncations +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types ``` diff --git a/src/elementary-number-theory/legendre-symbol.lagda.md b/src/elementary-number-theory/legendre-symbol.lagda.md index 57f91cb937..11cc6f82f0 100644 --- a/src/elementary-number-theory/legendre-symbol.lagda.md +++ b/src/elementary-number-theory/legendre-symbol.lagda.md @@ -1,23 +1,31 @@ # The Legendre symbol ```agda -module elementary-number-theory.legendre-symbol where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.legendre-symbol + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import elementary-number-theory.integers -open import elementary-number-theory.modular-arithmetic +open import elementary-number-theory.modular-arithmetic funext univalence truncations open import elementary-number-theory.natural-numbers -open import elementary-number-theory.prime-numbers -open import elementary-number-theory.squares-modular-arithmetic +open import elementary-number-theory.prime-numbers funext univalence truncations +open import elementary-number-theory.squares-modular-arithmetic funext univalence truncations open import foundation.action-on-identifications-functions -open import foundation.coproduct-types -open import foundation.decidable-types +open import foundation.coproduct-types funext univalence truncations +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext ```
diff --git a/src/elementary-number-theory/lower-bounds-natural-numbers.lagda.md b/src/elementary-number-theory/lower-bounds-natural-numbers.lagda.md index 1a84c70750..f3c6bbb1e5 100644 --- a/src/elementary-number-theory/lower-bounds-natural-numbers.lagda.md +++ b/src/elementary-number-theory/lower-bounds-natural-numbers.lagda.md @@ -1,17 +1,26 @@ # Lower bounds of type families over the natural numbers ```agda -module elementary-number-theory.lower-bounds-natural-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.lower-bounds-natural-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.inequality-natural-numbers funext univalence truncations open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.propositions funext univalence open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/maximum-natural-numbers.lagda.md b/src/elementary-number-theory/maximum-natural-numbers.lagda.md index 97038be80f..141b43bb73 100644 --- a/src/elementary-number-theory/maximum-natural-numbers.lagda.md +++ b/src/elementary-number-theory/maximum-natural-numbers.lagda.md @@ -1,26 +1,34 @@ # Maximum on the natural numbers ```agda -module elementary-number-theory.maximum-natural-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.maximum-natural-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.inequality-natural-numbers funext univalence truncations open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.coproduct-types +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.unit-type -open import order-theory.least-upper-bounds-posets +open import order-theory.least-upper-bounds-posets funext univalence truncations -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/elementary-number-theory/maximum-rational-numbers.lagda.md b/src/elementary-number-theory/maximum-rational-numbers.lagda.md index 59124d8e82..ffab4dd225 100644 --- a/src/elementary-number-theory/maximum-rational-numbers.lagda.md +++ b/src/elementary-number-theory/maximum-rational-numbers.lagda.md @@ -1,22 +1,30 @@ # Maximum on the rational numbers ```agda -module elementary-number-theory.maximum-rational-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.maximum-rational-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.decidable-total-order-rational-numbers -open import elementary-number-theory.inequality-rational-numbers -open import elementary-number-theory.rational-numbers -open import elementary-number-theory.strict-inequality-rational-numbers +open import elementary-number-theory.decidable-total-order-rational-numbers funext univalence truncations +open import elementary-number-theory.inequality-rational-numbers funext univalence truncations +open import elementary-number-theory.rational-numbers funext univalence truncations +open import elementary-number-theory.strict-inequality-rational-numbers funext univalence truncations -open import foundation.coproduct-types -open import foundation.identity-types +open import foundation.coproduct-types funext univalence truncations +open import foundation.identity-types funext open import foundation.transport-along-identifications -open import order-theory.decidable-total-orders +open import order-theory.decidable-total-orders funext univalence truncations ```
diff --git a/src/elementary-number-theory/maximum-standard-finite-types.lagda.md b/src/elementary-number-theory/maximum-standard-finite-types.lagda.md index 160a0de610..16e2bbe2b9 100644 --- a/src/elementary-number-theory/maximum-standard-finite-types.lagda.md +++ b/src/elementary-number-theory/maximum-standard-finite-types.lagda.md @@ -1,22 +1,30 @@ # Maximum on the standard finite types ```agda -module elementary-number-theory.maximum-standard-finite-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.maximum-standard-finite-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.inequality-standard-finite-types +open import elementary-number-theory.inequality-standard-finite-types funext univalence truncations open import elementary-number-theory.natural-numbers -open import foundation.coproduct-types +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types open import foundation.unit-type -open import order-theory.least-upper-bounds-posets +open import order-theory.least-upper-bounds-posets funext univalence truncations -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/elementary-number-theory/mediant-integer-fractions.lagda.md b/src/elementary-number-theory/mediant-integer-fractions.lagda.md index 96adcb2df1..95f6d80398 100644 --- a/src/elementary-number-theory/mediant-integer-fractions.lagda.md +++ b/src/elementary-number-theory/mediant-integer-fractions.lagda.md @@ -1,21 +1,29 @@ # The mediant fraction of two integer fractions ```agda -module elementary-number-theory.mediant-integer-fractions where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.mediant-integer-fractions + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.addition-integers -open import elementary-number-theory.addition-positive-and-negative-integers -open import elementary-number-theory.cross-multiplication-difference-integer-fractions -open import elementary-number-theory.difference-integers -open import elementary-number-theory.integer-fractions -open import elementary-number-theory.multiplication-integers +open import elementary-number-theory.addition-integers funext univalence truncations +open import elementary-number-theory.addition-positive-and-negative-integers funext univalence truncations +open import elementary-number-theory.cross-multiplication-difference-integer-fractions funext univalence truncations +open import elementary-number-theory.difference-integers funext univalence truncations +open import elementary-number-theory.integer-fractions funext univalence truncations +open import elementary-number-theory.multiplication-integers funext univalence truncations open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext ```
diff --git a/src/elementary-number-theory/mersenne-primes.lagda.md b/src/elementary-number-theory/mersenne-primes.lagda.md index 072edc42fe..b97ff62735 100644 --- a/src/elementary-number-theory/mersenne-primes.lagda.md +++ b/src/elementary-number-theory/mersenne-primes.lagda.md @@ -1,20 +1,28 @@ # Mersenne primes ```agda -module elementary-number-theory.mersenne-primes where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.mersenne-primes + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.distance-natural-numbers -open import elementary-number-theory.exponentiation-natural-numbers +open import elementary-number-theory.distance-natural-numbers funext univalence truncations +open import elementary-number-theory.exponentiation-natural-numbers funext univalence truncations open import elementary-number-theory.natural-numbers -open import elementary-number-theory.prime-numbers +open import elementary-number-theory.prime-numbers funext univalence truncations -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/minimum-natural-numbers.lagda.md b/src/elementary-number-theory/minimum-natural-numbers.lagda.md index 71d9c60530..6de68483a9 100644 --- a/src/elementary-number-theory/minimum-natural-numbers.lagda.md +++ b/src/elementary-number-theory/minimum-natural-numbers.lagda.md @@ -1,26 +1,34 @@ # Minimum on the natural numbers ```agda -module elementary-number-theory.minimum-natural-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.minimum-natural-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.inequality-natural-numbers funext univalence truncations open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.coproduct-types +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.unit-type -open import order-theory.greatest-lower-bounds-posets +open import order-theory.greatest-lower-bounds-posets funext univalence truncations -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/elementary-number-theory/minimum-rational-numbers.lagda.md b/src/elementary-number-theory/minimum-rational-numbers.lagda.md index a0e9cf67da..b0c6ca4d54 100644 --- a/src/elementary-number-theory/minimum-rational-numbers.lagda.md +++ b/src/elementary-number-theory/minimum-rational-numbers.lagda.md @@ -1,22 +1,30 @@ # Minimum on the rational numbers ```agda -module elementary-number-theory.minimum-rational-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.minimum-rational-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.decidable-total-order-rational-numbers -open import elementary-number-theory.inequality-rational-numbers -open import elementary-number-theory.rational-numbers -open import elementary-number-theory.strict-inequality-rational-numbers +open import elementary-number-theory.decidable-total-order-rational-numbers funext univalence truncations +open import elementary-number-theory.inequality-rational-numbers funext univalence truncations +open import elementary-number-theory.rational-numbers funext univalence truncations +open import elementary-number-theory.strict-inequality-rational-numbers funext univalence truncations -open import foundation.coproduct-types -open import foundation.identity-types +open import foundation.coproduct-types funext univalence truncations +open import foundation.identity-types funext open import foundation.transport-along-identifications -open import order-theory.decidable-total-orders +open import order-theory.decidable-total-orders funext univalence truncations ```
diff --git a/src/elementary-number-theory/minimum-standard-finite-types.lagda.md b/src/elementary-number-theory/minimum-standard-finite-types.lagda.md index d2eef65a72..b2396e5723 100644 --- a/src/elementary-number-theory/minimum-standard-finite-types.lagda.md +++ b/src/elementary-number-theory/minimum-standard-finite-types.lagda.md @@ -1,22 +1,30 @@ # Minimum on the standard finite types ```agda -module elementary-number-theory.minimum-standard-finite-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.minimum-standard-finite-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.inequality-standard-finite-types +open import elementary-number-theory.inequality-standard-finite-types funext univalence truncations open import elementary-number-theory.natural-numbers -open import foundation.coproduct-types +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types open import foundation.unit-type -open import order-theory.greatest-lower-bounds-posets +open import order-theory.greatest-lower-bounds-posets funext univalence truncations -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/elementary-number-theory/modular-arithmetic-standard-finite-types.lagda.md b/src/elementary-number-theory/modular-arithmetic-standard-finite-types.lagda.md index e7205258f8..7693b3264d 100644 --- a/src/elementary-number-theory/modular-arithmetic-standard-finite-types.lagda.md +++ b/src/elementary-number-theory/modular-arithmetic-standard-finite-types.lagda.md @@ -1,38 +1,45 @@ # Modular arithmetic on the standard finite types ```agda -module elementary-number-theory.modular-arithmetic-standard-finite-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.modular-arithmetic-standard-finite-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.congruence-natural-numbers -open import elementary-number-theory.distance-natural-numbers -open import elementary-number-theory.divisibility-natural-numbers -open import elementary-number-theory.equality-natural-numbers -open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.congruence-natural-numbers funext univalence truncations +open import elementary-number-theory.distance-natural-numbers funext univalence truncations +open import elementary-number-theory.divisibility-natural-numbers funext univalence truncations +open import elementary-number-theory.equality-natural-numbers funext univalence truncations +open import elementary-number-theory.inequality-natural-numbers funext univalence truncations open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.coproduct-types -open import foundation.decidable-propositions -open import foundation.decidable-types +open import foundation.coproduct-types funext univalence truncations +open import foundation.decidable-propositions funext univalence truncations +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.sets +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.injective-maps funext open import foundation.split-surjective-maps -open import foundation.surjective-maps +open import foundation.surjective-maps funext univalence truncations open import foundation.universe-levels -open import univalent-combinatorics.equality-standard-finite-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.equality-standard-finite-types funext univalence truncations +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/elementary-number-theory/modular-arithmetic.lagda.md b/src/elementary-number-theory/modular-arithmetic.lagda.md index b75b74c017..880678e5fb 100644 --- a/src/elementary-number-theory/modular-arithmetic.lagda.md +++ b/src/elementary-number-theory/modular-arithmetic.lagda.md @@ -1,50 +1,58 @@ # Modular arithmetic ```agda -module elementary-number-theory.modular-arithmetic where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.modular-arithmetic + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.absolute-value-integers -open import elementary-number-theory.addition-integers -open import elementary-number-theory.congruence-integers -open import elementary-number-theory.congruence-natural-numbers -open import elementary-number-theory.divisibility-integers -open import elementary-number-theory.equality-integers -open import elementary-number-theory.inequality-integers +open import elementary-number-theory.absolute-value-integers funext univalence truncations +open import elementary-number-theory.addition-integers funext univalence truncations +open import elementary-number-theory.congruence-integers funext univalence truncations +open import elementary-number-theory.congruence-natural-numbers funext univalence truncations +open import elementary-number-theory.divisibility-integers funext univalence truncations +open import elementary-number-theory.equality-integers funext univalence truncations +open import elementary-number-theory.inequality-integers funext univalence truncations open import elementary-number-theory.integers -open import elementary-number-theory.modular-arithmetic-standard-finite-types -open import elementary-number-theory.multiplication-integers +open import elementary-number-theory.modular-arithmetic-standard-finite-types funext univalence truncations +open import elementary-number-theory.multiplication-integers funext univalence truncations open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.nonnegative-integers +open import elementary-number-theory.nonnegative-integers funext univalence truncations open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.coproduct-types -open import foundation.decidable-equality -open import foundation.decidable-types +open import foundation.coproduct-types funext univalence truncations +open import foundation.decidable-equality funext univalence truncations +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.discrete-types -open import foundation.empty-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.negated-equality -open import foundation.negation -open import foundation.sets -open import foundation.surjective-maps +open import foundation.discrete-types funext univalence truncations +open import foundation.empty-types funext univalence truncations +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.negated-equality funext univalence truncations +open import foundation.negation funext +open import foundation.sets funext univalence +open import foundation.surjective-maps funext univalence truncations open import foundation.unit-type open import foundation.universe-levels -open import structured-types.types-equipped-with-endomorphisms +open import structured-types.types-equipped-with-endomorphisms funext univalence -open import univalent-combinatorics.equality-standard-finite-types -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.equality-standard-finite-types funext univalence truncations +open import univalent-combinatorics.finite-types funext univalence truncations +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/elementary-number-theory/monoid-of-natural-numbers-with-addition.lagda.md b/src/elementary-number-theory/monoid-of-natural-numbers-with-addition.lagda.md index da4c41ed15..d37821d4ae 100644 --- a/src/elementary-number-theory/monoid-of-natural-numbers-with-addition.lagda.md +++ b/src/elementary-number-theory/monoid-of-natural-numbers-with-addition.lagda.md @@ -1,21 +1,29 @@ # The monoid of natural numbers with addition ```agda -module elementary-number-theory.monoid-of-natural-numbers-with-addition where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.monoid-of-natural-numbers-with-addition + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.equality-natural-numbers +open import elementary-number-theory.equality-natural-numbers funext univalence truncations open import foundation.dependent-pair-types open import foundation.universe-levels -open import group-theory.commutative-monoids -open import group-theory.monoids -open import group-theory.semigroups +open import group-theory.commutative-monoids funext univalence truncations +open import group-theory.monoids funext univalence truncations +open import group-theory.semigroups funext univalence ```
diff --git a/src/elementary-number-theory/monoid-of-natural-numbers-with-maximum.lagda.md b/src/elementary-number-theory/monoid-of-natural-numbers-with-maximum.lagda.md index ae0b8fe991..925cef1487 100644 --- a/src/elementary-number-theory/monoid-of-natural-numbers-with-maximum.lagda.md +++ b/src/elementary-number-theory/monoid-of-natural-numbers-with-maximum.lagda.md @@ -1,25 +1,33 @@ # The monoid of the natural numbers with maximum ```agda -module elementary-number-theory.monoid-of-natural-numbers-with-maximum where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.monoid-of-natural-numbers-with-maximum + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.equality-natural-numbers -open import elementary-number-theory.initial-segments-natural-numbers -open import elementary-number-theory.maximum-natural-numbers +open import elementary-number-theory.equality-natural-numbers funext univalence truncations +open import elementary-number-theory.initial-segments-natural-numbers funext univalence truncations +open import elementary-number-theory.maximum-natural-numbers funext univalence truncations open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types open import foundation.universe-levels -open import group-theory.commutative-monoids -open import group-theory.monoids -open import group-theory.normal-submonoids-commutative-monoids -open import group-theory.semigroups -open import group-theory.submonoids-commutative-monoids +open import group-theory.commutative-monoids funext univalence truncations +open import group-theory.monoids funext univalence truncations +open import group-theory.normal-submonoids-commutative-monoids funext univalence truncations +open import group-theory.semigroups funext univalence +open import group-theory.submonoids-commutative-monoids funext univalence truncations ```
diff --git a/src/elementary-number-theory/multiplication-integer-fractions.lagda.md b/src/elementary-number-theory/multiplication-integer-fractions.lagda.md index 33ca87b0b6..fcbf5deccd 100644 --- a/src/elementary-number-theory/multiplication-integer-fractions.lagda.md +++ b/src/elementary-number-theory/multiplication-integer-fractions.lagda.md @@ -1,23 +1,31 @@ # Multiplication on integer fractions ```agda -module elementary-number-theory.multiplication-integer-fractions where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.multiplication-integer-fractions + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.addition-integer-fractions -open import elementary-number-theory.addition-integers -open import elementary-number-theory.integer-fractions +open import elementary-number-theory.addition-integer-fractions funext univalence truncations +open import elementary-number-theory.addition-integers funext univalence truncations +open import elementary-number-theory.integer-fractions funext univalence truncations open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-integers -open import elementary-number-theory.multiplication-positive-and-negative-integers +open import elementary-number-theory.multiplication-integers funext univalence truncations +open import elementary-number-theory.multiplication-positive-and-negative-integers funext univalence truncations open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext ```
diff --git a/src/elementary-number-theory/multiplication-integers.lagda.md b/src/elementary-number-theory/multiplication-integers.lagda.md index d8c89edf3b..eaf023c903 100644 --- a/src/elementary-number-theory/multiplication-integers.lagda.md +++ b/src/elementary-number-theory/multiplication-integers.lagda.md @@ -1,37 +1,39 @@ # Multiplication of integers ```agda -module elementary-number-theory.multiplication-integers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.multiplication-integers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.addition-integers +open import elementary-number-theory.addition-integers funext univalence truncations open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.addition-positive-and-negative-integers -open import elementary-number-theory.difference-integers -open import elementary-number-theory.equality-integers -open import elementary-number-theory.inequality-integers +open import elementary-number-theory.difference-integers funext univalence truncations +open import elementary-number-theory.equality-integers funext univalence truncations open import elementary-number-theory.integers open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.nonnegative-integers -open import elementary-number-theory.nonzero-integers -open import elementary-number-theory.positive-integers +open import elementary-number-theory.nonzero-integers funext univalence truncations open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.coproduct-types -open import foundation.embeddings -open import foundation.empty-types -open import foundation.function-types -open import foundation.identity-types -open import foundation.injective-maps +open import foundation.coproduct-types funext univalence truncations +open import foundation.embeddings funext +open import foundation.empty-types funext univalence truncations +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.injective-maps funext open import foundation.interchange-law -open import foundation.sets -open import foundation.transport-along-identifications -open import foundation.type-arithmetic-empty-type +open import foundation.type-arithmetic-empty-type funext univalence truncations open import foundation.unit-type open import foundation.universe-levels ``` @@ -53,7 +55,7 @@ and derive its basic properties with respect to `succ-ℤ`, `pred-ℤ`, `neg-ℤ mul-ℤ : ℤ → ℤ → ℤ mul-ℤ (inl zero-ℕ) l = neg-ℤ l mul-ℤ (inl (succ-ℕ x)) l = (neg-ℤ l) +ℤ (mul-ℤ (inl x) l) -mul-ℤ (inr (inl star)) l = zero-ℤ +mul-ℤ (inr (inl _)) l = zero-ℤ mul-ℤ (inr (inr zero-ℕ)) l = l mul-ℤ (inr (inr (succ-ℕ x))) l = l +ℤ (mul-ℤ (inr (inr x)) l) @@ -73,13 +75,13 @@ ap-mul-ℤ p q = ap-binary mul-ℤ p q ```agda explicit-mul-ℤ : ℤ → ℤ → ℤ explicit-mul-ℤ (inl x) (inl y) = int-ℕ ((succ-ℕ x) *ℕ (succ-ℕ y)) -explicit-mul-ℤ (inl x) (inr (inl star)) = zero-ℤ +explicit-mul-ℤ (inl x) (inr (inl _)) = zero-ℤ explicit-mul-ℤ (inl x) (inr (inr y)) = neg-ℤ (int-ℕ ((succ-ℕ x) *ℕ (succ-ℕ y))) -explicit-mul-ℤ (inr (inl star)) (inl y) = zero-ℤ +explicit-mul-ℤ (inr (inl _)) (inl y) = zero-ℤ explicit-mul-ℤ (inr (inr x)) (inl y) = neg-ℤ (int-ℕ ((succ-ℕ x) *ℕ (succ-ℕ y))) -explicit-mul-ℤ (inr (inl star)) (inr (inl star)) = zero-ℤ -explicit-mul-ℤ (inr (inl star)) (inr (inr y)) = zero-ℤ -explicit-mul-ℤ (inr (inr x)) (inr (inl star)) = zero-ℤ +explicit-mul-ℤ (inr (inl _)) (inr (inl _)) = zero-ℤ +explicit-mul-ℤ (inr (inl _)) (inr (inr y)) = zero-ℤ +explicit-mul-ℤ (inr (inr x)) (inr (inl _)) = zero-ℤ explicit-mul-ℤ (inr (inr x)) (inr (inr y)) = int-ℕ ((succ-ℕ x) *ℕ (succ-ℕ y)) explicit-mul-ℤ' : ℤ → ℤ → ℤ @@ -105,7 +107,7 @@ right-zero-law-mul-ℤ : (k : ℤ) → k *ℤ zero-ℤ ＝ zero-ℤ right-zero-law-mul-ℤ (inl zero-ℕ) = refl right-zero-law-mul-ℤ (inl (succ-ℕ n)) = right-zero-law-mul-ℤ (inl n) -right-zero-law-mul-ℤ (inr (inl star)) = refl +right-zero-law-mul-ℤ (inr (inl _)) = refl right-zero-law-mul-ℤ (inr (inr zero-ℕ)) = refl right-zero-law-mul-ℤ (inr (inr (succ-ℕ n))) = right-zero-law-mul-ℤ (inr (inr n)) @@ -121,7 +123,7 @@ right-unit-law-mul-ℤ : (k : ℤ) → k *ℤ one-ℤ ＝ k right-unit-law-mul-ℤ (inl zero-ℕ) = refl right-unit-law-mul-ℤ (inl (succ-ℕ n)) = ap ((neg-one-ℤ) +ℤ_) (right-unit-law-mul-ℤ (inl n)) -right-unit-law-mul-ℤ (inr (inl star)) = refl +right-unit-law-mul-ℤ (inr (inl _)) = refl right-unit-law-mul-ℤ (inr (inr zero-ℕ)) = refl right-unit-law-mul-ℤ (inr (inr (succ-ℕ n))) = ap (one-ℤ +ℤ_) (right-unit-law-mul-ℤ (inr (inr n))) @@ -137,7 +139,7 @@ right-neg-unit-law-mul-ℤ : (k : ℤ) → k *ℤ neg-one-ℤ ＝ neg-ℤ k right-neg-unit-law-mul-ℤ (inl zero-ℕ) = refl right-neg-unit-law-mul-ℤ (inl (succ-ℕ n)) = ap (one-ℤ +ℤ_) (right-neg-unit-law-mul-ℤ (inl n)) -right-neg-unit-law-mul-ℤ (inr (inl star)) = refl +right-neg-unit-law-mul-ℤ (inr (inl _)) = refl right-neg-unit-law-mul-ℤ (inr (inr zero-ℕ)) = refl right-neg-unit-law-mul-ℤ (inr (inr (succ-ℕ n))) = ap (neg-one-ℤ +ℤ_) (right-neg-unit-law-mul-ℤ (inr (inr n))) @@ -156,7 +158,7 @@ left-successor-law-mul-ℤ (inl (succ-ℕ n)) l = ( _+ℤ ((inl n) *ℤ l)) ( inv (right-inverse-law-add-ℤ l)))) ∙ ( associative-add-ℤ l (neg-ℤ l) ((inl n) *ℤ l)) -left-successor-law-mul-ℤ (inr (inl star)) l = +left-successor-law-mul-ℤ (inr (inl _)) l = inv (right-unit-law-add-ℤ l) left-successor-law-mul-ℤ (inr (inr n)) l = refl @@ -169,7 +171,7 @@ left-successor-law-mul-ℤ' k l = left-predecessor-law-mul-ℤ : (k l : ℤ) → (pred-ℤ k) *ℤ l ＝ (neg-ℤ l) +ℤ (k *ℤ l) left-predecessor-law-mul-ℤ (inl n) l = refl -left-predecessor-law-mul-ℤ (inr (inl star)) l = +left-predecessor-law-mul-ℤ (inr (inl _)) l = ( left-neg-unit-law-mul-ℤ l) ∙ ( inv (right-unit-law-add-ℤ (neg-ℤ l))) left-predecessor-law-mul-ℤ (inr (inr zero-ℕ)) l = @@ -209,7 +211,7 @@ right-successor-law-mul-ℤ (inl (succ-ℕ n)) l = ( ( ap succ-ℤ (inv (pred-neg-ℤ l))) ∙ ( is-section-pred-ℤ (neg-ℤ l)))))))) ∙ ( associative-add-ℤ (inl (succ-ℕ n)) (neg-ℤ l) ((inl n) *ℤ l))))) -right-successor-law-mul-ℤ (inr (inl star)) l = refl +right-successor-law-mul-ℤ (inr (inl _)) l = refl right-successor-law-mul-ℤ (inr (inr zero-ℕ)) l = refl right-successor-law-mul-ℤ (inr (inr (succ-ℕ n))) l = ( left-successor-law-mul-ℤ (in-pos-ℤ n) (succ-ℤ l)) ∙ @@ -249,7 +251,7 @@ right-predecessor-law-mul-ℤ (inl (succ-ℕ n)) l = ( ( ap succ-ℤ (commutative-add-ℤ (neg-ℤ l) (in-pos-ℤ n))) ∙ ( inv (left-successor-law-add-ℤ (in-pos-ℤ n) (neg-ℤ l))))))) ∙ ( associative-add-ℤ (in-pos-ℤ (succ-ℕ n)) (neg-ℤ l) ((inl n) *ℤ l))))) -right-predecessor-law-mul-ℤ (inr (inl star)) l = refl +right-predecessor-law-mul-ℤ (inr (inl _)) l = refl right-predecessor-law-mul-ℤ (inr (inr zero-ℕ)) l = refl right-predecessor-law-mul-ℤ (inr (inr (succ-ℕ n))) l = ( left-successor-law-mul-ℤ (in-pos-ℤ n) (pred-ℤ l)) ∙ @@ -287,7 +289,7 @@ right-distributive-mul-add-ℤ (inl (succ-ℕ x)) l m = ( left-predecessor-law-mul-ℤ ((inl x) +ℤ l) m) ∙ ( ( ap ((neg-ℤ m) +ℤ_) (right-distributive-mul-add-ℤ (inl x) l m)) ∙ ( inv (associative-add-ℤ (neg-ℤ m) ((inl x) *ℤ m) (l *ℤ m)))) -right-distributive-mul-add-ℤ (inr (inl star)) l m = refl +right-distributive-mul-add-ℤ (inr (inl _)) l m = refl right-distributive-mul-add-ℤ (inr (inr zero-ℕ)) l m = left-successor-law-mul-ℤ l m right-distributive-mul-add-ℤ (inr (inr (succ-ℕ n))) l m = @@ -309,7 +311,7 @@ left-negative-law-mul-ℤ (inl (succ-ℕ n)) l = ( ( left-successor-law-mul-ℤ (neg-ℤ (inl n)) l) ∙ ( ( ap (l +ℤ_) (left-negative-law-mul-ℤ (inl n) l)) ∙ ( right-negative-law-add-ℤ l ((inl n) *ℤ l)))) -left-negative-law-mul-ℤ (inr (inl star)) l = refl +left-negative-law-mul-ℤ (inr (inl _)) l = refl left-negative-law-mul-ℤ (inr (inr zero-ℕ)) l = refl left-negative-law-mul-ℤ (inr (inr (succ-ℕ n))) l = ( left-predecessor-law-mul-ℤ (inl n) l) ∙ @@ -330,7 +332,7 @@ associative-mul-ℤ (inl (succ-ℕ n)) l m = ( ap ( _+ℤ ((inl n) *ℤ (l *ℤ m))) ( left-negative-law-mul-ℤ l m))) -associative-mul-ℤ (inr (inl star)) l m = refl +associative-mul-ℤ (inr (inl _)) l m = refl associative-mul-ℤ (inr (inr zero-ℕ)) l m = refl associative-mul-ℤ (inr (inr (succ-ℕ n))) l m = ( right-distributive-mul-add-ℤ l ((in-pos-ℤ n) *ℤ l) m) ∙ @@ -346,7 +348,7 @@ commutative-mul-ℤ (inl zero-ℕ) l = inv (right-neg-unit-law-mul-ℤ l) commutative-mul-ℤ (inl (succ-ℕ n)) l = ( ap ((neg-ℤ l) +ℤ_) (commutative-mul-ℤ (inl n) l)) ∙ ( inv (right-predecessor-law-mul-ℤ l (inl n))) -commutative-mul-ℤ (inr (inl star)) l = inv (right-zero-law-mul-ℤ l) +commutative-mul-ℤ (inr (inl _)) l = inv (right-zero-law-mul-ℤ l) commutative-mul-ℤ (inr (inr zero-ℕ)) l = inv (right-unit-law-mul-ℤ l) commutative-mul-ℤ (inr (inr (succ-ℕ n))) l = ( ap (l +ℤ_) (commutative-mul-ℤ (inr (inr n)) l)) ∙ @@ -423,9 +425,9 @@ compute-mul-ℤ (inl (succ-ℕ x)) (inl y) = ( int-ℕ (succ-ℕ y)) ( int-ℕ ((succ-ℕ x) *ℕ (succ-ℕ y))))) ∙ ( add-int-ℕ ((succ-ℕ x) *ℕ (succ-ℕ y)) (succ-ℕ y)) -compute-mul-ℤ (inl zero-ℕ) (inr (inl star)) = refl +compute-mul-ℤ (inl zero-ℕ) (inr (inl _)) = refl compute-mul-ℤ (inl zero-ℕ) (inr (inr x)) = ap inl (inv (left-unit-law-add-ℕ x)) -compute-mul-ℤ (inl (succ-ℕ x)) (inr (inl star)) = right-zero-law-mul-ℤ (inl x) +compute-mul-ℤ (inl (succ-ℕ x)) (inr (inl _)) = right-zero-law-mul-ℤ (inl x) compute-mul-ℤ (inl (succ-ℕ x)) (inr (inr y)) = ( ( ( ap ((inl y) +ℤ_) (compute-mul-ℤ (inl x) (inr (inr y)))) ∙ ( inv @@ -438,7 +440,7 @@ compute-mul-ℤ (inl (succ-ℕ x)) (inr (inr y)) = ( int-ℕ (succ-ℕ y)) ( int-ℕ ((succ-ℕ x) *ℕ (succ-ℕ y)))))) ∙ ( ap neg-ℤ (add-int-ℕ ((succ-ℕ x) *ℕ (succ-ℕ y)) (succ-ℕ y))) -compute-mul-ℤ (inr (inl star)) (inl y) = refl +compute-mul-ℤ (inr (inl _)) (inl y) = refl compute-mul-ℤ (inr (inr zero-ℕ)) (inl y) = ap inl (inv (left-unit-law-add-ℕ y)) compute-mul-ℤ (inr (inr (succ-ℕ x))) (inl y) = ( ap ((inl y) +ℤ_) (compute-mul-ℤ (inr (inr x)) (inl y))) ∙ @@ -453,10 +455,10 @@ compute-mul-ℤ (inr (inr (succ-ℕ x))) (inl y) = ( inr ∘ inr) ( left-successor-law-add-ℕ y ((x *ℕ (succ-ℕ y)) +ℕ y)))))) ∙ ( ap inl (commutative-add-ℕ y ((succ-ℕ x) *ℕ (succ-ℕ y))))) -compute-mul-ℤ (inr (inl star)) (inr (inl star)) = refl -compute-mul-ℤ (inr (inl star)) (inr (inr y)) = refl -compute-mul-ℤ (inr (inr zero-ℕ)) (inr (inl star)) = refl -compute-mul-ℤ (inr (inr (succ-ℕ x))) (inr (inl star)) = +compute-mul-ℤ (inr (inl _)) (inr (inl _)) = refl +compute-mul-ℤ (inr (inl _)) (inr (inr y)) = refl +compute-mul-ℤ (inr (inr zero-ℕ)) (inr (inl _)) = refl +compute-mul-ℤ (inr (inr (succ-ℕ x))) (inr (inl _)) = right-zero-law-mul-ℤ (inr (inr (succ-ℕ x))) compute-mul-ℤ (inr (inr zero-ℕ)) (inr (inr y)) = ap @@ -493,13 +495,13 @@ is-zero-is-zero-mul-ℤ : (x y : ℤ) → is-zero-ℤ (x *ℤ y) → (is-zero-ℤ x) + (is-zero-ℤ y) is-zero-is-zero-mul-ℤ (inl x) (inl y) H = ex-falso (Eq-eq-ℤ (inv (compute-mul-ℤ (inl x) (inl y)) ∙ H)) -is-zero-is-zero-mul-ℤ (inl x) (inr (inl star)) H = inr refl +is-zero-is-zero-mul-ℤ (inl x) (inr (inl _)) H = inr refl is-zero-is-zero-mul-ℤ (inl x) (inr (inr y)) H = ex-falso (Eq-eq-ℤ (inv (compute-mul-ℤ (inl x) (inr (inr y))) ∙ H)) -is-zero-is-zero-mul-ℤ (inr (inl star)) y H = inl refl +is-zero-is-zero-mul-ℤ (inr (inl _)) y H = inl refl is-zero-is-zero-mul-ℤ (inr (inr x)) (inl y) H = ex-falso (Eq-eq-ℤ (inv (compute-mul-ℤ (inr (inr x)) (inl y)) ∙ H)) -is-zero-is-zero-mul-ℤ (inr (inr x)) (inr (inl star)) H = inr refl +is-zero-is-zero-mul-ℤ (inr (inr x)) (inr (inl _)) H = inr refl is-zero-is-zero-mul-ℤ (inr (inr x)) (inr (inr y)) H = ex-falso (Eq-eq-ℤ (inv (compute-mul-ℤ (inr (inr x)) (inr (inr y))) ∙ H)) ``` diff --git a/src/elementary-number-theory/multiplication-lists-of-natural-numbers.lagda.md b/src/elementary-number-theory/multiplication-lists-of-natural-numbers.lagda.md index 85b452a28c..b2bb2710f2 100644 --- a/src/elementary-number-theory/multiplication-lists-of-natural-numbers.lagda.md +++ b/src/elementary-number-theory/multiplication-lists-of-natural-numbers.lagda.md @@ -1,7 +1,15 @@ # Multiplication of the elements of a list of natural numbers ```agda -module elementary-number-theory.multiplication-lists-of-natural-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.multiplication-lists-of-natural-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -11,14 +19,14 @@ open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import finite-group-theory.permutations-standard-finite-types +open import finite-group-theory.permutations-standard-finite-types funext univalence truncations open import foundation.action-on-identifications-functions -open import foundation.identity-types +open import foundation.identity-types funext -open import lists.concatenation-lists +open import lists.concatenation-lists funext univalence truncations open import lists.lists -open import lists.permutation-lists +open import lists.permutation-lists funext univalence truncations ```
diff --git a/src/elementary-number-theory/multiplication-natural-numbers.lagda.md b/src/elementary-number-theory/multiplication-natural-numbers.lagda.md index c4d6dd3e5f..c6b37aa41d 100644 --- a/src/elementary-number-theory/multiplication-natural-numbers.lagda.md +++ b/src/elementary-number-theory/multiplication-natural-numbers.lagda.md @@ -8,19 +8,17 @@ module elementary-number-theory.multiplication-natural-numbers where ```agda open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.equality-natural-numbers open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.identity-types -open import foundation.injective-maps open import foundation.interchange-law -open import foundation.negated-equality -open import foundation.sets + +open import foundation-core.coproduct-types +open import foundation-core.identity-types +open import foundation-core.injective-maps +open import foundation-core.negation ```
@@ -194,14 +192,6 @@ is-injective-left-mul-ℕ k H p with is-successor-is-nonzero-ℕ H ... | pair l refl = is-injective-left-mul-succ-ℕ l p -is-emb-left-mul-ℕ : (x : ℕ) → is-nonzero-ℕ x → is-emb (x *ℕ_) -is-emb-left-mul-ℕ x H = - is-emb-is-injective is-set-ℕ (is-injective-left-mul-ℕ x H) - -is-emb-right-mul-ℕ : (x : ℕ) → is-nonzero-ℕ x → is-emb (_*ℕ x) -is-emb-right-mul-ℕ x H = - is-emb-is-injective is-set-ℕ (is-injective-right-mul-ℕ x H) - is-nonzero-mul-ℕ : (x y : ℕ) → is-nonzero-ℕ x → is-nonzero-ℕ y → is-nonzero-ℕ (x *ℕ y) is-nonzero-mul-ℕ x y H K p = @@ -251,7 +241,7 @@ is-one-mul-ℕ : is-one-mul-ℕ .1 .1 refl refl = refl neq-mul-ℕ : - (m n : ℕ) → succ-ℕ m ≠ (succ-ℕ m *ℕ (succ-ℕ (succ-ℕ n))) + (m n : ℕ) → ¬ (succ-ℕ m ＝ succ-ℕ m *ℕ (succ-ℕ (succ-ℕ n))) neq-mul-ℕ m n p = neq-add-ℕ ( succ-ℕ m) diff --git a/src/elementary-number-theory/multiplication-positive-and-negative-integers.lagda.md b/src/elementary-number-theory/multiplication-positive-and-negative-integers.lagda.md index a8c0e801c0..cd94cfe79f 100644 --- a/src/elementary-number-theory/multiplication-positive-and-negative-integers.lagda.md +++ b/src/elementary-number-theory/multiplication-positive-and-negative-integers.lagda.md @@ -1,28 +1,36 @@ # Multiplication of positive, negative, nonnegative and nonpositive integers ```agda -module elementary-number-theory.multiplication-positive-and-negative-integers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.multiplication-positive-and-negative-integers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.addition-positive-and-negative-integers -open import elementary-number-theory.inequality-integers +open import elementary-number-theory.addition-positive-and-negative-integers funext univalence truncations +open import elementary-number-theory.inequality-integers funext univalence truncations open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-integers +open import elementary-number-theory.multiplication-integers funext univalence truncations open import elementary-number-theory.natural-numbers -open import elementary-number-theory.negative-integers -open import elementary-number-theory.nonnegative-integers -open import elementary-number-theory.nonpositive-integers -open import elementary-number-theory.positive-and-negative-integers -open import elementary-number-theory.positive-integers -open import elementary-number-theory.strict-inequality-integers - -open import foundation.coproduct-types +open import elementary-number-theory.negative-integers funext univalence truncations +open import elementary-number-theory.nonnegative-integers funext univalence truncations +open import elementary-number-theory.nonpositive-integers funext univalence truncations +open import elementary-number-theory.positive-and-negative-integers funext univalence truncations +open import elementary-number-theory.positive-integers funext univalence truncations +open import elementary-number-theory.strict-inequality-integers funext univalence truncations + +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.identity-types +open import foundation.empty-types funext univalence truncations +open import foundation.identity-types funext open import foundation.unit-type ``` diff --git a/src/elementary-number-theory/multiplication-rational-numbers.lagda.md b/src/elementary-number-theory/multiplication-rational-numbers.lagda.md index 367d83d9a5..04fb50ab6f 100644 --- a/src/elementary-number-theory/multiplication-rational-numbers.lagda.md +++ b/src/elementary-number-theory/multiplication-rational-numbers.lagda.md @@ -2,29 +2,36 @@ ```agda {-# OPTIONS --lossy-unification #-} - -module elementary-number-theory.multiplication-rational-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.multiplication-rational-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.addition-integer-fractions -open import elementary-number-theory.addition-rational-numbers -open import elementary-number-theory.difference-rational-numbers -open import elementary-number-theory.greatest-common-divisor-integers -open import elementary-number-theory.integer-fractions +open import elementary-number-theory.addition-integer-fractions funext univalence truncations +open import elementary-number-theory.addition-rational-numbers funext univalence truncations +open import elementary-number-theory.difference-rational-numbers funext univalence truncations +open import elementary-number-theory.greatest-common-divisor-integers funext univalence truncations +open import elementary-number-theory.integer-fractions funext univalence truncations open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-integer-fractions -open import elementary-number-theory.multiplication-integers -open import elementary-number-theory.rational-numbers -open import elementary-number-theory.reduced-integer-fractions +open import elementary-number-theory.multiplication-integer-fractions funext univalence truncations +open import elementary-number-theory.multiplication-integers funext univalence truncations +open import elementary-number-theory.rational-numbers funext univalence truncations +open import elementary-number-theory.reduced-integer-fractions funext univalence truncations open import foundation.action-on-identifications-functions -open import foundation.coproduct-types +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.identity-types +open import foundation.function-types funext +open import foundation.identity-types funext open import foundation.interchange-law ``` diff --git a/src/elementary-number-theory/multiplicative-group-of-positive-rational-numbers.lagda.md b/src/elementary-number-theory/multiplicative-group-of-positive-rational-numbers.lagda.md index 5c6d0553be..b1008008eb 100644 --- a/src/elementary-number-theory/multiplicative-group-of-positive-rational-numbers.lagda.md +++ b/src/elementary-number-theory/multiplicative-group-of-positive-rational-numbers.lagda.md @@ -2,27 +2,34 @@ ```agda {-# OPTIONS --lossy-unification #-} - -module elementary-number-theory.multiplicative-group-of-positive-rational-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.multiplicative-group-of-positive-rational-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.multiplication-rational-numbers -open import elementary-number-theory.multiplicative-monoid-of-rational-numbers -open import elementary-number-theory.positive-rational-numbers -open import elementary-number-theory.rational-numbers +open import elementary-number-theory.multiplication-rational-numbers funext univalence truncations +open import elementary-number-theory.multiplicative-monoid-of-rational-numbers funext univalence truncations +open import elementary-number-theory.positive-rational-numbers funext univalence truncations +open import elementary-number-theory.rational-numbers funext univalence truncations -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.groups -open import group-theory.monoids -open import group-theory.submonoids +open import group-theory.abelian-groups funext univalence truncations +open import group-theory.groups funext univalence truncations +open import group-theory.monoids funext univalence truncations +open import group-theory.submonoids funext univalence truncations ```
diff --git a/src/elementary-number-theory/multiplicative-group-of-rational-numbers.lagda.md b/src/elementary-number-theory/multiplicative-group-of-rational-numbers.lagda.md index 9fd3c96f59..9af9ffb22e 100644 --- a/src/elementary-number-theory/multiplicative-group-of-rational-numbers.lagda.md +++ b/src/elementary-number-theory/multiplicative-group-of-rational-numbers.lagda.md @@ -2,34 +2,41 @@ ```agda {-# OPTIONS --lossy-unification #-} - -module elementary-number-theory.multiplicative-group-of-rational-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.multiplicative-group-of-rational-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.multiplicative-monoid-of-rational-numbers -open import elementary-number-theory.nonzero-rational-numbers -open import elementary-number-theory.positive-rational-numbers -open import elementary-number-theory.rational-numbers -open import elementary-number-theory.ring-of-rational-numbers +open import elementary-number-theory.multiplicative-monoid-of-rational-numbers funext univalence truncations +open import elementary-number-theory.nonzero-rational-numbers funext univalence truncations +open import elementary-number-theory.positive-rational-numbers funext univalence truncations +open import elementary-number-theory.rational-numbers funext univalence truncations +open import elementary-number-theory.ring-of-rational-numbers funext univalence truncations -open import foundation.coproduct-types +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.identity-types -open import foundation.subtypes +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.cores-monoids -open import group-theory.groups -open import group-theory.submonoids-commutative-monoids +open import group-theory.abelian-groups funext univalence truncations +open import group-theory.cores-monoids funext univalence truncations +open import group-theory.groups funext univalence truncations +open import group-theory.submonoids-commutative-monoids funext univalence truncations -open import ring-theory.groups-of-units-rings -open import ring-theory.invertible-elements-rings -open import ring-theory.trivial-rings +open import ring-theory.groups-of-units-rings funext univalence truncations +open import ring-theory.invertible-elements-rings funext univalence truncations +open import ring-theory.trivial-rings funext univalence truncations ```
diff --git a/src/elementary-number-theory/multiplicative-inverses-positive-integer-fractions.lagda.md b/src/elementary-number-theory/multiplicative-inverses-positive-integer-fractions.lagda.md index 8f8e78a309..cfcb0fb842 100644 --- a/src/elementary-number-theory/multiplicative-inverses-positive-integer-fractions.lagda.md +++ b/src/elementary-number-theory/multiplicative-inverses-positive-integer-fractions.lagda.md @@ -1,22 +1,30 @@ # Multiplicative inverses of positive integer fractions ```agda -module elementary-number-theory.multiplicative-inverses-positive-integer-fractions where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.multiplicative-inverses-positive-integer-fractions + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.greatest-common-divisor-integers -open import elementary-number-theory.integer-fractions +open import elementary-number-theory.greatest-common-divisor-integers funext univalence truncations +open import elementary-number-theory.integer-fractions funext univalence truncations open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-integer-fractions -open import elementary-number-theory.multiplication-integers -open import elementary-number-theory.positive-integer-fractions -open import elementary-number-theory.reduced-integer-fractions +open import elementary-number-theory.multiplication-integer-fractions funext univalence truncations +open import elementary-number-theory.multiplication-integers funext univalence truncations +open import elementary-number-theory.positive-integer-fractions funext univalence truncations +open import elementary-number-theory.reduced-integer-fractions funext univalence truncations open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.transport-along-identifications ``` diff --git a/src/elementary-number-theory/multiplicative-monoid-of-natural-numbers.lagda.md b/src/elementary-number-theory/multiplicative-monoid-of-natural-numbers.lagda.md index 691a9935fd..f425afd67e 100644 --- a/src/elementary-number-theory/multiplicative-monoid-of-natural-numbers.lagda.md +++ b/src/elementary-number-theory/multiplicative-monoid-of-natural-numbers.lagda.md @@ -1,20 +1,28 @@ # The multiplicative monoid of natural numbers ```agda -module elementary-number-theory.multiplicative-monoid-of-natural-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.multiplicative-monoid-of-natural-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.equality-natural-numbers +open import elementary-number-theory.equality-natural-numbers funext univalence truncations open import elementary-number-theory.multiplication-natural-numbers open import foundation.dependent-pair-types open import foundation.universe-levels -open import group-theory.monoids -open import group-theory.semigroups +open import group-theory.monoids funext univalence truncations +open import group-theory.semigroups funext univalence ```
diff --git a/src/elementary-number-theory/multiplicative-monoid-of-rational-numbers.lagda.md b/src/elementary-number-theory/multiplicative-monoid-of-rational-numbers.lagda.md index 781ac3df4c..0210e6e177 100644 --- a/src/elementary-number-theory/multiplicative-monoid-of-rational-numbers.lagda.md +++ b/src/elementary-number-theory/multiplicative-monoid-of-rational-numbers.lagda.md @@ -2,23 +2,30 @@ ```agda {-# OPTIONS --lossy-unification #-} - -module elementary-number-theory.multiplicative-monoid-of-rational-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.multiplicative-monoid-of-rational-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.multiplication-rational-numbers -open import elementary-number-theory.rational-numbers +open import elementary-number-theory.multiplication-rational-numbers funext univalence truncations +open import elementary-number-theory.rational-numbers funext univalence truncations open import foundation.dependent-pair-types open import foundation.unital-binary-operations open import foundation.universe-levels -open import group-theory.commutative-monoids -open import group-theory.monoids -open import group-theory.semigroups +open import group-theory.commutative-monoids funext univalence truncations +open import group-theory.monoids funext univalence truncations +open import group-theory.semigroups funext univalence ```
diff --git a/src/elementary-number-theory/negative-integers.lagda.md b/src/elementary-number-theory/negative-integers.lagda.md index a549a3ae37..59431817b9 100644 --- a/src/elementary-number-theory/negative-integers.lagda.md +++ b/src/elementary-number-theory/negative-integers.lagda.md @@ -1,30 +1,40 @@ # The negative integers ```agda -module elementary-number-theory.negative-integers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.negative-integers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda +open import elementary-number-theory.equality-integers funext univalence truncations open import elementary-number-theory.integers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.nonzero-integers +open import elementary-number-theory.nonzero-integers funext univalence truncations open import foundation.action-on-identifications-functions -open import foundation.coproduct-types -open import foundation.decidable-subtypes -open import foundation.decidable-types +open import foundation.coproduct-types funext univalence truncations +open import foundation.decidable-subtypes funext univalence truncations +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.retractions -open import foundation.sections -open import foundation.sets -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.empty-types funext univalence truncations +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.retractions funext +open import foundation.sections funext +open import foundation.sets funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.transport-along-identifications open import foundation.unit-type open import foundation.universe-levels diff --git a/src/elementary-number-theory/nonnegative-integers.lagda.md b/src/elementary-number-theory/nonnegative-integers.lagda.md index 6f9d446eca..056784b9ac 100644 --- a/src/elementary-number-theory/nonnegative-integers.lagda.md +++ b/src/elementary-number-theory/nonnegative-integers.lagda.md @@ -1,29 +1,39 @@ # The nonnegative integers ```agda -module elementary-number-theory.nonnegative-integers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.nonnegative-integers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda +open import elementary-number-theory.equality-integers funext univalence truncations open import elementary-number-theory.integers open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.coproduct-types -open import foundation.decidable-subtypes -open import foundation.decidable-types +open import foundation.coproduct-types funext univalence truncations +open import foundation.decidable-subtypes funext univalence truncations +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.retractions -open import foundation.sections -open import foundation.sets -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.empty-types funext univalence truncations +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.retractions funext +open import foundation.sections funext +open import foundation.sets funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.transport-along-identifications open import foundation.unit-type open import foundation.universe-levels diff --git a/src/elementary-number-theory/nonpositive-integers.lagda.md b/src/elementary-number-theory/nonpositive-integers.lagda.md index 423216dbe2..9ca06299ee 100644 --- a/src/elementary-number-theory/nonpositive-integers.lagda.md +++ b/src/elementary-number-theory/nonpositive-integers.lagda.md @@ -1,29 +1,39 @@ # The nonpositive integers ```agda -module elementary-number-theory.nonpositive-integers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.nonpositive-integers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda +open import elementary-number-theory.equality-integers funext univalence truncations open import elementary-number-theory.integers open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.coproduct-types -open import foundation.decidable-subtypes -open import foundation.decidable-types +open import foundation.coproduct-types funext univalence truncations +open import foundation.decidable-subtypes funext univalence truncations +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.retractions -open import foundation.sections -open import foundation.sets -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.empty-types funext univalence truncations +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.retractions funext +open import foundation.sections funext +open import foundation.sets funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.transport-along-identifications open import foundation.unit-type open import foundation.universe-levels diff --git a/src/elementary-number-theory/nonzero-integers.lagda.md b/src/elementary-number-theory/nonzero-integers.lagda.md index 2d7dd2e4a9..ea58e99f8c 100644 --- a/src/elementary-number-theory/nonzero-integers.lagda.md +++ b/src/elementary-number-theory/nonzero-integers.lagda.md @@ -1,7 +1,15 @@ # Nonzero integers ```agda -module elementary-number-theory.nonzero-integers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.nonzero-integers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,12 +18,13 @@ module elementary-number-theory.nonzero-integers where open import elementary-number-theory.integers open import elementary-number-theory.natural-numbers -open import foundation.coproduct-types +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.negation -open import foundation.propositions -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.identity-types funext +open import foundation.negation funext +open import foundation.propositions funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/nonzero-natural-numbers.lagda.md b/src/elementary-number-theory/nonzero-natural-numbers.lagda.md index 9e4dc8c215..d7caa2b9b7 100644 --- a/src/elementary-number-theory/nonzero-natural-numbers.lagda.md +++ b/src/elementary-number-theory/nonzero-natural-numbers.lagda.md @@ -1,27 +1,35 @@ # Nonzero natural numbers ```agda -module elementary-number-theory.nonzero-natural-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.nonzero-natural-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.divisibility-natural-numbers -open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.divisibility-natural-numbers funext univalence truncations +open import elementary-number-theory.inequality-natural-numbers funext univalence truncations open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.strict-inequality-natural-numbers +open import elementary-number-theory.strict-inequality-natural-numbers funext univalence truncations -open import foundation.coproduct-types +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.equality-dependent-pair-types -open import foundation.identity-types -open import foundation.negated-equality -open import foundation.propositions -open import foundation.sections +open import foundation.empty-types funext univalence truncations +open import foundation.equality-dependent-pair-types funext +open import foundation.identity-types funext +open import foundation.negated-equality funext univalence truncations +open import foundation.propositions funext univalence +open import foundation.sections funext open import foundation.transport-along-identifications open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/nonzero-rational-numbers.lagda.md b/src/elementary-number-theory/nonzero-rational-numbers.lagda.md index 29defc2276..6a060e485b 100644 --- a/src/elementary-number-theory/nonzero-rational-numbers.lagda.md +++ b/src/elementary-number-theory/nonzero-rational-numbers.lagda.md @@ -2,35 +2,43 @@ ```agda {-# OPTIONS --lossy-unification #-} - -module elementary-number-theory.nonzero-rational-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.nonzero-rational-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.integer-fractions +open import elementary-number-theory.integer-fractions funext univalence truncations open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-integers -open import elementary-number-theory.multiplication-rational-numbers -open import elementary-number-theory.multiplicative-monoid-of-rational-numbers -open import elementary-number-theory.nonzero-integers -open import elementary-number-theory.rational-numbers -open import elementary-number-theory.reduced-integer-fractions +open import elementary-number-theory.multiplication-integers funext univalence truncations +open import elementary-number-theory.multiplication-rational-numbers funext univalence truncations +open import elementary-number-theory.multiplicative-monoid-of-rational-numbers funext univalence truncations +open import elementary-number-theory.nonzero-integers funext univalence truncations +open import elementary-number-theory.rational-numbers funext univalence truncations +open import elementary-number-theory.reduced-integer-fractions funext univalence truncations open import foundation.action-on-identifications-functions -open import foundation.coproduct-types +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.function-types -open import foundation.functoriality-coproduct-types -open import foundation.identity-types -open import foundation.negation -open import foundation.propositions -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.empty-types funext univalence truncations +open import foundation.function-types funext +open import foundation.functoriality-coproduct-types funext univalence truncations +open import foundation.identity-types funext +open import foundation.negation funext +open import foundation.propositions funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels -open import group-theory.submonoids +open import group-theory.submonoids funext univalence truncations ```
diff --git a/src/elementary-number-theory/ordinal-induction-natural-numbers.lagda.md b/src/elementary-number-theory/ordinal-induction-natural-numbers.lagda.md index 80761f26c3..85be391fa2 100644 --- a/src/elementary-number-theory/ordinal-induction-natural-numbers.lagda.md +++ b/src/elementary-number-theory/ordinal-induction-natural-numbers.lagda.md @@ -1,16 +1,24 @@ # The ordinal induction principle for the natural numbers ```agda -module elementary-number-theory.ordinal-induction-natural-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.ordinal-induction-natural-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import elementary-number-theory.natural-numbers -open import elementary-number-theory.strict-inequality-natural-numbers +open import elementary-number-theory.strict-inequality-natural-numbers funext univalence truncations -open import foundation.empty-types +open import foundation.empty-types funext univalence truncations open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/parity-natural-numbers.lagda.md b/src/elementary-number-theory/parity-natural-numbers.lagda.md index 78da36cfb4..3dcb4d7e37 100644 --- a/src/elementary-number-theory/parity-natural-numbers.lagda.md +++ b/src/elementary-number-theory/parity-natural-numbers.lagda.md @@ -1,25 +1,33 @@ # Parity of the natural numbers ```agda -module elementary-number-theory.parity-natural-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.parity-natural-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.divisibility-natural-numbers -open import elementary-number-theory.equality-natural-numbers -open import elementary-number-theory.modular-arithmetic-standard-finite-types +open import elementary-number-theory.divisibility-natural-numbers funext univalence truncations +open import elementary-number-theory.equality-natural-numbers funext univalence truncations +open import elementary-number-theory.modular-arithmetic-standard-finite-types funext univalence truncations open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.decidable-types +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.function-types -open import foundation.identity-types -open import foundation.negation +open import foundation.empty-types funext univalence truncations +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.negation funext open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/peano-arithmetic.lagda.md b/src/elementary-number-theory/peano-arithmetic.lagda.md index 97139b2a63..5b478c7866 100644 --- a/src/elementary-number-theory/peano-arithmetic.lagda.md +++ b/src/elementary-number-theory/peano-arithmetic.lagda.md @@ -1,7 +1,15 @@ # Peano arithmetic ```agda -module elementary-number-theory.peano-arithmetic where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.peano-arithmetic + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,11 +18,12 @@ module elementary-number-theory.peano-arithmetic where open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.negated-equality -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.negated-equality funext univalence truncations +open import foundation.propositions funext univalence open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/pisano-periods.lagda.md b/src/elementary-number-theory/pisano-periods.lagda.md index f765a59fb3..8f17b61a2c 100644 --- a/src/elementary-number-theory/pisano-periods.lagda.md +++ b/src/elementary-number-theory/pisano-periods.lagda.md @@ -1,37 +1,45 @@ # Pisano periods ```agda -module elementary-number-theory.pisano-periods where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.pisano-periods + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.divisibility-natural-numbers -open import elementary-number-theory.fibonacci-sequence -open import elementary-number-theory.inequality-natural-numbers -open import elementary-number-theory.lower-bounds-natural-numbers -open import elementary-number-theory.modular-arithmetic-standard-finite-types +open import elementary-number-theory.divisibility-natural-numbers funext univalence truncations +open import elementary-number-theory.fibonacci-sequence funext univalence truncations +open import elementary-number-theory.inequality-natural-numbers funext univalence truncations +open import elementary-number-theory.lower-bounds-natural-numbers funext univalence truncations +open import elementary-number-theory.modular-arithmetic-standard-finite-types funext univalence truncations open import elementary-number-theory.natural-numbers -open import elementary-number-theory.strict-inequality-natural-numbers -open import elementary-number-theory.well-ordering-principle-natural-numbers +open import elementary-number-theory.strict-inequality-natural-numbers funext univalence truncations +open import elementary-number-theory.well-ordering-principle-natural-numbers funext univalence truncations open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.equivalences -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.repetitions-sequences -open import foundation.sets +open import foundation.empty-types funext univalence truncations +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.repetitions-sequences funext univalence truncations +open import foundation.sets funext univalence open import foundation.universe-levels -open import univalent-combinatorics.cartesian-product-types -open import univalent-combinatorics.counting -open import univalent-combinatorics.sequences-finite-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.cartesian-product-types funext univalence truncations +open import univalent-combinatorics.counting funext univalence truncations +open import univalent-combinatorics.sequences-finite-types funext univalence truncations +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/elementary-number-theory/poset-of-natural-numbers-ordered-by-divisibility.lagda.md b/src/elementary-number-theory/poset-of-natural-numbers-ordered-by-divisibility.lagda.md index 4977a5e18b..f5e77731a2 100644 --- a/src/elementary-number-theory/poset-of-natural-numbers-ordered-by-divisibility.lagda.md +++ b/src/elementary-number-theory/poset-of-natural-numbers-ordered-by-divisibility.lagda.md @@ -9,21 +9,22 @@ module
Imports ```agda -open import elementary-number-theory.divisibility-natural-numbers -open import elementary-number-theory.equality-natural-numbers +open import elementary-number-theory.divisibility-natural-numbers funext univalence truncations +open import elementary-number-theory.equality-natural-numbers funext univalence truncations open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.identity-types -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.sets +open import foundation.dependent-products-propositions funext +open import foundation.empty-types funext univalence truncations +open import foundation.identity-types funext +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence +open import foundation.sets funext univalence open import foundation.universe-levels -open import order-theory.posets -open import order-theory.preorders +open import order-theory.posets funext univalence truncations +open import order-theory.preorders funext univalence truncations ```
diff --git a/src/elementary-number-theory/positive-and-negative-integers.lagda.md b/src/elementary-number-theory/positive-and-negative-integers.lagda.md index 844b95a8b8..55256e638f 100644 --- a/src/elementary-number-theory/positive-and-negative-integers.lagda.md +++ b/src/elementary-number-theory/positive-and-negative-integers.lagda.md @@ -1,7 +1,15 @@ # The positive, negative, nonnegative and nonpositive integers ```agda -module elementary-number-theory.positive-and-negative-integers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.positive-and-negative-integers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,20 +17,20 @@ module elementary-number-theory.positive-and-negative-integers where ```agda open import elementary-number-theory.integers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.negative-integers -open import elementary-number-theory.nonnegative-integers -open import elementary-number-theory.nonpositive-integers -open import elementary-number-theory.nonzero-integers -open import elementary-number-theory.positive-integers - -open import foundation.cartesian-product-types -open import foundation.coproduct-types +open import elementary-number-theory.negative-integers funext univalence truncations +open import elementary-number-theory.nonnegative-integers funext univalence truncations +open import elementary-number-theory.nonpositive-integers funext univalence truncations +open import elementary-number-theory.nonzero-integers funext univalence truncations +open import elementary-number-theory.positive-integers funext univalence truncations + +open import foundation.cartesian-product-types funext univalence +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.function-types -open import foundation.identity-types -open import foundation.negated-equality -open import foundation.negation +open import foundation.empty-types funext univalence truncations +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.negated-equality funext univalence truncations +open import foundation.negation funext open import foundation.unit-type ``` diff --git a/src/elementary-number-theory/positive-conatural-numbers.lagda.md b/src/elementary-number-theory/positive-conatural-numbers.lagda.md index d50eb34f27..ea924942ed 100644 --- a/src/elementary-number-theory/positive-conatural-numbers.lagda.md +++ b/src/elementary-number-theory/positive-conatural-numbers.lagda.md @@ -2,25 +2,32 @@ ```agda {-# OPTIONS --guardedness #-} - -module elementary-number-theory.positive-conatural-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.positive-conatural-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.conatural-numbers -open import elementary-number-theory.zero-conatural-numbers +open import elementary-number-theory.conatural-numbers funext univalence truncations +open import elementary-number-theory.zero-conatural-numbers funext univalence truncations -open import foundation.coproduct-types -open import foundation.decidable-types +open import foundation.coproduct-types funext univalence truncations +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.maybe -open import foundation.negation +open import foundation.negation funext open import foundation.universe-levels open import foundation-core.empty-types open import foundation-core.identity-types +open import foundation-core.maybe ```
diff --git a/src/elementary-number-theory/positive-integer-fractions.lagda.md b/src/elementary-number-theory/positive-integer-fractions.lagda.md index 7e92ff3e65..7a75b94556 100644 --- a/src/elementary-number-theory/positive-integer-fractions.lagda.md +++ b/src/elementary-number-theory/positive-integer-fractions.lagda.md @@ -1,23 +1,32 @@ # Positive integer fractions ```agda -module elementary-number-theory.positive-integer-fractions where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.positive-integer-fractions + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.addition-integer-fractions -open import elementary-number-theory.addition-positive-and-negative-integers -open import elementary-number-theory.integer-fractions +open import elementary-number-theory.addition-integer-fractions funext univalence truncations +open import elementary-number-theory.addition-positive-and-negative-integers funext univalence truncations +open import elementary-number-theory.integer-fractions funext univalence truncations open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-integer-fractions -open import elementary-number-theory.multiplication-positive-and-negative-integers -open import elementary-number-theory.positive-integers -open import elementary-number-theory.reduced-integer-fractions - -open import foundation.propositions -open import foundation.subtypes +open import elementary-number-theory.multiplication-integer-fractions funext univalence truncations +open import elementary-number-theory.multiplication-positive-and-negative-integers funext univalence truncations +open import elementary-number-theory.positive-integers funext univalence truncations +open import elementary-number-theory.reduced-integer-fractions funext univalence truncations + +open import foundation.dependent-products-propositions funext +open import foundation.propositions funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/positive-integers.lagda.md b/src/elementary-number-theory/positive-integers.lagda.md index bc942b406f..fb78f28b0a 100644 --- a/src/elementary-number-theory/positive-integers.lagda.md +++ b/src/elementary-number-theory/positive-integers.lagda.md @@ -1,38 +1,46 @@ # The positive integers ```agda -module elementary-number-theory.positive-integers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.positive-integers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda +open import elementary-number-theory.equality-integers funext univalence truncations open import elementary-number-theory.integers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.nonzero-integers -open import elementary-number-theory.nonzero-natural-numbers +open import elementary-number-theory.nonzero-integers funext univalence truncations +open import elementary-number-theory.nonzero-natural-numbers funext univalence truncations open import foundation.action-on-identifications-functions -open import foundation.coproduct-types -open import foundation.decidable-subtypes -open import foundation.decidable-types +open import foundation.coproduct-types funext univalence truncations +open import foundation.decidable-subtypes funext univalence truncations +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.equivalences -open import foundation.existential-quantification -open import foundation.function-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.retractions -open import foundation.sections -open import foundation.sets -open import foundation.subtypes -open import foundation.surjective-maps +open import foundation.dependent-products-propositions funext +open import foundation.empty-types funext univalence truncations +open import foundation.equivalences funext +open import foundation.existential-quantification funext univalence truncations +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.subtypes funext univalence truncations +open import foundation.surjective-maps funext univalence truncations open import foundation.transport-along-identifications open import foundation.unit-type open import foundation.universe-levels -open import set-theory.countable-sets +open import set-theory.countable-sets funext univalence truncations ```
diff --git a/src/elementary-number-theory/positive-rational-numbers.lagda.md b/src/elementary-number-theory/positive-rational-numbers.lagda.md index a30df38014..0e8b18f898 100644 --- a/src/elementary-number-theory/positive-rational-numbers.lagda.md +++ b/src/elementary-number-theory/positive-rational-numbers.lagda.md @@ -2,64 +2,70 @@ ```agda {-# OPTIONS --lossy-unification #-} - -module elementary-number-theory.positive-rational-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.positive-rational-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.addition-integer-fractions -open import elementary-number-theory.addition-rational-numbers -open import elementary-number-theory.additive-group-of-rational-numbers -open import elementary-number-theory.cross-multiplication-difference-integer-fractions -open import elementary-number-theory.difference-rational-numbers -open import elementary-number-theory.inequality-rational-numbers -open import elementary-number-theory.integer-fractions +open import elementary-number-theory.addition-rational-numbers funext univalence truncations +open import elementary-number-theory.additive-group-of-rational-numbers funext univalence truncations +open import elementary-number-theory.cross-multiplication-difference-integer-fractions funext univalence truncations +open import elementary-number-theory.difference-rational-numbers funext univalence truncations +open import elementary-number-theory.inequality-rational-numbers funext univalence truncations +open import elementary-number-theory.integer-fractions funext univalence truncations open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-integer-fractions -open import elementary-number-theory.multiplication-integers -open import elementary-number-theory.multiplication-positive-and-negative-integers -open import elementary-number-theory.multiplication-rational-numbers -open import elementary-number-theory.multiplicative-inverses-positive-integer-fractions -open import elementary-number-theory.multiplicative-monoid-of-rational-numbers -open import elementary-number-theory.negative-integers -open import elementary-number-theory.nonzero-natural-numbers -open import elementary-number-theory.nonzero-rational-numbers -open import elementary-number-theory.positive-and-negative-integers -open import elementary-number-theory.positive-integer-fractions -open import elementary-number-theory.positive-integers -open import elementary-number-theory.rational-numbers -open import elementary-number-theory.reduced-integer-fractions -open import elementary-number-theory.strict-inequality-integers -open import elementary-number-theory.strict-inequality-rational-numbers +open import elementary-number-theory.multiplication-integer-fractions funext univalence truncations +open import elementary-number-theory.multiplication-integers funext univalence truncations +open import elementary-number-theory.multiplication-positive-and-negative-integers funext univalence truncations +open import elementary-number-theory.multiplication-rational-numbers funext univalence truncations +open import elementary-number-theory.multiplicative-inverses-positive-integer-fractions funext univalence truncations +open import elementary-number-theory.multiplicative-monoid-of-rational-numbers funext univalence truncations +open import elementary-number-theory.negative-integers funext univalence truncations +open import elementary-number-theory.nonzero-natural-numbers funext univalence truncations +open import elementary-number-theory.nonzero-rational-numbers funext univalence truncations +open import elementary-number-theory.positive-and-negative-integers funext univalence truncations +open import elementary-number-theory.positive-integer-fractions funext univalence truncations +open import elementary-number-theory.positive-integers funext univalence truncations +open import elementary-number-theory.rational-numbers funext univalence truncations +open import elementary-number-theory.strict-inequality-integers funext univalence truncations +open import elementary-number-theory.strict-inequality-rational-numbers funext univalence truncations open import foundation.action-on-identifications-functions open import foundation.binary-transport -open import foundation.cartesian-product-types -open import foundation.coproduct-types +open import foundation.cartesian-product-types funext univalence +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.equivalences -open import foundation.existential-quantification -open import foundation.function-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.negation -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.sets -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.empty-types funext univalence truncations +open import foundation.equivalences funext +open import foundation.existential-quantification funext univalence truncations +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.negation funext +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.transport-along-identifications open import foundation.universe-levels -open import group-theory.commutative-monoids -open import group-theory.invertible-elements-monoids -open import group-theory.monoids -open import group-theory.semigroups -open import group-theory.submonoids -open import group-theory.submonoids-commutative-monoids -open import group-theory.subsemigroups +open import group-theory.commutative-monoids funext univalence truncations +open import group-theory.invertible-elements-monoids funext univalence truncations +open import group-theory.monoids funext univalence truncations +open import group-theory.semigroups funext univalence +open import group-theory.submonoids funext univalence truncations +open import group-theory.submonoids-commutative-monoids funext univalence truncations +open import group-theory.subsemigroups funext univalence truncations ```
diff --git a/src/elementary-number-theory/powers-integers.lagda.md b/src/elementary-number-theory/powers-integers.lagda.md index 05ec3f9e69..4b0e014bfa 100644 --- a/src/elementary-number-theory/powers-integers.lagda.md +++ b/src/elementary-number-theory/powers-integers.lagda.md @@ -1,20 +1,28 @@ # Powers of integers ```agda -module elementary-number-theory.powers-integers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.powers-integers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import commutative-algebra.powers-of-elements-commutative-rings +open import commutative-algebra.powers-of-elements-commutative-rings funext univalence truncations open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-integers +open import elementary-number-theory.multiplication-integers funext univalence truncations open import elementary-number-theory.natural-numbers -open import elementary-number-theory.ring-of-integers +open import elementary-number-theory.ring-of-integers funext univalence truncations -open import foundation.identity-types +open import foundation.identity-types funext ```
diff --git a/src/elementary-number-theory/powers-of-two.lagda.md b/src/elementary-number-theory/powers-of-two.lagda.md index d856d60206..eaefc96e2b 100644 --- a/src/elementary-number-theory/powers-of-two.lagda.md +++ b/src/elementary-number-theory/powers-of-two.lagda.md @@ -1,25 +1,33 @@ # Powers of two ```agda -module elementary-number-theory.powers-of-two where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.powers-of-two + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.divisibility-natural-numbers -open import elementary-number-theory.exponentiation-natural-numbers -open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.divisibility-natural-numbers funext univalence truncations +open import elementary-number-theory.exponentiation-natural-numbers funext univalence truncations +open import elementary-number-theory.inequality-natural-numbers funext univalence truncations open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.parity-natural-numbers -open import elementary-number-theory.strong-induction-natural-numbers +open import elementary-number-theory.parity-natural-numbers funext univalence truncations +open import elementary-number-theory.strong-induction-natural-numbers funext univalence truncations open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types open import foundation.equality-cartesian-product-types -open import foundation.function-types +open import foundation.function-types funext open import foundation.split-surjective-maps open import foundation.transport-along-identifications open import foundation.universe-levels diff --git a/src/elementary-number-theory/prime-numbers.lagda.md b/src/elementary-number-theory/prime-numbers.lagda.md index 930d240933..17c0da196c 100644 --- a/src/elementary-number-theory/prime-numbers.lagda.md +++ b/src/elementary-number-theory/prime-numbers.lagda.md @@ -1,34 +1,44 @@ # Prime numbers ```agda -module elementary-number-theory.prime-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.prime-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.decidable-types -open import elementary-number-theory.divisibility-natural-numbers -open import elementary-number-theory.equality-natural-numbers -open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.decidable-types funext univalence truncations +open import elementary-number-theory.divisibility-natural-numbers funext univalence truncations +open import elementary-number-theory.equality-natural-numbers funext univalence truncations +open import elementary-number-theory.inequality-natural-numbers funext univalence truncations open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.proper-divisors-natural-numbers -open import elementary-number-theory.strict-inequality-natural-numbers +open import elementary-number-theory.proper-divisors-natural-numbers funext univalence truncations +open import elementary-number-theory.strict-inequality-natural-numbers funext univalence truncations open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types -open import foundation.contractible-types -open import foundation.coproduct-types -open import foundation.decidable-types +open import foundation.cartesian-product-types funext univalence +open import foundation.contractible-types funext univalence +open import foundation.coproduct-types funext univalence truncations +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.empty-types +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.empty-types funext univalence truncations open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.negated-equality -open import foundation.propositions -open import foundation.torsorial-type-families +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.negated-equality funext univalence truncations +open import foundation.propositions funext univalence +open import foundation.torsorial-type-families funext univalence truncations open import foundation.transport-along-identifications open import foundation.unit-type open import foundation.universe-levels diff --git a/src/elementary-number-theory/products-of-natural-numbers.lagda.md b/src/elementary-number-theory/products-of-natural-numbers.lagda.md index bf853f365e..076e71c9ac 100644 --- a/src/elementary-number-theory/products-of-natural-numbers.lagda.md +++ b/src/elementary-number-theory/products-of-natural-numbers.lagda.md @@ -1,7 +1,15 @@ # Products of natural numbers ```agda -module elementary-number-theory.products-of-natural-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.products-of-natural-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,16 +17,16 @@ module elementary-number-theory.products-of-natural-numbers where ```agda open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.strict-inequality-natural-numbers +open import elementary-number-theory.strict-inequality-natural-numbers funext univalence truncations -open import foundation.coproduct-types -open import foundation.function-types -open import foundation.identity-types +open import foundation.coproduct-types funext univalence truncations +open import foundation.function-types funext +open import foundation.identity-types funext open import foundation.unit-type open import lists.lists -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/elementary-number-theory/proper-divisors-natural-numbers.lagda.md b/src/elementary-number-theory/proper-divisors-natural-numbers.lagda.md index 0f35339378..a6aa1fca10 100644 --- a/src/elementary-number-theory/proper-divisors-natural-numbers.lagda.md +++ b/src/elementary-number-theory/proper-divisors-natural-numbers.lagda.md @@ -1,29 +1,38 @@ # Proper divisors of natural numbers ```agda -module elementary-number-theory.proper-divisors-natural-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.proper-divisors-natural-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.divisibility-natural-numbers -open import elementary-number-theory.equality-natural-numbers -open import elementary-number-theory.inequality-natural-numbers -open import elementary-number-theory.modular-arithmetic-standard-finite-types +open import elementary-number-theory.divisibility-natural-numbers funext univalence truncations +open import elementary-number-theory.equality-natural-numbers funext univalence truncations +open import elementary-number-theory.inequality-natural-numbers funext univalence truncations +open import elementary-number-theory.modular-arithmetic-standard-finite-types funext univalence truncations open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.strict-inequality-natural-numbers +open import elementary-number-theory.strict-inequality-natural-numbers funext univalence truncations -open import foundation.cartesian-product-types -open import foundation.decidable-types +open import foundation.cartesian-product-types funext univalence +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.identity-types -open import foundation.negated-equality -open import foundation.negation -open import foundation.propositions -open import foundation.type-arithmetic-empty-type +open import foundation.dependent-products-propositions funext +open import foundation.empty-types funext univalence truncations +open import foundation.identity-types funext +open import foundation.negated-equality funext univalence truncations +open import foundation.negation funext +open import foundation.propositions funext univalence +open import foundation.type-arithmetic-empty-type funext univalence truncations open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/pythagorean-triples.lagda.md b/src/elementary-number-theory/pythagorean-triples.lagda.md index bc76529522..7bdd0dd2c1 100644 --- a/src/elementary-number-theory/pythagorean-triples.lagda.md +++ b/src/elementary-number-theory/pythagorean-triples.lagda.md @@ -1,7 +1,15 @@ # Pythagorean triples ```agda -module elementary-number-theory.pythagorean-triples where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.pythagorean-triples + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,9 +17,9 @@ module elementary-number-theory.pythagorean-triples where ```agda open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.squares-natural-numbers +open import elementary-number-theory.squares-natural-numbers funext univalence truncations -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/rational-numbers.lagda.md b/src/elementary-number-theory/rational-numbers.lagda.md index 001db38b16..8e6f5f629f 100644 --- a/src/elementary-number-theory/rational-numbers.lagda.md +++ b/src/elementary-number-theory/rational-numbers.lagda.md @@ -1,38 +1,44 @@ # The rational numbers ```agda -module elementary-number-theory.rational-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.rational-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.divisibility-integers -open import elementary-number-theory.greatest-common-divisor-integers -open import elementary-number-theory.integer-fractions +open import elementary-number-theory.divisibility-integers funext univalence truncations +open import elementary-number-theory.greatest-common-divisor-integers funext univalence truncations +open import elementary-number-theory.integer-fractions funext univalence truncations open import elementary-number-theory.integers -open import elementary-number-theory.mediant-integer-fractions -open import elementary-number-theory.multiplication-integers -open import elementary-number-theory.positive-and-negative-integers -open import elementary-number-theory.positive-integers -open import elementary-number-theory.reduced-integer-fractions +open import elementary-number-theory.mediant-integer-fractions funext univalence truncations +open import elementary-number-theory.multiplication-integers funext univalence truncations +open import elementary-number-theory.positive-integers funext univalence truncations +open import elementary-number-theory.reduced-integer-fractions funext univalence truncations open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions funext open import foundation.equality-cartesian-product-types -open import foundation.equality-dependent-pair-types -open import foundation.identity-types -open import foundation.negation -open import foundation.propositions -open import foundation.reflecting-maps-equivalence-relations -open import foundation.retracts-of-types -open import foundation.sections -open import foundation.sets -open import foundation.subtypes -open import foundation.surjective-maps +open import foundation.equality-dependent-pair-types funext +open import foundation.identity-types funext +open import foundation.negation funext +open import foundation.propositions funext univalence +open import foundation.reflecting-maps-equivalence-relations funext univalence truncations +open import foundation.retracts-of-types funext univalence +open import foundation.sections funext +open import foundation.sets funext univalence open import foundation.universe-levels -open import set-theory.countable-sets +open import set-theory.countable-sets funext univalence truncations ```
diff --git a/src/elementary-number-theory/reduced-integer-fractions.lagda.md b/src/elementary-number-theory/reduced-integer-fractions.lagda.md index b74d316dd3..1d1617f44d 100644 --- a/src/elementary-number-theory/reduced-integer-fractions.lagda.md +++ b/src/elementary-number-theory/reduced-integer-fractions.lagda.md @@ -1,35 +1,44 @@ # Reduced integer fractions ```agda -module elementary-number-theory.reduced-integer-fractions where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.reduced-integer-fractions + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.bezouts-lemma-integers -open import elementary-number-theory.divisibility-integers -open import elementary-number-theory.equality-integers -open import elementary-number-theory.greatest-common-divisor-integers -open import elementary-number-theory.integer-fractions +open import elementary-number-theory.bezouts-lemma-integers funext univalence truncations +open import elementary-number-theory.divisibility-integers funext univalence truncations +open import elementary-number-theory.equality-integers funext univalence truncations +open import elementary-number-theory.greatest-common-divisor-integers funext univalence truncations +open import elementary-number-theory.integer-fractions funext univalence truncations open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-integers -open import elementary-number-theory.multiplication-positive-and-negative-integers +open import elementary-number-theory.multiplication-integers funext univalence truncations +open import elementary-number-theory.multiplication-positive-and-negative-integers funext univalence truncations open import elementary-number-theory.natural-numbers -open import elementary-number-theory.positive-and-negative-integers -open import elementary-number-theory.positive-integers -open import elementary-number-theory.relatively-prime-integers +open import elementary-number-theory.positive-and-negative-integers funext univalence truncations +open import elementary-number-theory.positive-integers funext univalence truncations +open import elementary-number-theory.relatively-prime-integers funext univalence truncations open import foundation.action-on-identifications-functions -open import foundation.coproduct-types +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.empty-types +open import foundation.dependent-products-propositions funext +open import foundation.empty-types funext univalence truncations open import foundation.equality-cartesian-product-types -open import foundation.equality-dependent-pair-types -open import foundation.identity-types -open import foundation.negation -open import foundation.propositions -open import foundation.subtypes +open import foundation.equality-dependent-pair-types funext +open import foundation.identity-types funext +open import foundation.negation funext +open import foundation.propositions funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.transport-along-identifications open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/relatively-prime-integers.lagda.md b/src/elementary-number-theory/relatively-prime-integers.lagda.md index 56ab84992a..e731328f91 100644 --- a/src/elementary-number-theory/relatively-prime-integers.lagda.md +++ b/src/elementary-number-theory/relatively-prime-integers.lagda.md @@ -1,19 +1,29 @@ # Relatively prime integers ```agda -module elementary-number-theory.relatively-prime-integers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.relatively-prime-integers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.absolute-value-integers -open import elementary-number-theory.greatest-common-divisor-integers +open import elementary-number-theory.absolute-value-integers funext univalence truncations +open import elementary-number-theory.equality-integers funext univalence truncations +open import elementary-number-theory.greatest-common-divisor-integers funext univalence truncations open import elementary-number-theory.integers -open import elementary-number-theory.relatively-prime-natural-numbers +open import elementary-number-theory.relatively-prime-natural-numbers funext univalence truncations open import foundation.action-on-identifications-functions -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.propositions funext univalence open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/relatively-prime-natural-numbers.lagda.md b/src/elementary-number-theory/relatively-prime-natural-numbers.lagda.md index 01f59c2f4b..7295532b0a 100644 --- a/src/elementary-number-theory/relatively-prime-natural-numbers.lagda.md +++ b/src/elementary-number-theory/relatively-prime-natural-numbers.lagda.md @@ -1,25 +1,34 @@ # Relatively prime natural numbers ```agda -module elementary-number-theory.relatively-prime-natural-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.relatively-prime-natural-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.divisibility-natural-numbers -open import elementary-number-theory.equality-natural-numbers -open import elementary-number-theory.greatest-common-divisor-natural-numbers +open import elementary-number-theory.divisibility-natural-numbers funext univalence truncations +open import elementary-number-theory.equality-natural-numbers funext univalence truncations +open import elementary-number-theory.greatest-common-divisor-natural-numbers funext univalence truncations open import elementary-number-theory.natural-numbers -open import elementary-number-theory.prime-numbers +open import elementary-number-theory.prime-numbers funext univalence truncations -open import foundation.decidable-propositions -open import foundation.decidable-types +open import foundation.decidable-propositions funext univalence truncations +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.negated-equality -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.identity-types funext +open import foundation.negated-equality funext univalence truncations +open import foundation.propositions funext univalence open import foundation.transport-along-identifications open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/repeating-element-standard-finite-type.lagda.md b/src/elementary-number-theory/repeating-element-standard-finite-type.lagda.md index d8a354ec93..533245d582 100644 --- a/src/elementary-number-theory/repeating-element-standard-finite-type.lagda.md +++ b/src/elementary-number-theory/repeating-element-standard-finite-type.lagda.md @@ -1,7 +1,15 @@ # Repeating an element in a standard finite type ```agda -module elementary-number-theory.repeating-element-standard-finite-type where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.repeating-element-standard-finite-type + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,14 +18,14 @@ module elementary-number-theory.repeating-element-standard-finite-type where open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.coproduct-types -open import foundation.empty-types -open import foundation.identity-types -open import foundation.negated-equality +open import foundation.coproduct-types funext univalence truncations +open import foundation.empty-types funext univalence truncations +open import foundation.identity-types funext +open import foundation.negated-equality funext univalence truncations open import foundation.unit-type -open import univalent-combinatorics.equality-standard-finite-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.equality-standard-finite-types funext univalence truncations +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/elementary-number-theory/retracts-of-natural-numbers.lagda.md b/src/elementary-number-theory/retracts-of-natural-numbers.lagda.md index f6fc313258..1811b95989 100644 --- a/src/elementary-number-theory/retracts-of-natural-numbers.lagda.md +++ b/src/elementary-number-theory/retracts-of-natural-numbers.lagda.md @@ -1,17 +1,25 @@ # Retracts of the type of natural numbers ```agda -module elementary-number-theory.retracts-of-natural-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.retracts-of-natural-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.equality-natural-numbers +open import elementary-number-theory.equality-natural-numbers funext univalence truncations open import elementary-number-theory.natural-numbers -open import foundation.decidable-maps -open import foundation.retractions +open import foundation.decidable-maps funext univalence truncations +open import foundation.retractions funext open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/ring-of-integers.lagda.md b/src/elementary-number-theory/ring-of-integers.lagda.md index 1ef3b8fff6..2b7afdd8c3 100644 --- a/src/elementary-number-theory/ring-of-integers.lagda.md +++ b/src/elementary-number-theory/ring-of-integers.lagda.md @@ -1,35 +1,43 @@ # The ring of integers ```agda -module elementary-number-theory.ring-of-integers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.ring-of-integers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import commutative-algebra.commutative-rings +open import commutative-algebra.commutative-rings funext univalence truncations -open import elementary-number-theory.addition-integers -open import elementary-number-theory.group-of-integers +open import elementary-number-theory.addition-integers funext univalence truncations +open import elementary-number-theory.group-of-integers funext univalence truncations open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-integers +open import elementary-number-theory.multiplication-integers funext univalence truncations open import elementary-number-theory.natural-numbers -open import elementary-number-theory.nonzero-integers +open import elementary-number-theory.nonzero-integers funext univalence truncations open import foundation.action-on-identifications-functions -open import foundation.coproduct-types +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import group-theory.free-groups-with-one-generator -open import group-theory.homomorphisms-groups +open import group-theory.free-groups-with-one-generator funext univalence truncations +open import group-theory.homomorphisms-groups funext univalence truncations -open import ring-theory.homomorphisms-rings -open import ring-theory.initial-rings -open import ring-theory.integer-multiples-of-elements-rings -open import ring-theory.rings -open import ring-theory.trivial-rings +open import ring-theory.homomorphisms-rings funext univalence truncations +open import ring-theory.initial-rings funext univalence truncations +open import ring-theory.integer-multiples-of-elements-rings funext univalence truncations +open import ring-theory.rings funext univalence truncations +open import ring-theory.trivial-rings funext univalence truncations ```
diff --git a/src/elementary-number-theory/ring-of-rational-numbers.lagda.md b/src/elementary-number-theory/ring-of-rational-numbers.lagda.md index d0e4e6f220..139c8317f6 100644 --- a/src/elementary-number-theory/ring-of-rational-numbers.lagda.md +++ b/src/elementary-number-theory/ring-of-rational-numbers.lagda.md @@ -2,27 +2,34 @@ ```agda {-# OPTIONS --lossy-unification #-} - -module elementary-number-theory.ring-of-rational-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.ring-of-rational-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import commutative-algebra.commutative-rings +open import commutative-algebra.commutative-rings funext univalence truncations -open import elementary-number-theory.additive-group-of-rational-numbers -open import elementary-number-theory.multiplication-rational-numbers -open import elementary-number-theory.multiplicative-monoid-of-rational-numbers +open import elementary-number-theory.additive-group-of-rational-numbers funext univalence truncations +open import elementary-number-theory.multiplication-rational-numbers funext univalence truncations +open import elementary-number-theory.multiplicative-monoid-of-rational-numbers funext univalence truncations -open import foundation.coproduct-types +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types open import foundation.unital-binary-operations open import foundation.universe-levels -open import group-theory.semigroups +open import group-theory.semigroups funext univalence -open import ring-theory.rings +open import ring-theory.rings funext univalence truncations ```
diff --git a/src/elementary-number-theory/sieve-of-eratosthenes.lagda.md b/src/elementary-number-theory/sieve-of-eratosthenes.lagda.md index 1727176161..16dcecd872 100644 --- a/src/elementary-number-theory/sieve-of-eratosthenes.lagda.md +++ b/src/elementary-number-theory/sieve-of-eratosthenes.lagda.md @@ -1,29 +1,37 @@ # The sieve of Eratosthenes ```agda -module elementary-number-theory.sieve-of-eratosthenes where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.sieve-of-eratosthenes + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.decidable-types -open import elementary-number-theory.divisibility-natural-numbers -open import elementary-number-theory.equality-natural-numbers -open import elementary-number-theory.factorials -open import elementary-number-theory.inequality-natural-numbers -open import elementary-number-theory.modular-arithmetic-standard-finite-types +open import elementary-number-theory.decidable-types funext univalence truncations +open import elementary-number-theory.divisibility-natural-numbers funext univalence truncations +open import elementary-number-theory.equality-natural-numbers funext univalence truncations +open import elementary-number-theory.factorials funext univalence truncations +open import elementary-number-theory.inequality-natural-numbers funext univalence truncations +open import elementary-number-theory.modular-arithmetic-standard-finite-types funext univalence truncations open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.strict-inequality-natural-numbers +open import elementary-number-theory.strict-inequality-natural-numbers funext univalence truncations -open import foundation.cartesian-product-types -open import foundation.coproduct-types -open import foundation.decidable-types +open import foundation.cartesian-product-types funext univalence +open import foundation.coproduct-types funext univalence truncations +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.function-types -open import foundation.identity-types +open import foundation.empty-types funext univalence truncations +open import foundation.function-types funext +open import foundation.identity-types funext open import foundation.unit-type open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/square-free-natural-numbers.lagda.md b/src/elementary-number-theory/square-free-natural-numbers.lagda.md index c168fab9ea..517ec7f5c8 100644 --- a/src/elementary-number-theory/square-free-natural-numbers.lagda.md +++ b/src/elementary-number-theory/square-free-natural-numbers.lagda.md @@ -1,15 +1,23 @@ # Square-free natural numbers ```agda -module elementary-number-theory.square-free-natural-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.square-free-natural-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.divisibility-natural-numbers +open import elementary-number-theory.divisibility-natural-numbers funext univalence truncations open import elementary-number-theory.natural-numbers -open import elementary-number-theory.squares-natural-numbers +open import elementary-number-theory.squares-natural-numbers funext univalence truncations open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/squares-integers.lagda.md b/src/elementary-number-theory/squares-integers.lagda.md index 2497b17b33..868ecad8bd 100644 --- a/src/elementary-number-theory/squares-integers.lagda.md +++ b/src/elementary-number-theory/squares-integers.lagda.md @@ -1,29 +1,37 @@ # Squares in the integers ```agda -module elementary-number-theory.squares-integers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.squares-integers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.absolute-value-integers +open import elementary-number-theory.absolute-value-integers funext univalence truncations open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-integers -open import elementary-number-theory.multiplication-positive-and-negative-integers +open import elementary-number-theory.multiplication-integers funext univalence truncations +open import elementary-number-theory.multiplication-positive-and-negative-integers funext univalence truncations open import elementary-number-theory.natural-numbers -open import elementary-number-theory.nonnegative-integers -open import elementary-number-theory.positive-and-negative-integers -open import elementary-number-theory.positive-integers -open import elementary-number-theory.squares-natural-numbers +open import elementary-number-theory.nonnegative-integers funext univalence truncations +open import elementary-number-theory.positive-and-negative-integers funext univalence truncations +open import elementary-number-theory.positive-integers funext univalence truncations +open import elementary-number-theory.squares-natural-numbers funext univalence truncations open import foundation.action-on-identifications-functions -open import foundation.coproduct-types -open import foundation.decidable-types +open import foundation.coproduct-types funext univalence truncations +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.negation +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.negation funext open import foundation.universe-levels open import foundation-core.cartesian-product-types diff --git a/src/elementary-number-theory/squares-modular-arithmetic.lagda.md b/src/elementary-number-theory/squares-modular-arithmetic.lagda.md index 7d77108c0c..4fe55fcaa9 100644 --- a/src/elementary-number-theory/squares-modular-arithmetic.lagda.md +++ b/src/elementary-number-theory/squares-modular-arithmetic.lagda.md @@ -1,22 +1,30 @@ # Squares in ℤₚ ```agda -module elementary-number-theory.squares-modular-arithmetic where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.squares-modular-arithmetic + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.modular-arithmetic +open import elementary-number-theory.modular-arithmetic funext univalence truncations open import elementary-number-theory.natural-numbers -open import elementary-number-theory.squares-integers +open import elementary-number-theory.squares-integers funext univalence truncations -open import foundation.decidable-types +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import univalent-combinatorics.fibers-of-maps +open import univalent-combinatorics.fibers-of-maps funext univalence truncations ```
diff --git a/src/elementary-number-theory/squares-natural-numbers.lagda.md b/src/elementary-number-theory/squares-natural-numbers.lagda.md index f8afd7063e..9ed1348972 100644 --- a/src/elementary-number-theory/squares-natural-numbers.lagda.md +++ b/src/elementary-number-theory/squares-natural-numbers.lagda.md @@ -1,24 +1,32 @@ # Squares in the natural numbers ```agda -module elementary-number-theory.squares-natural-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.squares-natural-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.decidable-types -open import elementary-number-theory.equality-natural-numbers -open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.decidable-types funext univalence truncations +open import elementary-number-theory.equality-natural-numbers funext univalence truncations +open import elementary-number-theory.inequality-natural-numbers funext univalence truncations open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import foundation.coproduct-types -open import foundation.decidable-types +open import foundation.coproduct-types funext univalence truncations +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.negation +open import foundation.identity-types funext +open import foundation.negation funext open import foundation.unit-type open import foundation.universe-levels diff --git a/src/elementary-number-theory/standard-cyclic-groups.lagda.md b/src/elementary-number-theory/standard-cyclic-groups.lagda.md index dc65ddde36..99d0516a13 100644 --- a/src/elementary-number-theory/standard-cyclic-groups.lagda.md +++ b/src/elementary-number-theory/standard-cyclic-groups.lagda.md @@ -1,21 +1,29 @@ # The standard cyclic groups ```agda -module elementary-number-theory.standard-cyclic-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.standard-cyclic-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.modular-arithmetic +open import elementary-number-theory.modular-arithmetic funext univalence truncations open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.groups -open import group-theory.semigroups +open import group-theory.abelian-groups funext univalence truncations +open import group-theory.groups funext univalence truncations +open import group-theory.semigroups funext univalence ```
diff --git a/src/elementary-number-theory/standard-cyclic-rings.lagda.md b/src/elementary-number-theory/standard-cyclic-rings.lagda.md index 60ffeb3ce6..8a1579fd47 100644 --- a/src/elementary-number-theory/standard-cyclic-rings.lagda.md +++ b/src/elementary-number-theory/standard-cyclic-rings.lagda.md @@ -1,37 +1,45 @@ # The standard cyclic rings ```agda -module elementary-number-theory.standard-cyclic-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.standard-cyclic-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import commutative-algebra.commutative-rings +open import commutative-algebra.commutative-rings funext univalence truncations -open import elementary-number-theory.addition-integers +open import elementary-number-theory.addition-integers funext univalence truncations open import elementary-number-theory.integers -open import elementary-number-theory.modular-arithmetic -open import elementary-number-theory.modular-arithmetic-standard-finite-types +open import elementary-number-theory.modular-arithmetic funext univalence truncations +open import elementary-number-theory.modular-arithmetic-standard-finite-types funext univalence truncations open import elementary-number-theory.natural-numbers -open import elementary-number-theory.ring-of-integers -open import elementary-number-theory.standard-cyclic-groups +open import elementary-number-theory.ring-of-integers funext univalence truncations +open import elementary-number-theory.standard-cyclic-groups funext univalence truncations open import foundation.action-on-identifications-functions -open import foundation.coproduct-types +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.existential-quantification -open import foundation.homotopies -open import foundation.identity-types -open import foundation.surjective-maps +open import foundation.existential-quantification funext univalence truncations +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.surjective-maps funext univalence truncations open import foundation.universe-levels -open import group-theory.cyclic-groups -open import group-theory.generating-elements-groups +open import group-theory.cyclic-groups funext univalence truncations +open import group-theory.generating-elements-groups funext univalence truncations -open import ring-theory.cyclic-rings -open import ring-theory.integer-multiples-of-elements-rings -open import ring-theory.rings +open import ring-theory.cyclic-rings funext univalence truncations +open import ring-theory.integer-multiples-of-elements-rings funext univalence truncations +open import ring-theory.rings funext univalence truncations ```
diff --git a/src/elementary-number-theory/strict-inequality-integer-fractions.lagda.md b/src/elementary-number-theory/strict-inequality-integer-fractions.lagda.md index d58fbf1f4c..3801316ddd 100644 --- a/src/elementary-number-theory/strict-inequality-integer-fractions.lagda.md +++ b/src/elementary-number-theory/strict-inequality-integer-fractions.lagda.md @@ -1,45 +1,54 @@ # Strict inequality on the integer fractions ```agda -module elementary-number-theory.strict-inequality-integer-fractions where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.strict-inequality-integer-fractions + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.addition-integer-fractions -open import elementary-number-theory.addition-integers -open import elementary-number-theory.addition-positive-and-negative-integers -open import elementary-number-theory.cross-multiplication-difference-integer-fractions -open import elementary-number-theory.difference-integers -open import elementary-number-theory.inequality-integer-fractions -open import elementary-number-theory.inequality-integers -open import elementary-number-theory.integer-fractions +open import elementary-number-theory.addition-integer-fractions funext univalence truncations +open import elementary-number-theory.addition-integers funext univalence truncations +open import elementary-number-theory.addition-positive-and-negative-integers funext univalence truncations +open import elementary-number-theory.cross-multiplication-difference-integer-fractions funext univalence truncations +open import elementary-number-theory.difference-integers funext univalence truncations +open import elementary-number-theory.inequality-integer-fractions funext univalence truncations +open import elementary-number-theory.inequality-integers funext univalence truncations +open import elementary-number-theory.integer-fractions funext univalence truncations open import elementary-number-theory.integers -open import elementary-number-theory.mediant-integer-fractions -open import elementary-number-theory.multiplication-integers -open import elementary-number-theory.multiplication-positive-and-negative-integers -open import elementary-number-theory.nonnegative-integers -open import elementary-number-theory.nonpositive-integers -open import elementary-number-theory.positive-and-negative-integers -open import elementary-number-theory.positive-integers -open import elementary-number-theory.strict-inequality-integers +open import elementary-number-theory.mediant-integer-fractions funext univalence truncations +open import elementary-number-theory.multiplication-integers funext univalence truncations +open import elementary-number-theory.multiplication-positive-and-negative-integers funext univalence truncations +open import elementary-number-theory.nonnegative-integers funext univalence truncations +open import elementary-number-theory.nonpositive-integers funext univalence truncations +open import elementary-number-theory.positive-and-negative-integers funext univalence truncations +open import elementary-number-theory.positive-integers funext univalence truncations +open import elementary-number-theory.strict-inequality-integers funext univalence truncations open import foundation.action-on-identifications-functions open import foundation.binary-transport -open import foundation.cartesian-product-types -open import foundation.conjunction -open import foundation.coproduct-types -open import foundation.decidable-propositions +open import foundation.cartesian-product-types funext univalence +open import foundation.conjunction funext univalence truncations +open import foundation.coproduct-types funext univalence truncations +open import foundation.decidable-propositions funext univalence truncations open import foundation.dependent-pair-types -open import foundation.disjunction -open import foundation.existential-quantification -open import foundation.function-types -open import foundation.functoriality-coproduct-types -open import foundation.identity-types -open import foundation.negation -open import foundation.propositional-truncations -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.disjunction funext univalence truncations +open import foundation.existential-quantification funext univalence truncations +open import foundation.function-types funext +open import foundation.functoriality-coproduct-types funext univalence truncations +open import foundation.identity-types funext +open import foundation.negation funext +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence open import foundation.transport-along-identifications open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/strict-inequality-integers.lagda.md b/src/elementary-number-theory/strict-inequality-integers.lagda.md index 107592ee5c..3d6f137e1c 100644 --- a/src/elementary-number-theory/strict-inequality-integers.lagda.md +++ b/src/elementary-number-theory/strict-inequality-integers.lagda.md @@ -1,44 +1,53 @@ # Strict inequality on the integers ```agda -module elementary-number-theory.strict-inequality-integers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.strict-inequality-integers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.addition-integers -open import elementary-number-theory.addition-positive-and-negative-integers -open import elementary-number-theory.difference-integers -open import elementary-number-theory.inequality-integers -open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.addition-integers funext univalence truncations +open import elementary-number-theory.addition-positive-and-negative-integers funext univalence truncations +open import elementary-number-theory.difference-integers funext univalence truncations +open import elementary-number-theory.inequality-integers funext univalence truncations +open import elementary-number-theory.inequality-natural-numbers funext univalence truncations open import elementary-number-theory.integers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.negative-integers -open import elementary-number-theory.nonnegative-integers -open import elementary-number-theory.nonpositive-integers -open import elementary-number-theory.positive-and-negative-integers -open import elementary-number-theory.positive-integers -open import elementary-number-theory.strict-inequality-natural-numbers +open import elementary-number-theory.negative-integers funext univalence truncations +open import elementary-number-theory.nonnegative-integers funext univalence truncations +open import elementary-number-theory.nonpositive-integers funext univalence truncations +open import elementary-number-theory.positive-and-negative-integers funext univalence truncations +open import elementary-number-theory.positive-integers funext univalence truncations +open import elementary-number-theory.strict-inequality-natural-numbers funext univalence truncations open import foundation.action-on-identifications-functions open import foundation.binary-transport -open import foundation.coproduct-types -open import foundation.decidable-propositions +open import foundation.coproduct-types funext univalence truncations +open import foundation.decidable-propositions funext univalence truncations open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.functoriality-coproduct-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.negated-equality -open import foundation.negation -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.function-types funext +open import foundation.functoriality-coproduct-types funext univalence truncations +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.negated-equality funext univalence truncations +open import foundation.negation funext +open import foundation.propositions funext univalence open import foundation.transport-along-identifications open import foundation.unit-type open import foundation.universe-levels -open import order-theory.posets -open import order-theory.preorders +open import order-theory.posets funext univalence truncations +open import order-theory.preorders funext univalence truncations ```
diff --git a/src/elementary-number-theory/strict-inequality-natural-numbers.lagda.md b/src/elementary-number-theory/strict-inequality-natural-numbers.lagda.md index 623bc26c65..4e64cf51f2 100644 --- a/src/elementary-number-theory/strict-inequality-natural-numbers.lagda.md +++ b/src/elementary-number-theory/strict-inequality-natural-numbers.lagda.md @@ -1,31 +1,40 @@ # Strict inequality on the natural numbers ```agda -module elementary-number-theory.strict-inequality-natural-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.strict-inequality-natural-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.inequality-natural-numbers funext univalence truncations open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions open import foundation.binary-transport -open import foundation.cartesian-product-types -open import foundation.coproduct-types -open import foundation.decidable-types +open import foundation.cartesian-product-types funext univalence +open import foundation.coproduct-types funext univalence truncations +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.function-types -open import foundation.functoriality-coproduct-types -open import foundation.identity-types -open import foundation.negated-equality -open import foundation.negation -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.empty-types funext univalence truncations +open import foundation.function-types funext +open import foundation.functoriality-coproduct-types funext univalence truncations +open import foundation.identity-types funext +open import foundation.negated-equality funext univalence truncations +open import foundation.negation funext +open import foundation.propositions funext univalence open import foundation.transport-along-identifications open import foundation.unit-type open import foundation.universe-levels diff --git a/src/elementary-number-theory/strict-inequality-rational-numbers.lagda.md b/src/elementary-number-theory/strict-inequality-rational-numbers.lagda.md index 8f5c5545e7..39a0fbbfa3 100644 --- a/src/elementary-number-theory/strict-inequality-rational-numbers.lagda.md +++ b/src/elementary-number-theory/strict-inequality-rational-numbers.lagda.md @@ -2,55 +2,63 @@ ```agda {-# OPTIONS --lossy-unification #-} - -module elementary-number-theory.strict-inequality-rational-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.strict-inequality-rational-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.addition-integer-fractions -open import elementary-number-theory.addition-rational-numbers -open import elementary-number-theory.additive-group-of-rational-numbers -open import elementary-number-theory.cross-multiplication-difference-integer-fractions -open import elementary-number-theory.difference-integers -open import elementary-number-theory.difference-rational-numbers -open import elementary-number-theory.inequality-integer-fractions -open import elementary-number-theory.inequality-integers -open import elementary-number-theory.inequality-rational-numbers -open import elementary-number-theory.integer-fractions +open import elementary-number-theory.addition-integer-fractions funext univalence truncations +open import elementary-number-theory.addition-rational-numbers funext univalence truncations +open import elementary-number-theory.additive-group-of-rational-numbers funext univalence truncations +open import elementary-number-theory.cross-multiplication-difference-integer-fractions funext univalence truncations +open import elementary-number-theory.difference-integers funext univalence truncations +open import elementary-number-theory.difference-rational-numbers funext univalence truncations +open import elementary-number-theory.inequality-integer-fractions funext univalence truncations +open import elementary-number-theory.inequality-integers funext univalence truncations +open import elementary-number-theory.inequality-rational-numbers funext univalence truncations +open import elementary-number-theory.integer-fractions funext univalence truncations open import elementary-number-theory.integers -open import elementary-number-theory.mediant-integer-fractions -open import elementary-number-theory.multiplication-integers -open import elementary-number-theory.nonnegative-integers -open import elementary-number-theory.nonpositive-integers -open import elementary-number-theory.positive-and-negative-integers -open import elementary-number-theory.positive-integers -open import elementary-number-theory.rational-numbers -open import elementary-number-theory.reduced-integer-fractions -open import elementary-number-theory.strict-inequality-integer-fractions -open import elementary-number-theory.strict-inequality-integers +open import elementary-number-theory.mediant-integer-fractions funext univalence truncations +open import elementary-number-theory.multiplication-integers funext univalence truncations +open import elementary-number-theory.nonnegative-integers funext univalence truncations +open import elementary-number-theory.nonpositive-integers funext univalence truncations +open import elementary-number-theory.positive-and-negative-integers funext univalence truncations +open import elementary-number-theory.positive-integers funext univalence truncations +open import elementary-number-theory.rational-numbers funext univalence truncations +open import elementary-number-theory.reduced-integer-fractions funext univalence truncations +open import elementary-number-theory.strict-inequality-integer-fractions funext univalence truncations +open import elementary-number-theory.strict-inequality-integers funext univalence truncations open import foundation.action-on-identifications-functions -open import foundation.binary-relations -open import foundation.cartesian-product-types -open import foundation.conjunction -open import foundation.coproduct-types -open import foundation.decidable-propositions +open import foundation.binary-relations funext univalence truncations +open import foundation.cartesian-product-types funext univalence +open import foundation.conjunction funext univalence truncations +open import foundation.coproduct-types funext univalence truncations +open import foundation.decidable-propositions funext univalence truncations open import foundation.dependent-pair-types -open import foundation.disjunction -open import foundation.existential-quantification -open import foundation.function-types -open import foundation.functoriality-coproduct-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.negation -open import foundation.propositional-truncations -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.disjunction funext univalence truncations +open import foundation.existential-quantification funext univalence truncations +open import foundation.function-types funext +open import foundation.functoriality-coproduct-types funext univalence truncations +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.negation funext +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence open import foundation.transport-along-identifications open import foundation.universe-levels -open import group-theory.groups +open import group-theory.groups funext univalence truncations ```
diff --git a/src/elementary-number-theory/strict-inequality-standard-finite-types.lagda.md b/src/elementary-number-theory/strict-inequality-standard-finite-types.lagda.md index 5083034a1f..0bca20a9a1 100644 --- a/src/elementary-number-theory/strict-inequality-standard-finite-types.lagda.md +++ b/src/elementary-number-theory/strict-inequality-standard-finite-types.lagda.md @@ -1,26 +1,35 @@ # Strict inequality on the standard finite types ```agda -module elementary-number-theory.strict-inequality-standard-finite-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.strict-inequality-standard-finite-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.inequality-natural-numbers funext univalence truncations open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.coproduct-types -open import foundation.empty-types -open import foundation.function-types -open import foundation.identity-types -open import foundation.propositions +open import foundation.coproduct-types funext univalence truncations +open import foundation.dependent-products-propositions funext +open import foundation.empty-types funext univalence truncations +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence open import foundation.transport-along-identifications open import foundation.unit-type open import foundation.universe-levels -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/elementary-number-theory/strictly-ordered-pairs-of-natural-numbers.lagda.md b/src/elementary-number-theory/strictly-ordered-pairs-of-natural-numbers.lagda.md index faab496e28..e6f36719de 100644 --- a/src/elementary-number-theory/strictly-ordered-pairs-of-natural-numbers.lagda.md +++ b/src/elementary-number-theory/strictly-ordered-pairs-of-natural-numbers.lagda.md @@ -1,23 +1,31 @@ # Strictly ordered pairs of natural numbers ```agda -module elementary-number-theory.strictly-ordered-pairs-of-natural-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.strictly-ordered-pairs-of-natural-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import elementary-number-theory.natural-numbers -open import elementary-number-theory.strict-inequality-natural-numbers +open import elementary-number-theory.strict-inequality-natural-numbers funext univalence truncations open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.identity-types -open import foundation.negated-equality -open import foundation.pairs-of-distinct-elements +open import foundation.empty-types funext univalence truncations +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.identity-types funext +open import foundation.negated-equality funext univalence truncations +open import foundation.pairs-of-distinct-elements funext univalence truncations open import foundation.unit-type open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/strong-induction-natural-numbers.lagda.md b/src/elementary-number-theory/strong-induction-natural-numbers.lagda.md index 6a0bf777c5..811e77e9b9 100644 --- a/src/elementary-number-theory/strong-induction-natural-numbers.lagda.md +++ b/src/elementary-number-theory/strong-induction-natural-numbers.lagda.md @@ -1,25 +1,34 @@ # The strong induction principle for the natural numbers ```agda -module elementary-number-theory.strong-induction-natural-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.strong-induction-natural-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.equality-natural-numbers -open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.equality-natural-numbers funext univalence truncations +open import elementary-number-theory.inequality-natural-numbers funext univalence truncations open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types -open import foundation.coproduct-types +open import foundation.cartesian-product-types funext univalence +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.identity-types -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.empty-types funext univalence truncations +open import foundation.function-extensionality funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/sums-of-natural-numbers.lagda.md b/src/elementary-number-theory/sums-of-natural-numbers.lagda.md index a026d32a7c..01f29918a3 100644 --- a/src/elementary-number-theory/sums-of-natural-numbers.lagda.md +++ b/src/elementary-number-theory/sums-of-natural-numbers.lagda.md @@ -1,7 +1,15 @@ # Sums of natural numbers ```agda -module elementary-number-theory.sums-of-natural-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.sums-of-natural-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,24 +18,24 @@ module elementary-number-theory.sums-of-natural-numbers where open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.strict-inequality-natural-numbers +open import elementary-number-theory.strict-inequality-natural-numbers funext univalence truncations open import foundation.action-on-identifications-functions -open import foundation.constant-maps -open import foundation.coproduct-types +open import foundation.constant-maps funext univalence truncations +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.unit-type open import foundation.universe-levels open import foundation.whiskering-homotopies-composition open import lists.lists -open import univalent-combinatorics.counting -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.counting funext univalence truncations +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/elementary-number-theory/sylvesters-sequence.lagda.md b/src/elementary-number-theory/sylvesters-sequence.lagda.md index 5b7094c31d..c6239eac47 100644 --- a/src/elementary-number-theory/sylvesters-sequence.lagda.md +++ b/src/elementary-number-theory/sylvesters-sequence.lagda.md @@ -1,17 +1,25 @@ # Sylvester's sequence ```agda -module elementary-number-theory.sylvesters-sequence where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.sylvesters-sequence + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import elementary-number-theory.natural-numbers -open import elementary-number-theory.ordinal-induction-natural-numbers -open import elementary-number-theory.products-of-natural-numbers +open import elementary-number-theory.ordinal-induction-natural-numbers funext univalence truncations +open import elementary-number-theory.products-of-natural-numbers funext univalence truncations -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/elementary-number-theory/taxicab-numbers.lagda.md b/src/elementary-number-theory/taxicab-numbers.lagda.md index 6c89d1db21..ee2c1e12d5 100644 --- a/src/elementary-number-theory/taxicab-numbers.lagda.md +++ b/src/elementary-number-theory/taxicab-numbers.lagda.md @@ -1,25 +1,33 @@ # Taxicab numbers ```agda -module elementary-number-theory.taxicab-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.taxicab-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.cubes-natural-numbers -open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.cubes-natural-numbers funext univalence truncations +open import elementary-number-theory.inequality-natural-numbers funext univalence truncations open import elementary-number-theory.natural-numbers -open import elementary-number-theory.nonzero-natural-numbers +open import elementary-number-theory.nonzero-natural-numbers funext univalence truncations -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.identity-types +open import foundation.equivalences funext +open import foundation.identity-types funext open import foundation.universe-levels -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/elementary-number-theory/twin-prime-conjecture.lagda.md b/src/elementary-number-theory/twin-prime-conjecture.lagda.md index a3c6993cca..67c7852d72 100644 --- a/src/elementary-number-theory/twin-prime-conjecture.lagda.md +++ b/src/elementary-number-theory/twin-prime-conjecture.lagda.md @@ -1,17 +1,25 @@ # The Twin Prime conjecture ```agda -module elementary-number-theory.twin-prime-conjecture where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.twin-prime-conjecture + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.inequality-natural-numbers funext univalence truncations open import elementary-number-theory.natural-numbers -open import elementary-number-theory.prime-numbers +open import elementary-number-theory.prime-numbers funext univalence truncations -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/type-arithmetic-natural-numbers.lagda.md b/src/elementary-number-theory/type-arithmetic-natural-numbers.lagda.md index 9d3fa6833f..1fb6319351 100644 --- a/src/elementary-number-theory/type-arithmetic-natural-numbers.lagda.md +++ b/src/elementary-number-theory/type-arithmetic-natural-numbers.lagda.md @@ -1,30 +1,38 @@ # Type arithmetic with natural numbers ```agda -module elementary-number-theory.type-arithmetic-natural-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.type-arithmetic-natural-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.divisibility-natural-numbers +open import elementary-number-theory.divisibility-natural-numbers funext univalence truncations open import elementary-number-theory.integers open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.parity-natural-numbers -open import elementary-number-theory.powers-of-two +open import elementary-number-theory.parity-natural-numbers funext univalence truncations +open import elementary-number-theory.powers-of-two funext univalence truncations open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.functoriality-cartesian-product-types -open import foundation.functoriality-coproduct-types -open import foundation.iterating-functions +open import foundation.function-types funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.functoriality-coproduct-types funext univalence truncations +open import foundation.iterating-functions funext univalence truncations open import foundation.split-surjective-maps -open import foundation.type-arithmetic-coproduct-types -open import foundation.type-arithmetic-empty-type -open import foundation.type-arithmetic-unit-type +open import foundation.type-arithmetic-coproduct-types funext univalence truncations +open import foundation.type-arithmetic-empty-type funext univalence truncations +open import foundation.type-arithmetic-unit-type funext open import foundation.unit-type open import foundation-core.cartesian-product-types @@ -36,7 +44,7 @@ open import foundation-core.identity-types open import foundation-core.injective-maps open import foundation-core.negation -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/elementary-number-theory/unit-elements-standard-finite-types.lagda.md b/src/elementary-number-theory/unit-elements-standard-finite-types.lagda.md index 4b6f36cc3b..b0068b158a 100644 --- a/src/elementary-number-theory/unit-elements-standard-finite-types.lagda.md +++ b/src/elementary-number-theory/unit-elements-standard-finite-types.lagda.md @@ -1,26 +1,34 @@ # Unit elements in the standard finite types ```agda -module elementary-number-theory.unit-elements-standard-finite-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.unit-elements-standard-finite-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.congruence-natural-numbers -open import elementary-number-theory.distance-natural-numbers -open import elementary-number-theory.divisibility-standard-finite-types -open import elementary-number-theory.modular-arithmetic-standard-finite-types +open import elementary-number-theory.congruence-natural-numbers funext univalence truncations +open import elementary-number-theory.distance-natural-numbers funext univalence truncations +open import elementary-number-theory.divisibility-standard-finite-types funext univalence truncations +open import elementary-number-theory.modular-arithmetic-standard-finite-types funext univalence truncations open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.squares-natural-numbers +open import elementary-number-theory.squares-natural-numbers funext univalence truncations open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/elementary-number-theory/unit-fractions-rational-numbers.lagda.md b/src/elementary-number-theory/unit-fractions-rational-numbers.lagda.md index 6740932fae..640e6d2408 100644 --- a/src/elementary-number-theory/unit-fractions-rational-numbers.lagda.md +++ b/src/elementary-number-theory/unit-fractions-rational-numbers.lagda.md @@ -2,32 +2,39 @@ ```agda {-# OPTIONS --lossy-unification #-} - -module elementary-number-theory.unit-fractions-rational-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.unit-fractions-rational-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.archimedean-property-positive-rational-numbers -open import elementary-number-theory.inequality-integers -open import elementary-number-theory.inequality-rational-numbers +open import elementary-number-theory.archimedean-property-positive-rational-numbers funext univalence truncations +open import elementary-number-theory.inequality-integers funext univalence truncations +open import elementary-number-theory.inequality-rational-numbers funext univalence truncations open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-integers -open import elementary-number-theory.multiplication-rational-numbers -open import elementary-number-theory.multiplicative-group-of-positive-rational-numbers -open import elementary-number-theory.nonzero-natural-numbers -open import elementary-number-theory.positive-rational-numbers -open import elementary-number-theory.rational-numbers -open import elementary-number-theory.strict-inequality-integers -open import elementary-number-theory.strict-inequality-rational-numbers +open import elementary-number-theory.multiplication-integers funext univalence truncations +open import elementary-number-theory.multiplication-rational-numbers funext univalence truncations +open import elementary-number-theory.multiplicative-group-of-positive-rational-numbers funext univalence truncations +open import elementary-number-theory.nonzero-natural-numbers funext univalence truncations +open import elementary-number-theory.positive-rational-numbers funext univalence truncations +open import elementary-number-theory.rational-numbers funext univalence truncations +open import elementary-number-theory.strict-inequality-integers funext univalence truncations +open import elementary-number-theory.strict-inequality-rational-numbers funext univalence truncations open import foundation.action-on-identifications-functions open import foundation.binary-transport open import foundation.dependent-pair-types -open import foundation.functoriality-dependent-pair-types +open import foundation.functoriality-dependent-pair-types funext -open import group-theory.groups +open import group-theory.groups funext univalence truncations ```
diff --git a/src/elementary-number-theory/unit-similarity-standard-finite-types.lagda.md b/src/elementary-number-theory/unit-similarity-standard-finite-types.lagda.md index 3830ea8381..907599739d 100644 --- a/src/elementary-number-theory/unit-similarity-standard-finite-types.lagda.md +++ b/src/elementary-number-theory/unit-similarity-standard-finite-types.lagda.md @@ -1,25 +1,33 @@ # Unit similarity on the standard finite types ```agda -module elementary-number-theory.unit-similarity-standard-finite-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.unit-similarity-standard-finite-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.congruence-natural-numbers -open import elementary-number-theory.modular-arithmetic-standard-finite-types +open import elementary-number-theory.congruence-natural-numbers funext univalence truncations +open import elementary-number-theory.modular-arithmetic-standard-finite-types funext univalence truncations open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.unit-elements-standard-finite-types +open import elementary-number-theory.unit-elements-standard-finite-types funext univalence truncations open import foundation.action-on-identifications-functions -open import foundation.binary-relations +open import foundation.binary-relations funext univalence truncations open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/elementary-number-theory/universal-property-conatural-numbers.lagda.md b/src/elementary-number-theory/universal-property-conatural-numbers.lagda.md index c593269a23..ad952ca119 100644 --- a/src/elementary-number-theory/universal-property-conatural-numbers.lagda.md +++ b/src/elementary-number-theory/universal-property-conatural-numbers.lagda.md @@ -1,15 +1,22 @@ # The universal property of the conatural numbers ```agda -module elementary-number-theory.universal-property-conatural-numbers where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.universal-property-conatural-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda -open import foundation.coalgebras-maybe -open import foundation.contractible-types -open import foundation.morphisms-coalgebras-maybe +open import foundation.coalgebras-maybe funext univalence +open import foundation.contractible-types funext univalence +open import foundation.dependent-products-contractible-types funext +open import foundation.morphisms-coalgebras-maybe funext univalence open import foundation.universe-levels ``` @@ -23,7 +30,7 @@ enjoys many universal properties, among others: 1. It is the one-point compactification of the [natural numbers](elementary-number-theory.natural-numbers.md). 2. It classifies downward-stable subsets of the natural numbers. -3. It is the final coalgebra of the [maybe monad](foundation.maybe.md). +3. It is the final coalgebra of the [maybe monad](foundation-core.maybe.md). On this page we consider the last of these. Thus, a `Maybe`-[coalgebra](foundation.coalgebras-maybe.md) `η : X → Maybe X` satisfies diff --git a/src/elementary-number-theory/universal-property-integers.lagda.md b/src/elementary-number-theory/universal-property-integers.lagda.md index 2d36403b4e..8113ba794d 100644 --- a/src/elementary-number-theory/universal-property-integers.lagda.md +++ b/src/elementary-number-theory/universal-property-integers.lagda.md @@ -1,7 +1,15 @@ # The universal property of the integers ```agda -module elementary-number-theory.universal-property-integers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.universal-property-integers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,20 +18,22 @@ module elementary-number-theory.universal-property-integers where open import elementary-number-theory.integers open import elementary-number-theory.natural-numbers -open import foundation.cartesian-product-types -open import foundation.contractible-types -open import foundation.coproduct-types +open import foundation.cartesian-product-types funext univalence +open import foundation.contractible-types funext univalence +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types -open import foundation.propositions +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence open import foundation.structure-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext univalence truncations open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/universal-property-natural-numbers.lagda.md b/src/elementary-number-theory/universal-property-natural-numbers.lagda.md index 69460d3015..49211d5738 100644 --- a/src/elementary-number-theory/universal-property-natural-numbers.lagda.md +++ b/src/elementary-number-theory/universal-property-natural-numbers.lagda.md @@ -1,7 +1,15 @@ # The universal property of the natural numbers ```agda -module elementary-number-theory.universal-property-natural-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.universal-property-natural-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,19 +18,20 @@ module elementary-number-theory.universal-property-natural-numbers where open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types -open import foundation.contractible-types +open import foundation.cartesian-product-types funext univalence +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types +open import foundation.dependent-products-contractible-types funext +open import foundation.equivalences funext +open import foundation.function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext open import foundation.structure-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext univalence truncations open import foundation.universe-levels -open import foundation.whiskering-identifications-concatenation +open import foundation.whiskering-identifications-concatenation funext ```
diff --git a/src/elementary-number-theory/upper-bounds-natural-numbers.lagda.md b/src/elementary-number-theory/upper-bounds-natural-numbers.lagda.md index 2a0529164b..501d985973 100644 --- a/src/elementary-number-theory/upper-bounds-natural-numbers.lagda.md +++ b/src/elementary-number-theory/upper-bounds-natural-numbers.lagda.md @@ -1,15 +1,23 @@ # Upper bounds for type families over the natural numbers ```agda -module elementary-number-theory.upper-bounds-natural-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.upper-bounds-natural-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.inequality-natural-numbers funext univalence truncations open import elementary-number-theory.natural-numbers -open import elementary-number-theory.strict-inequality-natural-numbers +open import elementary-number-theory.strict-inequality-natural-numbers funext univalence truncations open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/well-ordering-principle-natural-numbers.lagda.md b/src/elementary-number-theory/well-ordering-principle-natural-numbers.lagda.md index a72905645f..89ea43f93b 100644 --- a/src/elementary-number-theory/well-ordering-principle-natural-numbers.lagda.md +++ b/src/elementary-number-theory/well-ordering-principle-natural-numbers.lagda.md @@ -1,28 +1,37 @@ # The well-ordering principle of the natural numbers ```agda -module elementary-number-theory.well-ordering-principle-natural-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.well-ordering-principle-natural-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.inequality-natural-numbers -open import elementary-number-theory.lower-bounds-natural-numbers +open import elementary-number-theory.inequality-natural-numbers funext univalence truncations +open import elementary-number-theory.lower-bounds-natural-numbers funext univalence truncations open import elementary-number-theory.natural-numbers -open import foundation.cartesian-product-types -open import foundation.coproduct-types -open import foundation.decidable-types +open import foundation.cartesian-product-types funext univalence +open import foundation.coproduct-types funext univalence truncations +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.functoriality-dependent-pair-types -open import foundation.hilberts-epsilon-operators -open import foundation.identity-types -open import foundation.negation -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.empty-types funext univalence truncations +open import foundation.functoriality-dependent-pair-types funext +open import foundation.hilberts-epsilon-operators funext univalence truncations +open import foundation.identity-types funext +open import foundation.negation funext +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/well-ordering-principle-standard-finite-types.lagda.md b/src/elementary-number-theory/well-ordering-principle-standard-finite-types.lagda.md index a422c722f0..26779ceef0 100644 --- a/src/elementary-number-theory/well-ordering-principle-standard-finite-types.lagda.md +++ b/src/elementary-number-theory/well-ordering-principle-standard-finite-types.lagda.md @@ -1,46 +1,55 @@ # The well-ordering principle of the standard finite types ```agda -module elementary-number-theory.well-ordering-principle-standard-finite-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.well-ordering-principle-standard-finite-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.inequality-standard-finite-types -open import elementary-number-theory.modular-arithmetic-standard-finite-types +open import elementary-number-theory.inequality-standard-finite-types funext univalence truncations +open import elementary-number-theory.modular-arithmetic-standard-finite-types funext univalence truncations open import elementary-number-theory.natural-numbers -open import elementary-number-theory.well-ordering-principle-natural-numbers +open import elementary-number-theory.well-ordering-principle-natural-numbers funext univalence truncations -open import foundation.cartesian-product-types -open import foundation.coproduct-types -open import foundation.decidable-subtypes -open import foundation.decidable-types +open import foundation.cartesian-product-types funext univalence +open import foundation.coproduct-types funext univalence truncations +open import foundation.decidable-subtypes funext univalence truncations +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.equivalence-extensionality -open import foundation.equivalences -open import foundation.existential-quantification -open import foundation.function-types -open import foundation.functoriality-coproduct-types -open import foundation.functoriality-dependent-pair-types -open import foundation.functoriality-propositional-truncation -open import foundation.hilberts-epsilon-operators -open import foundation.identity-types -open import foundation.negation -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.empty-types funext univalence truncations +open import foundation.equivalence-extensionality funext +open import foundation.equivalences funext +open import foundation.existential-quantification funext univalence truncations +open import foundation.function-types funext +open import foundation.functoriality-coproduct-types funext univalence truncations +open import foundation.functoriality-dependent-pair-types funext +open import foundation.functoriality-propositional-truncation funext univalence truncations +open import foundation.hilberts-epsilon-operators funext univalence truncations +open import foundation.identity-types funext +open import foundation.negation funext +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.transport-along-identifications -open import foundation.type-arithmetic-coproduct-types -open import foundation.type-arithmetic-empty-type -open import foundation.type-arithmetic-unit-type +open import foundation.type-arithmetic-coproduct-types funext univalence truncations +open import foundation.type-arithmetic-empty-type funext univalence truncations +open import foundation.type-arithmetic-unit-type funext open import foundation.unit-type open import foundation.universe-levels -open import univalent-combinatorics.counting -open import univalent-combinatorics.decidable-dependent-pair-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.counting funext univalence truncations +open import univalent-combinatorics.decidable-dependent-pair-types funext univalence truncations +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/elementary-number-theory/zero-conatural-numbers.lagda.md b/src/elementary-number-theory/zero-conatural-numbers.lagda.md index ea40798173..b979f5b103 100644 --- a/src/elementary-number-theory/zero-conatural-numbers.lagda.md +++ b/src/elementary-number-theory/zero-conatural-numbers.lagda.md @@ -2,23 +2,30 @@ ```agda {-# OPTIONS --guardedness #-} - -module elementary-number-theory.zero-conatural-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module elementary-number-theory.zero-conatural-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.conatural-numbers +open import elementary-number-theory.conatural-numbers funext univalence truncations -open import foundation.coproduct-types -open import foundation.decidable-types -open import foundation.function-types -open import foundation.maybe -open import foundation.negation +open import foundation.coproduct-types funext univalence truncations +open import foundation.decidable-types funext univalence truncations +open import foundation.function-types funext +open import foundation.negation funext open import foundation.universe-levels open import foundation-core.identity-types +open import foundation-core.maybe open import foundation-core.propositions ``` diff --git a/src/finite-algebra.lagda.md b/src/finite-algebra.lagda.md index 3e2d66d204..39baed7272 100644 --- a/src/finite-algebra.lagda.md +++ b/src/finite-algebra.lagda.md @@ -3,16 +3,24 @@ ## Modules in the finite algebra namespace ```agda -module finite-algebra where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom -open import finite-algebra.commutative-finite-rings public -open import finite-algebra.dependent-products-commutative-finite-rings public -open import finite-algebra.dependent-products-finite-rings public -open import finite-algebra.finite-fields public -open import finite-algebra.finite-rings public -open import finite-algebra.homomorphisms-commutative-finite-rings public -open import finite-algebra.homomorphisms-finite-rings public -open import finite-algebra.products-commutative-finite-rings public -open import finite-algebra.products-finite-rings public -open import finite-algebra.semisimple-commutative-finite-rings public +module finite-algebra + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where + +open import finite-algebra.commutative-finite-rings funext univalence truncations public +open import finite-algebra.dependent-products-commutative-finite-rings funext univalence truncations public +open import finite-algebra.dependent-products-finite-rings funext univalence truncations public +open import finite-algebra.finite-fields funext univalence truncations public +open import finite-algebra.finite-rings funext univalence truncations public +open import finite-algebra.homomorphisms-commutative-finite-rings funext univalence truncations public +open import finite-algebra.homomorphisms-finite-rings funext univalence truncations public +open import finite-algebra.products-commutative-finite-rings funext univalence truncations public +open import finite-algebra.products-finite-rings funext univalence truncations public +open import finite-algebra.semisimple-commutative-finite-rings funext univalence truncations public ``` diff --git a/src/finite-algebra/commutative-finite-rings.lagda.md b/src/finite-algebra/commutative-finite-rings.lagda.md index 035aeea3e7..1ee40b4b98 100644 --- a/src/finite-algebra/commutative-finite-rings.lagda.md +++ b/src/finite-algebra/commutative-finite-rings.lagda.md @@ -1,51 +1,60 @@ # Commutative finite rings ```agda -module finite-algebra.commutative-finite-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module finite-algebra.commutative-finite-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import commutative-algebra.commutative-rings -open import commutative-algebra.commutative-semirings +open import commutative-algebra.commutative-rings funext univalence truncations +open import commutative-algebra.commutative-semirings funext univalence truncations open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.natural-numbers -open import finite-algebra.finite-rings +open import finite-algebra.finite-rings funext univalence truncations open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.binary-embeddings +open import foundation.binary-embeddings funext open import foundation.binary-equivalences -open import foundation.embeddings -open import foundation.equivalences -open import foundation.identity-types -open import foundation.injective-maps +open import foundation.dependent-products-propositions funext +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.injective-maps funext open import foundation.interchange-law -open import foundation.involutions -open import foundation.propositions -open import foundation.sets +open import foundation.involutions funext univalence +open import foundation.propositions funext univalence +open import foundation.sets funext univalence open import foundation.unital-binary-operations open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.commutative-monoids -open import group-theory.groups -open import group-theory.monoids -open import group-theory.semigroups +open import group-theory.abelian-groups funext univalence truncations +open import group-theory.commutative-monoids funext univalence truncations +open import group-theory.groups funext univalence truncations +open import group-theory.monoids funext univalence truncations +open import group-theory.semigroups funext univalence -open import lists.concatenation-lists +open import lists.concatenation-lists funext univalence truncations open import lists.lists -open import ring-theory.rings -open import ring-theory.semirings +open import ring-theory.rings funext univalence truncations +open import ring-theory.semirings funext univalence truncations -open import univalent-combinatorics.dependent-function-types -open import univalent-combinatorics.dependent-pair-types -open import univalent-combinatorics.equality-finite-types -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.dependent-function-types funext univalence truncations +open import univalent-combinatorics.dependent-pair-types funext univalence truncations +open import univalent-combinatorics.equality-finite-types funext univalence truncations +open import univalent-combinatorics.finite-types funext univalence truncations ```
diff --git a/src/finite-algebra/dependent-products-commutative-finite-rings.lagda.md b/src/finite-algebra/dependent-products-commutative-finite-rings.lagda.md index 82cdf56aa9..072a95b656 100644 --- a/src/finite-algebra/dependent-products-commutative-finite-rings.lagda.md +++ b/src/finite-algebra/dependent-products-commutative-finite-rings.lagda.md @@ -1,32 +1,40 @@ # Dependent products of commutative finit rings ```agda -module finite-algebra.dependent-products-commutative-finite-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module finite-algebra.dependent-products-commutative-finite-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import commutative-algebra.commutative-rings -open import commutative-algebra.dependent-products-commutative-rings +open import commutative-algebra.commutative-rings funext univalence truncations +open import commutative-algebra.dependent-products-commutative-rings funext univalence truncations -open import finite-algebra.commutative-finite-rings -open import finite-algebra.dependent-products-finite-rings -open import finite-algebra.finite-rings +open import finite-algebra.commutative-finite-rings funext univalence truncations +open import finite-algebra.dependent-products-finite-rings funext univalence truncations +open import finite-algebra.finite-rings funext univalence truncations open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.identity-types -open import foundation.sets +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.sets funext univalence open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.commutative-monoids +open import group-theory.abelian-groups funext univalence truncations +open import group-theory.commutative-monoids funext univalence truncations -open import ring-theory.dependent-products-rings -open import ring-theory.rings +open import ring-theory.dependent-products-rings funext univalence truncations +open import ring-theory.rings funext univalence truncations -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.finite-types funext univalence truncations ```
diff --git a/src/finite-algebra/dependent-products-finite-rings.lagda.md b/src/finite-algebra/dependent-products-finite-rings.lagda.md index a1c2f98a52..9db14cfc5a 100644 --- a/src/finite-algebra/dependent-products-finite-rings.lagda.md +++ b/src/finite-algebra/dependent-products-finite-rings.lagda.md @@ -1,31 +1,39 @@ # Dependent products of finite rings ```agda -module finite-algebra.dependent-products-finite-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module finite-algebra.dependent-products-finite-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import finite-algebra.finite-rings +open import finite-algebra.finite-rings funext univalence truncations open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.identity-types -open import foundation.sets +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.sets funext univalence open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.groups -open import group-theory.monoids -open import group-theory.semigroups +open import group-theory.abelian-groups funext univalence truncations +open import group-theory.groups funext univalence truncations +open import group-theory.monoids funext univalence truncations +open import group-theory.semigroups funext univalence -open import ring-theory.dependent-products-rings -open import ring-theory.rings -open import ring-theory.semirings +open import ring-theory.dependent-products-rings funext univalence truncations +open import ring-theory.rings funext univalence truncations +open import ring-theory.semirings funext univalence truncations -open import univalent-combinatorics.dependent-function-types -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.dependent-function-types funext univalence truncations +open import univalent-combinatorics.finite-types funext univalence truncations ```
diff --git a/src/finite-algebra/finite-fields.lagda.md b/src/finite-algebra/finite-fields.lagda.md index 27425b25c9..72635ce27a 100644 --- a/src/finite-algebra/finite-fields.lagda.md +++ b/src/finite-algebra/finite-fields.lagda.md @@ -1,47 +1,56 @@ # Finite fields ```agda -module finite-algebra.finite-fields where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module finite-algebra.finite-fields + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import commutative-algebra.commutative-rings -open import commutative-algebra.commutative-semirings +open import commutative-algebra.commutative-rings funext univalence truncations +open import commutative-algebra.commutative-semirings funext univalence truncations open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.natural-numbers -open import finite-algebra.commutative-finite-rings -open import finite-algebra.finite-rings +open import finite-algebra.commutative-finite-rings funext univalence truncations +open import finite-algebra.finite-rings funext univalence truncations open import foundation.action-on-identifications-binary-functions -open import foundation.binary-embeddings +open import foundation.binary-embeddings funext open import foundation.binary-equivalences open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalences -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.involutions -open import foundation.propositions -open import foundation.sets +open import foundation.dependent-products-propositions funext +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.involutions funext univalence +open import foundation.propositions funext univalence +open import foundation.sets funext univalence open import foundation.unital-binary-operations open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.commutative-monoids -open import group-theory.groups -open import group-theory.monoids -open import group-theory.semigroups +open import group-theory.abelian-groups funext univalence truncations +open import group-theory.commutative-monoids funext univalence truncations +open import group-theory.groups funext univalence truncations +open import group-theory.monoids funext univalence truncations +open import group-theory.semigroups funext univalence -open import lists.concatenation-lists +open import lists.concatenation-lists funext univalence truncations open import lists.lists -open import ring-theory.division-rings -open import ring-theory.rings -open import ring-theory.semirings +open import ring-theory.division-rings funext univalence truncations +open import ring-theory.rings funext univalence truncations +open import ring-theory.semirings funext univalence truncations ```
diff --git a/src/finite-algebra/finite-rings.lagda.md b/src/finite-algebra/finite-rings.lagda.md index e78ca56b4d..94639bf31b 100644 --- a/src/finite-algebra/finite-rings.lagda.md +++ b/src/finite-algebra/finite-rings.lagda.md @@ -1,7 +1,15 @@ # Finite rings ```agda -module finite-algebra.finite-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module finite-algebra.finite-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,39 +18,40 @@ module finite-algebra.finite-rings where open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.natural-numbers -open import finite-group-theory.finite-abelian-groups -open import finite-group-theory.finite-groups -open import finite-group-theory.finite-monoids +open import finite-group-theory.finite-abelian-groups funext univalence truncations +open import finite-group-theory.finite-groups funext univalence truncations +open import finite-group-theory.finite-monoids funext univalence truncations -open import foundation.binary-embeddings +open import foundation.binary-embeddings funext open import foundation.binary-equivalences -open import foundation.embeddings -open import foundation.equivalences -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.involutions -open import foundation.propositions -open import foundation.sets +open import foundation.dependent-products-propositions funext +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.involutions funext univalence +open import foundation.propositions funext univalence +open import foundation.sets funext univalence open import foundation.unital-binary-operations open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.commutative-monoids -open import group-theory.groups -open import group-theory.monoids -open import group-theory.semigroups +open import group-theory.abelian-groups funext univalence truncations +open import group-theory.commutative-monoids funext univalence truncations +open import group-theory.groups funext univalence truncations +open import group-theory.monoids funext univalence truncations +open import group-theory.semigroups funext univalence -open import lists.concatenation-lists +open import lists.concatenation-lists funext univalence truncations open import lists.lists -open import ring-theory.rings -open import ring-theory.semirings +open import ring-theory.rings funext univalence truncations +open import ring-theory.semirings funext univalence truncations -open import univalent-combinatorics.cartesian-product-types -open import univalent-combinatorics.dependent-function-types -open import univalent-combinatorics.dependent-pair-types -open import univalent-combinatorics.equality-finite-types -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.cartesian-product-types funext univalence truncations +open import univalent-combinatorics.dependent-function-types funext univalence truncations +open import univalent-combinatorics.dependent-pair-types funext univalence truncations +open import univalent-combinatorics.equality-finite-types funext univalence truncations +open import univalent-combinatorics.finite-types funext univalence truncations ```
diff --git a/src/finite-algebra/homomorphisms-commutative-finite-rings.lagda.md b/src/finite-algebra/homomorphisms-commutative-finite-rings.lagda.md index 21ac9504c6..f8a66960f6 100644 --- a/src/finite-algebra/homomorphisms-commutative-finite-rings.lagda.md +++ b/src/finite-algebra/homomorphisms-commutative-finite-rings.lagda.md @@ -1,28 +1,37 @@ # Homomorphisms of commutative finite rings ```agda -module finite-algebra.homomorphisms-commutative-finite-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module finite-algebra.homomorphisms-commutative-finite-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import commutative-algebra.homomorphisms-commutative-rings -open import commutative-algebra.homomorphisms-commutative-semirings +open import commutative-algebra.homomorphisms-commutative-rings funext univalence truncations +open import commutative-algebra.homomorphisms-commutative-semirings funext univalence truncations -open import finite-algebra.commutative-finite-rings +open import finite-algebra.commutative-finite-rings funext univalence truncations -open import foundation.equivalences -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets -open import foundation.torsorial-type-families +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.torsorial-type-families funext univalence truncations open import foundation.universe-levels -open import group-theory.homomorphisms-abelian-groups -open import group-theory.homomorphisms-monoids +open import group-theory.homomorphisms-abelian-groups funext univalence truncations +open import group-theory.homomorphisms-monoids funext univalence truncations -open import ring-theory.homomorphisms-rings +open import ring-theory.homomorphisms-rings funext univalence truncations ```
diff --git a/src/finite-algebra/homomorphisms-finite-rings.lagda.md b/src/finite-algebra/homomorphisms-finite-rings.lagda.md index 9cc03a1249..e0fda50492 100644 --- a/src/finite-algebra/homomorphisms-finite-rings.lagda.md +++ b/src/finite-algebra/homomorphisms-finite-rings.lagda.md @@ -1,25 +1,34 @@ # Homomorphisms of finite rings ```agda -module finite-algebra.homomorphisms-finite-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module finite-algebra.homomorphisms-finite-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import finite-algebra.finite-rings - -open import foundation.equivalences -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets -open import foundation.torsorial-type-families +open import finite-algebra.finite-rings funext univalence truncations + +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.torsorial-type-families funext univalence truncations open import foundation.universe-levels -open import group-theory.homomorphisms-abelian-groups -open import group-theory.homomorphisms-monoids +open import group-theory.homomorphisms-abelian-groups funext univalence truncations +open import group-theory.homomorphisms-monoids funext univalence truncations -open import ring-theory.homomorphisms-rings +open import ring-theory.homomorphisms-rings funext univalence truncations ```
diff --git a/src/finite-algebra/products-commutative-finite-rings.lagda.md b/src/finite-algebra/products-commutative-finite-rings.lagda.md index 46ad564c75..16f6e7c93f 100644 --- a/src/finite-algebra/products-commutative-finite-rings.lagda.md +++ b/src/finite-algebra/products-commutative-finite-rings.lagda.md @@ -1,28 +1,36 @@ # Products of commutative finite rings ```agda -module finite-algebra.products-commutative-finite-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module finite-algebra.products-commutative-finite-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import commutative-algebra.commutative-rings -open import commutative-algebra.products-commutative-rings +open import commutative-algebra.commutative-rings funext univalence truncations +open import commutative-algebra.products-commutative-rings funext univalence truncations -open import finite-algebra.commutative-finite-rings -open import finite-algebra.products-finite-rings +open import finite-algebra.commutative-finite-rings funext univalence truncations +open import finite-algebra.products-finite-rings funext univalence truncations open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.sets +open import foundation.identity-types funext +open import foundation.sets funext univalence open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.groups -open import group-theory.semigroups +open import group-theory.abelian-groups funext univalence truncations +open import group-theory.groups funext univalence truncations +open import group-theory.semigroups funext univalence -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.finite-types funext univalence truncations ```
diff --git a/src/finite-algebra/products-finite-rings.lagda.md b/src/finite-algebra/products-finite-rings.lagda.md index 4555ad4b74..173955f2f9 100644 --- a/src/finite-algebra/products-finite-rings.lagda.md +++ b/src/finite-algebra/products-finite-rings.lagda.md @@ -1,28 +1,36 @@ # Products of finite rings ```agda -module finite-algebra.products-finite-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module finite-algebra.products-finite-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import finite-algebra.finite-rings +open import finite-algebra.finite-rings funext univalence truncations open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.sets +open import foundation.identity-types funext +open import foundation.sets funext univalence open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.groups -open import group-theory.semigroups +open import group-theory.abelian-groups funext univalence truncations +open import group-theory.groups funext univalence truncations +open import group-theory.semigroups funext univalence -open import ring-theory.products-rings -open import ring-theory.rings +open import ring-theory.products-rings funext univalence truncations +open import ring-theory.rings funext univalence truncations -open import univalent-combinatorics.cartesian-product-types -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.cartesian-product-types funext univalence truncations +open import univalent-combinatorics.finite-types funext univalence truncations ```
diff --git a/src/finite-algebra/semisimple-commutative-finite-rings.lagda.md b/src/finite-algebra/semisimple-commutative-finite-rings.lagda.md index 7c72cb1712..81d24b45e3 100644 --- a/src/finite-algebra/semisimple-commutative-finite-rings.lagda.md +++ b/src/finite-algebra/semisimple-commutative-finite-rings.lagda.md @@ -1,7 +1,15 @@ # Semisimple commutative finite rings ```agda -module finite-algebra.semisimple-commutative-finite-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module finite-algebra.semisimple-commutative-finite-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,20 +17,20 @@ module finite-algebra.semisimple-commutative-finite-rings where ```agda open import elementary-number-theory.natural-numbers -open import finite-algebra.commutative-finite-rings -open import finite-algebra.dependent-products-commutative-finite-rings -open import finite-algebra.finite-fields -open import finite-algebra.homomorphisms-commutative-finite-rings +open import finite-algebra.commutative-finite-rings funext univalence truncations +open import finite-algebra.dependent-products-commutative-finite-rings funext univalence truncations +open import finite-algebra.finite-fields funext univalence truncations +open import finite-algebra.homomorphisms-commutative-finite-rings funext univalence truncations open import foundation.dependent-pair-types -open import foundation.existential-quantification -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.propositional-truncations +open import foundation.existential-quantification funext univalence truncations +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.propositional-truncations funext univalence open import foundation.universe-levels -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.finite-types funext univalence truncations +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/finite-group-theory.lagda.md b/src/finite-group-theory.lagda.md index 8c555ee159..ac41053ff0 100644 --- a/src/finite-group-theory.lagda.md +++ b/src/finite-group-theory.lagda.md @@ -3,28 +3,36 @@ ## Modules in the finite group theory namespace ```agda -module finite-group-theory where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom -open import finite-group-theory.abstract-quaternion-group public -open import finite-group-theory.alternating-concrete-groups public -open import finite-group-theory.alternating-groups public -open import finite-group-theory.cartier-delooping-sign-homomorphism public -open import finite-group-theory.concrete-quaternion-group public -open import finite-group-theory.delooping-sign-homomorphism public -open import finite-group-theory.finite-abelian-groups public -open import finite-group-theory.finite-commutative-monoids public -open import finite-group-theory.finite-groups public -open import finite-group-theory.finite-monoids public -open import finite-group-theory.finite-semigroups public -open import finite-group-theory.finite-type-groups public -open import finite-group-theory.groups-of-order-2 public -open import finite-group-theory.orbits-permutations public -open import finite-group-theory.permutations public -open import finite-group-theory.permutations-standard-finite-types public -open import finite-group-theory.sign-homomorphism public -open import finite-group-theory.simpson-delooping-sign-homomorphism public -open import finite-group-theory.subgroups-finite-groups public -open import finite-group-theory.tetrahedra-in-3-space public -open import finite-group-theory.transpositions public -open import finite-group-theory.transpositions-standard-finite-types public +module finite-group-theory + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where + +open import finite-group-theory.abstract-quaternion-group funext univalence truncations public +open import finite-group-theory.alternating-concrete-groups funext univalence truncations public +open import finite-group-theory.alternating-groups funext univalence truncations public +open import finite-group-theory.cartier-delooping-sign-homomorphism funext univalence truncations public +open import finite-group-theory.concrete-quaternion-group funext univalence truncations public +open import finite-group-theory.delooping-sign-homomorphism funext univalence truncations public +open import finite-group-theory.finite-abelian-groups funext univalence truncations public +open import finite-group-theory.finite-commutative-monoids funext univalence truncations public +open import finite-group-theory.finite-groups funext univalence truncations public +open import finite-group-theory.finite-monoids funext univalence truncations public +open import finite-group-theory.finite-semigroups funext univalence truncations public +open import finite-group-theory.finite-type-groups funext univalence truncations public +open import finite-group-theory.groups-of-order-2 funext univalence truncations public +open import finite-group-theory.orbits-permutations funext univalence truncations public +open import finite-group-theory.permutations funext univalence truncations public +open import finite-group-theory.permutations-standard-finite-types funext univalence truncations public +open import finite-group-theory.sign-homomorphism funext univalence truncations public +open import finite-group-theory.simpson-delooping-sign-homomorphism funext univalence truncations public +open import finite-group-theory.subgroups-finite-groups funext univalence truncations public +open import finite-group-theory.tetrahedra-in-3-space funext univalence truncations public +open import finite-group-theory.transpositions funext univalence truncations public +open import finite-group-theory.transpositions-standard-finite-types funext univalence truncations public ``` diff --git a/src/finite-group-theory/abstract-quaternion-group.lagda.md b/src/finite-group-theory/abstract-quaternion-group.lagda.md index c8a8199ee7..f453f91611 100644 --- a/src/finite-group-theory/abstract-quaternion-group.lagda.md +++ b/src/finite-group-theory/abstract-quaternion-group.lagda.md @@ -1,33 +1,41 @@ # The abstract quaternion group of order `8` ```agda -module finite-group-theory.abstract-quaternion-group where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module finite-group-theory.abstract-quaternion-group + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.coproduct-types -open import foundation.decidable-equality -open import foundation.decidable-types +open import foundation.coproduct-types funext univalence truncations +open import foundation.decidable-equality funext univalence truncations +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.negation -open import foundation.propositional-truncations -open import foundation.sets +open import foundation.empty-types funext univalence truncations +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.negation funext +open import foundation.propositional-truncations funext univalence +open import foundation.sets funext univalence open import foundation.unit-type open import foundation.universe-levels -open import group-theory.groups -open import group-theory.semigroups +open import group-theory.groups funext univalence truncations +open import group-theory.semigroups funext univalence -open import univalent-combinatorics.counting -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.counting funext univalence truncations +open import univalent-combinatorics.finite-types funext univalence truncations +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/finite-group-theory/alternating-concrete-groups.lagda.md b/src/finite-group-theory/alternating-concrete-groups.lagda.md index 388be53b80..9b9fc13ed6 100644 --- a/src/finite-group-theory/alternating-concrete-groups.lagda.md +++ b/src/finite-group-theory/alternating-concrete-groups.lagda.md @@ -1,7 +1,15 @@ # Alternating concrete groups ```agda -module finite-group-theory.alternating-concrete-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module finite-group-theory.alternating-concrete-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,13 +17,13 @@ module finite-group-theory.alternating-concrete-groups where ```agda open import elementary-number-theory.natural-numbers -open import finite-group-theory.cartier-delooping-sign-homomorphism -open import finite-group-theory.finite-type-groups +open import finite-group-theory.cartier-delooping-sign-homomorphism funext univalence truncations +open import finite-group-theory.finite-type-groups funext univalence truncations open import foundation.universe-levels -open import group-theory.concrete-groups -open import group-theory.kernels-homomorphisms-concrete-groups +open import group-theory.concrete-groups funext univalence truncations +open import group-theory.kernels-homomorphisms-concrete-groups funext univalence truncations ```
diff --git a/src/finite-group-theory/alternating-groups.lagda.md b/src/finite-group-theory/alternating-groups.lagda.md index 975c699ac4..de5fe06961 100644 --- a/src/finite-group-theory/alternating-groups.lagda.md +++ b/src/finite-group-theory/alternating-groups.lagda.md @@ -1,7 +1,15 @@ # Alternating groups ```agda -module finite-group-theory.alternating-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module finite-group-theory.alternating-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,14 +17,14 @@ module finite-group-theory.alternating-groups where ```agda open import elementary-number-theory.natural-numbers -open import finite-group-theory.sign-homomorphism +open import finite-group-theory.sign-homomorphism funext univalence truncations -open import group-theory.groups -open import group-theory.kernels-homomorphisms-groups -open import group-theory.symmetric-groups +open import group-theory.groups funext univalence truncations +open import group-theory.kernels-homomorphisms-groups funext univalence truncations +open import group-theory.symmetric-groups funext univalence truncations -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.finite-types funext univalence truncations +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/finite-group-theory/cartier-delooping-sign-homomorphism.lagda.md b/src/finite-group-theory/cartier-delooping-sign-homomorphism.lagda.md index ecac11c0d1..a82fef943a 100644 --- a/src/finite-group-theory/cartier-delooping-sign-homomorphism.lagda.md +++ b/src/finite-group-theory/cartier-delooping-sign-homomorphism.lagda.md @@ -2,8 +2,15 @@ ```agda {-# OPTIONS --lossy-unification #-} - -module finite-group-theory.cartier-delooping-sign-homomorphism where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module finite-group-theory.cartier-delooping-sign-homomorphism + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -12,37 +19,38 @@ module finite-group-theory.cartier-delooping-sign-homomorphism where open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.natural-numbers -open import finite-group-theory.delooping-sign-homomorphism -open import finite-group-theory.finite-type-groups -open import finite-group-theory.sign-homomorphism -open import finite-group-theory.transpositions +open import finite-group-theory.delooping-sign-homomorphism funext univalence truncations +open import finite-group-theory.finite-type-groups funext univalence truncations +open import finite-group-theory.sign-homomorphism funext univalence truncations +open import finite-group-theory.transpositions funext univalence truncations -open import foundation.action-on-equivalences-type-families-over-subuniverses +open import foundation.action-on-equivalences-type-families-over-subuniverses funext univalence open import foundation.action-on-identifications-functions -open import foundation.contractible-types +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalence-relations -open import foundation.equivalences -open import foundation.identity-types -open import foundation.mere-equivalences -open import foundation.negation -open import foundation.propositional-truncations -open import foundation.raising-universe-levels +open import foundation.dependent-products-contractible-types funext +open import foundation.equivalence-relations funext univalence truncations +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.mere-equivalences funext univalence truncations +open import foundation.negation funext +open import foundation.propositional-truncations funext univalence open import foundation.transport-along-identifications -open import foundation.type-theoretic-principle-of-choice +open import foundation.type-theoretic-principle-of-choice funext open import foundation.unit-type open import foundation.universe-levels -open import group-theory.concrete-groups -open import group-theory.homomorphisms-concrete-groups -open import group-theory.homomorphisms-groups -open import group-theory.isomorphisms-groups -open import group-theory.loop-groups-sets -open import group-theory.symmetric-groups +open import foundation-core.raising-universe-levels + +open import group-theory.homomorphisms-concrete-groups funext univalence truncations +open import group-theory.homomorphisms-groups funext univalence truncations +open import group-theory.isomorphisms-groups funext univalence truncations +open import group-theory.loop-groups-sets funext univalence truncations +open import group-theory.symmetric-groups funext univalence truncations -open import univalent-combinatorics.2-element-decidable-subtypes -open import univalent-combinatorics.orientations-complete-undirected-graph -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.2-element-decidable-subtypes funext univalence truncations +open import univalent-combinatorics.orientations-complete-undirected-graph funext univalence truncations +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/finite-group-theory/concrete-quaternion-group.lagda.md b/src/finite-group-theory/concrete-quaternion-group.lagda.md index d424d3600b..5f5a604acb 100644 --- a/src/finite-group-theory/concrete-quaternion-group.lagda.md +++ b/src/finite-group-theory/concrete-quaternion-group.lagda.md @@ -1,7 +1,15 @@ # The concrete quaternion group ```agda -module finite-group-theory.concrete-quaternion-group where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module finite-group-theory.concrete-quaternion-group + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,16 +18,16 @@ module finite-group-theory.concrete-quaternion-group where open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.identity-types -open import foundation.isolated-elements +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.isolated-elements funext univalence truncations open import foundation.transport-along-identifications open import foundation.universe-levels -open import univalent-combinatorics.complements-isolated-elements -open import univalent-combinatorics.cubes -open import univalent-combinatorics.equality-finite-types -open import univalent-combinatorics.equivalences-cubes +open import univalent-combinatorics.complements-isolated-elements funext univalence truncations +open import univalent-combinatorics.cubes funext univalence truncations +open import univalent-combinatorics.equality-finite-types funext univalence truncations +open import univalent-combinatorics.equivalences-cubes funext univalence truncations ```
diff --git a/src/finite-group-theory/delooping-sign-homomorphism.lagda.md b/src/finite-group-theory/delooping-sign-homomorphism.lagda.md index cdb615bc50..cb0815b8f4 100644 --- a/src/finite-group-theory/delooping-sign-homomorphism.lagda.md +++ b/src/finite-group-theory/delooping-sign-homomorphism.lagda.md @@ -2,82 +2,92 @@ ```agda {-# OPTIONS --lossy-unification #-} +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom -module finite-group-theory.delooping-sign-homomorphism where +module finite-group-theory.delooping-sign-homomorphism + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.inequality-natural-numbers funext univalence truncations open import elementary-number-theory.natural-numbers -open import finite-group-theory.finite-type-groups -open import finite-group-theory.permutations -open import finite-group-theory.sign-homomorphism -open import finite-group-theory.transpositions +open import finite-group-theory.finite-type-groups funext univalence truncations +open import finite-group-theory.permutations funext univalence truncations +open import finite-group-theory.sign-homomorphism funext univalence truncations +open import finite-group-theory.transpositions funext univalence truncations -open import foundation.action-on-equivalences-type-families-over-subuniverses +open import foundation.action-on-equivalences-type-families-over-subuniverses funext univalence open import foundation.action-on-identifications-functions open import foundation.binary-transport -open import foundation.commuting-squares-of-maps -open import foundation.contractible-types -open import foundation.coproduct-types -open import foundation.decidable-propositions -open import foundation.decidable-types +open import foundation.commuting-squares-of-maps funext univalence +open import foundation.contractible-types funext univalence +open import foundation.coproduct-types funext univalence truncations +open import foundation.decidable-propositions funext univalence truncations +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.empty-types -open import foundation.equality-dependent-pair-types -open import foundation.equivalence-classes -open import foundation.equivalence-extensionality -open import foundation.equivalence-induction -open import foundation.equivalence-relations -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.functoriality-propositional-truncation -open import foundation.functoriality-set-quotients -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.involutions -open import foundation.logical-equivalences -open import foundation.mere-equivalences -open import foundation.negated-equality -open import foundation.negation -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.raising-universe-levels -open import foundation.reflecting-maps-equivalence-relations -open import foundation.sets +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.dependent-products-truncated-types funext +open import foundation.embeddings funext +open import foundation.empty-types funext univalence truncations +open import foundation.equality-dependent-pair-types funext +open import foundation.equivalence-classes funext univalence truncations +open import foundation.equivalence-extensionality funext +open import foundation.equivalence-induction funext univalence +open import foundation.equivalence-relations funext univalence truncations +open import foundation.equivalences funext +open import foundation.function-extensionality funext +open import foundation.function-types funext +open import foundation.functoriality-propositional-truncation funext univalence truncations +open import foundation.functoriality-set-quotients funext univalence truncations +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.involutions funext univalence +open import foundation.logical-equivalences funext +open import foundation.mere-equivalences funext univalence truncations +open import foundation.negated-equality funext univalence truncations +open import foundation.negation funext +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence +open import foundation.reflecting-maps-equivalence-relations funext univalence truncations +open import foundation.sets funext univalence open import foundation.transport-along-identifications -open import foundation.truncated-types -open import foundation.uniqueness-set-quotients +open import foundation.truncated-types funext univalence +open import foundation.uniqueness-set-quotients funext univalence truncations open import foundation.unit-type -open import foundation.univalence -open import foundation.universal-property-set-quotients +open import foundation.univalence funext univalence +open import foundation.universal-property-set-quotients funext univalence truncations open import foundation.universe-levels -open import foundation.whiskering-identifications-concatenation +open import foundation.whiskering-identifications-concatenation funext + +open import foundation-core.raising-universe-levels -open import group-theory.concrete-groups -open import group-theory.generating-sets-groups -open import group-theory.groups -open import group-theory.homomorphisms-concrete-groups -open import group-theory.homomorphisms-generated-subgroups -open import group-theory.homomorphisms-groups -open import group-theory.homomorphisms-semigroups -open import group-theory.isomorphisms-groups -open import group-theory.loop-groups-sets -open import group-theory.symmetric-groups +open import group-theory.generating-sets-groups funext univalence truncations +open import group-theory.groups funext univalence truncations +open import group-theory.homomorphisms-concrete-groups funext univalence truncations +open import group-theory.homomorphisms-generated-subgroups funext univalence truncations +open import group-theory.homomorphisms-groups funext univalence truncations +open import group-theory.homomorphisms-semigroups funext univalence truncations +open import group-theory.isomorphisms-groups funext univalence truncations +open import group-theory.loop-groups-sets funext univalence truncations +open import group-theory.symmetric-groups funext univalence truncations -open import synthetic-homotopy-theory.loop-spaces +open import synthetic-homotopy-theory.loop-spaces funext univalence truncations -open import univalent-combinatorics.2-element-decidable-subtypes -open import univalent-combinatorics.equality-finite-types -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.set-quotients-of-index-two -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.2-element-decidable-subtypes funext univalence truncations +open import univalent-combinatorics.equality-finite-types funext univalence truncations +open import univalent-combinatorics.finite-types funext univalence truncations +open import univalent-combinatorics.set-quotients-of-index-two funext univalence truncations +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/finite-group-theory/finite-abelian-groups.lagda.md b/src/finite-group-theory/finite-abelian-groups.lagda.md index 51bc616d82..cf1aa7aa5c 100644 --- a/src/finite-group-theory/finite-abelian-groups.lagda.md +++ b/src/finite-group-theory/finite-abelian-groups.lagda.md @@ -1,31 +1,40 @@ # Abelian groups ```agda -module finite-group-theory.finite-abelian-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module finite-group-theory.finite-abelian-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import finite-group-theory.finite-groups +open import finite-group-theory.finite-groups funext univalence truncations -open import foundation.equivalences -open import foundation.identity-types +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.identity-types funext open import foundation.interchange-law -open import foundation.propositions -open import foundation.sets +open import foundation.propositions funext univalence +open import foundation.sets funext univalence open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.conjugation -open import group-theory.groups -open import group-theory.monoids -open import group-theory.semigroups +open import group-theory.abelian-groups funext univalence truncations +open import group-theory.conjugation funext univalence truncations +open import group-theory.groups funext univalence truncations +open import group-theory.monoids funext univalence truncations +open import group-theory.semigroups funext univalence -open import univalent-combinatorics.dependent-function-types -open import univalent-combinatorics.dependent-pair-types -open import univalent-combinatorics.equality-finite-types -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.dependent-function-types funext univalence truncations +open import univalent-combinatorics.dependent-pair-types funext univalence truncations +open import univalent-combinatorics.equality-finite-types funext univalence truncations +open import univalent-combinatorics.finite-types funext univalence truncations ```
diff --git a/src/finite-group-theory/finite-commutative-monoids.lagda.md b/src/finite-group-theory/finite-commutative-monoids.lagda.md index d66dd10353..7025c8ab9d 100644 --- a/src/finite-group-theory/finite-commutative-monoids.lagda.md +++ b/src/finite-group-theory/finite-commutative-monoids.lagda.md @@ -1,27 +1,35 @@ # Finite Commutative monoids ```agda -module finite-group-theory.finite-commutative-monoids where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module finite-group-theory.finite-commutative-monoids + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import finite-group-theory.finite-monoids +open import finite-group-theory.finite-monoids funext univalence truncations -open import foundation.identity-types -open import foundation.sets +open import foundation.identity-types funext +open import foundation.sets funext univalence open import foundation.unital-binary-operations open import foundation.universe-levels -open import group-theory.commutative-monoids -open import group-theory.monoids -open import group-theory.semigroups +open import group-theory.commutative-monoids funext univalence truncations +open import group-theory.monoids funext univalence truncations +open import group-theory.semigroups funext univalence -open import univalent-combinatorics.dependent-function-types -open import univalent-combinatorics.dependent-pair-types -open import univalent-combinatorics.equality-finite-types -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.dependent-function-types funext univalence truncations +open import univalent-combinatorics.dependent-pair-types funext univalence truncations +open import univalent-combinatorics.equality-finite-types funext univalence truncations +open import univalent-combinatorics.finite-types funext univalence truncations ```
diff --git a/src/finite-group-theory/finite-groups.lagda.md b/src/finite-group-theory/finite-groups.lagda.md index b52469f559..0218e06e25 100644 --- a/src/finite-group-theory/finite-groups.lagda.md +++ b/src/finite-group-theory/finite-groups.lagda.md @@ -1,7 +1,15 @@ # Finite groups ```agda -module finite-group-theory.finite-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module finite-group-theory.finite-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,51 +17,52 @@ module finite-group-theory.finite-groups where ```agda open import elementary-number-theory.natural-numbers -open import finite-group-theory.finite-monoids -open import finite-group-theory.finite-semigroups +open import finite-group-theory.finite-monoids funext univalence truncations +open import finite-group-theory.finite-semigroups funext univalence truncations -open import foundation.1-types -open import foundation.binary-embeddings +open import foundation.1-types funext univalence +open import foundation.binary-embeddings funext open import foundation.binary-equivalences -open import foundation.decidable-equality -open import foundation.decidable-types -open import foundation.embeddings -open import foundation.equivalences -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.mere-equivalences -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.set-truncations -open import foundation.sets +open import foundation.decidable-equality funext univalence truncations +open import foundation.decidable-types funext univalence truncations +open import foundation.dependent-products-propositions funext +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.mere-equivalences funext univalence truncations +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence +open import foundation.set-truncations funext univalence +open import foundation.sets funext univalence open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels -open import group-theory.category-of-groups -open import group-theory.commuting-elements-groups -open import group-theory.groups -open import group-theory.monoids -open import group-theory.semigroups +open import group-theory.category-of-groups funext univalence truncations +open import group-theory.commuting-elements-groups funext univalence truncations +open import group-theory.groups funext univalence truncations +open import group-theory.monoids funext univalence truncations +open import group-theory.semigroups funext univalence open import structured-types.pointed-types -open import univalent-combinatorics.cartesian-product-types -open import univalent-combinatorics.counting -open import univalent-combinatorics.counting-dependent-pair-types -open import univalent-combinatorics.decidable-dependent-function-types -open import univalent-combinatorics.decidable-dependent-pair-types -open import univalent-combinatorics.decidable-propositions -open import univalent-combinatorics.dependent-function-types -open import univalent-combinatorics.dependent-pair-types -open import univalent-combinatorics.equality-finite-types -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.finitely-many-connected-components -open import univalent-combinatorics.function-types -open import univalent-combinatorics.pi-finite-types -open import univalent-combinatorics.standard-finite-types -open import univalent-combinatorics.untruncated-pi-finite-types +open import univalent-combinatorics.cartesian-product-types funext univalence truncations +open import univalent-combinatorics.counting funext univalence truncations +open import univalent-combinatorics.counting-dependent-pair-types funext univalence truncations +open import univalent-combinatorics.decidable-dependent-function-types funext univalence truncations +open import univalent-combinatorics.decidable-dependent-pair-types funext univalence truncations +open import univalent-combinatorics.decidable-propositions funext univalence truncations +open import univalent-combinatorics.dependent-function-types funext univalence truncations +open import univalent-combinatorics.dependent-pair-types funext univalence truncations +open import univalent-combinatorics.equality-finite-types funext univalence truncations +open import univalent-combinatorics.finite-types funext univalence truncations +open import univalent-combinatorics.finitely-many-connected-components funext univalence truncations +open import univalent-combinatorics.function-types funext univalence truncations +open import univalent-combinatorics.pi-finite-types funext univalence truncations +open import univalent-combinatorics.standard-finite-types funext univalence truncations +open import univalent-combinatorics.untruncated-pi-finite-types funext univalence truncations ```
diff --git a/src/finite-group-theory/finite-monoids.lagda.md b/src/finite-group-theory/finite-monoids.lagda.md index 36b3f1e29b..16c907cb9d 100644 --- a/src/finite-group-theory/finite-monoids.lagda.md +++ b/src/finite-group-theory/finite-monoids.lagda.md @@ -1,7 +1,15 @@ # Finite monoids ```agda -module finite-group-theory.finite-monoids where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module finite-group-theory.finite-monoids + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,38 +17,39 @@ module finite-group-theory.finite-monoids where ```agda open import elementary-number-theory.natural-numbers -open import finite-group-theory.finite-semigroups +open import finite-group-theory.finite-semigroups funext univalence truncations -open import foundation.1-types -open import foundation.decidable-propositions -open import foundation.decidable-types +open import foundation.1-types funext univalence +open import foundation.decidable-propositions funext univalence truncations +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.identity-types -open import foundation.mere-equivalences -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.set-truncations -open import foundation.sets +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.mere-equivalences funext univalence truncations +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence +open import foundation.set-truncations funext univalence +open import foundation.sets funext univalence open import foundation.type-arithmetic-dependent-pair-types open import foundation.unital-binary-operations open import foundation.universe-levels -open import group-theory.monoids -open import group-theory.semigroups - -open import univalent-combinatorics.cartesian-product-types -open import univalent-combinatorics.counting -open import univalent-combinatorics.decidable-dependent-function-types -open import univalent-combinatorics.decidable-dependent-pair-types -open import univalent-combinatorics.dependent-function-types -open import univalent-combinatorics.dependent-pair-types -open import univalent-combinatorics.equality-finite-types -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.finitely-many-connected-components -open import univalent-combinatorics.pi-finite-types -open import univalent-combinatorics.standard-finite-types -open import univalent-combinatorics.untruncated-pi-finite-types +open import group-theory.monoids funext univalence truncations +open import group-theory.semigroups funext univalence + +open import univalent-combinatorics.cartesian-product-types funext univalence truncations +open import univalent-combinatorics.counting funext univalence truncations +open import univalent-combinatorics.decidable-dependent-function-types funext univalence truncations +open import univalent-combinatorics.decidable-dependent-pair-types funext univalence truncations +open import univalent-combinatorics.dependent-function-types funext univalence truncations +open import univalent-combinatorics.dependent-pair-types funext univalence truncations +open import univalent-combinatorics.equality-finite-types funext univalence truncations +open import univalent-combinatorics.finite-types funext univalence truncations +open import univalent-combinatorics.finitely-many-connected-components funext univalence truncations +open import univalent-combinatorics.pi-finite-types funext univalence truncations +open import univalent-combinatorics.standard-finite-types funext univalence truncations +open import univalent-combinatorics.untruncated-pi-finite-types funext univalence truncations ```
diff --git a/src/finite-group-theory/finite-semigroups.lagda.md b/src/finite-group-theory/finite-semigroups.lagda.md index 80e46d4e23..cd77185a02 100644 --- a/src/finite-group-theory/finite-semigroups.lagda.md +++ b/src/finite-group-theory/finite-semigroups.lagda.md @@ -1,7 +1,15 @@ # Finite semigroups ```agda -module finite-group-theory.finite-semigroups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module finite-group-theory.finite-semigroups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,32 +17,32 @@ module finite-group-theory.finite-semigroups where ```agda open import elementary-number-theory.natural-numbers -open import foundation.1-types -open import foundation.decidable-propositions -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.identity-types -open import foundation.mere-equivalences -open import foundation.propositions -open import foundation.set-truncations -open import foundation.sets -open import foundation.subtypes +open import foundation.1-types funext univalence +open import foundation.decidable-propositions funext univalence truncations +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.identity-types funext +open import foundation.mere-equivalences funext univalence truncations +open import foundation.propositions funext univalence +open import foundation.set-truncations funext univalence +open import foundation.sets funext univalence open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels -open import group-theory.category-of-semigroups -open import group-theory.semigroups - -open import univalent-combinatorics.dependent-function-types -open import univalent-combinatorics.dependent-pair-types -open import univalent-combinatorics.equality-finite-types -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.finitely-many-connected-components -open import univalent-combinatorics.function-types -open import univalent-combinatorics.pi-finite-types -open import univalent-combinatorics.standard-finite-types -open import univalent-combinatorics.untruncated-pi-finite-types +open import group-theory.category-of-semigroups funext univalence truncations +open import group-theory.semigroups funext univalence + +open import univalent-combinatorics.dependent-function-types funext univalence truncations +open import univalent-combinatorics.dependent-pair-types funext univalence truncations +open import univalent-combinatorics.equality-finite-types funext univalence truncations +open import univalent-combinatorics.finite-types funext univalence truncations +open import univalent-combinatorics.finitely-many-connected-components funext univalence truncations +open import univalent-combinatorics.function-types funext univalence truncations +open import univalent-combinatorics.pi-finite-types funext univalence truncations +open import univalent-combinatorics.standard-finite-types funext univalence truncations +open import univalent-combinatorics.untruncated-pi-finite-types funext univalence truncations ```
diff --git a/src/finite-group-theory/finite-type-groups.lagda.md b/src/finite-group-theory/finite-type-groups.lagda.md index 4a1905d8df..a8d6dbe089 100644 --- a/src/finite-group-theory/finite-type-groups.lagda.md +++ b/src/finite-group-theory/finite-type-groups.lagda.md @@ -2,8 +2,15 @@ ```agda {-# OPTIONS --lossy-unification #-} - -module finite-group-theory.finite-type-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module finite-group-theory.finite-type-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -11,36 +18,38 @@ module finite-group-theory.finite-type-groups where ```agda open import elementary-number-theory.natural-numbers -open import foundation.0-connected-types -open import foundation.1-types +open import foundation.0-connected-types funext univalence truncations open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.identity-types -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.raising-universe-levels -open import foundation.sets -open import foundation.truncated-types +open import foundation.dependent-products-propositions funext +open import foundation.dependent-products-truncated-types funext +open import foundation.equality-dependent-pair-types funext +open import foundation.function-extensionality funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.truncated-types funext univalence open import foundation.universe-levels -open import group-theory.concrete-groups -open import group-theory.groups -open import group-theory.homomorphisms-groups -open import group-theory.homomorphisms-semigroups -open import group-theory.isomorphisms-groups -open import group-theory.loop-groups-sets -open import group-theory.monoids -open import group-theory.semigroups +open import foundation-core.raising-universe-levels + +open import group-theory.concrete-groups funext univalence truncations +open import group-theory.groups funext univalence truncations +open import group-theory.homomorphisms-groups funext univalence truncations +open import group-theory.homomorphisms-semigroups funext univalence truncations +open import group-theory.isomorphisms-groups funext univalence truncations +open import group-theory.loop-groups-sets funext univalence truncations +open import group-theory.monoids funext univalence truncations +open import group-theory.semigroups funext univalence -open import higher-group-theory.higher-groups +open import higher-group-theory.higher-groups funext univalence truncations open import structured-types.pointed-types -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.finite-types funext univalence truncations +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/finite-group-theory/groups-of-order-2.lagda.md b/src/finite-group-theory/groups-of-order-2.lagda.md index 05de139f31..918098ce78 100644 --- a/src/finite-group-theory/groups-of-order-2.lagda.md +++ b/src/finite-group-theory/groups-of-order-2.lagda.md @@ -2,35 +2,42 @@ ```agda {-# OPTIONS --lossy-unification #-} - -module finite-group-theory.groups-of-order-2 where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module finite-group-theory.groups-of-order-2 + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.standard-cyclic-groups +open import elementary-number-theory.standard-cyclic-groups funext univalence truncations -open import finite-group-theory.finite-groups +open import finite-group-theory.finite-groups funext univalence truncations open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalences +open import foundation.equivalences funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types -open import foundation.mere-equivalences -open import foundation.propositional-truncations -open import foundation.sets +open import foundation.identity-types funext +open import foundation.mere-equivalences funext univalence truncations +open import foundation.propositional-truncations funext univalence +open import foundation.sets funext univalence open import foundation.subtype-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext univalence truncations open import foundation.universe-levels -open import group-theory.groups -open import group-theory.isomorphisms-groups -open import group-theory.symmetric-groups +open import group-theory.groups funext univalence truncations +open import group-theory.isomorphisms-groups funext univalence truncations +open import group-theory.symmetric-groups funext univalence truncations -open import univalent-combinatorics.2-element-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.2-element-types funext univalence truncations +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/finite-group-theory/orbits-permutations.lagda.md b/src/finite-group-theory/orbits-permutations.lagda.md index 06919a3b39..e34f6ff4cc 100644 --- a/src/finite-group-theory/orbits-permutations.lagda.md +++ b/src/finite-group-theory/orbits-permutations.lagda.md @@ -2,67 +2,75 @@ ```agda {-# OPTIONS --lossy-unification #-} - -module finite-group-theory.orbits-permutations where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module finite-group-theory.orbits-permutations + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.decidable-types -open import elementary-number-theory.equality-natural-numbers -open import elementary-number-theory.euclidean-division-natural-numbers -open import elementary-number-theory.inequality-natural-numbers -open import elementary-number-theory.lower-bounds-natural-numbers +open import elementary-number-theory.decidable-types funext univalence truncations +open import elementary-number-theory.equality-natural-numbers funext univalence truncations +open import elementary-number-theory.euclidean-division-natural-numbers funext univalence truncations +open import elementary-number-theory.inequality-natural-numbers funext univalence truncations +open import elementary-number-theory.lower-bounds-natural-numbers funext univalence truncations open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.strict-inequality-natural-numbers -open import elementary-number-theory.well-ordering-principle-natural-numbers +open import elementary-number-theory.strict-inequality-natural-numbers funext univalence truncations +open import elementary-number-theory.well-ordering-principle-natural-numbers funext univalence truncations -open import finite-group-theory.transpositions +open import finite-group-theory.transpositions funext univalence truncations open import foundation.action-on-identifications-functions -open import foundation.automorphisms -open import foundation.cartesian-product-types -open import foundation.coproduct-types -open import foundation.decidable-equality -open import foundation.decidable-equivalence-relations -open import foundation.decidable-propositions -open import foundation.decidable-types +open import foundation.automorphisms funext univalence +open import foundation.cartesian-product-types funext univalence +open import foundation.coproduct-types funext univalence truncations +open import foundation.decidable-equality funext univalence truncations +open import foundation.decidable-equivalence-relations funext univalence truncations +open import foundation.decidable-propositions funext univalence truncations +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.double-negation -open import foundation.empty-types -open import foundation.equality-dependent-pair-types -open import foundation.equivalence-classes -open import foundation.equivalence-extensionality -open import foundation.equivalence-relations -open import foundation.equivalences -open import foundation.function-types -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.iterating-functions -open import foundation.logical-equivalences -open import foundation.negated-equality -open import foundation.negation -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.repetitions-of-values -open import foundation.sets +open import foundation.dependent-products-propositions funext +open import foundation.double-negation funext univalence truncations +open import foundation.empty-types funext univalence truncations +open import foundation.equality-dependent-pair-types funext +open import foundation.equivalence-classes funext univalence truncations +open import foundation.equivalence-extensionality funext +open import foundation.equivalence-relations funext univalence truncations +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.iterating-functions funext univalence truncations +open import foundation.logical-equivalences funext +open import foundation.negated-equality funext univalence truncations +open import foundation.negation funext +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence +open import foundation.repetitions-of-values funext univalence truncations +open import foundation.sets funext univalence open import foundation.transport-along-identifications open import foundation.unit-type open import foundation.universe-levels open import lists.lists -open import univalent-combinatorics.2-element-decidable-subtypes -open import univalent-combinatorics.2-element-types -open import univalent-combinatorics.counting -open import univalent-combinatorics.equality-standard-finite-types -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.image-of-maps -open import univalent-combinatorics.pigeonhole-principle -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.2-element-decidable-subtypes funext univalence truncations +open import univalent-combinatorics.2-element-types funext univalence truncations +open import univalent-combinatorics.counting funext univalence truncations +open import univalent-combinatorics.equality-standard-finite-types funext univalence truncations +open import univalent-combinatorics.finite-types funext univalence truncations +open import univalent-combinatorics.image-of-maps funext univalence truncations +open import univalent-combinatorics.pigeonhole-principle funext univalence truncations +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/finite-group-theory/permutations-standard-finite-types.lagda.md b/src/finite-group-theory/permutations-standard-finite-types.lagda.md index 0be0d3314d..609e7c87bb 100644 --- a/src/finite-group-theory/permutations-standard-finite-types.lagda.md +++ b/src/finite-group-theory/permutations-standard-finite-types.lagda.md @@ -2,8 +2,15 @@ ```agda {-# OPTIONS --lossy-unification #-} +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom -module finite-group-theory.permutations-standard-finite-types where +module finite-group-theory.permutations-standard-finite-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -11,37 +18,38 @@ module finite-group-theory.permutations-standard-finite-types where ```agda open import elementary-number-theory.natural-numbers -open import finite-group-theory.transpositions +open import finite-group-theory.transpositions funext univalence truncations open import foundation.action-on-identifications-functions -open import foundation.automorphisms -open import foundation.cartesian-product-types -open import foundation.coproduct-types -open import foundation.decidable-propositions +open import foundation.automorphisms funext univalence +open import foundation.cartesian-product-types funext univalence +open import foundation.coproduct-types funext univalence truncations +open import foundation.decidable-propositions funext univalence truncations open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.equality-dependent-pair-types -open import foundation.equivalence-extensionality -open import foundation.equivalences -open import foundation.equivalences-maybe -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.negated-equality -open import foundation.propositions -open import foundation.sets +open import foundation.dependent-products-propositions funext +open import foundation.empty-types funext univalence truncations +open import foundation.equality-dependent-pair-types funext +open import foundation.equivalence-extensionality funext +open import foundation.equivalences funext +open import foundation.equivalences-maybe funext univalence truncations +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.negated-equality funext univalence truncations +open import foundation.propositions funext univalence +open import foundation.sets funext univalence open import foundation.unit-type open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import lists.functoriality-lists +open import lists.functoriality-lists funext univalence truncations open import lists.lists -open import univalent-combinatorics.2-element-decidable-subtypes -open import univalent-combinatorics.equality-standard-finite-types -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.2-element-decidable-subtypes funext univalence truncations +open import univalent-combinatorics.equality-standard-finite-types funext univalence truncations +open import univalent-combinatorics.finite-types funext univalence truncations +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/finite-group-theory/permutations.lagda.md b/src/finite-group-theory/permutations.lagda.md index 02097ffebf..ba99bc6936 100644 --- a/src/finite-group-theory/permutations.lagda.md +++ b/src/finite-group-theory/permutations.lagda.md @@ -2,54 +2,64 @@ ```agda {-# OPTIONS --lossy-unification #-} +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom -module finite-group-theory.permutations where +module finite-group-theory.permutations + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.modular-arithmetic-standard-finite-types +open import elementary-number-theory.modular-arithmetic-standard-finite-types funext univalence truncations open import elementary-number-theory.natural-numbers -open import finite-group-theory.orbits-permutations -open import finite-group-theory.permutations-standard-finite-types -open import finite-group-theory.transpositions +open import finite-group-theory.orbits-permutations funext univalence truncations +open import finite-group-theory.permutations-standard-finite-types funext univalence truncations +open import finite-group-theory.transpositions funext univalence truncations open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types -open import foundation.contractible-types -open import foundation.coproduct-types -open import foundation.decidable-propositions +open import foundation.cartesian-product-types funext univalence +open import foundation.contractible-types funext univalence +open import foundation.coproduct-types funext univalence truncations +open import foundation.decidable-propositions funext univalence truncations open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.equality-dependent-pair-types -open import foundation.equivalence-extensionality -open import foundation.equivalences -open import foundation.function-types -open import foundation.identity-types -open import foundation.iterating-functions -open import foundation.iterating-involutions -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.sets -open import foundation.truncated-types +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.dependent-products-truncated-types funext +open import foundation.empty-types funext univalence truncations +open import foundation.equality-dependent-pair-types funext +open import foundation.equivalence-extensionality funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.iterating-functions funext univalence truncations +open import foundation.iterating-involutions funext univalence truncations +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.truncated-types funext univalence open import foundation.truncation-levels open import foundation.unit-type open import foundation.universe-levels -open import group-theory.generating-sets-groups -open import group-theory.subgroups-generated-by-subsets-groups -open import group-theory.symmetric-groups +open import group-theory.generating-sets-groups funext univalence truncations +open import group-theory.subgroups-generated-by-subsets-groups funext univalence truncations +open import group-theory.symmetric-groups funext univalence truncations -open import lists.functoriality-lists +open import lists.functoriality-lists funext univalence truncations open import lists.lists -open import univalent-combinatorics.2-element-decidable-subtypes -open import univalent-combinatorics.2-element-types -open import univalent-combinatorics.counting -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.2-element-decidable-subtypes funext univalence truncations +open import univalent-combinatorics.2-element-types funext univalence truncations +open import univalent-combinatorics.counting funext univalence truncations +open import univalent-combinatorics.finite-types funext univalence truncations +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/finite-group-theory/sign-homomorphism.lagda.md b/src/finite-group-theory/sign-homomorphism.lagda.md index 877705c2d4..010f9dfd79 100644 --- a/src/finite-group-theory/sign-homomorphism.lagda.md +++ b/src/finite-group-theory/sign-homomorphism.lagda.md @@ -1,45 +1,54 @@ # The sign homomorphism ```agda -module finite-group-theory.sign-homomorphism where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module finite-group-theory.sign-homomorphism + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.modular-arithmetic-standard-finite-types +open import elementary-number-theory.modular-arithmetic-standard-finite-types funext univalence truncations open import elementary-number-theory.natural-numbers -open import finite-group-theory.permutations -open import finite-group-theory.transpositions +open import finite-group-theory.permutations funext univalence truncations +open import finite-group-theory.transpositions funext univalence truncations open import foundation.action-on-identifications-functions -open import foundation.automorphisms -open import foundation.contractible-types -open import foundation.coproduct-types -open import foundation.decidable-propositions +open import foundation.automorphisms funext univalence +open import foundation.contractible-types funext univalence +open import foundation.coproduct-types funext univalence truncations +open import foundation.decidable-propositions funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalence-extensionality -open import foundation.equivalences -open import foundation.function-types -open import foundation.identity-types -open import foundation.propositional-truncations -open import foundation.sets +open import foundation.dependent-products-contractible-types funext +open import foundation.equivalence-extensionality funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.propositional-truncations funext univalence +open import foundation.sets funext univalence open import foundation.unit-type open import foundation.universe-levels -open import group-theory.homomorphisms-groups -open import group-theory.homomorphisms-semigroups -open import group-theory.symmetric-groups +open import group-theory.homomorphisms-groups funext univalence truncations +open import group-theory.homomorphisms-semigroups funext univalence truncations +open import group-theory.symmetric-groups funext univalence truncations -open import lists.concatenation-lists -open import lists.functoriality-lists +open import lists.concatenation-lists funext univalence truncations +open import lists.functoriality-lists funext univalence truncations open import lists.lists -open import univalent-combinatorics.2-element-decidable-subtypes -open import univalent-combinatorics.2-element-types -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.2-element-decidable-subtypes funext univalence truncations +open import univalent-combinatorics.2-element-types funext univalence truncations +open import univalent-combinatorics.finite-types funext univalence truncations +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/finite-group-theory/simpson-delooping-sign-homomorphism.lagda.md b/src/finite-group-theory/simpson-delooping-sign-homomorphism.lagda.md index 5e6d56f993..f7be993ff2 100644 --- a/src/finite-group-theory/simpson-delooping-sign-homomorphism.lagda.md +++ b/src/finite-group-theory/simpson-delooping-sign-homomorphism.lagda.md @@ -2,67 +2,75 @@ ```agda {-# OPTIONS --lossy-unification #-} - -module finite-group-theory.simpson-delooping-sign-homomorphism where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module finite-group-theory.simpson-delooping-sign-homomorphism + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.congruence-natural-numbers -open import elementary-number-theory.inequality-natural-numbers -open import elementary-number-theory.modular-arithmetic-standard-finite-types +open import elementary-number-theory.congruence-natural-numbers funext univalence truncations +open import elementary-number-theory.inequality-natural-numbers funext univalence truncations +open import elementary-number-theory.modular-arithmetic-standard-finite-types funext univalence truncations open import elementary-number-theory.natural-numbers -open import finite-group-theory.delooping-sign-homomorphism -open import finite-group-theory.finite-type-groups -open import finite-group-theory.permutations -open import finite-group-theory.sign-homomorphism -open import finite-group-theory.transpositions +open import finite-group-theory.delooping-sign-homomorphism funext univalence truncations +open import finite-group-theory.finite-type-groups funext univalence truncations +open import finite-group-theory.permutations funext univalence truncations +open import finite-group-theory.sign-homomorphism funext univalence truncations +open import finite-group-theory.transpositions funext univalence truncations -open import foundation.action-on-equivalences-type-families-over-subuniverses +open import foundation.action-on-equivalences-type-families-over-subuniverses funext univalence open import foundation.action-on-identifications-functions -open import foundation.contractible-types -open import foundation.coproduct-types -open import foundation.decidable-equivalence-relations -open import foundation.decidable-types +open import foundation.contractible-types funext univalence +open import foundation.coproduct-types funext univalence truncations +open import foundation.decidable-equivalence-relations funext univalence truncations +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.equivalence-classes -open import foundation.equivalence-extensionality -open import foundation.equivalence-relations -open import foundation.equivalences -open import foundation.function-types -open import foundation.identity-types -open import foundation.involutions -open import foundation.logical-equivalences -open import foundation.mere-equivalences -open import foundation.negation -open import foundation.propositional-truncations -open import foundation.raising-universe-levels -open import foundation.sets +open import foundation.dependent-products-contractible-types funext +open import foundation.empty-types funext univalence truncations +open import foundation.equivalence-classes funext univalence truncations +open import foundation.equivalence-extensionality funext +open import foundation.equivalence-relations funext univalence truncations +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.involutions funext univalence +open import foundation.logical-equivalences funext +open import foundation.mere-equivalences funext univalence truncations +open import foundation.negation funext +open import foundation.propositional-truncations funext univalence +open import foundation.sets funext univalence open import foundation.transport-along-identifications -open import foundation.type-theoretic-principle-of-choice +open import foundation.type-theoretic-principle-of-choice funext open import foundation.unit-type open import foundation.universe-levels -open import group-theory.concrete-groups -open import group-theory.groups -open import group-theory.homomorphisms-concrete-groups -open import group-theory.homomorphisms-groups -open import group-theory.isomorphisms-groups -open import group-theory.loop-groups-sets -open import group-theory.symmetric-groups +open import foundation-core.raising-universe-levels + +open import group-theory.groups funext univalence truncations +open import group-theory.homomorphisms-concrete-groups funext univalence truncations +open import group-theory.homomorphisms-groups funext univalence truncations +open import group-theory.isomorphisms-groups funext univalence truncations +open import group-theory.loop-groups-sets funext univalence truncations +open import group-theory.symmetric-groups funext univalence truncations open import lists.lists -open import univalent-combinatorics.2-element-decidable-subtypes -open import univalent-combinatorics.counting -open import univalent-combinatorics.equality-finite-types -open import univalent-combinatorics.equality-standard-finite-types -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.2-element-decidable-subtypes funext univalence truncations +open import univalent-combinatorics.counting funext univalence truncations +open import univalent-combinatorics.equality-finite-types funext univalence truncations +open import univalent-combinatorics.equality-standard-finite-types funext univalence truncations +open import univalent-combinatorics.finite-types funext univalence truncations +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/finite-group-theory/subgroups-finite-groups.lagda.md b/src/finite-group-theory/subgroups-finite-groups.lagda.md index e693dcaa67..523cb55c78 100644 --- a/src/finite-group-theory/subgroups-finite-groups.lagda.md +++ b/src/finite-group-theory/subgroups-finite-groups.lagda.md @@ -1,34 +1,43 @@ # Subgroups of finite groups ```agda -module finite-group-theory.subgroups-finite-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module finite-group-theory.subgroups-finite-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import finite-group-theory.finite-groups -open import finite-group-theory.finite-semigroups +open import finite-group-theory.finite-groups funext univalence truncations +open import finite-group-theory.finite-semigroups funext univalence truncations -open import foundation.binary-relations +open import foundation.binary-relations funext univalence truncations open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalence-relations -open import foundation.equivalences -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets +open import foundation.dependent-products-propositions funext +open import foundation.embeddings funext +open import foundation.equivalence-relations funext univalence truncations +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence open import foundation.universe-levels -open import group-theory.decidable-subgroups -open import group-theory.groups -open import group-theory.homomorphisms-groups -open import group-theory.semigroups -open import group-theory.subgroups -open import group-theory.subsets-groups +open import group-theory.decidable-subgroups funext univalence truncations +open import group-theory.groups funext univalence truncations +open import group-theory.homomorphisms-groups funext univalence truncations +open import group-theory.semigroups funext univalence +open import group-theory.subgroups funext univalence truncations +open import group-theory.subsets-groups funext univalence truncations -open import univalent-combinatorics.decidable-subtypes -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.decidable-subtypes funext univalence truncations +open import univalent-combinatorics.finite-types funext univalence truncations ```
diff --git a/src/finite-group-theory/tetrahedra-in-3-space.lagda.md b/src/finite-group-theory/tetrahedra-in-3-space.lagda.md index 6fac18a6da..ef6e219cb0 100644 --- a/src/finite-group-theory/tetrahedra-in-3-space.lagda.md +++ b/src/finite-group-theory/tetrahedra-in-3-space.lagda.md @@ -1,19 +1,27 @@ # Tetrahedra in `3`-dimensional space ```agda -module finite-group-theory.tetrahedra-in-3-space where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module finite-group-theory.tetrahedra-in-3-space + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.empty-types +open import foundation.empty-types funext univalence truncations open import foundation.universe-levels -open import univalent-combinatorics.2-element-decidable-subtypes -open import univalent-combinatorics.cyclic-finite-types -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.2-element-decidable-subtypes funext univalence truncations +open import univalent-combinatorics.cyclic-finite-types funext univalence truncations +open import univalent-combinatorics.finite-types funext univalence truncations ```
diff --git a/src/finite-group-theory/transpositions-standard-finite-types.lagda.md b/src/finite-group-theory/transpositions-standard-finite-types.lagda.md index bd345f2692..470c2df57d 100644 --- a/src/finite-group-theory/transpositions-standard-finite-types.lagda.md +++ b/src/finite-group-theory/transpositions-standard-finite-types.lagda.md @@ -2,8 +2,15 @@ ```agda {-# OPTIONS --lossy-unification #-} - -module finite-group-theory.transpositions-standard-finite-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module finite-group-theory.transpositions-standard-finite-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -11,31 +18,32 @@ module finite-group-theory.transpositions-standard-finite-types where ```agda open import elementary-number-theory.natural-numbers -open import finite-group-theory.permutations-standard-finite-types -open import finite-group-theory.transpositions +open import finite-group-theory.permutations-standard-finite-types funext univalence truncations +open import finite-group-theory.transpositions funext univalence truncations open import foundation.action-on-identifications-functions -open import foundation.coproduct-types +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.equivalence-extensionality -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-coproduct-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.negated-equality -open import foundation.negation -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.empty-types funext univalence truncations +open import foundation.equivalence-extensionality funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-coproduct-types funext univalence truncations +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.negated-equality funext univalence truncations +open import foundation.negation funext +open import foundation.propositions funext univalence open import foundation.unit-type open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import lists.functoriality-lists +open import lists.functoriality-lists funext univalence truncations open import lists.lists -open import univalent-combinatorics.equality-standard-finite-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.equality-standard-finite-types funext univalence truncations +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/finite-group-theory/transpositions.lagda.md b/src/finite-group-theory/transpositions.lagda.md index 1900b49eed..7920d7d65d 100644 --- a/src/finite-group-theory/transpositions.lagda.md +++ b/src/finite-group-theory/transpositions.lagda.md @@ -1,61 +1,71 @@ # Transpositions ```agda -module finite-group-theory.transpositions where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module finite-group-theory.transpositions + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import elementary-number-theory.natural-numbers -open import elementary-number-theory.well-ordering-principle-standard-finite-types +open import elementary-number-theory.well-ordering-principle-standard-finite-types funext univalence truncations open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.automorphisms -open import foundation.cartesian-product-types -open import foundation.coproduct-types -open import foundation.decidable-equality -open import foundation.decidable-propositions -open import foundation.decidable-subtypes -open import foundation.decidable-types +open import foundation.automorphisms funext univalence +open import foundation.cartesian-product-types funext univalence +open import foundation.coproduct-types funext univalence truncations +open import foundation.decidable-equality funext univalence truncations +open import foundation.decidable-propositions funext univalence truncations +open import foundation.decidable-subtypes funext univalence truncations +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.equality-dependent-pair-types -open import foundation.equivalence-extensionality -open import foundation.equivalences -open import foundation.equivalences-maybe -open import foundation.fibers-of-maps -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.functoriality-coproduct-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.involutions -open import foundation.logical-equivalences -open import foundation.negated-equality -open import foundation.propositional-extensionality -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.raising-universe-levels -open import foundation.sets +open import foundation.dependent-products-propositions funext +open import foundation.empty-types funext univalence truncations +open import foundation.equality-dependent-pair-types funext +open import foundation.equivalence-extensionality funext +open import foundation.equivalences funext +open import foundation.equivalences-maybe funext univalence truncations +open import foundation.fibers-of-maps funext +open import foundation.function-extensionality funext +open import foundation.function-types funext +open import foundation.functoriality-coproduct-types funext univalence truncations +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.involutions funext univalence +open import foundation.logical-equivalences funext +open import foundation.negated-equality funext univalence truncations +open import foundation.propositional-extensionality funext univalence truncations +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence +open import foundation.sets funext univalence open import foundation.transport-along-identifications -open import foundation.type-arithmetic-empty-type +open import foundation.type-arithmetic-empty-type funext univalence truncations open import foundation.unit-type -open import foundation.univalence +open import foundation.univalence funext univalence open import foundation.universe-levels -open import lists.concatenation-lists -open import lists.functoriality-lists +open import foundation-core.raising-universe-levels + +open import lists.concatenation-lists funext univalence truncations +open import lists.functoriality-lists funext univalence truncations open import lists.lists -open import univalent-combinatorics.2-element-decidable-subtypes -open import univalent-combinatorics.2-element-types -open import univalent-combinatorics.counting -open import univalent-combinatorics.equality-standard-finite-types -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.2-element-decidable-subtypes funext univalence truncations +open import univalent-combinatorics.2-element-types funext univalence truncations +open import univalent-combinatorics.counting funext univalence truncations +open import univalent-combinatorics.equality-standard-finite-types funext univalence truncations +open import univalent-combinatorics.finite-types funext univalence truncations +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/foundation-core.lagda.md b/src/foundation-core.lagda.md index 9b9dd2512c..780e6876fd 100644 --- a/src/foundation-core.lagda.md +++ b/src/foundation-core.lagda.md @@ -3,42 +3,54 @@ ## Modules in the foundation-core namespace ```agda -module foundation-core where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom -open import foundation-core.1-types public +module foundation-core + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where + +open import foundation-core.1-types funext univalence public +open import foundation-core.booleans public open import foundation-core.cartesian-product-types public open import foundation-core.coherently-invertible-maps public -open import foundation-core.commuting-prisms-of-maps public +open import foundation-core.commuting-prisms-of-maps funext public open import foundation-core.commuting-squares-of-homotopies public open import foundation-core.commuting-squares-of-identifications public -open import foundation-core.commuting-squares-of-maps public +open import foundation-core.commuting-squares-of-maps funext public open import foundation-core.commuting-triangles-of-maps public open import foundation-core.constant-maps public open import foundation-core.contractible-maps public open import foundation-core.contractible-types public open import foundation-core.coproduct-types public -open import foundation-core.decidable-propositions public +open import foundation-core.decidable-propositions funext univalence truncations public open import foundation-core.dependent-identifications public open import foundation-core.diagonal-maps-cartesian-products-of-types public -open import foundation-core.discrete-types public +open import foundation-core.diagonal-maps-of-types public +open import foundation-core.discrete-types funext univalence truncations public open import foundation-core.embeddings public open import foundation-core.empty-types public -open import foundation-core.endomorphisms public +open import foundation-core.endomorphisms funext univalence public open import foundation-core.equality-dependent-pair-types public -open import foundation-core.equivalence-relations public +open import foundation-core.equivalence-relations funext univalence truncations public open import foundation-core.equivalences public open import foundation-core.families-of-equivalences public open import foundation-core.fibers-of-maps public open import foundation-core.function-types public -open import foundation-core.functoriality-dependent-function-types public +open import foundation-core.functoriality-dependent-function-types funext public open import foundation-core.functoriality-dependent-pair-types public open import foundation-core.homotopies public open import foundation-core.identity-types public open import foundation-core.injective-maps public open import foundation-core.invertible-maps public +open import foundation-core.logical-equivalences public +open import foundation-core.maybe public open import foundation-core.negation public -open import foundation-core.operations-span-diagrams public -open import foundation-core.operations-spans public +open import foundation-core.operations-span-diagrams funext univalence truncations public +open import foundation-core.operations-spans funext public open import foundation-core.path-split-maps public open import foundation-core.postcomposition-dependent-functions public open import foundation-core.postcomposition-functions public @@ -46,22 +58,23 @@ open import foundation-core.precomposition-dependent-functions public open import foundation-core.precomposition-functions public open import foundation-core.propositional-maps public open import foundation-core.propositions public -open import foundation-core.pullbacks public +open import foundation-core.pullbacks funext public +open import foundation-core.raising-universe-levels public open import foundation-core.retractions public open import foundation-core.retracts-of-types public open import foundation-core.sections public open import foundation-core.sets public -open import foundation-core.small-types public -open import foundation-core.subtypes public +open import foundation-core.small-types funext univalence truncations public +open import foundation-core.subtypes funext public open import foundation-core.torsorial-type-families public open import foundation-core.transport-along-identifications public -open import foundation-core.truncated-maps public +open import foundation-core.truncated-maps funext public open import foundation-core.truncated-types public open import foundation-core.truncation-levels public open import foundation-core.type-theoretic-principle-of-choice public open import foundation-core.univalence public -open import foundation-core.universal-property-pullbacks public -open import foundation-core.universal-property-truncation public +open import foundation-core.universal-property-pullbacks funext public +open import foundation-core.universal-property-truncation funext public open import foundation-core.whiskering-homotopies-concatenation public open import foundation-core.whiskering-identifications-concatenation public ``` diff --git a/src/foundation-core/1-types.lagda.md b/src/foundation-core/1-types.lagda.md index 79ac7bd491..2c32d3593c 100644 --- a/src/foundation-core/1-types.lagda.md +++ b/src/foundation-core/1-types.lagda.md @@ -1,15 +1,23 @@ # `1`-Types ```agda -module foundation-core.1-types where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation-core.1-types + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda -open import foundation.contractible-types +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.truncated-types +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-truncated-types funext +open import foundation.truncated-types funext univalence open import foundation.universe-levels open import foundation-core.equivalences diff --git a/src/foundation-core/booleans.lagda.md b/src/foundation-core/booleans.lagda.md new file mode 100644 index 0000000000..c952e4b34a --- /dev/null +++ b/src/foundation-core/booleans.lagda.md @@ -0,0 +1,235 @@ +# The booleans + +```agda +module foundation-core.booleans where +``` + +
Imports + +```agda +open import foundation.dependent-pair-types +open import foundation.unit-type +open import foundation.universe-levels + +open import foundation-core.constant-maps +open import foundation-core.empty-types +open import foundation-core.equivalences +open import foundation-core.function-types +open import foundation-core.identity-types +open import foundation-core.negation +open import foundation-core.propositions +open import foundation-core.sections +open import foundation-core.sets +``` + +
+ +## Idea + +The type of **booleans** is a +[2-element type](univalent-combinatorics.2-element-types.md) with elements +`true false : bool`, which is used for reasoning with +[decidable propositions](foundation-core.decidable-propositions.md). + +## Definition + +### The booleans + +```agda +data bool : UU lzero where + true false : bool + +{-# BUILTIN BOOL bool #-} +{-# BUILTIN TRUE true #-} +{-# BUILTIN FALSE false #-} +``` + +### The induction principle of the booleans + +```agda +module _ + {l : Level} (P : bool → UU l) + where + + ind-bool : P true → P false → (b : bool) → P b + ind-bool pt pf true = pt + ind-bool pt pf false = pf +``` + +### The recursion principle of the booleans + +```agda +module _ + {l : Level} {P : UU l} + where + + rec-bool : P → P → bool → P + rec-bool = ind-bool (λ _ → P) +``` + +### The `if_then_else` function + +```agda +module _ + {l : Level} {A : UU l} + where + + if_then_else_ : bool → A → A → A + if b then x else y = rec-bool x y b +``` + +### The standard propositions associated to the constructors of bool + +```agda +prop-bool : bool → Prop lzero +prop-bool true = unit-Prop +prop-bool false = empty-Prop + +type-prop-bool : bool → UU lzero +type-prop-bool = type-Prop ∘ prop-bool +``` + +### Equality on the booleans + +```agda +Eq-bool : bool → bool → UU lzero +Eq-bool true true = unit +Eq-bool true false = empty +Eq-bool false true = empty +Eq-bool false false = unit + +refl-Eq-bool : (x : bool) → Eq-bool x x +refl-Eq-bool true = star +refl-Eq-bool false = star + +Eq-eq-bool : + {x y : bool} → x ＝ y → Eq-bool x y +Eq-eq-bool {x = x} refl = refl-Eq-bool x + +eq-Eq-bool : + {x y : bool} → Eq-bool x y → x ＝ y +eq-Eq-bool {true} {true} star = refl +eq-Eq-bool {false} {false} star = refl + +neq-false-true-bool : ¬ (false ＝ true) +neq-false-true-bool () + +neq-true-false-bool : ¬ (true ＝ false) +neq-true-false-bool () +``` + +## Structure + +### The boolean operators + +```agda +neg-bool : bool → bool +neg-bool true = false +neg-bool false = true + +conjunction-bool : bool → bool → bool +conjunction-bool true true = true +conjunction-bool true false = false +conjunction-bool false true = false +conjunction-bool false false = false + +disjunction-bool : bool → bool → bool +disjunction-bool true true = true +disjunction-bool true false = true +disjunction-bool false true = true +disjunction-bool false false = false + +implication-bool : bool → bool → bool +implication-bool true true = true +implication-bool true false = false +implication-bool false true = true +implication-bool false false = true +``` + +## Properties + +### The booleans are a set + +```agda +abstract + is-prop-Eq-bool : (x y : bool) → is-prop (Eq-bool x y) + is-prop-Eq-bool true true = is-prop-unit + is-prop-Eq-bool true false = is-prop-empty + is-prop-Eq-bool false true = is-prop-empty + is-prop-Eq-bool false false = is-prop-unit + +abstract + is-set-bool : is-set bool + is-set-bool = + is-set-prop-in-id + ( Eq-bool) + ( is-prop-Eq-bool) + ( refl-Eq-bool) + ( λ x y → eq-Eq-bool) + +bool-Set : Set lzero +bool-Set = bool , is-set-bool +``` + +### The "is true" predicate on booleans + +```agda +is-true : bool → UU lzero +is-true = _＝ true + +is-prop-is-true : (b : bool) → is-prop (is-true b) +is-prop-is-true b = is-set-bool b true + +is-true-Prop : bool → Prop lzero +is-true-Prop b = is-true b , is-prop-is-true b +``` + +### The "is false" predicate on booleans + +```agda +is-false : bool → UU lzero +is-false = _＝ false + +is-prop-is-false : (b : bool) → is-prop (is-false b) +is-prop-is-false b = is-set-bool b false + +is-false-Prop : bool → Prop lzero +is-false-Prop b = is-false b , is-prop-is-false b +``` + +### A boolean cannot be both true and false + +```agda +not-is-false-is-true : (x : bool) → is-true x → ¬ (is-false x) +not-is-false-is-true true t () +not-is-false-is-true false () f + +not-is-true-is-false : (x : bool) → is-false x → ¬ (is-true x) +not-is-true-is-false true () f +not-is-true-is-false false t () +``` + +### Boolean negation has no fixed points + +```agda +neq-neg-bool : (b : bool) → ¬ (b ＝ neg-bool b) +neq-neg-bool true () +neq-neg-bool false () + +neq-neg-bool' : (b : bool) → ¬ (neg-bool b ＝ b) +neq-neg-bool' b = neq-neg-bool b ∘ inv +``` + +### The constant function `const bool b` is not an equivalence + +```agda +abstract + no-section-const-bool : (b : bool) → ¬ (section (const bool b)) + no-section-const-bool true (g , G) = neq-true-false-bool (G false) + no-section-const-bool false (g , G) = neq-false-true-bool (G true) + +abstract + is-not-equiv-const-bool : + (b : bool) → ¬ (is-equiv (const bool b)) + is-not-equiv-const-bool b e = no-section-const-bool b (section-is-equiv e) +``` diff --git a/src/foundation-core/commuting-prisms-of-maps.lagda.md b/src/foundation-core/commuting-prisms-of-maps.lagda.md index 68a2637fd1..ce691c1f1e 100644 --- a/src/foundation-core/commuting-prisms-of-maps.lagda.md +++ b/src/foundation-core/commuting-prisms-of-maps.lagda.md @@ -1,7 +1,11 @@ # Commuting prisms of maps ```agda -module foundation-core.commuting-prisms-of-maps where +open import foundation.function-extensionality-axiom + +module foundation-core.commuting-prisms-of-maps + (funext : function-extensionality) + where ```
Imports @@ -9,14 +13,14 @@ module foundation-core.commuting-prisms-of-maps where ```agda open import foundation.action-on-identifications-functions open import foundation.commuting-pentagons-of-identifications -open import foundation.identity-types open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import foundation.whiskering-identifications-concatenation -open import foundation-core.commuting-squares-of-maps +open import foundation-core.commuting-squares-of-maps funext open import foundation-core.commuting-triangles-of-maps open import foundation-core.homotopies +open import foundation-core.identity-types +open import foundation-core.whiskering-identifications-concatenation ```
diff --git a/src/foundation-core/commuting-squares-of-maps.lagda.md b/src/foundation-core/commuting-squares-of-maps.lagda.md index 6cce4fb386..73c5951b23 100644 --- a/src/foundation-core/commuting-squares-of-maps.lagda.md +++ b/src/foundation-core/commuting-squares-of-maps.lagda.md @@ -1,14 +1,18 @@ # Commuting squares of maps ```agda -module foundation-core.commuting-squares-of-maps where +open import foundation.function-extensionality-axiom + +module foundation-core.commuting-squares-of-maps + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.transposition-identifications-along-equivalences +open import foundation.transposition-identifications-along-equivalences funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition diff --git a/src/foundation-core/contractible-maps.lagda.md b/src/foundation-core/contractible-maps.lagda.md index 2c2d1e9c41..12610e8c3d 100644 --- a/src/foundation-core/contractible-maps.lagda.md +++ b/src/foundation-core/contractible-maps.lagda.md @@ -16,7 +16,6 @@ open import foundation-core.contractible-types open import foundation-core.equivalences open import foundation-core.fibers-of-maps open import foundation-core.function-types -open import foundation-core.homotopies open import foundation-core.identity-types open import foundation-core.retractions open import foundation-core.sections diff --git a/src/foundation-core/contractible-types.lagda.md b/src/foundation-core/contractible-types.lagda.md index d86bdea803..f6b56e6169 100644 --- a/src/foundation-core/contractible-types.lagda.md +++ b/src/foundation-core/contractible-types.lagda.md @@ -10,8 +10,6 @@ module foundation-core.contractible-types where open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types open import foundation.equality-cartesian-product-types -open import foundation.function-extensionality -open import foundation.implicit-function-types open import foundation.universe-levels open import foundation-core.cartesian-product-types @@ -256,75 +254,3 @@ is-prop-is-contr : pr1 (is-prop-is-contr H x y) = eq-is-contr H pr2 (is-prop-is-contr H x .x) refl = left-inv (pr2 H x) ``` - -### Products of families of contractible types are contractible - -```agda -abstract - is-contr-Π : - {l1 l2 : Level} {A : UU l1} {B : A → UU l2} → - ((x : A) → is-contr (B x)) → is-contr ((x : A) → B x) - pr1 (is-contr-Π {A = A} {B = B} H) x = center (H x) - pr2 (is-contr-Π {A = A} {B = B} H) f = - eq-htpy (λ x → contraction (H x) (f x)) - -abstract - is-contr-implicit-Π : - {l1 l2 : Level} {A : UU l1} {B : A → UU l2} → - ((x : A) → is-contr (B x)) → is-contr ({x : A} → B x) - is-contr-implicit-Π H = - is-contr-equiv _ equiv-explicit-implicit-Π (is-contr-Π H) -``` - -### The type of functions into a contractible type is contractible - -```agda -is-contr-function-type : - {l1 l2 : Level} {A : UU l1} {B : UU l2} → - is-contr B → is-contr (A → B) -is-contr-function-type is-contr-B = is-contr-Π (λ _ → is-contr-B) -``` - -### The type of equivalences between contractible types is contractible - -```agda -module _ - {l1 l2 : Level} {A : UU l1} {B : UU l2} - where - - is-contr-equiv-is-contr : - is-contr A → is-contr B → is-contr (A ≃ B) - is-contr-equiv-is-contr (pair a α) (pair b β) = - is-contr-Σ - ( is-contr-function-type (pair b β)) - ( λ x → b) - ( is-contr-product - ( is-contr-Σ - ( is-contr-function-type (pair a α)) - ( λ y → a) - ( is-contr-Π (is-prop-is-contr (pair b β) b))) - ( is-contr-Σ - ( is-contr-function-type (pair a α)) - ( λ y → a) - ( is-contr-Π (is-prop-is-contr (pair a α) a)))) -``` - -### Being contractible is a proposition - -```agda -module _ - {l : Level} {A : UU l} - where - - abstract - is-contr-is-contr : is-contr A → is-contr (is-contr A) - is-contr-is-contr (pair a α) = - is-contr-Σ - ( pair a α) - ( a) - ( is-contr-Π (is-prop-is-contr (pair a α) a)) - - abstract - is-property-is-contr : (H K : is-contr A) → is-contr (H ＝ K) - is-property-is-contr H = is-prop-is-contr (is-contr-is-contr H) H -``` diff --git a/src/foundation-core/decidable-propositions.lagda.md b/src/foundation-core/decidable-propositions.lagda.md index eb48a26b7d..6879d1a02b 100644 --- a/src/foundation-core/decidable-propositions.lagda.md +++ b/src/foundation-core/decidable-propositions.lagda.md @@ -1,18 +1,27 @@ # Decidable propositions ```agda -module foundation-core.decidable-propositions where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation-core.decidable-propositions + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.coproduct-types -open import foundation.decidable-types +open import foundation.coproduct-types funext univalence truncations +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.double-negation -open import foundation.negation -open import foundation.propositional-truncations +open import foundation.dependent-products-propositions funext +open import foundation.double-negation funext univalence truncations +open import foundation.negation funext +open import foundation.propositional-truncations funext univalence open import foundation.transport-along-identifications open import foundation.unit-type open import foundation.universe-levels @@ -23,7 +32,7 @@ open import foundation-core.empty-types open import foundation-core.function-types open import foundation-core.functoriality-dependent-pair-types open import foundation-core.propositions -open import foundation-core.subtypes +open import foundation-core.subtypes funext ```
diff --git a/src/foundation-core/diagonal-maps-cartesian-products-of-types.lagda.md b/src/foundation-core/diagonal-maps-cartesian-products-of-types.lagda.md index afab6f6e6a..7674be4787 100644 --- a/src/foundation-core/diagonal-maps-cartesian-products-of-types.lagda.md +++ b/src/foundation-core/diagonal-maps-cartesian-products-of-types.lagda.md @@ -15,8 +15,6 @@ open import foundation.universe-levels open import foundation-core.cartesian-product-types open import foundation-core.equivalences open import foundation-core.fibers-of-maps -open import foundation-core.function-types -open import foundation-core.homotopies open import foundation-core.identity-types open import foundation-core.propositions open import foundation-core.retractions diff --git a/src/foundation-core/diagonal-maps-of-types.lagda.md b/src/foundation-core/diagonal-maps-of-types.lagda.md new file mode 100644 index 0000000000..3e09e621f5 --- /dev/null +++ b/src/foundation-core/diagonal-maps-of-types.lagda.md @@ -0,0 +1,92 @@ +# Diagonal maps of types + +```agda +module foundation-core.diagonal-maps-of-types where +``` + +
Imports + +```agda +open import foundation.action-on-identifications-functions +open import foundation.dependent-pair-types +open import foundation.function-extensionality-axiom +open import foundation.universe-levels + +open import foundation-core.constant-maps +open import foundation-core.function-types +open import foundation-core.homotopies +open import foundation-core.identity-types +open import foundation-core.injective-maps +``` + +
+ +## Idea + +The +{{#concept "diagonal map" Disambiguation="of a type into exponentials" Agda=diagonal-exponential}} +of a type `A` is the map that includes the points of `A` into the exponential +`X → A`. + +## Definitions + +```agda +module _ + {l1 l2 : Level} (A : UU l1) (X : UU l2) + where + + diagonal-exponential : A → X → A + diagonal-exponential = const X +``` + +## Properties + +### The action on identifications of a diagonal map is another diagonal map + +```agda +module _ + {l1 l2 : Level} {A : UU l1} (x y : A) (B : UU l2) + where + + htpy-diagonal-exponential-Id-ap-diagonal-exponential-htpy-eq : + htpy-eq ∘ ap (diagonal-exponential A B) ~ diagonal-exponential (x ＝ y) B + htpy-diagonal-exponential-Id-ap-diagonal-exponential-htpy-eq refl = refl + + htpy-ap-diagonal-exponential-htpy-eq-diagonal-exponential-Id : + diagonal-exponential (x ＝ y) B ~ htpy-eq ∘ ap (diagonal-exponential A B) + htpy-ap-diagonal-exponential-htpy-eq-diagonal-exponential-Id = + inv-htpy htpy-diagonal-exponential-Id-ap-diagonal-exponential-htpy-eq +``` + +### Given an element of the exponent the diagonal map is injective + +```agda +module _ + {l1 l2 : Level} (A : UU l1) (B : UU l2) (b : B) + where + + is-injective-diagonal-exponential : + is-injective (diagonal-exponential A B) + is-injective-diagonal-exponential p = htpy-eq p b + + diagonal-exponential-injection : injection A (B → A) + pr1 diagonal-exponential-injection = diagonal-exponential A B + pr2 diagonal-exponential-injection = is-injective-diagonal-exponential +``` + +### The action on identifications of an (exponential) diagonal is a diagonal + +```agda +module _ + {l1 l2 : Level} (A : UU l1) {B : UU l2} (x y : B) + where + + compute-htpy-eq-ap-diagonal-exponential : + htpy-eq ∘ ap (diagonal-exponential B A) ~ diagonal-exponential (x ＝ y) A + compute-htpy-eq-ap-diagonal-exponential refl = refl + + inv-compute-htpy-eq-ap-diagonal-exponential : + diagonal-exponential (x ＝ y) A ~ htpy-eq ∘ ap (diagonal-exponential B A) + inv-compute-htpy-eq-ap-diagonal-exponential = + inv-htpy compute-htpy-eq-ap-diagonal-exponential +``` diff --git a/src/foundation-core/discrete-types.lagda.md b/src/foundation-core/discrete-types.lagda.md index 6ace450fc3..f5fe143fd4 100644 --- a/src/foundation-core/discrete-types.lagda.md +++ b/src/foundation-core/discrete-types.lagda.md @@ -1,13 +1,21 @@ # Discrete types ```agda -module foundation-core.discrete-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation-core.discrete-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.decidable-equality +open import foundation.decidable-equality funext univalence truncations open import foundation.dependent-pair-types open import foundation.universe-levels diff --git a/src/foundation-core/endomorphisms.lagda.md b/src/foundation-core/endomorphisms.lagda.md index 0f59be9040..d8024c0d58 100644 --- a/src/foundation-core/endomorphisms.lagda.md +++ b/src/foundation-core/endomorphisms.lagda.md @@ -1,14 +1,21 @@ # Endomorphisms ```agda -module foundation-core.endomorphisms where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation-core.endomorphisms + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.sets +open import foundation.dependent-products-truncated-types funext +open import foundation.sets funext univalence open import foundation.universe-levels open import foundation-core.function-types diff --git a/src/foundation-core/equivalence-relations.lagda.md b/src/foundation-core/equivalence-relations.lagda.md index 28396e95f5..52a1cd3b5d 100644 --- a/src/foundation-core/equivalence-relations.lagda.md +++ b/src/foundation-core/equivalence-relations.lagda.md @@ -1,18 +1,27 @@ # Equivalence relations ```agda -module foundation-core.equivalence-relations where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation-core.equivalence-relations + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.binary-relations +open import foundation.binary-relations funext univalence truncations open import foundation.dependent-pair-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.inhabited-subtypes -open import foundation.logical-equivalences -open import foundation.propositional-truncations +open import foundation.inhabited-subtypes funext univalence truncations +open import foundation.logical-equivalences funext +open import foundation.propositional-truncations funext univalence +open import foundation.raising-universe-levels-unit-type open import foundation.subtype-identity-principle open import foundation.unit-type open import foundation.universe-levels diff --git a/src/foundation-core/fibers-of-maps.lagda.md b/src/foundation-core/fibers-of-maps.lagda.md index 12a441cd2d..4728163858 100644 --- a/src/foundation-core/fibers-of-maps.lagda.md +++ b/src/foundation-core/fibers-of-maps.lagda.md @@ -16,7 +16,6 @@ open import foundation-core.equivalences open import foundation-core.function-types open import foundation-core.homotopies open import foundation-core.identity-types -open import foundation-core.postcomposition-functions open import foundation-core.retractions open import foundation-core.sections open import foundation-core.transport-along-identifications diff --git a/src/foundation-core/functoriality-dependent-function-types.lagda.md b/src/foundation-core/functoriality-dependent-function-types.lagda.md index 1ed18e0b4c..b7b3b0e0bf 100644 --- a/src/foundation-core/functoriality-dependent-function-types.lagda.md +++ b/src/foundation-core/functoriality-dependent-function-types.lagda.md @@ -1,14 +1,19 @@ # Functoriality of dependent function types ```agda -module foundation-core.functoriality-dependent-function-types where +open import foundation.function-extensionality-axiom + +module foundation-core.functoriality-dependent-function-types + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-extensionality +open import foundation.dependent-products-contractible-types funext +open import foundation.function-extensionality funext open import foundation.implicit-function-types open import foundation.universe-levels diff --git a/src/foundation-core/functoriality-dependent-pair-types.lagda.md b/src/foundation-core/functoriality-dependent-pair-types.lagda.md index f3d941d326..9e6ceb2fb5 100644 --- a/src/foundation-core/functoriality-dependent-pair-types.lagda.md +++ b/src/foundation-core/functoriality-dependent-pair-types.lagda.md @@ -7,7 +7,6 @@ module foundation-core.functoriality-dependent-pair-types where
Imports ```agda -open import foundation.action-on-identifications-dependent-functions open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types open import foundation.transport-along-identifications diff --git a/src/foundation-core/invertible-maps.lagda.md b/src/foundation-core/invertible-maps.lagda.md index c4af35f5a7..b958fa00ab 100644 --- a/src/foundation-core/invertible-maps.lagda.md +++ b/src/foundation-core/invertible-maps.lagda.md @@ -7,7 +7,6 @@ module foundation-core.invertible-maps where
Imports ```agda -open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types open import foundation.universe-levels open import foundation.whiskering-homotopies-composition diff --git a/src/foundation-core/logical-equivalences.lagda.md b/src/foundation-core/logical-equivalences.lagda.md new file mode 100644 index 0000000000..bbfe9f6441 --- /dev/null +++ b/src/foundation-core/logical-equivalences.lagda.md @@ -0,0 +1,227 @@ +# Logical equivalences + +```agda +module foundation-core.logical-equivalences where +``` + +
Imports + +```agda +open import foundation.dependent-pair-types +open import foundation.equality-cartesian-product-types +open import foundation.type-arithmetic-dependent-pair-types +open import foundation.universe-levels + +open import foundation-core.cartesian-product-types +open import foundation-core.equivalences +open import foundation-core.fibers-of-maps +open import foundation-core.function-types +open import foundation-core.functoriality-dependent-pair-types +open import foundation-core.homotopies +open import foundation-core.identity-types +open import foundation-core.propositions +open import foundation-core.torsorial-type-families +``` + +
+ +## Idea + +{{#concept "Logical equivalences" Disambiguation="of types" Agda=iff}} between +two types `A` and `B` consist of a map `A → B` and a map `B → A`. The type of +logical equivalences between types is the +[Curry–Howard interpretation](https://en.wikipedia.org/wiki/Curry–Howard_correspondence) +of logical equivalences between [propositions](foundation-core.propositions.md). + +## Definition + +### The structure on a map of being a logical equivalence + +```agda +has-converse : {l1 l2 : Level} {A : UU l1} {B : UU l2} → (A → B) → UU (l1 ⊔ l2) +has-converse {A = A} {B} f = (B → A) +``` + +### Logical equivalences between types + +```agda +iff : {l1 l2 : Level} → UU l1 → UU l2 → UU (l1 ⊔ l2) +iff A B = Σ (A → B) has-converse + +infix 6 _↔_ + +_↔_ : {l1 l2 : Level} → UU l1 → UU l2 → UU (l1 ⊔ l2) +_↔_ = iff + +module _ + {l1 l2 : Level} {A : UU l1} {B : UU l2} (H : A ↔ B) + where + + forward-implication : A → B + forward-implication = pr1 H + + backward-implication : B → A + backward-implication = pr2 H +``` + +### The identity logical equivalence + +```agda +id-iff : {l1 : Level} {A : UU l1} → A ↔ A +id-iff = (id , id) +``` + +### Composition of logical equivalences + +```agda +infixr 15 _∘iff_ + +_∘iff_ : + {l1 l2 l3 : Level} {A : UU l1} {B : UU l2} {C : UU l3} → + (B ↔ C) → (A ↔ B) → (A ↔ C) +pr1 ((g1 , g2) ∘iff (f1 , f2)) = g1 ∘ f1 +pr2 ((g1 , g2) ∘iff (f1 , f2)) = f2 ∘ g2 +``` + +### Inverting a logical equivalence + +```agda +inv-iff : + {l1 l2 : Level} {A : UU l1} {B : UU l2} → (A ↔ B) → (B ↔ A) +pr1 (inv-iff (f , g)) = g +pr2 (inv-iff (f , g)) = f +``` + +## Properties + +### Homotopies of logical equivalences + +```agda +module _ + {l1 l2 : Level} {A : UU l1} {B : UU l2} + where + + htpy-iff : (f g : A ↔ B) → UU (l1 ⊔ l2) + htpy-iff f g = + ( forward-implication f ~ forward-implication g) × + ( backward-implication f ~ backward-implication g) +``` + +### Logical equivalences between propositions induce equivalences + +```agda +module _ + {l1 l2 : Level} {A : UU l1} {B : UU l2} + where + + abstract + is-equiv-has-converse-is-prop : + is-prop A → is-prop B → {f : A → B} → (B → A) → is-equiv f + is-equiv-has-converse-is-prop is-prop-A is-prop-B {f} g = + is-equiv-is-invertible + ( g) + ( λ y → eq-is-prop is-prop-B) + ( λ x → eq-is-prop is-prop-A) + + abstract + equiv-iff-is-prop : is-prop A → is-prop B → (A → B) → (B → A) → A ≃ B + pr1 (equiv-iff-is-prop is-prop-A is-prop-B f g) = f + pr2 (equiv-iff-is-prop is-prop-A is-prop-B f g) = + is-equiv-has-converse-is-prop is-prop-A is-prop-B g + +module _ + {l1 l2 : Level} (P : Prop l1) (Q : Prop l2) + where + + abstract + is-equiv-has-converse : + {f : type-Prop P → type-Prop Q} → (type-Prop Q → type-Prop P) → is-equiv f + is-equiv-has-converse = + is-equiv-has-converse-is-prop + ( is-prop-type-Prop P) + ( is-prop-type-Prop Q) + + equiv-iff' : (type-Prop P ↔ type-Prop Q) → (type-Prop P ≃ type-Prop Q) + pr1 (equiv-iff' t) = forward-implication t + pr2 (equiv-iff' t) = + is-equiv-has-converse-is-prop + ( is-prop-type-Prop P) + ( is-prop-type-Prop Q) + ( backward-implication t) + + equiv-iff : + (type-Prop P → type-Prop Q) → (type-Prop Q → type-Prop P) → + type-Prop P ≃ type-Prop Q + equiv-iff f g = equiv-iff' (f , g) +``` + +### Equivalences are logical equivalences + +```agda +iff-equiv : {l1 l2 : Level} {A : UU l1} {B : UU l2} → (A ≃ B) → (A ↔ B) +pr1 (iff-equiv e) = map-equiv e +pr2 (iff-equiv e) = map-inv-equiv e + +iff-equiv' : {l1 l2 : Level} {A : UU l1} {B : UU l2} → (A ≃ B) → (B ↔ A) +pr1 (iff-equiv' e) = map-inv-equiv e +pr2 (iff-equiv' e) = map-equiv e + +compute-fiber-iff-equiv' : + {l1 l2 : Level} {A : UU l1} {B : UU l2} ((f , g) : A ↔ B) → + fiber (iff-equiv) (f , g) ≃ Σ (is-equiv f) (λ f' → map-inv-is-equiv f' ＝ g) +compute-fiber-iff-equiv' {A = A} {B} (f , g) = + ( left-unit-law-Σ-is-contr (is-torsorial-Id' f) (f , refl)) ∘e + ( inv-associative-Σ (A → B) (_＝ f) _) ∘e + ( equiv-tot (λ _ → equiv-left-swap-Σ)) ∘e + ( associative-Σ (A → B) _ _) ∘e + ( equiv-tot (λ e → equiv-pair-eq (iff-equiv e) (f , g))) +``` + +### Two equal propositions are logically equivalent + +```agda +iff-eq : {l1 : Level} {P Q : Prop l1} → P ＝ Q → (type-Prop P ↔ type-Prop Q) +pr1 (iff-eq refl) = id +pr2 (iff-eq refl) = id +``` + +## Logical equivalences between dependent function types + +```agda +module _ + {l1 l2 l3 : Level} {I : UU l1} {A : I → UU l2} {B : I → UU l3} + where + + iff-Π-iff-family : ((i : I) → A i ↔ B i) → ((i : I) → A i) ↔ ((i : I) → B i) + pr1 (iff-Π-iff-family e) a i = forward-implication (e i) (a i) + pr2 (iff-Π-iff-family e) b i = backward-implication (e i) (b i) +``` + +## Reasoning with logical equivalences + +Logical equivalences can be constructed by equational reasoning in the following +way: + +```text +logical-equivalence-reasoning + X ↔ Y by equiv-1 + ↔ Z by equiv-2 + ↔ V by equiv-3 +``` + +```agda +infixl 1 logical-equivalence-reasoning_ +infixl 0 step-logical-equivalence-reasoning + +logical-equivalence-reasoning_ : + {l1 : Level} (X : UU l1) → X ↔ X +pr1 (logical-equivalence-reasoning X) = id +pr2 (logical-equivalence-reasoning X) = id + +step-logical-equivalence-reasoning : + {l1 l2 l3 : Level} {X : UU l1} {Y : UU l2} → + (X ↔ Y) → (Z : UU l3) → (Y ↔ Z) → (X ↔ Z) +step-logical-equivalence-reasoning e Z f = f ∘iff e + +syntax step-logical-equivalence-reasoning e Z f = e ↔ Z by f +``` diff --git a/src/foundation-core/maybe.lagda.md b/src/foundation-core/maybe.lagda.md new file mode 100644 index 0000000000..ca3502824d --- /dev/null +++ b/src/foundation-core/maybe.lagda.md @@ -0,0 +1,212 @@ +# The maybe monad + +```agda +module foundation-core.maybe where +``` + +
Imports + +```agda +open import foundation.dependent-pair-types +open import foundation.unit-type +open import foundation.universe-levels + +open import foundation-core.cartesian-product-types +open import foundation-core.coproduct-types +open import foundation-core.equivalences +open import foundation-core.identity-types +open import foundation-core.negation +open import foundation-core.propositions +open import foundation-core.retractions +open import foundation-core.sections +``` + +
+ +## Idea + +The +{{#concept "maybe monad" Disambiguation="on types" Agda=Maybe WD="option type" WDID=Q7099015}} +is an operation on types that adds one point. This is used, for example, to +define [partial functions](foundation.partial-functions.md), where a partial +function `f : X ⇀ Y` is a map `f : X → Maybe Y`. + +The maybe monad is an example of a monad that is not a +[modality](orthogonal-factorization-systems.higher-modalities.md), since it is +not [idempotent](foundation.idempotent-maps.md). + +## Definitions + +### The maybe monad + +```agda +Maybe : {l : Level} → UU l → UU l +Maybe X = X + unit + +unit-Maybe : {l : Level} {X : UU l} → X → Maybe X +unit-Maybe = inl + +exception-Maybe : {l : Level} {X : UU l} → Maybe X +exception-Maybe = inr star + +extend-Maybe : + {l1 l2 : Level} {X : UU l1} {Y : UU l2} → (X → Maybe Y) → Maybe X → Maybe Y +extend-Maybe f (inl x) = f x +extend-Maybe f (inr *) = inr * + +map-Maybe : + {l1 l2 : Level} {X : UU l1} {Y : UU l2} → (X → Y) → Maybe X → Maybe Y +map-Maybe f (inl x) = inl (f x) +map-Maybe f (inr *) = inr * +``` + +### The inductive definition of the maybe monad + +```agda +data Maybe' {l : Level} (X : UU l) : UU l where + unit-Maybe' : X → Maybe' X + exception-Maybe' : Maybe' X + +{-# BUILTIN MAYBE Maybe' #-} +``` + +### The predicate of being an exception + +```agda +is-exception-Maybe : {l : Level} {X : UU l} → Maybe X → UU l +is-exception-Maybe {l} {X} x = (x ＝ exception-Maybe) + +is-not-exception-Maybe : {l : Level} {X : UU l} → Maybe X → UU l +is-not-exception-Maybe x = ¬ (is-exception-Maybe x) + +abstract + is-prop-is-exception-Maybe : + {l : Level} {X : UU l} (x : Maybe X) → is-prop (is-exception-Maybe x) + is-prop-is-exception-Maybe (inl x) () + is-prop-is-exception-Maybe (inr star) refl refl = refl , (λ where refl → refl) +``` + +### The predicate of being a value + +```agda +is-value-Maybe : {l : Level} {X : UU l} → Maybe X → UU l +is-value-Maybe {l} {X} x = Σ X (λ y → inl y ＝ x) + +value-is-value-Maybe : + {l : Level} {X : UU l} (x : Maybe X) → is-value-Maybe x → X +value-is-value-Maybe x = pr1 + +eq-is-value-Maybe : + {l : Level} {X : UU l} (x : Maybe X) (H : is-value-Maybe x) → + inl (value-is-value-Maybe x H) ＝ x +eq-is-value-Maybe x H = pr2 H +``` + +### Maybe structure on a type + +```agda +maybe-structure : {l1 : Level} (X : UU l1) → UU (lsuc l1) +maybe-structure {l1} X = Σ (UU l1) (λ Y → Maybe Y ≃ X) +``` + +## Properties + +### The values of the unit of the `Maybe` monad are not exceptions + +```agda +abstract + is-not-exception-unit-Maybe : + {l : Level} {X : UU l} (x : X) → is-not-exception-Maybe (unit-Maybe x) + is-not-exception-unit-Maybe x () +``` + +### For any element of type `Maybe X` we can decide whether it is a value or an exception + +```agda +decide-Maybe : + {l : Level} {X : UU l} (x : Maybe X) → is-value-Maybe x + is-exception-Maybe x +decide-Maybe (inl x) = inl (x , refl) +decide-Maybe (inr star) = inr refl +``` + +### Values are not exceptions + +```agda +abstract + is-not-exception-is-value-Maybe : + {l1 : Level} {X : UU l1} (x : Maybe X) → + is-value-Maybe x → is-not-exception-Maybe x + is-not-exception-is-value-Maybe {l1} {X} .(inl x) (x , refl) = + is-not-exception-unit-Maybe x +``` + +### The two definitions of `Maybe` are equivalent + +```agda +module _ + {l1 l2 : Level} {X : UU l1} + where + + map-Maybe-Maybe' : Maybe X → Maybe' X + map-Maybe-Maybe' (inl x) = unit-Maybe' x + map-Maybe-Maybe' (inr _) = exception-Maybe' + + map-inv-Maybe-Maybe' : Maybe' X → Maybe X + map-inv-Maybe-Maybe' (unit-Maybe' x) = inl x + map-inv-Maybe-Maybe' exception-Maybe' = inr star + + is-section-map-inv-Maybe-Maybe' : + is-section map-Maybe-Maybe' map-inv-Maybe-Maybe' + is-section-map-inv-Maybe-Maybe' (unit-Maybe' x) = refl + is-section-map-inv-Maybe-Maybe' exception-Maybe' = refl + + is-retraction-map-inv-Maybe-Maybe' : + is-retraction map-Maybe-Maybe' map-inv-Maybe-Maybe' + is-retraction-map-inv-Maybe-Maybe' (inl x) = refl + is-retraction-map-inv-Maybe-Maybe' (inr x) = refl + + is-equiv-map-Maybe-Maybe' : is-equiv map-Maybe-Maybe' + is-equiv-map-Maybe-Maybe' = + is-equiv-is-invertible + ( map-inv-Maybe-Maybe') + ( is-section-map-inv-Maybe-Maybe') + ( is-retraction-map-inv-Maybe-Maybe') + + equiv-Maybe-Maybe' : Maybe X ≃ Maybe' X + equiv-Maybe-Maybe' = (map-Maybe-Maybe' , is-equiv-map-Maybe-Maybe') +``` + +### There is a surjection from `Maybe A + Maybe B` to `Maybe (A + B)` + +```agda +module _ + {l1 l2 : Level} {A : UU l1} {B : UU l2} + where + + map-maybe-coproduct : Maybe A + Maybe B → Maybe (A + B) + map-maybe-coproduct (inl (inl x)) = inl (inl x) + map-maybe-coproduct (inl (inr star)) = inr star + map-maybe-coproduct (inr (inl x)) = inl (inr x) + map-maybe-coproduct (inr (inr star)) = inr star +``` + +### There is a surjection from `Maybe A × Maybe B` to `Maybe (A × B)` + +```agda +module _ + {l1 l2 : Level} {A : UU l1} {B : UU l2} + where + + map-maybe-product : Maybe A × Maybe B → Maybe (A × B) + map-maybe-product (inl a , inl b) = inl (a , b) + map-maybe-product (inl a , inr star) = inr star + map-maybe-product (inr star , inl b) = inr star + map-maybe-product (inr star , inr star) = inr star +``` + +## External links + +- [maybe monad](https://ncatlab.org/nlab/show/maybe+monad) at $n$Lab +- [Monad (category theory)#The maybe monad]() + at Wikipedia +- [Option type](https://en.wikipedia.org/wiki/Option_type) at Wikipedia diff --git a/src/foundation-core/negation.lagda.md b/src/foundation-core/negation.lagda.md index 620f220429..720d64e266 100644 --- a/src/foundation-core/negation.lagda.md +++ b/src/foundation-core/negation.lagda.md @@ -10,6 +10,7 @@ module foundation-core.negation where open import foundation.universe-levels open import foundation-core.empty-types +open import foundation-core.logical-equivalences ```
@@ -23,7 +24,7 @@ using propositions as types. Thus, the {{#concept "negation" Disambiguation="of a type" WDID=Q190558 WD="logical negation" Agda=¬_}} of a type `A` is the type `A → empty`. -## Definition +## Definitions ```agda infix 25 ¬_ @@ -37,6 +38,23 @@ map-neg : map-neg f nq p = nq (f p) ``` +### Reductio ad absurdum + +```agda +reductio-ad-absurdum : {l1 l2 : Level} {P : UU l1} {Q : UU l2} → P → ¬ P → Q +reductio-ad-absurdum p np = ex-falso (np p) +``` + +### Negation has no fixed points + +```agda +no-fixed-points-neg : + {l : Level} (A : UU l) → ¬ (A ↔ ¬ A) +no-fixed-points-neg A e = + ( λ (h : ¬ A) → h (backward-implication e h)) + ( λ (a : A) → forward-implication e a a) +``` + ## External links - [negation](https://ncatlab.org/nlab/show/negation) at $n$Lab diff --git a/src/foundation-core/operations-span-diagrams.lagda.md b/src/foundation-core/operations-span-diagrams.lagda.md index 78b68e8722..9b4a2f9ae0 100644 --- a/src/foundation-core/operations-span-diagrams.lagda.md +++ b/src/foundation-core/operations-span-diagrams.lagda.md @@ -1,16 +1,24 @@ # Operations on span diagrams ```agda -module foundation-core.operations-span-diagrams where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation-core.operations-span-diagrams + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.morphisms-arrows -open import foundation.operations-spans -open import foundation.span-diagrams +open import foundation.morphisms-arrows funext +open import foundation.operations-spans funext univalence truncations +open import foundation.span-diagrams funext open import foundation.spans open import foundation.universe-levels diff --git a/src/foundation-core/operations-spans.lagda.md b/src/foundation-core/operations-spans.lagda.md index 47e60de4d7..352897d8c3 100644 --- a/src/foundation-core/operations-spans.lagda.md +++ b/src/foundation-core/operations-spans.lagda.md @@ -1,14 +1,18 @@ # Operations on spans ```agda -module foundation-core.operations-spans where +open import foundation.function-extensionality-axiom + +module foundation-core.operations-spans + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.morphisms-arrows +open import foundation.morphisms-arrows funext open import foundation.spans open import foundation.universe-levels diff --git a/src/foundation-core/propositions.lagda.md b/src/foundation-core/propositions.lagda.md index 5aeafc52d4..c35bb3436e 100644 --- a/src/foundation-core/propositions.lagda.md +++ b/src/foundation-core/propositions.lagda.md @@ -8,7 +8,7 @@ module foundation-core.propositions where ```agda open import foundation.dependent-pair-types -open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.universe-levels open import foundation-core.cartesian-product-types @@ -16,7 +16,6 @@ open import foundation-core.contractible-types open import foundation-core.equality-dependent-pair-types open import foundation-core.equivalences open import foundation-core.function-types -open import foundation-core.homotopies open import foundation-core.identity-types open import foundation-core.transport-along-identifications ``` @@ -236,141 +235,7 @@ module _ product-Prop = (type-product-Prop , is-prop-product-Prop) ``` -### Products of families of propositions are propositions - -```agda -abstract - is-prop-Π : - {l1 l2 : Level} {A : UU l1} {B : A → UU l2} → - ((x : A) → is-prop (B x)) → is-prop ((x : A) → B x) - is-prop-Π H = - is-prop-is-proof-irrelevant - ( λ f → is-contr-Π (λ x → is-proof-irrelevant-is-prop (H x) (f x))) - -module _ - {l1 l2 : Level} (A : UU l1) (P : A → Prop l2) - where - - type-Π-Prop : UU (l1 ⊔ l2) - type-Π-Prop = (x : A) → type-Prop (P x) - - is-prop-Π-Prop : is-prop type-Π-Prop - is-prop-Π-Prop = is-prop-Π (λ x → is-prop-type-Prop (P x)) - - Π-Prop : Prop (l1 ⊔ l2) - pr1 Π-Prop = type-Π-Prop - pr2 Π-Prop = is-prop-Π-Prop -``` - -We now repeat the above for implicit Π-types. - -```agda -abstract - is-prop-implicit-Π : - {l1 l2 : Level} {A : UU l1} {B : A → UU l2} → - ((x : A) → is-prop (B x)) → is-prop ({x : A} → B x) - is-prop-implicit-Π H = - is-prop-equiv - ( ( λ f x → f {x}) , - ( is-equiv-is-invertible (λ g {x} → g x) (refl-htpy) (refl-htpy))) - ( is-prop-Π H) - -module _ - {l1 l2 : Level} (A : UU l1) (P : A → Prop l2) - where - - type-implicit-Π-Prop : UU (l1 ⊔ l2) - type-implicit-Π-Prop = {x : A} → type-Prop (P x) - - is-prop-implicit-Π-Prop : is-prop type-implicit-Π-Prop - is-prop-implicit-Π-Prop = - is-prop-implicit-Π (λ x → is-prop-type-Prop (P x)) - - implicit-Π-Prop : Prop (l1 ⊔ l2) - pr1 implicit-Π-Prop = type-implicit-Π-Prop - pr2 implicit-Π-Prop = is-prop-implicit-Π-Prop -``` - -### The type of functions into a proposition is a proposition - -```agda -abstract - is-prop-function-type : - {l1 l2 : Level} {A : UU l1} {B : UU l2} → - is-prop B → is-prop (A → B) - is-prop-function-type H = is-prop-Π (λ _ → H) - -type-function-Prop : - {l1 l2 : Level} → UU l1 → Prop l2 → UU (l1 ⊔ l2) -type-function-Prop A P = A → type-Prop P - -is-prop-function-Prop : - {l1 l2 : Level} {A : UU l1} (P : Prop l2) → - is-prop (type-function-Prop A P) -is-prop-function-Prop P = - is-prop-function-type (is-prop-type-Prop P) - -function-Prop : - {l1 l2 : Level} → UU l1 → Prop l2 → Prop (l1 ⊔ l2) -pr1 (function-Prop A P) = type-function-Prop A P -pr2 (function-Prop A P) = is-prop-function-Prop P - -type-hom-Prop : - {l1 l2 : Level} (P : Prop l1) (Q : Prop l2) → UU (l1 ⊔ l2) -type-hom-Prop P = type-function-Prop (type-Prop P) - -is-prop-hom-Prop : - {l1 l2 : Level} (P : Prop l1) (Q : Prop l2) → - is-prop (type-hom-Prop P Q) -is-prop-hom-Prop P = is-prop-function-Prop - -hom-Prop : - {l1 l2 : Level} → Prop l1 → Prop l2 → Prop (l1 ⊔ l2) -pr1 (hom-Prop P Q) = type-hom-Prop P Q -pr2 (hom-Prop P Q) = is-prop-hom-Prop P Q - -infixr 5 _⇒_ -_⇒_ = hom-Prop -``` - -### The type of equivalences between two propositions is a proposition - -```agda -module _ - {l1 l2 : Level} {A : UU l1} {B : UU l2} - where - - is-prop-equiv-is-prop : is-prop A → is-prop B → is-prop (A ≃ B) - is-prop-equiv-is-prop H K = - is-prop-Σ - ( is-prop-function-type K) - ( λ f → - is-prop-product - ( is-prop-Σ - ( is-prop-function-type H) - ( λ g → is-prop-is-contr (is-contr-Π (λ y → K (f (g y)) y)))) - ( is-prop-Σ - ( is-prop-function-type H) - ( λ h → is-prop-is-contr (is-contr-Π (λ x → H (h (f x)) x))))) - -type-equiv-Prop : - { l1 l2 : Level} (P : Prop l1) (Q : Prop l2) → UU (l1 ⊔ l2) -type-equiv-Prop P Q = (type-Prop P) ≃ (type-Prop Q) - -abstract - is-prop-type-equiv-Prop : - {l1 l2 : Level} (P : Prop l1) (Q : Prop l2) → - is-prop (type-equiv-Prop P Q) - is-prop-type-equiv-Prop P Q = - is-prop-equiv-is-prop (is-prop-type-Prop P) (is-prop-type-Prop Q) - -equiv-Prop : - { l1 l2 : Level} → Prop l1 → Prop l2 → Prop (l1 ⊔ l2) -pr1 (equiv-Prop P Q) = type-equiv-Prop P Q -pr2 (equiv-Prop P Q) = is-prop-type-equiv-Prop P Q -``` - -### A type is a proposition if and only if the type of its endomaps is contractible +### A type is a proposition if the type of its endomaps is contractible ```agda abstract @@ -378,25 +243,6 @@ abstract {l : Level} (P : UU l) → is-contr (P → P) → is-prop P is-prop-is-contr-endomaps P H = is-prop-all-elements-equal (λ x → htpy-eq (eq-is-contr H)) - -abstract - is-contr-endomaps-is-prop : - {l : Level} (P : UU l) → is-prop P → is-contr (P → P) - is-contr-endomaps-is-prop P is-prop-P = - is-proof-irrelevant-is-prop (is-prop-function-type is-prop-P) id -``` - -### Being a proposition is a proposition - -```agda -abstract - is-prop-is-prop : - {l : Level} (A : UU l) → is-prop (is-prop A) - is-prop-is-prop A = is-prop-Π (λ x → is-prop-Π (λ y → is-property-is-contr)) - -is-prop-Prop : {l : Level} (A : UU l) → Prop l -pr1 (is-prop-Prop A) = is-prop A -pr2 (is-prop-Prop A) = is-prop-is-prop A ``` ## See also diff --git a/src/foundation-core/pullbacks.lagda.md b/src/foundation-core/pullbacks.lagda.md index 332e6e96e2..179c5f29ae 100644 --- a/src/foundation-core/pullbacks.lagda.md +++ b/src/foundation-core/pullbacks.lagda.md @@ -1,21 +1,25 @@ # Pullbacks ```agda -module foundation-core.pullbacks where +open import foundation.function-extensionality-axiom + +module foundation-core.pullbacks + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cones-over-cospan-diagrams +open import foundation.cones-over-cospan-diagrams funext open import foundation.dependent-pair-types -open import foundation.functoriality-cartesian-product-types -open import foundation.functoriality-fibers-of-maps -open import foundation.identity-types -open import foundation.morphisms-arrows -open import foundation.standard-pullbacks -open import foundation.type-arithmetic-standard-pullbacks +open import foundation.functoriality-cartesian-product-types funext +open import foundation.functoriality-fibers-of-maps funext +open import foundation.identity-types funext +open import foundation.morphisms-arrows funext +open import foundation.standard-pullbacks funext +open import foundation.type-arithmetic-standard-pullbacks funext open import foundation.universe-levels open import foundation-core.commuting-triangles-of-maps @@ -27,7 +31,7 @@ open import foundation-core.fibers-of-maps open import foundation-core.function-types open import foundation-core.functoriality-dependent-pair-types open import foundation-core.homotopies -open import foundation-core.universal-property-pullbacks +open import foundation-core.universal-property-pullbacks funext ```
diff --git a/src/foundation-core/raising-universe-levels.lagda.md b/src/foundation-core/raising-universe-levels.lagda.md new file mode 100644 index 0000000000..15251fb47f --- /dev/null +++ b/src/foundation-core/raising-universe-levels.lagda.md @@ -0,0 +1,128 @@ +# Raising universe levels + +```agda +module foundation-core.raising-universe-levels where +``` + +
Imports + +```agda +open import foundation.action-on-identifications-functions +open import foundation.dependent-pair-types +open import foundation.universe-levels + +open import foundation-core.equivalences +open import foundation-core.function-types +open import foundation-core.homotopies +open import foundation-core.identity-types +open import foundation-core.propositions +open import foundation-core.sets +``` + +
+ +## Idea + +In Agda, types have a designated universe levels, and universes in Agda don't +overlap. Using `data` types we can construct for any type `A` of universe level +`l` an equivalent type in any higher universe. + +## Definition + +```agda +data raise (l : Level) {l1 : Level} (A : UU l1) : UU (l1 ⊔ l) where + map-raise : A → raise l A + +data raiseω {l1 : Level} (A : UU l1) : UUω where + map-raiseω : A → raiseω A +``` + +## Properties + +### Types are equivalent to their raised equivalents + +```agda +module _ + {l l1 : Level} {A : UU l1} + where + + map-inv-raise : raise l A → A + map-inv-raise (map-raise x) = x + + is-section-map-inv-raise : (map-raise ∘ map-inv-raise) ~ id + is-section-map-inv-raise (map-raise x) = refl + + is-retraction-map-inv-raise : (map-inv-raise ∘ map-raise) ~ id + is-retraction-map-inv-raise x = refl + + is-equiv-map-raise : is-equiv (map-raise {l} {l1} {A}) + is-equiv-map-raise = + is-equiv-is-invertible + map-inv-raise + is-section-map-inv-raise + is-retraction-map-inv-raise + +compute-raise : (l : Level) {l1 : Level} (A : UU l1) → A ≃ raise l A +pr1 (compute-raise l A) = map-raise +pr2 (compute-raise l A) = is-equiv-map-raise + +inv-compute-raise : (l : Level) {l1 : Level} (A : UU l1) → raise l A ≃ A +inv-compute-raise l A = inv-equiv (compute-raise l A) + +Raise : (l : Level) {l1 : Level} (A : UU l1) → Σ (UU (l1 ⊔ l)) (λ X → A ≃ X) +pr1 (Raise l A) = raise l A +pr2 (Raise l A) = compute-raise l A +``` + +### Raising universe levels of propositions + +```agda +raise-Prop : (l : Level) {l1 : Level} → Prop l1 → Prop (l ⊔ l1) +pr1 (raise-Prop l P) = raise l (type-Prop P) +pr2 (raise-Prop l P) = + is-prop-equiv' (compute-raise l (type-Prop P)) (is-prop-type-Prop P) +``` + +### Raising universe levels of sets + +```agda +raise-Set : (l : Level) {l1 : Level} → Set l1 → Set (l ⊔ l1) +pr1 (raise-Set l A) = raise l (type-Set A) +pr2 (raise-Set l A) = + is-set-equiv' (type-Set A) (compute-raise l (type-Set A)) (is-set-type-Set A) +``` + +### Raising equivalent types + +```agda +module _ + {l1 l2 : Level} (l3 l4 : Level) {A : UU l1} {B : UU l2} (e : A ≃ B) + where + + map-equiv-raise : raise l3 A → raise l4 B + map-equiv-raise (map-raise x) = map-raise (map-equiv e x) + + map-inv-equiv-raise : raise l4 B → raise l3 A + map-inv-equiv-raise (map-raise y) = map-raise (map-inv-equiv e y) + + is-section-map-inv-equiv-raise : + ( map-equiv-raise ∘ map-inv-equiv-raise) ~ id + is-section-map-inv-equiv-raise (map-raise y) = + ap map-raise (is-section-map-inv-equiv e y) + + is-retraction-map-inv-equiv-raise : + ( map-inv-equiv-raise ∘ map-equiv-raise) ~ id + is-retraction-map-inv-equiv-raise (map-raise x) = + ap map-raise (is-retraction-map-inv-equiv e x) + + is-equiv-map-equiv-raise : is-equiv map-equiv-raise + is-equiv-map-equiv-raise = + is-equiv-is-invertible + map-inv-equiv-raise + is-section-map-inv-equiv-raise + is-retraction-map-inv-equiv-raise + + equiv-raise : raise l3 A ≃ raise l4 B + pr1 equiv-raise = map-equiv-raise + pr2 equiv-raise = is-equiv-map-equiv-raise +``` diff --git a/src/foundation-core/retracts-of-types.lagda.md b/src/foundation-core/retracts-of-types.lagda.md index 43c71c5134..6aea379f91 100644 --- a/src/foundation-core/retracts-of-types.lagda.md +++ b/src/foundation-core/retracts-of-types.lagda.md @@ -9,15 +9,11 @@ module foundation-core.retracts-of-types where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-extensionality open import foundation.universe-levels -open import foundation.whiskering-homotopies-composition open import foundation-core.function-types open import foundation-core.homotopies open import foundation-core.identity-types -open import foundation-core.postcomposition-functions -open import foundation-core.precomposition-functions open import foundation-core.retractions open import foundation-core.sections ``` @@ -140,40 +136,6 @@ module _ pr2 retract-eq = retraction-ap (inclusion-retract R) (retraction-retract R) ``` -### If `A` is a retract of `B` then `A → S` is a retract of `B → S` via precomposition - -```agda -module _ - {l1 l2 l3 : Level} {A : UU l1} {B : UU l2} (R : A retract-of B) (S : UU l3) - where - - retract-precomp : - (A → S) retract-of (B → S) - pr1 retract-precomp = - precomp (map-retraction-retract R) S - pr1 (pr2 retract-precomp) = - precomp (inclusion-retract R) S - pr2 (pr2 retract-precomp) h = - eq-htpy (h ·l is-retraction-map-retraction-retract R) -``` - -### If `A` is a retract of `B` then `S → A` is a retract of `S → B` via postcomposition - -```agda -module _ - {l1 l2 l3 : Level} {A : UU l1} {B : UU l2} (S : UU l3) (R : A retract-of B) - where - - retract-postcomp : - (S → A) retract-of (S → B) - pr1 retract-postcomp = - postcomp S (inclusion-retract R) - pr1 (pr2 retract-postcomp) = - postcomp S (map-retraction-retract R) - pr2 (pr2 retract-postcomp) h = - eq-htpy (is-retraction-map-retraction-retract R ·r h) -``` - ### Every type is a retract of itself ```agda diff --git a/src/foundation-core/sets.lagda.md b/src/foundation-core/sets.lagda.md index def449a7a1..b05ea9bb42 100644 --- a/src/foundation-core/sets.lagda.md +++ b/src/foundation-core/sets.lagda.md @@ -12,7 +12,6 @@ open import foundation.fundamental-theorem-of-identity-types open import foundation.universe-levels open import foundation-core.contractible-types -open import foundation-core.embeddings open import foundation-core.equivalences open import foundation-core.identity-types open import foundation-core.injective-maps @@ -194,24 +193,6 @@ abstract {l1 l2 : Level} (A : UU l1) {B : UU l2} (e : A ≃ B) → is-set A → is-set B is-set-equiv' = is-trunc-equiv' zero-𝕋 - -abstract - is-set-equiv-is-set : - {l1 l2 : Level} {A : UU l1} {B : UU l2} → - is-set A → is-set B → is-set (A ≃ B) - is-set-equiv-is-set = is-trunc-equiv-is-trunc zero-𝕋 - -module _ - {l1 l2 : Level} (A : Set l1) (B : Set l2) - where - - equiv-Set : UU (l1 ⊔ l2) - equiv-Set = type-Set A ≃ type-Set B - - equiv-set-Set : Set (l1 ⊔ l2) - pr1 equiv-set-Set = equiv-Set - pr2 equiv-set-Set = - is-set-equiv-is-set (is-set-type-Set A) (is-set-type-Set B) ``` ### If a type injects into a set, then it is a set diff --git a/src/foundation-core/small-types.lagda.md b/src/foundation-core/small-types.lagda.md index 96a3cd8d75..c9eac1a3b1 100644 --- a/src/foundation-core/small-types.lagda.md +++ b/src/foundation-core/small-types.lagda.md @@ -1,24 +1,32 @@ # Small types ```agda -module foundation-core.small-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation-core.small-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.functoriality-coproduct-types -open import foundation.functoriality-dependent-function-types -open import foundation.logical-equivalences -open import foundation.mere-equivalences -open import foundation.propositional-truncations -open import foundation.raising-universe-levels +open import foundation.equivalences funext +open import foundation.functoriality-coproduct-types funext univalence truncations +open import foundation.functoriality-dependent-function-types funext univalence +open import foundation.logical-equivalences funext +open import foundation.mere-equivalences funext univalence truncations +open import foundation.propositional-truncations funext univalence +open import foundation.raising-universe-levels-unit-type open import foundation.transport-along-identifications open import foundation.type-arithmetic-dependent-pair-types open import foundation.unit-type -open import foundation.univalence +open import foundation.univalence funext univalence open import foundation.universe-levels open import foundation-core.cartesian-product-types @@ -28,6 +36,7 @@ open import foundation-core.coproduct-types open import foundation-core.functoriality-dependent-pair-types open import foundation-core.identity-types open import foundation-core.propositions +open import foundation-core.raising-universe-levels open import foundation-core.retractions open import foundation-core.sections ``` diff --git a/src/foundation-core/subtypes.lagda.md b/src/foundation-core/subtypes.lagda.md index 128f682668..cbe847292c 100644 --- a/src/foundation-core/subtypes.lagda.md +++ b/src/foundation-core/subtypes.lagda.md @@ -1,7 +1,11 @@ # Subtypes ```agda -module foundation-core.subtypes where +open import foundation.function-extensionality-axiom + +module foundation-core.subtypes + (funext : function-extensionality) + where ```
Imports @@ -9,7 +13,8 @@ module foundation-core.subtypes where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.logical-equivalences +open import foundation.dependent-products-propositions funext +open import foundation.logical-equivalences funext open import foundation.subtype-identity-principle open import foundation.universe-levels @@ -23,7 +28,7 @@ open import foundation-core.propositional-maps open import foundation-core.propositions open import foundation-core.sets open import foundation-core.transport-along-identifications -open import foundation-core.truncated-maps +open import foundation-core.truncated-maps funext open import foundation-core.truncated-types open import foundation-core.truncation-levels ``` diff --git a/src/foundation-core/truncated-maps.lagda.md b/src/foundation-core/truncated-maps.lagda.md index 6c68755acc..f784b05600 100644 --- a/src/foundation-core/truncated-maps.lagda.md +++ b/src/foundation-core/truncated-maps.lagda.md @@ -1,7 +1,11 @@ # Truncated maps ```agda -module foundation-core.truncated-maps where +open import foundation.function-extensionality-axiom + +module foundation-core.truncated-maps + (funext : function-extensionality) + where ```
Imports @@ -9,10 +13,10 @@ module foundation-core.truncated-maps where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equality-fibers-of-maps +open import foundation.equality-fibers-of-maps funext open import foundation.universe-levels -open import foundation-core.commuting-squares-of-maps +open import foundation-core.commuting-squares-of-maps funext open import foundation-core.contractible-maps open import foundation-core.equivalences open import foundation-core.fibers-of-maps diff --git a/src/foundation-core/truncated-types.lagda.md b/src/foundation-core/truncated-types.lagda.md index fb88b4c3df..a0c1773090 100644 --- a/src/foundation-core/truncated-types.lagda.md +++ b/src/foundation-core/truncated-types.lagda.md @@ -11,7 +11,6 @@ open import foundation.action-on-identifications-dependent-functions open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types open import foundation.equality-cartesian-product-types -open import foundation.function-extensionality open import foundation.universe-levels open import foundation-core.cartesian-product-types @@ -19,9 +18,7 @@ open import foundation-core.contractible-types open import foundation-core.embeddings open import foundation-core.equality-dependent-pair-types open import foundation-core.equivalences -open import foundation-core.homotopies open import foundation-core.identity-types -open import foundation-core.propositions open import foundation-core.retracts-of-types open import foundation-core.transport-along-identifications open import foundation-core.truncation-levels @@ -292,153 +289,3 @@ is-trunc-right-factor-product (succ-𝕋 k) {A} {B} H a b b' = ( H (pair a b) (pair a b'))) ( refl) ``` - -### Products of families of truncated types are truncated - -```agda -abstract - is-trunc-Π : - {l1 l2 : Level} (k : 𝕋) {A : UU l1} {B : A → UU l2} → - ((x : A) → is-trunc k (B x)) → is-trunc k ((x : A) → B x) - is-trunc-Π neg-two-𝕋 is-trunc-B = is-contr-Π is-trunc-B - is-trunc-Π (succ-𝕋 k) is-trunc-B f g = - is-trunc-is-equiv k (f ~ g) htpy-eq - ( funext f g) - ( is-trunc-Π k (λ x → is-trunc-B x (f x) (g x))) - -type-Π-Truncated-Type' : - (k : 𝕋) {l1 l2 : Level} (A : UU l1) (B : A → Truncated-Type l2 k) → - UU (l1 ⊔ l2) -type-Π-Truncated-Type' k A B = (x : A) → type-Truncated-Type (B x) - -is-trunc-type-Π-Truncated-Type' : - (k : 𝕋) {l1 l2 : Level} (A : UU l1) (B : A → Truncated-Type l2 k) → - is-trunc k (type-Π-Truncated-Type' k A B) -is-trunc-type-Π-Truncated-Type' k A B = - is-trunc-Π k (λ x → is-trunc-type-Truncated-Type (B x)) - -Π-Truncated-Type' : - (k : 𝕋) {l1 l2 : Level} (A : UU l1) (B : A → Truncated-Type l2 k) → - Truncated-Type (l1 ⊔ l2) k -pr1 (Π-Truncated-Type' k A B) = type-Π-Truncated-Type' k A B -pr2 (Π-Truncated-Type' k A B) = is-trunc-type-Π-Truncated-Type' k A B - -type-Π-Truncated-Type : - (k : 𝕋) {l1 l2 : Level} (A : Truncated-Type l1 k) - (B : type-Truncated-Type A → Truncated-Type l2 k) → - UU (l1 ⊔ l2) -type-Π-Truncated-Type k A B = - type-Π-Truncated-Type' k (type-Truncated-Type A) B - -is-trunc-type-Π-Truncated-Type : - (k : 𝕋) {l1 l2 : Level} (A : Truncated-Type l1 k) - (B : type-Truncated-Type A → Truncated-Type l2 k) → - is-trunc k (type-Π-Truncated-Type k A B) -is-trunc-type-Π-Truncated-Type k A B = - is-trunc-type-Π-Truncated-Type' k (type-Truncated-Type A) B - -Π-Truncated-Type : - (k : 𝕋) {l1 l2 : Level} (A : Truncated-Type l1 k) - (B : type-Truncated-Type A → Truncated-Type l2 k) → - Truncated-Type (l1 ⊔ l2) k -Π-Truncated-Type k A B = - Π-Truncated-Type' k (type-Truncated-Type A) B -``` - -### The type of functions into a truncated type is truncated - -```agda -abstract - is-trunc-function-type : - {l1 l2 : Level} (k : 𝕋) {A : UU l1} {B : UU l2} → - is-trunc k B → is-trunc k (A → B) - is-trunc-function-type k {A} {B} is-trunc-B = - is-trunc-Π k {B = λ (x : A) → B} (λ x → is-trunc-B) - -function-type-Truncated-Type : - {l1 l2 : Level} {k : 𝕋} (A : UU l1) (B : Truncated-Type l2 k) → - Truncated-Type (l1 ⊔ l2) k -pr1 (function-type-Truncated-Type A B) = A → type-Truncated-Type B -pr2 (function-type-Truncated-Type A B) = - is-trunc-function-type _ (is-trunc-type-Truncated-Type B) - -type-hom-Truncated-Type : - (k : 𝕋) {l1 l2 : Level} (A : Truncated-Type l1 k) - (B : Truncated-Type l2 k) → UU (l1 ⊔ l2) -type-hom-Truncated-Type k A B = - type-Truncated-Type A → type-Truncated-Type B - -is-trunc-type-hom-Truncated-Type : - (k : 𝕋) {l1 l2 : Level} (A : Truncated-Type l1 k) - (B : Truncated-Type l2 k) → - is-trunc k (type-hom-Truncated-Type k A B) -is-trunc-type-hom-Truncated-Type k A B = - is-trunc-function-type k (is-trunc-type-Truncated-Type B) - -hom-Truncated-Type : - (k : 𝕋) {l1 l2 : Level} (A : Truncated-Type l1 k) - (B : Truncated-Type l2 k) → Truncated-Type (l1 ⊔ l2) k -pr1 (hom-Truncated-Type k A B) = type-hom-Truncated-Type k A B -pr2 (hom-Truncated-Type k A B) = is-trunc-type-hom-Truncated-Type k A B -``` - -### Being truncated is a property - -```agda -abstract - is-prop-is-trunc : - {l : Level} (k : 𝕋) (A : UU l) → is-prop (is-trunc k A) - is-prop-is-trunc neg-two-𝕋 A = is-property-is-contr - is-prop-is-trunc (succ-𝕋 k) A = - is-trunc-Π neg-one-𝕋 - ( λ x → is-trunc-Π neg-one-𝕋 (λ y → is-prop-is-trunc k (x ＝ y))) - -is-trunc-Prop : {l : Level} (k : 𝕋) (A : UU l) → Σ (UU l) (is-trunc neg-one-𝕋) -pr1 (is-trunc-Prop k A) = is-trunc k A -pr2 (is-trunc-Prop k A) = is-prop-is-trunc k A -``` - -### The type of equivalences between truncated types is truncated - -```agda -module _ - {l1 l2 : Level} {A : UU l1} {B : UU l2} - where - - is-trunc-equiv-is-trunc : - (k : 𝕋) → is-trunc k A → is-trunc k B → is-trunc k (A ≃ B) - is-trunc-equiv-is-trunc k H K = - is-trunc-Σ - ( is-trunc-function-type k K) - ( λ f → - is-trunc-Σ - ( is-trunc-Σ - ( is-trunc-function-type k H) - ( λ g → - is-trunc-Π k (λ y → is-trunc-Id K (f (g y)) y))) - ( λ _ → - is-trunc-Σ - ( is-trunc-function-type k H) - ( λ h → - is-trunc-Π k (λ x → is-trunc-Id H (h (f x)) x)))) - -type-equiv-Truncated-Type : - {l1 l2 : Level} {k : 𝕋} (A : Truncated-Type l1 k) (B : Truncated-Type l2 k) → - UU (l1 ⊔ l2) -type-equiv-Truncated-Type A B = - type-Truncated-Type A ≃ type-Truncated-Type B - -is-trunc-type-equiv-Truncated-Type : - {l1 l2 : Level} {k : 𝕋} (A : Truncated-Type l1 k) (B : Truncated-Type l2 k) → - is-trunc k (type-equiv-Truncated-Type A B) -is-trunc-type-equiv-Truncated-Type A B = - is-trunc-equiv-is-trunc _ - ( is-trunc-type-Truncated-Type A) - ( is-trunc-type-Truncated-Type B) - -equiv-Truncated-Type : - {l1 l2 : Level} {k : 𝕋} (A : Truncated-Type l1 k) (B : Truncated-Type l2 k) → - Truncated-Type (l1 ⊔ l2) k -pr1 (equiv-Truncated-Type A B) = type-equiv-Truncated-Type A B -pr2 (equiv-Truncated-Type A B) = is-trunc-type-equiv-Truncated-Type A B -``` diff --git a/src/foundation-core/universal-property-pullbacks.lagda.md b/src/foundation-core/universal-property-pullbacks.lagda.md index 8ec97f1f27..f4e61c23fe 100644 --- a/src/foundation-core/universal-property-pullbacks.lagda.md +++ b/src/foundation-core/universal-property-pullbacks.lagda.md @@ -1,16 +1,20 @@ # The universal property of pullbacks ```agda -module foundation-core.universal-property-pullbacks where +open import foundation.function-extensionality-axiom + +module foundation-core.universal-property-pullbacks + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cones-over-cospan-diagrams +open import foundation.cones-over-cospan-diagrams funext open import foundation.dependent-pair-types -open import foundation.postcomposition-functions +open import foundation.postcomposition-functions funext open import foundation.universe-levels open import foundation-core.contractible-maps diff --git a/src/foundation-core/universal-property-truncation.lagda.md b/src/foundation-core/universal-property-truncation.lagda.md index 1f7366ca3a..1e7c991bb8 100644 --- a/src/foundation-core/universal-property-truncation.lagda.md +++ b/src/foundation-core/universal-property-truncation.lagda.md @@ -1,15 +1,20 @@ # The universal property of truncations ```agda -module foundation-core.universal-property-truncation where +open import foundation.function-extensionality-axiom + +module foundation-core.universal-property-truncation + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-extensionality -open import foundation.universal-property-equivalences +open import foundation.dependent-products-truncated-types funext +open import foundation.function-extensionality funext +open import foundation.universal-property-equivalences funext open import foundation.universe-levels open import foundation-core.contractible-maps diff --git a/src/foundation.lagda.md b/src/foundation.lagda.md index fa5ed4f5b6..c939cc1e9f 100644 --- a/src/foundation.lagda.md +++ b/src/foundation.lagda.md @@ -7,502 +7,516 @@ ## Modules in the foundation namespace ```agda -module foundation where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom -open import foundation.0-connected-types public -open import foundation.0-images-of-maps public -open import foundation.0-maps public -open import foundation.1-types public +module foundation + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where + +open import foundation.0-connected-types funext univalence truncations public +open import foundation.0-images-of-maps funext univalence truncations public +open import foundation.0-maps funext public +open import foundation.1-types funext univalence public open import foundation.2-types public -open import foundation.action-on-equivalences-functions public -open import foundation.action-on-equivalences-functions-out-of-subuniverses public -open import foundation.action-on-equivalences-type-families public -open import foundation.action-on-equivalences-type-families-over-subuniverses public -open import foundation.action-on-higher-identifications-functions public -open import foundation.action-on-homotopies-functions public +open import foundation.action-on-equivalences-functions funext univalence public +open import foundation.action-on-equivalences-functions-out-of-subuniverses funext univalence public +open import foundation.action-on-equivalences-type-families funext univalence public +open import foundation.action-on-equivalences-type-families-over-subuniverses funext univalence public +open import foundation.action-on-higher-identifications-functions funext public +open import foundation.action-on-homotopies-functions funext public open import foundation.action-on-identifications-binary-dependent-functions public open import foundation.action-on-identifications-binary-functions public open import foundation.action-on-identifications-dependent-functions public open import foundation.action-on-identifications-functions public -open import foundation.apartness-relations public -open import foundation.arithmetic-law-coproduct-and-sigma-decompositions public -open import foundation.arithmetic-law-product-and-pi-decompositions public -open import foundation.automorphisms public -open import foundation.axiom-of-choice public -open import foundation.bands public -open import foundation.base-changes-span-diagrams public -open import foundation.bicomposition-functions public +open import foundation.apartness-relations funext univalence truncations public +open import foundation.arithmetic-law-coproduct-and-sigma-decompositions funext univalence truncations public +open import foundation.arithmetic-law-product-and-pi-decompositions funext univalence truncations public +open import foundation.automorphisms funext univalence public +open import foundation.axiom-of-choice funext univalence truncations public +open import foundation.bands funext univalence truncations public +open import foundation.base-changes-span-diagrams funext univalence truncations public +open import foundation.bicomposition-functions funext public open import foundation.binary-dependent-identifications public -open import foundation.binary-embeddings public +open import foundation.binary-embeddings funext public open import foundation.binary-equivalences public -open import foundation.binary-equivalences-unordered-pairs-of-types public -open import foundation.binary-functoriality-set-quotients public -open import foundation.binary-homotopies public -open import foundation.binary-operations-unordered-pairs-of-types public -open import foundation.binary-reflecting-maps-equivalence-relations public -open import foundation.binary-relations public -open import foundation.binary-relations-with-extensions public -open import foundation.binary-relations-with-lifts public +open import foundation.binary-equivalences-unordered-pairs-of-types funext univalence truncations public +open import foundation.binary-functoriality-set-quotients funext univalence truncations public +open import foundation.binary-homotopies funext public +open import foundation.binary-operations-unordered-pairs-of-types funext univalence truncations public +open import foundation.binary-reflecting-maps-equivalence-relations funext univalence truncations public +open import foundation.binary-relations funext univalence truncations public +open import foundation.binary-relations-with-extensions funext univalence truncations public +open import foundation.binary-relations-with-lifts funext univalence truncations public open import foundation.binary-transport public -open import foundation.binary-type-duality public -open import foundation.booleans public -open import foundation.cantor-schroder-bernstein-escardo public -open import foundation.cantors-theorem public -open import foundation.cartesian-morphisms-arrows public -open import foundation.cartesian-morphisms-span-diagrams public -open import foundation.cartesian-product-types public -open import foundation.cartesian-products-set-quotients public -open import foundation.category-of-families-of-sets public -open import foundation.category-of-sets public -open import foundation.choice-of-representatives-equivalence-relation public -open import foundation.coalgebras-maybe public +open import foundation.binary-type-duality funext univalence public +open import foundation.booleans funext univalence truncations public +open import foundation.cantor-schroder-bernstein-escardo funext univalence truncations public +open import foundation.cantors-theorem funext univalence truncations public +open import foundation.cartesian-morphisms-arrows funext univalence truncations public +open import foundation.cartesian-morphisms-span-diagrams funext univalence truncations public +open import foundation.cartesian-product-types funext univalence public +open import foundation.cartesian-products-set-quotients funext univalence truncations public +open import foundation.category-of-families-of-sets funext univalence truncations public +open import foundation.category-of-sets funext univalence truncations public +open import foundation.choice-of-representatives-equivalence-relation funext univalence truncations public +open import foundation.coalgebras-maybe funext univalence public open import foundation.codiagonal-maps-of-types public -open import foundation.coherently-idempotent-maps public -open import foundation.coherently-invertible-maps public -open import foundation.coinhabited-pairs-of-types public -open import foundation.commuting-cubes-of-maps public +open import foundation.coherently-idempotent-maps funext univalence truncations public +open import foundation.coherently-invertible-maps funext public +open import foundation.coinhabited-pairs-of-types funext univalence truncations public +open import foundation.commuting-cubes-of-maps funext univalence public open import foundation.commuting-hexagons-of-identifications public open import foundation.commuting-pentagons-of-identifications public -open import foundation.commuting-prisms-of-maps public -open import foundation.commuting-squares-of-homotopies public -open import foundation.commuting-squares-of-identifications public -open import foundation.commuting-squares-of-maps public -open import foundation.commuting-tetrahedra-of-homotopies public +open import foundation.commuting-prisms-of-maps funext univalence public +open import foundation.commuting-squares-of-homotopies funext public +open import foundation.commuting-squares-of-identifications funext public +open import foundation.commuting-squares-of-maps funext univalence public +open import foundation.commuting-tetrahedra-of-homotopies funext public open import foundation.commuting-tetrahedra-of-maps public -open import foundation.commuting-triangles-of-homotopies public -open import foundation.commuting-triangles-of-identifications public -open import foundation.commuting-triangles-of-maps public -open import foundation.commuting-triangles-of-morphisms-arrows public +open import foundation.commuting-triangles-of-homotopies funext public +open import foundation.commuting-triangles-of-identifications funext public +open import foundation.commuting-triangles-of-maps funext univalence public +open import foundation.commuting-triangles-of-morphisms-arrows funext public open import foundation.complements public -open import foundation.complements-subtypes public -open import foundation.composite-maps-in-inverse-sequential-diagrams public -open import foundation.composition-algebra public -open import foundation.composition-spans public -open import foundation.computational-identity-types public -open import foundation.cones-over-cospan-diagrams public -open import foundation.cones-over-inverse-sequential-diagrams public -open import foundation.conjunction public -open import foundation.connected-components public -open import foundation.connected-components-universes public -open import foundation.connected-maps public -open import foundation.connected-types public -open import foundation.constant-maps public -open import foundation.constant-span-diagrams public -open import foundation.constant-type-families public -open import foundation.continuations public -open import foundation.contractible-maps public -open import foundation.contractible-types public -open import foundation.copartial-elements public -open import foundation.copartial-functions public -open import foundation.coproduct-decompositions public -open import foundation.coproduct-decompositions-subuniverse public -open import foundation.coproduct-types public -open import foundation.coproducts-pullbacks public -open import foundation.coslice public +open import foundation.complements-subtypes funext univalence truncations public +open import foundation.composite-maps-in-inverse-sequential-diagrams funext univalence truncations public +open import foundation.composition-algebra funext public +open import foundation.composition-spans funext univalence truncations public +open import foundation.computational-identity-types funext univalence public +open import foundation.cones-over-cospan-diagrams funext public +open import foundation.cones-over-inverse-sequential-diagrams funext univalence truncations public +open import foundation.conjunction funext univalence truncations public +open import foundation.connected-components funext univalence truncations public +open import foundation.connected-components-universes funext univalence truncations public +open import foundation.connected-maps funext univalence truncations public +open import foundation.connected-types funext univalence truncations public +open import foundation.constant-maps funext univalence truncations public +open import foundation.constant-span-diagrams funext univalence public +open import foundation.constant-type-families funext public +open import foundation.continuations funext univalence truncations public +open import foundation.contractible-maps funext public +open import foundation.contractible-types funext univalence public +open import foundation.copartial-elements funext univalence truncations public +open import foundation.copartial-functions funext univalence truncations public +open import foundation.coproduct-decompositions funext univalence truncations public +open import foundation.coproduct-decompositions-subuniverse funext univalence truncations public +open import foundation.coproduct-types funext univalence truncations public +open import foundation.coproducts-pullbacks funext univalence truncations public +open import foundation.coslice funext public open import foundation.cospan-diagrams public open import foundation.cospans public -open import foundation.decidable-dependent-function-types public -open import foundation.decidable-dependent-pair-types public -open import foundation.decidable-embeddings public -open import foundation.decidable-equality public -open import foundation.decidable-equivalence-relations public -open import foundation.decidable-maps public -open import foundation.decidable-propositions public -open import foundation.decidable-relations public -open import foundation.decidable-subtypes public -open import foundation.decidable-types public -open import foundation.dependent-binary-homotopies public -open import foundation.dependent-binomial-theorem public -open import foundation.dependent-epimorphisms public -open import foundation.dependent-epimorphisms-with-respect-to-truncated-types public -open import foundation.dependent-function-types public +open import foundation.decidable-dependent-function-types funext univalence truncations public +open import foundation.decidable-dependent-pair-types funext univalence truncations public +open import foundation.decidable-embeddings funext univalence truncations public +open import foundation.decidable-equality funext univalence truncations public +open import foundation.decidable-equivalence-relations funext univalence truncations public +open import foundation.decidable-maps funext univalence truncations public +open import foundation.decidable-propositions funext univalence truncations public +open import foundation.decidable-relations funext univalence truncations public +open import foundation.decidable-subtypes funext univalence truncations public +open import foundation.decidable-types funext univalence truncations public +open import foundation.dependent-binary-homotopies funext public +open import foundation.dependent-binomial-theorem funext univalence truncations public +open import foundation.dependent-epimorphisms funext univalence truncations public +open import foundation.dependent-epimorphisms-with-respect-to-truncated-types funext univalence truncations public +open import foundation.dependent-function-types funext univalence public open import foundation.dependent-homotopies public -open import foundation.dependent-identifications public -open import foundation.dependent-inverse-sequential-diagrams public +open import foundation.dependent-identifications funext public +open import foundation.dependent-inverse-sequential-diagrams funext univalence truncations public open import foundation.dependent-pair-types public -open import foundation.dependent-products-pullbacks public +open import foundation.dependent-products-contractible-types funext public +open import foundation.dependent-products-propositions funext public +open import foundation.dependent-products-pullbacks funext univalence public +open import foundation.dependent-products-truncated-types funext public open import foundation.dependent-sequences public -open import foundation.dependent-sums-pullbacks public +open import foundation.dependent-sums-pullbacks funext public open import foundation.dependent-telescopes public -open import foundation.dependent-universal-property-equivalences public -open import foundation.descent-coproduct-types public -open import foundation.descent-dependent-pair-types public -open import foundation.descent-empty-types public -open import foundation.descent-equivalences public -open import foundation.diaconescus-theorem public -open import foundation.diagonal-maps-cartesian-products-of-types public -open import foundation.diagonal-maps-of-types public -open import foundation.diagonal-span-diagrams public -open import foundation.diagonals-of-maps public +open import foundation.dependent-universal-property-equivalences funext public +open import foundation.descent-coproduct-types funext univalence truncations public +open import foundation.descent-dependent-pair-types funext public +open import foundation.descent-empty-types funext public +open import foundation.descent-equivalences funext public +open import foundation.diaconescus-theorem funext univalence truncations public +open import foundation.diagonal-maps-cartesian-products-of-types funext univalence public +open import foundation.diagonal-maps-of-types funext public +open import foundation.diagonal-span-diagrams funext public +open import foundation.diagonals-of-maps funext public open import foundation.diagonals-of-morphisms-arrows public -open import foundation.discrete-binary-relations public -open import foundation.discrete-reflexive-relations public -open import foundation.discrete-relaxed-sigma-decompositions public -open import foundation.discrete-sigma-decompositions public -open import foundation.discrete-types public -open import foundation.disjoint-subtypes public -open import foundation.disjunction public +open import foundation.discrete-binary-relations funext univalence truncations public +open import foundation.discrete-reflexive-relations funext univalence truncations public +open import foundation.discrete-relaxed-sigma-decompositions funext univalence public +open import foundation.discrete-sigma-decompositions funext univalence truncations public +open import foundation.discrete-types funext univalence truncations public +open import foundation.disjoint-subtypes funext univalence truncations public +open import foundation.disjunction funext univalence truncations public open import foundation.double-arrows public -open import foundation.double-negation public -open import foundation.double-negation-modality public -open import foundation.double-negation-stable-equality public -open import foundation.double-negation-stable-propositions public -open import foundation.double-powersets public -open import foundation.dubuc-penon-compact-types public -open import foundation.effective-maps-equivalence-relations public -open import foundation.embeddings public -open import foundation.empty-types public -open import foundation.endomorphisms public -open import foundation.epimorphisms public -open import foundation.epimorphisms-with-respect-to-sets public -open import foundation.epimorphisms-with-respect-to-truncated-types public +open import foundation.double-negation funext univalence truncations public +open import foundation.double-negation-modality funext univalence truncations public +open import foundation.double-negation-stable-equality funext univalence truncations public +open import foundation.double-negation-stable-propositions funext univalence truncations public +open import foundation.double-powersets funext univalence truncations public +open import foundation.dubuc-penon-compact-types funext univalence truncations public +open import foundation.effective-maps-equivalence-relations funext univalence truncations public +open import foundation.embeddings funext public +open import foundation.empty-types funext univalence truncations public +open import foundation.endomorphisms funext univalence truncations public +open import foundation.epimorphisms funext univalence truncations public +open import foundation.epimorphisms-with-respect-to-sets funext univalence truncations public +open import foundation.epimorphisms-with-respect-to-truncated-types funext univalence truncations public open import foundation.equality-cartesian-product-types public -open import foundation.equality-coproduct-types public -open import foundation.equality-dependent-function-types public -open import foundation.equality-dependent-pair-types public -open import foundation.equality-fibers-of-maps public -open import foundation.equivalence-classes public -open import foundation.equivalence-extensionality public -open import foundation.equivalence-induction public -open import foundation.equivalence-injective-type-families public -open import foundation.equivalence-relations public -open import foundation.equivalences public -open import foundation.equivalences-arrows public -open import foundation.equivalences-cospans public -open import foundation.equivalences-double-arrows public -open import foundation.equivalences-inverse-sequential-diagrams public -open import foundation.equivalences-maybe public -open import foundation.equivalences-span-diagrams public -open import foundation.equivalences-span-diagrams-families-of-types public -open import foundation.equivalences-spans public -open import foundation.equivalences-spans-families-of-types public +open import foundation.equality-coproduct-types funext univalence truncations public +open import foundation.equality-dependent-function-types funext public +open import foundation.equality-dependent-pair-types funext public +open import foundation.equality-fibers-of-maps funext public +open import foundation.equivalence-classes funext univalence truncations public +open import foundation.equivalence-extensionality funext public +open import foundation.equivalence-induction funext univalence public +open import foundation.equivalence-injective-type-families funext univalence public +open import foundation.equivalence-relations funext univalence truncations public +open import foundation.equivalences funext public +open import foundation.equivalences-arrows funext univalence truncations public +open import foundation.equivalences-cospans funext univalence public +open import foundation.equivalences-double-arrows funext univalence truncations public +open import foundation.equivalences-inverse-sequential-diagrams funext univalence truncations public +open import foundation.equivalences-maybe funext univalence truncations public +open import foundation.equivalences-span-diagrams funext univalence truncations public +open import foundation.equivalences-span-diagrams-families-of-types funext univalence public +open import foundation.equivalences-spans funext univalence public +open import foundation.equivalences-spans-families-of-types funext univalence public open import foundation.evaluation-functions public -open import foundation.exclusive-disjunction public -open import foundation.exclusive-sum public -open import foundation.existential-quantification public -open import foundation.exponents-set-quotients public -open import foundation.extensions-types public -open import foundation.extensions-types-global-subuniverses public -open import foundation.extensions-types-subuniverses public -open import foundation.faithful-maps public -open import foundation.families-of-equivalences public -open import foundation.families-of-maps public +open import foundation.exclusive-disjunction funext univalence truncations public +open import foundation.exclusive-sum funext univalence truncations public +open import foundation.existential-quantification funext univalence truncations public +open import foundation.exponents-set-quotients funext univalence truncations public +open import foundation.extensions-types funext univalence truncations public +open import foundation.extensions-types-global-subuniverses funext univalence truncations public +open import foundation.extensions-types-subuniverses funext univalence truncations public +open import foundation.faithful-maps funext public +open import foundation.families-of-equivalences funext public +open import foundation.families-of-maps funext public open import foundation.families-over-telescopes public -open import foundation.fiber-inclusions public -open import foundation.fibered-equivalences public -open import foundation.fibered-involutions public -open import foundation.fibered-maps public -open import foundation.fibers-of-maps public -open import foundation.finitely-coherent-equivalences public -open import foundation.finitely-coherently-invertible-maps public +open import foundation.fiber-inclusions funext univalence public +open import foundation.fibered-equivalences funext univalence truncations public +open import foundation.fibered-involutions funext univalence truncations public +open import foundation.fibered-maps funext univalence truncations public +open import foundation.fibers-of-maps funext public +open import foundation.finitely-coherent-equivalences funext public +open import foundation.finitely-coherently-invertible-maps funext public open import foundation.fixed-points-endofunctions public -open import foundation.full-subtypes public -open import foundation.function-extensionality public -open import foundation.function-types public -open import foundation.functional-correspondences public -open import foundation.functoriality-action-on-identifications-functions public -open import foundation.functoriality-cartesian-product-types public -open import foundation.functoriality-coproduct-types public -open import foundation.functoriality-dependent-function-types public -open import foundation.functoriality-dependent-pair-types public -open import foundation.functoriality-fibers-of-maps public -open import foundation.functoriality-function-types public -open import foundation.functoriality-morphisms-arrows public -open import foundation.functoriality-propositional-truncation public -open import foundation.functoriality-pullbacks public -open import foundation.functoriality-sequential-limits public -open import foundation.functoriality-set-quotients public -open import foundation.functoriality-set-truncation public -open import foundation.functoriality-truncation public -open import foundation.fundamental-theorem-of-equivalence-relations public +open import foundation.full-subtypes funext univalence truncations public +open import foundation.function-extensionality funext public +open import foundation.function-extensionality-axiom public +open import foundation.function-types funext public +open import foundation.functional-correspondences funext univalence truncations public +open import foundation.functoriality-action-on-identifications-functions funext public +open import foundation.functoriality-cartesian-product-types funext public +open import foundation.functoriality-coproduct-types funext univalence truncations public +open import foundation.functoriality-dependent-function-types funext univalence public +open import foundation.functoriality-dependent-pair-types funext public +open import foundation.functoriality-fibers-of-maps funext public +open import foundation.functoriality-function-types funext univalence public +open import foundation.functoriality-morphisms-arrows funext univalence truncations public +open import foundation.functoriality-propositional-truncation funext univalence truncations public +open import foundation.functoriality-pullbacks funext univalence truncations public +open import foundation.functoriality-sequential-limits funext univalence truncations public +open import foundation.functoriality-set-quotients funext univalence truncations public +open import foundation.functoriality-set-truncation funext univalence truncations public +open import foundation.functoriality-truncation funext univalence truncations public +open import foundation.fundamental-theorem-of-equivalence-relations funext univalence truncations public open import foundation.fundamental-theorem-of-identity-types public -open import foundation.global-choice public -open import foundation.global-subuniverses public -open import foundation.globular-type-of-dependent-functions public -open import foundation.globular-type-of-functions public -open import foundation.higher-homotopies-morphisms-arrows public -open import foundation.hilberts-epsilon-operators public -open import foundation.homotopies public -open import foundation.homotopies-morphisms-arrows public -open import foundation.homotopies-morphisms-cospan-diagrams public +open import foundation.global-choice funext univalence truncations public +open import foundation.global-subuniverses funext univalence public +open import foundation.globular-type-of-dependent-functions funext univalence truncations public +open import foundation.globular-type-of-functions funext univalence truncations public +open import foundation.higher-homotopies-morphisms-arrows funext univalence truncations public +open import foundation.hilberts-epsilon-operators funext univalence truncations public +open import foundation.homotopies funext public +open import foundation.homotopies-morphisms-arrows funext public +open import foundation.homotopies-morphisms-cospan-diagrams funext univalence truncations public open import foundation.homotopy-algebra public -open import foundation.homotopy-induction public -open import foundation.homotopy-preorder-of-types public -open import foundation.horizontal-composition-spans-of-spans public -open import foundation.idempotent-maps public +open import foundation.homotopy-induction funext public +open import foundation.homotopy-preorder-of-types funext univalence truncations public +open import foundation.horizontal-composition-spans-of-spans funext univalence truncations public +open import foundation.idempotent-maps funext public open import foundation.identity-systems public -open import foundation.identity-truncated-types public -open import foundation.identity-types public -open import foundation.images public -open import foundation.images-subtypes public +open import foundation.identity-truncated-types funext univalence public +open import foundation.identity-types funext public +open import foundation.images funext univalence truncations public +open import foundation.images-subtypes funext univalence truncations public open import foundation.implicit-function-types public -open import foundation.impredicative-encodings public -open import foundation.impredicative-universes public +open import foundation.impredicative-encodings funext univalence truncations public +open import foundation.impredicative-universes funext univalence truncations public open import foundation.induction-principle-propositional-truncation public -open import foundation.infinitely-coherent-equivalences public -open import foundation.inhabited-subtypes public -open import foundation.inhabited-types public -open import foundation.injective-maps public +open import foundation.infinitely-coherent-equivalences funext univalence public +open import foundation.inhabited-subtypes funext univalence truncations public +open import foundation.inhabited-types funext univalence truncations public +open import foundation.injective-maps funext public open import foundation.interchange-law public -open import foundation.intersections-subtypes public -open import foundation.inverse-sequential-diagrams public -open import foundation.invertible-maps public -open import foundation.involutions public -open import foundation.irrefutable-propositions public -open import foundation.isolated-elements public -open import foundation.isomorphisms-of-sets public -open import foundation.iterated-cartesian-product-types public +open import foundation.intersections-subtypes funext univalence truncations public +open import foundation.inverse-sequential-diagrams funext univalence truncations public +open import foundation.invertible-maps funext univalence truncations public +open import foundation.involutions funext univalence public +open import foundation.irrefutable-propositions funext univalence truncations public +open import foundation.isolated-elements funext univalence truncations public +open import foundation.isomorphisms-of-sets funext univalence public +open import foundation.iterated-cartesian-product-types funext univalence truncations public open import foundation.iterated-dependent-pair-types public -open import foundation.iterated-dependent-product-types public -open import foundation.iterating-automorphisms public -open import foundation.iterating-families-of-maps public -open import foundation.iterating-functions public -open import foundation.iterating-involutions public -open import foundation.kernel-span-diagrams-of-maps public -open import foundation.large-apartness-relations public -open import foundation.large-binary-relations public +open import foundation.iterated-dependent-product-types funext public +open import foundation.iterating-automorphisms funext univalence truncations public +open import foundation.iterating-families-of-maps funext univalence truncations public +open import foundation.iterating-functions funext univalence truncations public +open import foundation.iterating-involutions funext univalence truncations public +open import foundation.kernel-span-diagrams-of-maps funext public +open import foundation.large-apartness-relations funext univalence truncations public +open import foundation.large-binary-relations funext univalence truncations public open import foundation.large-dependent-pair-types public open import foundation.large-homotopies public open import foundation.large-identity-types public -open import foundation.large-locale-of-propositions public -open import foundation.large-locale-of-subtypes public -open import foundation.law-of-excluded-middle public -open import foundation.lawveres-fixed-point-theorem public -open import foundation.lesser-limited-principle-of-omniscience public +open import foundation.large-locale-of-propositions funext univalence truncations public +open import foundation.large-locale-of-subtypes funext univalence truncations public +open import foundation.law-of-excluded-middle funext univalence truncations public +open import foundation.lawveres-fixed-point-theorem funext univalence truncations public +open import foundation.lesser-limited-principle-of-omniscience funext univalence truncations public open import foundation.lifts-types public -open import foundation.limited-principle-of-omniscience public -open import foundation.locale-of-propositions public -open import foundation.locally-small-types public -open import foundation.logical-equivalences public -open import foundation.maps-in-global-subuniverses public -open import foundation.maps-in-subuniverses public -open import foundation.maybe public -open import foundation.mere-embeddings public -open import foundation.mere-equality public -open import foundation.mere-equivalences public -open import foundation.mere-functions public -open import foundation.mere-logical-equivalences public -open import foundation.mere-path-cosplit-maps public -open import foundation.monomorphisms public -open import foundation.morphisms-arrows public -open import foundation.morphisms-binary-relations public -open import foundation.morphisms-coalgebras-maybe public +open import foundation.limited-principle-of-omniscience funext univalence truncations public +open import foundation.locale-of-propositions funext univalence truncations public +open import foundation.locally-small-types funext univalence truncations public +open import foundation.logical-equivalences funext public +open import foundation.maps-in-global-subuniverses funext univalence truncations public +open import foundation.maps-in-subuniverses funext univalence public +open import foundation.maybe funext univalence truncations public +open import foundation.mere-embeddings funext univalence truncations public +open import foundation.mere-equality funext univalence truncations public +open import foundation.mere-equivalences funext univalence truncations public +open import foundation.mere-functions funext univalence truncations public +open import foundation.mere-logical-equivalences funext univalence truncations public +open import foundation.mere-path-cosplit-maps funext univalence truncations public +open import foundation.monomorphisms funext univalence public +open import foundation.morphisms-arrows funext public +open import foundation.morphisms-binary-relations funext univalence truncations public +open import foundation.morphisms-coalgebras-maybe funext univalence public open import foundation.morphisms-cospan-diagrams public open import foundation.morphisms-cospans public -open import foundation.morphisms-double-arrows public -open import foundation.morphisms-inverse-sequential-diagrams public -open import foundation.morphisms-span-diagrams public +open import foundation.morphisms-double-arrows funext univalence public +open import foundation.morphisms-inverse-sequential-diagrams funext univalence truncations public +open import foundation.morphisms-span-diagrams funext univalence truncations public open import foundation.morphisms-spans public -open import foundation.morphisms-spans-families-of-types public +open import foundation.morphisms-spans-families-of-types funext public open import foundation.morphisms-twisted-arrows public -open import foundation.multisubsets public -open import foundation.multivariable-correspondences public -open import foundation.multivariable-decidable-relations public -open import foundation.multivariable-functoriality-set-quotients public -open import foundation.multivariable-homotopies public -open import foundation.multivariable-operations public -open import foundation.multivariable-relations public -open import foundation.multivariable-sections public -open import foundation.negated-equality public -open import foundation.negation public -open import foundation.noncontractible-types public -open import foundation.null-homotopic-maps public -open import foundation.operations-span-diagrams public -open import foundation.operations-spans public +open import foundation.multisubsets funext univalence truncations public +open import foundation.multivariable-correspondences funext univalence truncations public +open import foundation.multivariable-decidable-relations funext univalence truncations public +open import foundation.multivariable-functoriality-set-quotients funext univalence truncations public +open import foundation.multivariable-homotopies funext public +open import foundation.multivariable-operations funext univalence truncations public +open import foundation.multivariable-relations funext univalence truncations public +open import foundation.multivariable-sections funext public +open import foundation.negated-equality funext univalence truncations public +open import foundation.negation funext public +open import foundation.noncontractible-types funext univalence truncations public +open import foundation.null-homotopic-maps funext univalence truncations public +open import foundation.operations-span-diagrams funext univalence truncations public +open import foundation.operations-spans funext univalence truncations public open import foundation.operations-spans-families-of-types public open import foundation.opposite-spans public -open import foundation.pairs-of-distinct-elements public +open import foundation.pairs-of-distinct-elements funext univalence truncations public open import foundation.partial-elements public open import foundation.partial-functions public open import foundation.partial-sequences public -open import foundation.partitions public -open import foundation.path-algebra public -open import foundation.path-cosplit-maps public -open import foundation.path-split-maps public -open import foundation.path-split-type-families public -open import foundation.perfect-images public +open import foundation.partitions funext univalence truncations public +open import foundation.path-algebra funext public +open import foundation.path-cosplit-maps funext univalence truncations public +open import foundation.path-split-maps funext public +open import foundation.path-split-type-families funext public +open import foundation.perfect-images funext univalence truncations public open import foundation.permutations-spans-families-of-types public -open import foundation.pi-decompositions public -open import foundation.pi-decompositions-subuniverse public -open import foundation.pointed-torsorial-type-families public -open import foundation.postcomposition-dependent-functions public -open import foundation.postcomposition-functions public -open import foundation.postcomposition-pullbacks public -open import foundation.powersets public -open import foundation.precomposition-dependent-functions public -open import foundation.precomposition-functions public -open import foundation.precomposition-functions-into-subuniverses public -open import foundation.precomposition-type-families public -open import foundation.preunivalence public -open import foundation.preunivalent-type-families public -open import foundation.principle-of-omniscience public +open import foundation.pi-decompositions funext univalence public +open import foundation.pi-decompositions-subuniverse funext univalence public +open import foundation.pointed-torsorial-type-families funext univalence truncations public +open import foundation.postcomposition-dependent-functions funext public +open import foundation.postcomposition-functions funext public +open import foundation.postcomposition-pullbacks funext public +open import foundation.powersets funext univalence truncations public +open import foundation.precomposition-dependent-functions funext public +open import foundation.precomposition-functions funext public +open import foundation.precomposition-functions-into-subuniverses funext public +open import foundation.precomposition-type-families funext public +open import foundation.preunivalence funext univalence public +open import foundation.preunivalent-type-families funext univalence public +open import foundation.principle-of-omniscience funext univalence truncations public open import foundation.product-decompositions public -open import foundation.product-decompositions-subuniverse public -open import foundation.products-binary-relations public -open import foundation.products-equivalence-relations public -open import foundation.products-of-tuples-of-types public -open import foundation.products-pullbacks public -open import foundation.products-unordered-pairs-of-types public -open import foundation.products-unordered-tuples-of-types public -open import foundation.projective-types public -open import foundation.proper-subtypes public -open import foundation.propositional-extensionality public -open import foundation.propositional-maps public -open import foundation.propositional-resizing public -open import foundation.propositional-truncations public -open import foundation.propositions public -open import foundation.pullback-cones public -open import foundation.pullbacks public -open import foundation.pullbacks-subtypes public -open import foundation.quasicoherently-idempotent-maps public -open import foundation.raising-universe-levels public -open import foundation.reflecting-maps-equivalence-relations public -open import foundation.reflexive-relations public -open import foundation.regensburg-extension-fundamental-theorem-of-identity-types public -open import foundation.relaxed-sigma-decompositions public -open import foundation.repetitions-of-values public -open import foundation.repetitions-sequences public -open import foundation.replacement public -open import foundation.retractions public -open import foundation.retracts-of-maps public -open import foundation.retracts-of-types public -open import foundation.sections public -open import foundation.separated-types-subuniverses public +open import foundation.product-decompositions-subuniverse funext univalence public +open import foundation.products-binary-relations funext univalence truncations public +open import foundation.products-equivalence-relations funext univalence truncations public +open import foundation.products-of-tuples-of-types funext univalence truncations public +open import foundation.products-pullbacks funext univalence truncations public +open import foundation.products-unordered-pairs-of-types funext univalence truncations public +open import foundation.products-unordered-tuples-of-types funext univalence truncations public +open import foundation.projective-types funext univalence truncations public +open import foundation.proper-subtypes funext univalence truncations public +open import foundation.propositional-extensionality funext univalence truncations public +open import foundation.propositional-maps funext public +open import foundation.propositional-resizing funext univalence truncations public +open import foundation.propositional-truncations funext univalence public +open import foundation.propositions funext univalence public +open import foundation.pullback-cones funext univalence truncations public +open import foundation.pullbacks funext univalence truncations public +open import foundation.pullbacks-subtypes funext univalence truncations public +open import foundation.quasicoherently-idempotent-maps funext univalence truncations public +open import foundation.raising-universe-levels funext univalence public +open import foundation.raising-universe-levels-booleans public +open import foundation.raising-universe-levels-unit-type public +open import foundation.reflecting-maps-equivalence-relations funext univalence truncations public +open import foundation.reflexive-relations funext univalence truncations public +open import foundation.regensburg-extension-fundamental-theorem-of-identity-types funext univalence truncations public +open import foundation.relaxed-sigma-decompositions funext univalence public +open import foundation.repetitions-of-values funext univalence truncations public +open import foundation.repetitions-sequences funext univalence truncations public +open import foundation.replacement funext univalence truncations public +open import foundation.retractions funext public +open import foundation.retracts-of-maps funext univalence public +open import foundation.retracts-of-types funext univalence public +open import foundation.sections funext public +open import foundation.separated-types-subuniverses funext univalence public open import foundation.sequences public -open import foundation.sequential-limits public -open import foundation.set-presented-types public -open import foundation.set-quotients public -open import foundation.set-truncations public -open import foundation.sets public +open import foundation.sequential-limits funext univalence truncations public +open import foundation.set-presented-types funext univalence truncations public +open import foundation.set-quotients funext univalence truncations public +open import foundation.set-truncations funext univalence public +open import foundation.sets funext univalence public open import foundation.shifting-sequences public -open import foundation.sigma-closed-subuniverses public -open import foundation.sigma-decomposition-subuniverse public -open import foundation.sigma-decompositions public +open import foundation.sigma-closed-subuniverses funext univalence public +open import foundation.sigma-decomposition-subuniverse funext univalence public +open import foundation.sigma-decompositions funext univalence truncations public open import foundation.singleton-induction public -open import foundation.singleton-subtypes public -open import foundation.slice public -open import foundation.small-maps public -open import foundation.small-types public -open import foundation.small-universes public +open import foundation.singleton-subtypes funext univalence truncations public +open import foundation.slice funext univalence public +open import foundation.small-maps funext univalence truncations public +open import foundation.small-types funext univalence truncations public +open import foundation.small-universes funext univalence truncations public open import foundation.sorial-type-families public -open import foundation.span-diagrams public +open import foundation.span-diagrams funext public open import foundation.span-diagrams-families-of-types public open import foundation.spans public open import foundation.spans-families-of-types public -open import foundation.spans-of-spans public -open import foundation.split-idempotent-maps public +open import foundation.spans-of-spans funext univalence public +open import foundation.split-idempotent-maps funext univalence truncations public open import foundation.split-surjective-maps public -open import foundation.standard-apartness-relations public -open import foundation.standard-pullbacks public -open import foundation.standard-ternary-pullbacks public -open import foundation.strict-symmetrization-binary-relations public -open import foundation.strictly-involutive-identity-types public +open import foundation.standard-apartness-relations funext univalence truncations public +open import foundation.standard-pullbacks funext public +open import foundation.standard-ternary-pullbacks funext public +open import foundation.strict-symmetrization-binary-relations funext univalence truncations public +open import foundation.strictly-involutive-identity-types funext univalence public open import foundation.strictly-right-unital-concatenation-identifications public -open import foundation.strong-preunivalence public -open import foundation.strongly-extensional-maps public -open import foundation.structure public +open import foundation.strong-preunivalence funext univalence truncations public +open import foundation.strongly-extensional-maps funext univalence truncations public +open import foundation.structure funext univalence public open import foundation.structure-identity-principle public -open import foundation.structured-equality-duality public -open import foundation.structured-type-duality public +open import foundation.structured-equality-duality funext univalence public +open import foundation.structured-type-duality funext univalence truncations public open import foundation.subsingleton-induction public open import foundation.subterminal-types public -open import foundation.subtype-duality public +open import foundation.subtype-duality funext univalence truncations public open import foundation.subtype-identity-principle public -open import foundation.subtypes public -open import foundation.subuniverses public -open import foundation.surjective-maps public -open import foundation.symmetric-binary-relations public -open import foundation.symmetric-cores-binary-relations public -open import foundation.symmetric-difference public -open import foundation.symmetric-identity-types public -open import foundation.symmetric-operations public +open import foundation.subtypes funext univalence truncations public +open import foundation.subuniverses funext univalence public +open import foundation.surjective-maps funext univalence truncations public +open import foundation.symmetric-binary-relations funext univalence truncations public +open import foundation.symmetric-cores-binary-relations funext univalence truncations public +open import foundation.symmetric-difference funext univalence truncations public +open import foundation.symmetric-identity-types funext univalence truncations public +open import foundation.symmetric-operations funext univalence truncations public open import foundation.telescopes public -open import foundation.terminal-spans-families-of-types public -open import foundation.tight-apartness-relations public -open import foundation.torsorial-type-families public +open import foundation.terminal-spans-families-of-types funext public +open import foundation.tight-apartness-relations funext univalence truncations public +open import foundation.torsorial-type-families funext univalence truncations public open import foundation.total-partial-elements public -open import foundation.total-partial-functions public -open import foundation.transfinite-cocomposition-of-maps public -open import foundation.transport-along-equivalences public -open import foundation.transport-along-higher-identifications public -open import foundation.transport-along-homotopies public +open import foundation.total-partial-functions funext public +open import foundation.transfinite-cocomposition-of-maps funext univalence truncations public +open import foundation.transport-along-equivalences funext univalence public +open import foundation.transport-along-higher-identifications funext public +open import foundation.transport-along-homotopies funext public open import foundation.transport-along-identifications public -open import foundation.transport-split-type-families public -open import foundation.transposition-identifications-along-equivalences public -open import foundation.transposition-identifications-along-retractions public -open import foundation.transposition-identifications-along-sections public -open import foundation.transposition-span-diagrams public -open import foundation.trivial-relaxed-sigma-decompositions public -open import foundation.trivial-sigma-decompositions public -open import foundation.truncated-equality public -open import foundation.truncated-maps public -open import foundation.truncated-types public -open import foundation.truncation-equivalences public -open import foundation.truncation-images-of-maps public +open import foundation.transport-split-type-families funext univalence public +open import foundation.transposition-identifications-along-equivalences funext public +open import foundation.transposition-identifications-along-retractions funext public +open import foundation.transposition-identifications-along-sections funext public +open import foundation.transposition-span-diagrams funext public +open import foundation.trivial-relaxed-sigma-decompositions funext univalence public +open import foundation.trivial-sigma-decompositions funext univalence truncations public +open import foundation.truncated-equality funext univalence truncations public +open import foundation.truncated-maps funext public +open import foundation.truncated-types funext univalence public +open import foundation.truncation-equivalences funext univalence truncations public +open import foundation.truncation-images-of-maps funext univalence truncations public open import foundation.truncation-levels public -open import foundation.truncation-modalities public -open import foundation.truncations public -open import foundation.tuples-of-types public +open import foundation.truncation-modalities funext univalence truncations public +open import foundation.truncations funext univalence truncations public +open import foundation.tuples-of-types funext univalence truncations public open import foundation.type-arithmetic-booleans public open import foundation.type-arithmetic-cartesian-product-types public -open import foundation.type-arithmetic-coproduct-types public -open import foundation.type-arithmetic-dependent-function-types public +open import foundation.type-arithmetic-coproduct-types funext univalence truncations public +open import foundation.type-arithmetic-dependent-function-types funext univalence public open import foundation.type-arithmetic-dependent-pair-types public -open import foundation.type-arithmetic-empty-type public -open import foundation.type-arithmetic-standard-pullbacks public -open import foundation.type-arithmetic-unit-type public -open import foundation.type-duality public -open import foundation.type-theoretic-principle-of-choice public -open import foundation.uniformly-decidable-type-families public -open import foundation.unions-subtypes public -open import foundation.uniqueness-image public -open import foundation.uniqueness-quantification public -open import foundation.uniqueness-set-quotients public -open import foundation.uniqueness-set-truncations public -open import foundation.uniqueness-truncation public +open import foundation.type-arithmetic-empty-type funext univalence truncations public +open import foundation.type-arithmetic-standard-pullbacks funext public +open import foundation.type-arithmetic-unit-type funext public +open import foundation.type-duality funext univalence truncations public +open import foundation.type-theoretic-principle-of-choice funext public +open import foundation.uniformly-decidable-type-families funext univalence truncations public +open import foundation.unions-subtypes funext univalence truncations public +open import foundation.uniqueness-image funext univalence truncations public +open import foundation.uniqueness-quantification funext univalence truncations public +open import foundation.uniqueness-set-quotients funext univalence truncations public +open import foundation.uniqueness-set-truncations funext univalence public +open import foundation.uniqueness-truncation funext public open import foundation.unit-type public open import foundation.unital-binary-operations public -open import foundation.univalence public -open import foundation.univalence-implies-function-extensionality public -open import foundation.univalent-type-families public -open import foundation.universal-property-booleans public -open import foundation.universal-property-cartesian-product-types public -open import foundation.universal-property-contractible-types public -open import foundation.universal-property-coproduct-types public -open import foundation.universal-property-dependent-function-types public -open import foundation.universal-property-dependent-pair-types public -open import foundation.universal-property-empty-type public -open import foundation.universal-property-equivalences public -open import foundation.universal-property-family-of-fibers-of-maps public -open import foundation.universal-property-fiber-products public -open import foundation.universal-property-identity-systems public -open import foundation.universal-property-identity-types public -open import foundation.universal-property-image public -open import foundation.universal-property-maybe public -open import foundation.universal-property-propositional-truncation public -open import foundation.universal-property-propositional-truncation-into-sets public -open import foundation.universal-property-pullbacks public -open import foundation.universal-property-sequential-limits public -open import foundation.universal-property-set-quotients public -open import foundation.universal-property-set-truncation public -open import foundation.universal-property-truncation public -open import foundation.universal-property-unit-type public -open import foundation.universal-quantification public +open import foundation.univalence funext univalence public +open import foundation.univalence-implies-function-extensionality funext univalence truncations public +open import foundation.univalent-type-families funext univalence public +open import foundation.universal-property-booleans funext public +open import foundation.universal-property-cartesian-product-types funext public +open import foundation.universal-property-contractible-types funext public +open import foundation.universal-property-coproduct-types funext public +open import foundation.universal-property-dependent-function-types funext public +open import foundation.universal-property-dependent-pair-types funext public +open import foundation.universal-property-empty-type funext public +open import foundation.universal-property-equivalences funext public +open import foundation.universal-property-family-of-fibers-of-maps funext public +open import foundation.universal-property-fiber-products funext public +open import foundation.universal-property-identity-systems funext public +open import foundation.universal-property-identity-types funext univalence truncations public +open import foundation.universal-property-image funext univalence truncations public +open import foundation.universal-property-maybe funext public +open import foundation.universal-property-propositional-truncation funext public +open import foundation.universal-property-propositional-truncation-into-sets funext univalence truncations public +open import foundation.universal-property-pullbacks funext public +open import foundation.universal-property-sequential-limits funext univalence truncations public +open import foundation.universal-property-set-quotients funext univalence truncations public +open import foundation.universal-property-set-truncation funext univalence truncations public +open import foundation.universal-property-truncation funext univalence truncations public +open import foundation.universal-property-unit-type funext public +open import foundation.universal-quantification funext univalence truncations public open import foundation.universe-levels public -open import foundation.unordered-pairs public -open import foundation.unordered-pairs-of-types public -open import foundation.unordered-tuples public -open import foundation.unordered-tuples-of-types public -open import foundation.vectors-set-quotients public -open import foundation.vertical-composition-spans-of-spans public -open import foundation.weak-function-extensionality public -open import foundation.weak-limited-principle-of-omniscience public -open import foundation.weakly-constant-maps public +open import foundation.unordered-pairs funext univalence truncations public +open import foundation.unordered-pairs-of-types funext univalence truncations public +open import foundation.unordered-tuples funext univalence truncations public +open import foundation.unordered-tuples-of-types funext univalence truncations public +open import foundation.vectors-set-quotients funext univalence truncations public +open import foundation.vertical-composition-spans-of-spans funext univalence truncations public +open import foundation.weak-function-extensionality funext univalence truncations public +open import foundation.weak-limited-principle-of-omniscience funext univalence truncations public +open import foundation.weakly-constant-maps funext public open import foundation.whiskering-higher-homotopies-composition public open import foundation.whiskering-homotopies-composition public -open import foundation.whiskering-homotopies-concatenation public -open import foundation.whiskering-identifications-concatenation public +open import foundation.whiskering-homotopies-concatenation funext public +open import foundation.whiskering-identifications-concatenation funext public open import foundation.whiskering-operations public -open import foundation.wild-category-of-types public -open import foundation.yoneda-identity-types public +open import foundation.wild-category-of-types funext univalence truncations public +open import foundation.yoneda-identity-types funext univalence public ``` diff --git a/src/foundation/0-connected-types.lagda.md b/src/foundation/0-connected-types.lagda.md index d2bdc9203d..939303423c 100644 --- a/src/foundation/0-connected-types.lagda.md +++ b/src/foundation/0-connected-types.lagda.md @@ -1,28 +1,37 @@ # `0`-Connected types ```agda -module foundation.0-connected-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.0-connected-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.constant-maps -open import foundation.contractible-types +open import foundation.constant-maps funext univalence truncations +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.fiber-inclusions -open import foundation.functoriality-set-truncation -open import foundation.images -open import foundation.inhabited-types -open import foundation.mere-equality -open import foundation.propositional-truncations -open import foundation.set-truncations -open import foundation.sets -open import foundation.surjective-maps +open import foundation.dependent-products-contractible-types funext +open import foundation.fiber-inclusions funext univalence +open import foundation.functoriality-set-truncation funext univalence truncations +open import foundation.images funext univalence truncations +open import foundation.inhabited-types funext univalence truncations +open import foundation.mere-equality funext univalence truncations +open import foundation.propositional-truncations funext univalence +open import foundation.set-truncations funext univalence +open import foundation.sets funext univalence +open import foundation.surjective-maps funext univalence truncations open import foundation.unit-type -open import foundation.universal-property-contractible-types -open import foundation.universal-property-unit-type +open import foundation.universal-property-contractible-types funext +open import foundation.universal-property-unit-type funext open import foundation.universe-levels open import foundation-core.cartesian-product-types @@ -32,7 +41,7 @@ open import foundation-core.function-types open import foundation-core.identity-types open import foundation-core.precomposition-functions open import foundation-core.propositions -open import foundation-core.truncated-maps +open import foundation-core.truncated-maps funext open import foundation-core.truncated-types open import foundation-core.truncation-levels ``` diff --git a/src/foundation/0-images-of-maps.lagda.md b/src/foundation/0-images-of-maps.lagda.md index 26121635f8..cc8e693cc4 100644 --- a/src/foundation/0-images-of-maps.lagda.md +++ b/src/foundation/0-images-of-maps.lagda.md @@ -1,13 +1,21 @@ # `0`-Images of maps ```agda -module foundation.0-images-of-maps where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.0-images-of-maps + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.truncation-images-of-maps +open import foundation.truncation-images-of-maps funext univalence truncations open import foundation.universe-levels open import foundation-core.truncation-levels diff --git a/src/foundation/0-maps.lagda.md b/src/foundation/0-maps.lagda.md index 365e87053d..6e3ce75e1a 100644 --- a/src/foundation/0-maps.lagda.md +++ b/src/foundation/0-maps.lagda.md @@ -1,21 +1,25 @@ # `0`-Maps ```agda -module foundation.0-maps where +open import foundation.function-extensionality-axiom + +module foundation.0-maps + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.functoriality-dependent-pair-types +open import foundation.functoriality-dependent-pair-types funext open import foundation.universe-levels open import foundation-core.fibers-of-maps open import foundation-core.function-types open import foundation-core.homotopies open import foundation-core.sets -open import foundation-core.truncated-maps +open import foundation-core.truncated-maps funext open import foundation-core.truncation-levels ``` diff --git a/src/foundation/1-types.lagda.md b/src/foundation/1-types.lagda.md index cdce9dfe87..99b156d374 100644 --- a/src/foundation/1-types.lagda.md +++ b/src/foundation/1-types.lagda.md @@ -1,24 +1,31 @@ # `1`-Types ```agda -module foundation.1-types where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom -open import foundation-core.1-types public +module foundation.1-types + (funext : function-extensionality) + (univalence : univalence-axiom) + where + +open import foundation-core.1-types funext univalence public ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.subuniverses -open import foundation.truncated-types +open import foundation.dependent-products-truncated-types funext +open import foundation.subuniverses funext univalence +open import foundation.truncated-types funext univalence open import foundation.universe-levels open import foundation-core.cartesian-product-types open import foundation-core.equivalences open import foundation-core.identity-types open import foundation-core.propositions -open import foundation-core.subtypes +open import foundation-core.subtypes funext open import foundation-core.torsorial-type-families open import foundation-core.truncation-levels ``` diff --git a/src/foundation/action-on-equivalences-functions-out-of-subuniverses.lagda.md b/src/foundation/action-on-equivalences-functions-out-of-subuniverses.lagda.md index 77d4813bf5..7c312efc2a 100644 --- a/src/foundation/action-on-equivalences-functions-out-of-subuniverses.lagda.md +++ b/src/foundation/action-on-equivalences-functions-out-of-subuniverses.lagda.md @@ -1,17 +1,23 @@ # The action on equivalences of functions out of subuniverses ```agda -module foundation.action-on-equivalences-functions-out-of-subuniverses where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.action-on-equivalences-functions-out-of-subuniverses + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda -open import foundation.action-on-higher-identifications-functions +open import foundation.action-on-higher-identifications-functions funext open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalence-induction -open import foundation.subuniverses +open import foundation.equivalence-induction funext univalence +open import foundation.subuniverses funext univalence open import foundation.universe-levels open import foundation-core.contractible-types diff --git a/src/foundation/action-on-equivalences-functions.lagda.md b/src/foundation/action-on-equivalences-functions.lagda.md index 497a160778..0c6552055e 100644 --- a/src/foundation/action-on-equivalences-functions.lagda.md +++ b/src/foundation/action-on-equivalences-functions.lagda.md @@ -1,17 +1,23 @@ # Action on equivalences of functions ```agda -module foundation.action-on-equivalences-functions where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.action-on-equivalences-functions + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda -open import foundation.action-on-higher-identifications-functions +open import foundation.action-on-higher-identifications-functions funext open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalence-induction -open import foundation.univalence +open import foundation.equivalence-induction funext univalence +open import foundation.univalence funext univalence open import foundation.universe-levels open import foundation-core.constant-maps diff --git a/src/foundation/action-on-equivalences-type-families-over-subuniverses.lagda.md b/src/foundation/action-on-equivalences-type-families-over-subuniverses.lagda.md index 9285de702a..51c9e6269e 100644 --- a/src/foundation/action-on-equivalences-type-families-over-subuniverses.lagda.md +++ b/src/foundation/action-on-equivalences-type-families-over-subuniverses.lagda.md @@ -1,7 +1,13 @@ # Action on equivalences in type families over subuniverses ```agda -module foundation.action-on-equivalences-type-families-over-subuniverses where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.action-on-equivalences-type-families-over-subuniverses + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports @@ -9,17 +15,16 @@ module foundation.action-on-equivalences-type-families-over-subuniverses where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalence-induction -open import foundation.subuniverses +open import foundation.equivalence-induction funext univalence +open import foundation.subuniverses funext univalence open import foundation.universe-levels -open import foundation-core.commuting-squares-of-maps +open import foundation-core.commuting-squares-of-maps funext open import foundation-core.contractible-types open import foundation-core.equivalences open import foundation-core.fibers-of-maps open import foundation-core.function-types open import foundation-core.identity-types -open import foundation-core.univalence ```
diff --git a/src/foundation/action-on-equivalences-type-families.lagda.md b/src/foundation/action-on-equivalences-type-families.lagda.md index 909f4c4011..a4cee05977 100644 --- a/src/foundation/action-on-equivalences-type-families.lagda.md +++ b/src/foundation/action-on-equivalences-type-families.lagda.md @@ -1,20 +1,26 @@ # Action on equivalences of type families ```agda -module foundation.action-on-equivalences-type-families where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.action-on-equivalences-type-families + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda -open import foundation.action-on-equivalences-functions +open import foundation.action-on-equivalences-functions funext univalence open import foundation.action-on-identifications-functions -open import foundation.equivalence-induction -open import foundation.univalence +open import foundation.equivalence-induction funext univalence +open import foundation.univalence funext univalence open import foundation.universe-levels open import foundation.whiskering-higher-homotopies-composition -open import foundation-core.commuting-squares-of-maps +open import foundation-core.commuting-squares-of-maps funext open import foundation-core.constant-maps open import foundation-core.contractible-types open import foundation-core.equivalences diff --git a/src/foundation/action-on-higher-identifications-functions.lagda.md b/src/foundation/action-on-higher-identifications-functions.lagda.md index ad3c91bea7..8b63d6656b 100644 --- a/src/foundation/action-on-higher-identifications-functions.lagda.md +++ b/src/foundation/action-on-higher-identifications-functions.lagda.md @@ -1,14 +1,18 @@ # The action of functions on higher identifications ```agda -module foundation.action-on-higher-identifications-functions where +open import foundation.function-extensionality-axiom + +module foundation.action-on-higher-identifications-functions + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.path-algebra +open import foundation.path-algebra funext open import foundation.universe-levels open import foundation-core.commuting-squares-of-identifications diff --git a/src/foundation/action-on-homotopies-functions.lagda.md b/src/foundation/action-on-homotopies-functions.lagda.md index 0bb5100c4c..86c46a040d 100644 --- a/src/foundation/action-on-homotopies-functions.lagda.md +++ b/src/foundation/action-on-homotopies-functions.lagda.md @@ -1,22 +1,24 @@ # The action on homotopies of functions ```agda -module foundation.action-on-homotopies-functions where +open import foundation.function-extensionality-axiom + +module foundation.action-on-homotopies-functions + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.action-on-higher-identifications-functions +open import foundation.action-on-higher-identifications-functions funext open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-extensionality -open import foundation.homotopy-induction +open import foundation.function-extensionality funext +open import foundation.homotopy-induction funext open import foundation.universe-levels -open import foundation-core.constant-maps open import foundation-core.contractible-types -open import foundation-core.function-types open import foundation-core.homotopies open import foundation-core.identity-types ``` diff --git a/src/foundation/apartness-relations.lagda.md b/src/foundation/apartness-relations.lagda.md index ed13a9135d..3ccb1ffed5 100644 --- a/src/foundation/apartness-relations.lagda.md +++ b/src/foundation/apartness-relations.lagda.md @@ -1,18 +1,27 @@ # Apartness relations ```agda -module foundation.apartness-relations where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.apartness-relations + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.binary-relations +open import foundation.binary-relations funext univalence truncations open import foundation.dependent-pair-types -open import foundation.disjunction -open import foundation.existential-quantification -open import foundation.propositional-truncations -open import foundation.universal-quantification +open import foundation.dependent-products-propositions funext +open import foundation.disjunction funext univalence truncations +open import foundation.existential-quantification funext univalence truncations +open import foundation.propositional-truncations funext univalence +open import foundation.universal-quantification funext univalence truncations open import foundation.universe-levels open import foundation-core.cartesian-product-types diff --git a/src/foundation/arithmetic-law-coproduct-and-sigma-decompositions.lagda.md b/src/foundation/arithmetic-law-coproduct-and-sigma-decompositions.lagda.md index c29be5ba4a..3777f146f3 100644 --- a/src/foundation/arithmetic-law-coproduct-and-sigma-decompositions.lagda.md +++ b/src/foundation/arithmetic-law-coproduct-and-sigma-decompositions.lagda.md @@ -1,21 +1,29 @@ # Arithmetic law for coproduct decomposition and Σ-decomposition ```agda -module foundation.arithmetic-law-coproduct-and-sigma-decompositions where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.arithmetic-law-coproduct-and-sigma-decompositions + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.coproduct-decompositions +open import foundation.coproduct-decompositions funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.functoriality-coproduct-types -open import foundation.relaxed-sigma-decompositions -open import foundation.type-arithmetic-coproduct-types +open import foundation.equivalences funext +open import foundation.functoriality-coproduct-types funext univalence truncations +open import foundation.relaxed-sigma-decompositions funext univalence +open import foundation.type-arithmetic-coproduct-types funext univalence truncations open import foundation.type-arithmetic-dependent-pair-types -open import foundation.univalence -open import foundation.universal-property-coproduct-types +open import foundation.univalence funext univalence +open import foundation.universal-property-coproduct-types funext open import foundation.universe-levels open import foundation-core.cartesian-product-types diff --git a/src/foundation/arithmetic-law-product-and-pi-decompositions.lagda.md b/src/foundation/arithmetic-law-product-and-pi-decompositions.lagda.md index 2f70b0a358..27d7963966 100644 --- a/src/foundation/arithmetic-law-product-and-pi-decompositions.lagda.md +++ b/src/foundation/arithmetic-law-product-and-pi-decompositions.lagda.md @@ -1,21 +1,29 @@ # Arithmetic law for product decomposition and Π-decomposition ```agda -module foundation.arithmetic-law-product-and-pi-decompositions where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.arithmetic-law-product-and-pi-decompositions + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.coproduct-decompositions +open import foundation.coproduct-decompositions funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.functoriality-cartesian-product-types -open import foundation.pi-decompositions +open import foundation.equivalences funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.pi-decompositions funext univalence open import foundation.product-decompositions open import foundation.type-arithmetic-dependent-pair-types -open import foundation.univalence -open import foundation.universal-property-coproduct-types +open import foundation.univalence funext univalence +open import foundation.universal-property-coproduct-types funext open import foundation.universe-levels open import foundation-core.cartesian-product-types diff --git a/src/foundation/automorphisms.lagda.md b/src/foundation/automorphisms.lagda.md index 183752d129..5a7209c603 100644 --- a/src/foundation/automorphisms.lagda.md +++ b/src/foundation/automorphisms.lagda.md @@ -1,17 +1,23 @@ # Automorphisms ```agda -module foundation.automorphisms where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.automorphisms + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda open import foundation.dependent-pair-types +open import foundation.sets funext univalence open import foundation.universe-levels open import foundation-core.equivalences -open import foundation-core.sets open import structured-types.pointed-types ``` diff --git a/src/foundation/axiom-of-choice.lagda.md b/src/foundation/axiom-of-choice.lagda.md index 26774379b7..e474f41d56 100644 --- a/src/foundation/axiom-of-choice.lagda.md +++ b/src/foundation/axiom-of-choice.lagda.md @@ -1,22 +1,28 @@ # The axiom of choice ```agda -module foundation.axiom-of-choice where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.axiom-of-choice + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-extensionality -open import foundation.functoriality-propositional-truncation -open import foundation.inhabited-types -open import foundation.postcomposition-functions -open import foundation.projective-types -open import foundation.propositional-truncations -open import foundation.sections +open import foundation.functoriality-propositional-truncation funext univalence truncations +open import foundation.inhabited-types funext univalence truncations +open import foundation.postcomposition-functions funext +open import foundation.projective-types funext univalence truncations +open import foundation.sections funext open import foundation.split-surjective-maps -open import foundation.surjective-maps +open import foundation.surjective-maps funext univalence truncations open import foundation.universe-levels open import foundation-core.equivalences diff --git a/src/foundation/bands.lagda.md b/src/foundation/bands.lagda.md index 9b846f6934..a3945c0e79 100644 --- a/src/foundation/bands.lagda.md +++ b/src/foundation/bands.lagda.md @@ -1,13 +1,21 @@ # Bands ```agda -module foundation.bands where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.bands + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.set-truncations +open import foundation.set-truncations funext univalence open import foundation.universe-levels open import foundation-core.equivalences diff --git a/src/foundation/base-changes-span-diagrams.lagda.md b/src/foundation/base-changes-span-diagrams.lagda.md index 10882ba5e2..3a9f87c847 100644 --- a/src/foundation/base-changes-span-diagrams.lagda.md +++ b/src/foundation/base-changes-span-diagrams.lagda.md @@ -1,19 +1,27 @@ # Base changes of span diagrams ```agda -module foundation.base-changes-span-diagrams where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.base-changes-span-diagrams + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.cartesian-morphisms-arrows -open import foundation.cartesian-morphisms-span-diagrams -open import foundation.commuting-squares-of-maps +open import foundation.cartesian-morphisms-arrows funext univalence truncations +open import foundation.cartesian-morphisms-span-diagrams funext univalence truncations +open import foundation.commuting-squares-of-maps funext univalence open import foundation.dependent-pair-types -open import foundation.morphisms-arrows -open import foundation.morphisms-span-diagrams -open import foundation.span-diagrams +open import foundation.morphisms-arrows funext +open import foundation.morphisms-span-diagrams funext univalence truncations +open import foundation.span-diagrams funext open import foundation.universe-levels ``` diff --git a/src/foundation/bicomposition-functions.lagda.md b/src/foundation/bicomposition-functions.lagda.md index fceca92642..c48cb683b7 100644 --- a/src/foundation/bicomposition-functions.lagda.md +++ b/src/foundation/bicomposition-functions.lagda.md @@ -1,7 +1,11 @@ # Bicomposition of functions ```agda -module foundation.bicomposition-functions where +open import foundation.function-extensionality-axiom + +module foundation.bicomposition-functions + (funext : function-extensionality) + where ```
Imports @@ -9,19 +13,19 @@ module foundation.bicomposition-functions where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-extensionality -open import foundation.postcomposition-dependent-functions +open import foundation.function-extensionality funext +open import foundation.postcomposition-dependent-functions funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import foundation-core.commuting-squares-of-maps +open import foundation-core.commuting-squares-of-maps funext open import foundation-core.commuting-triangles-of-maps open import foundation-core.contractible-maps open import foundation-core.contractible-types open import foundation-core.equivalences open import foundation-core.fibers-of-maps open import foundation-core.function-types -open import foundation-core.functoriality-dependent-function-types +open import foundation-core.functoriality-dependent-function-types funext open import foundation-core.functoriality-dependent-pair-types open import foundation-core.homotopies open import foundation-core.identity-types diff --git a/src/foundation/binary-dependent-identifications.lagda.md b/src/foundation/binary-dependent-identifications.lagda.md index 28877b6bcd..325d574d1e 100644 --- a/src/foundation/binary-dependent-identifications.lagda.md +++ b/src/foundation/binary-dependent-identifications.lagda.md @@ -8,8 +8,9 @@ module foundation.binary-dependent-identifications where ```agda open import foundation.binary-transport -open import foundation.identity-types open import foundation.universe-levels + +open import foundation-core.identity-types ```
diff --git a/src/foundation/binary-embeddings.lagda.md b/src/foundation/binary-embeddings.lagda.md index fb822a3918..78548ae40b 100644 --- a/src/foundation/binary-embeddings.lagda.md +++ b/src/foundation/binary-embeddings.lagda.md @@ -1,7 +1,11 @@ # Binary embeddings ```agda -module foundation.binary-embeddings where +open import foundation.function-extensionality-axiom + +module foundation.binary-embeddings + (funext : function-extensionality) + where ```
Imports @@ -11,7 +15,7 @@ open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions open import foundation.binary-equivalences open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels open import foundation-core.embeddings diff --git a/src/foundation/binary-equivalences-unordered-pairs-of-types.lagda.md b/src/foundation/binary-equivalences-unordered-pairs-of-types.lagda.md index 8f52b2aee3..c68b67f9d0 100644 --- a/src/foundation/binary-equivalences-unordered-pairs-of-types.lagda.md +++ b/src/foundation/binary-equivalences-unordered-pairs-of-types.lagda.md @@ -1,16 +1,24 @@ # Binary equivalences on unordered pairs of types ```agda -module foundation.binary-equivalences-unordered-pairs-of-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.binary-equivalences-unordered-pairs-of-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.binary-operations-unordered-pairs-of-types -open import foundation.products-unordered-pairs-of-types +open import foundation.binary-operations-unordered-pairs-of-types funext univalence truncations +open import foundation.products-unordered-pairs-of-types funext univalence truncations open import foundation.universe-levels -open import foundation.unordered-pairs +open import foundation.unordered-pairs funext univalence truncations open import foundation-core.equivalences open import foundation-core.function-types diff --git a/src/foundation/binary-functoriality-set-quotients.lagda.md b/src/foundation/binary-functoriality-set-quotients.lagda.md index 43c1441aa4..97577f0e1a 100644 --- a/src/foundation/binary-functoriality-set-quotients.lagda.md +++ b/src/foundation/binary-functoriality-set-quotients.lagda.md @@ -2,37 +2,45 @@ ```agda {-# OPTIONS --lossy-unification #-} - -module foundation.binary-functoriality-set-quotients where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.binary-functoriality-set-quotients + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.binary-homotopies +open import foundation.binary-homotopies funext open import foundation.dependent-pair-types -open import foundation.exponents-set-quotients -open import foundation.function-extensionality -open import foundation.functoriality-set-quotients +open import foundation.dependent-products-propositions funext +open import foundation.exponents-set-quotients funext univalence truncations +open import foundation.function-extensionality funext +open import foundation.functoriality-set-quotients funext univalence truncations open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.reflecting-maps-equivalence-relations -open import foundation.set-quotients -open import foundation.sets +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.reflecting-maps-equivalence-relations funext univalence truncations +open import foundation.set-quotients funext univalence truncations +open import foundation.sets funext univalence open import foundation.subtype-identity-principle -open import foundation.surjective-maps -open import foundation.universal-property-set-quotients +open import foundation.surjective-maps funext univalence truncations +open import foundation.universal-property-set-quotients funext univalence truncations open import foundation.universe-levels open import foundation-core.contractible-types -open import foundation-core.equivalence-relations +open import foundation-core.equivalence-relations funext univalence truncations open import foundation-core.equivalences open import foundation-core.function-types -open import foundation-core.functoriality-dependent-function-types +open import foundation-core.functoriality-dependent-function-types funext open import foundation-core.functoriality-dependent-pair-types open import foundation-core.propositions -open import foundation-core.subtypes +open import foundation-core.subtypes funext open import foundation-core.torsorial-type-families ``` diff --git a/src/foundation/binary-homotopies.lagda.md b/src/foundation/binary-homotopies.lagda.md index bbfde019b4..41b3ff6a00 100644 --- a/src/foundation/binary-homotopies.lagda.md +++ b/src/foundation/binary-homotopies.lagda.md @@ -1,17 +1,21 @@ # Homotopies of binary operations ```agda -module foundation.binary-homotopies where +open import foundation.function-extensionality-axiom + +module foundation.binary-homotopies + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types -open import foundation.function-extensionality +open import foundation.equality-dependent-function-types funext +open import foundation.function-extensionality funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopy-induction +open import foundation.homotopy-induction funext open import foundation.universe-levels open import foundation-core.equivalences diff --git a/src/foundation/binary-operations-unordered-pairs-of-types.lagda.md b/src/foundation/binary-operations-unordered-pairs-of-types.lagda.md index 2f5a31ac3c..b4bf92b03b 100644 --- a/src/foundation/binary-operations-unordered-pairs-of-types.lagda.md +++ b/src/foundation/binary-operations-unordered-pairs-of-types.lagda.md @@ -1,15 +1,23 @@ # Binary operations on unordered pairs of types ```agda -module foundation.binary-operations-unordered-pairs-of-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.binary-operations-unordered-pairs-of-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.products-unordered-pairs-of-types +open import foundation.products-unordered-pairs-of-types funext univalence truncations open import foundation.universe-levels -open import foundation.unordered-pairs +open import foundation.unordered-pairs funext univalence truncations ```
diff --git a/src/foundation/binary-reflecting-maps-equivalence-relations.lagda.md b/src/foundation/binary-reflecting-maps-equivalence-relations.lagda.md index eb1244a707..51537ea7f8 100644 --- a/src/foundation/binary-reflecting-maps-equivalence-relations.lagda.md +++ b/src/foundation/binary-reflecting-maps-equivalence-relations.lagda.md @@ -1,20 +1,29 @@ # Binary reflecting maps of equivalence relations ```agda -module foundation.binary-reflecting-maps-equivalence-relations where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.binary-reflecting-maps-equivalence-relations + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types +open import foundation.dependent-products-propositions funext +open import foundation.equality-dependent-function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopy-induction +open import foundation.homotopy-induction funext open import foundation.subtype-identity-principle open import foundation.universe-levels -open import foundation-core.equivalence-relations +open import foundation-core.equivalence-relations funext univalence truncations open import foundation-core.equivalences open import foundation-core.homotopies open import foundation-core.identity-types diff --git a/src/foundation/binary-relations-with-extensions.lagda.md b/src/foundation/binary-relations-with-extensions.lagda.md index 50543f32af..4b9275bed1 100644 --- a/src/foundation/binary-relations-with-extensions.lagda.md +++ b/src/foundation/binary-relations-with-extensions.lagda.md @@ -1,15 +1,23 @@ # Binary relations with extensions ```agda -module foundation.binary-relations-with-extensions where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.binary-relations-with-extensions + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.binary-relations +open import foundation.binary-relations funext univalence truncations open import foundation.dependent-pair-types -open import foundation.iterated-dependent-product-types +open import foundation.iterated-dependent-product-types funext open import foundation.universe-levels open import foundation-core.propositions diff --git a/src/foundation/binary-relations-with-lifts.lagda.md b/src/foundation/binary-relations-with-lifts.lagda.md index f6ef244510..295b749a60 100644 --- a/src/foundation/binary-relations-with-lifts.lagda.md +++ b/src/foundation/binary-relations-with-lifts.lagda.md @@ -1,15 +1,23 @@ # Binary relations with lifts ```agda -module foundation.binary-relations-with-lifts where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.binary-relations-with-lifts + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.binary-relations +open import foundation.binary-relations funext univalence truncations open import foundation.dependent-pair-types -open import foundation.iterated-dependent-product-types +open import foundation.iterated-dependent-product-types funext open import foundation.universe-levels open import foundation-core.propositions diff --git a/src/foundation/binary-relations.lagda.md b/src/foundation/binary-relations.lagda.md index b9ad577958..52761bb2f7 100644 --- a/src/foundation/binary-relations.lagda.md +++ b/src/foundation/binary-relations.lagda.md @@ -1,18 +1,28 @@ # Binary relations ```agda -module foundation.binary-relations where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.binary-relations + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types +open import foundation.dependent-products-propositions funext +open import foundation.equality-dependent-function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.iterated-dependent-product-types -open import foundation.subtypes -open import foundation.univalence +open import foundation.iterated-dependent-product-types funext +open import foundation.subtypes funext univalence truncations +open import foundation.telescopes +open import foundation.univalence funext univalence open import foundation.universe-levels open import foundation-core.cartesian-product-types diff --git a/src/foundation/binary-type-duality.lagda.md b/src/foundation/binary-type-duality.lagda.md index 20a23bc58d..da1b73a2b7 100644 --- a/src/foundation/binary-type-duality.lagda.md +++ b/src/foundation/binary-type-duality.lagda.md @@ -1,22 +1,28 @@ # Binary type duality ```agda -module foundation.binary-type-duality where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.binary-type-duality + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.equivalences-spans -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.multivariable-homotopies -open import foundation.retractions -open import foundation.sections +open import foundation.equivalences funext +open import foundation.equivalences-spans funext univalence +open import foundation.function-types funext +open import foundation.multivariable-homotopies funext +open import foundation.retractions funext +open import foundation.sections funext open import foundation.spans -open import foundation.univalence +open import foundation.telescopes +open import foundation.univalence funext univalence open import foundation.universe-levels open import foundation-core.cartesian-product-types diff --git a/src/foundation/booleans.lagda.md b/src/foundation/booleans.lagda.md index 712d69cc6b..1fec43c378 100644 --- a/src/foundation/booleans.lagda.md +++ b/src/foundation/booleans.lagda.md @@ -1,19 +1,27 @@ # The booleans ```agda -module foundation.booleans where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.booleans + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where + +open import foundation-core.booleans public ```
Imports ```agda -open import foundation.decidable-equality -open import foundation.decidable-types +open import foundation.decidable-equality funext univalence truncations open import foundation.dependent-pair-types -open import foundation.discrete-types -open import foundation.involutions -open import foundation.negated-equality -open import foundation.raising-universe-levels +open import foundation.discrete-types funext univalence truncations +open import foundation.involutions funext univalence +open import foundation.negated-equality funext univalence truncations open import foundation.unit-type open import foundation.universe-levels @@ -24,14 +32,13 @@ open import foundation-core.equivalences open import foundation-core.function-types open import foundation-core.homotopies open import foundation-core.identity-types -open import foundation-core.injective-maps open import foundation-core.negation open import foundation-core.propositions open import foundation-core.sections open import foundation-core.sets -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.finite-types funext univalence truncations +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
@@ -43,162 +50,8 @@ The type of **booleans** is a `true false : bool`, which is used for reasoning with [decidable propositions](foundation-core.decidable-propositions.md). -## Definition - -### The booleans - -```agda -data bool : UU lzero where - true false : bool - -{-# BUILTIN BOOL bool #-} -{-# BUILTIN TRUE true #-} -{-# BUILTIN FALSE false #-} -``` - -### The induction principle of the booleans - -```agda -module _ - {l : Level} (P : bool → UU l) - where - - ind-bool : P true → P false → (b : bool) → P b - ind-bool pt pf true = pt - ind-bool pt pf false = pf -``` - -### The recursion principle of the booleans - -```agda -module _ - {l : Level} {P : UU l} - where - - rec-bool : P → P → bool → P - rec-bool = ind-bool (λ _ → P) -``` - -### The `if_then_else` function - -```agda -module _ - {l : Level} {A : UU l} - where - - if_then_else_ : bool → A → A → A - if b then x else y = rec-bool x y b -``` - -### Raising universe levels of the booleans - -```agda -raise-bool : (l : Level) → UU l -raise-bool l = raise l bool - -raise-true : (l : Level) → raise-bool l -raise-true l = map-raise true - -raise-false : (l : Level) → raise-bool l -raise-false l = map-raise false - -compute-raise-bool : (l : Level) → bool ≃ raise-bool l -compute-raise-bool l = compute-raise l bool -``` - -### The standard propositions associated to the constructors of bool - -```agda -prop-bool : bool → Prop lzero -prop-bool true = unit-Prop -prop-bool false = empty-Prop - -type-prop-bool : bool → UU lzero -type-prop-bool = type-Prop ∘ prop-bool -``` - -### Equality on the booleans - -```agda -Eq-bool : bool → bool → UU lzero -Eq-bool true true = unit -Eq-bool true false = empty -Eq-bool false true = empty -Eq-bool false false = unit - -refl-Eq-bool : (x : bool) → Eq-bool x x -refl-Eq-bool true = star -refl-Eq-bool false = star - -Eq-eq-bool : - {x y : bool} → x ＝ y → Eq-bool x y -Eq-eq-bool {x = x} refl = refl-Eq-bool x - -eq-Eq-bool : - {x y : bool} → Eq-bool x y → x ＝ y -eq-Eq-bool {true} {true} star = refl -eq-Eq-bool {false} {false} star = refl - -neq-false-true-bool : false ≠ true -neq-false-true-bool () - -neq-true-false-bool : true ≠ false -neq-true-false-bool () -``` - -## Structure - -### The boolean operators - -```agda -neg-bool : bool → bool -neg-bool true = false -neg-bool false = true - -conjunction-bool : bool → bool → bool -conjunction-bool true true = true -conjunction-bool true false = false -conjunction-bool false true = false -conjunction-bool false false = false - -disjunction-bool : bool → bool → bool -disjunction-bool true true = true -disjunction-bool true false = true -disjunction-bool false true = true -disjunction-bool false false = false - -implication-bool : bool → bool → bool -implication-bool true true = true -implication-bool true false = false -implication-bool false true = true -implication-bool false false = true -``` - ## Properties -### The booleans are a set - -```agda -abstract - is-prop-Eq-bool : (x y : bool) → is-prop (Eq-bool x y) - is-prop-Eq-bool true true = is-prop-unit - is-prop-Eq-bool true false = is-prop-empty - is-prop-Eq-bool false true = is-prop-empty - is-prop-Eq-bool false false = is-prop-unit - -abstract - is-set-bool : is-set bool - is-set-bool = - is-set-prop-in-id - ( Eq-bool) - ( is-prop-Eq-bool) - ( refl-Eq-bool) - ( λ x y → eq-Eq-bool) - -bool-Set : Set lzero -bool-Set = bool , is-set-bool -``` - ### The booleans have decidable equality ```agda @@ -212,44 +65,6 @@ bool-Discrete-Type : Discrete-Type lzero bool-Discrete-Type = bool , has-decidable-equality-bool ``` -### The "is true" predicate on booleans - -```agda -is-true : bool → UU lzero -is-true = _＝ true - -is-prop-is-true : (b : bool) → is-prop (is-true b) -is-prop-is-true b = is-set-bool b true - -is-true-Prop : bool → Prop lzero -is-true-Prop b = is-true b , is-prop-is-true b -``` - -### The "is false" predicate on booleans - -```agda -is-false : bool → UU lzero -is-false = _＝ false - -is-prop-is-false : (b : bool) → is-prop (is-false b) -is-prop-is-false b = is-set-bool b false - -is-false-Prop : bool → Prop lzero -is-false-Prop b = is-false b , is-prop-is-false b -``` - -### A boolean cannot be both true and false - -```agda -not-is-false-is-true : (x : bool) → is-true x → ¬ (is-false x) -not-is-false-is-true true t () -not-is-false-is-true false () f - -not-is-true-is-false : (x : bool) → is-false x → ¬ (is-true x) -not-is-true-is-false true () f -not-is-true-is-false false t () -``` - ### The type of booleans is equivalent to `Fin 2` ```agda @@ -298,17 +113,6 @@ pr1 bool-Finite-Type = bool pr2 bool-Finite-Type = is-finite-bool ``` -### Boolean negation has no fixed points - -```agda -neq-neg-bool : (b : bool) → b ≠ neg-bool b -neq-neg-bool true () -neq-neg-bool false () - -neq-neg-bool' : (b : bool) → neg-bool b ≠ b -neq-neg-bool' b = neq-neg-bool b ∘ inv -``` - ### Boolean negation is an involution ```agda @@ -328,17 +132,3 @@ equiv-neg-bool : bool ≃ bool pr1 equiv-neg-bool = neg-bool pr2 equiv-neg-bool = is-equiv-neg-bool ``` - -### The constant function `const bool b` is not an equivalence - -```agda -abstract - no-section-const-bool : (b : bool) → ¬ (section (const bool b)) - no-section-const-bool true (g , G) = neq-true-false-bool (G false) - no-section-const-bool false (g , G) = neq-false-true-bool (G true) - -abstract - is-not-equiv-const-bool : - (b : bool) → ¬ (is-equiv (const bool b)) - is-not-equiv-const-bool b e = no-section-const-bool b (section-is-equiv e) -``` diff --git a/src/foundation/cantor-schroder-bernstein-escardo.lagda.md b/src/foundation/cantor-schroder-bernstein-escardo.lagda.md index c48597b785..e61f9b32a3 100644 --- a/src/foundation/cantor-schroder-bernstein-escardo.lagda.md +++ b/src/foundation/cantor-schroder-bernstein-escardo.lagda.md @@ -1,18 +1,26 @@ # The Cantor–Schröder–Bernstein–Escardó theorem ```agda -module foundation.cantor-schroder-bernstein-escardo where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.cantor-schroder-bernstein-escardo + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.decidable-types +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.injective-maps -open import foundation.law-of-excluded-middle -open import foundation.perfect-images +open import foundation.injective-maps funext +open import foundation.law-of-excluded-middle funext univalence truncations +open import foundation.perfect-images funext univalence truncations open import foundation.split-surjective-maps open import foundation.universe-levels diff --git a/src/foundation/cantors-theorem.lagda.md b/src/foundation/cantors-theorem.lagda.md index 499ebf65d6..8f2a584ff5 100644 --- a/src/foundation/cantors-theorem.lagda.md +++ b/src/foundation/cantors-theorem.lagda.md @@ -1,32 +1,38 @@ # Cantor's theorem ```agda -module foundation.cantors-theorem where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.cantors-theorem + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.decidable-propositions -open import foundation.decidable-subtypes +open import foundation.decidable-propositions funext univalence truncations +open import foundation.decidable-subtypes funext univalence truncations open import foundation.dependent-pair-types -open import foundation.double-negation-stable-propositions -open import foundation.function-extensionality -open import foundation.logical-equivalences -open import foundation.negation -open import foundation.powersets -open import foundation.propositional-truncations -open import foundation.surjective-maps +open import foundation.double-negation-stable-propositions funext univalence truncations +open import foundation.logical-equivalences funext +open import foundation.negation funext +open import foundation.powersets funext univalence truncations +open import foundation.propositional-truncations funext univalence +open import foundation.surjective-maps funext univalence truncations open import foundation.universe-levels open import foundation-core.empty-types open import foundation-core.fibers-of-maps -open import foundation-core.propositions -open import logic.de-morgan-propositions -open import logic.de-morgan-subtypes -open import logic.double-negation-stable-subtypes +open import logic.de-morgan-propositions funext univalence truncations +open import logic.de-morgan-subtypes funext univalence truncations +open import logic.double-negation-stable-subtypes funext univalence truncations ```
diff --git a/src/foundation/cartesian-morphisms-arrows.lagda.md b/src/foundation/cartesian-morphisms-arrows.lagda.md index 58ea9ebfbb..a61a110268 100644 --- a/src/foundation/cartesian-morphisms-arrows.lagda.md +++ b/src/foundation/cartesian-morphisms-arrows.lagda.md @@ -1,44 +1,52 @@ # Cartesian morphisms of arrows ```agda -module foundation.cartesian-morphisms-arrows where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.cartesian-morphisms-arrows + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-triangles-of-maps -open import foundation.commuting-triangles-of-morphisms-arrows -open import foundation.cones-over-cospan-diagrams -open import foundation.coproducts-pullbacks +open import foundation.commuting-triangles-of-maps funext univalence +open import foundation.commuting-triangles-of-morphisms-arrows funext +open import foundation.cones-over-cospan-diagrams funext +open import foundation.coproducts-pullbacks funext univalence truncations open import foundation.dependent-pair-types -open import foundation.dependent-products-pullbacks -open import foundation.dependent-sums-pullbacks -open import foundation.diagonal-maps-cartesian-products-of-types -open import foundation.equivalences -open import foundation.fibers-of-maps -open import foundation.function-types -open import foundation.functoriality-cartesian-product-types -open import foundation.functoriality-coproduct-types -open import foundation.functoriality-dependent-pair-types -open import foundation.functoriality-fibers-of-maps -open import foundation.homotopies-morphisms-arrows -open import foundation.identity-types -open import foundation.morphisms-arrows -open import foundation.postcomposition-functions -open import foundation.postcomposition-pullbacks -open import foundation.products-pullbacks -open import foundation.pullbacks -open import foundation.standard-pullbacks +open import foundation.dependent-products-pullbacks funext univalence +open import foundation.dependent-sums-pullbacks funext +open import foundation.diagonal-maps-cartesian-products-of-types funext univalence +open import foundation.equivalences funext +open import foundation.fibers-of-maps funext +open import foundation.function-types funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.functoriality-coproduct-types funext univalence truncations +open import foundation.functoriality-dependent-pair-types funext +open import foundation.functoriality-fibers-of-maps funext +open import foundation.homotopies-morphisms-arrows funext +open import foundation.identity-types funext +open import foundation.morphisms-arrows funext +open import foundation.postcomposition-functions funext +open import foundation.postcomposition-pullbacks funext +open import foundation.products-pullbacks funext univalence truncations +open import foundation.pullbacks funext univalence truncations +open import foundation.standard-pullbacks funext open import foundation.unit-type open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import foundation-core.commuting-squares-of-maps +open import foundation-core.commuting-squares-of-maps funext open import foundation-core.homotopies open import foundation-core.propositions -open import foundation-core.universal-property-pullbacks +open import foundation-core.universal-property-pullbacks funext ```
diff --git a/src/foundation/cartesian-morphisms-span-diagrams.lagda.md b/src/foundation/cartesian-morphisms-span-diagrams.lagda.md index 0441d162f7..5086304d02 100644 --- a/src/foundation/cartesian-morphisms-span-diagrams.lagda.md +++ b/src/foundation/cartesian-morphisms-span-diagrams.lagda.md @@ -1,19 +1,27 @@ # Cartesian morphisms of span diagrams ```agda -module foundation.cartesian-morphisms-span-diagrams where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.cartesian-morphisms-span-diagrams + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.cartesian-morphisms-arrows -open import foundation.cartesian-product-types -open import foundation.commuting-squares-of-maps +open import foundation.cartesian-morphisms-arrows funext univalence truncations +open import foundation.cartesian-product-types funext univalence +open import foundation.commuting-squares-of-maps funext univalence open import foundation.dependent-pair-types -open import foundation.morphisms-arrows -open import foundation.morphisms-span-diagrams -open import foundation.span-diagrams +open import foundation.morphisms-arrows funext +open import foundation.morphisms-span-diagrams funext univalence truncations +open import foundation.span-diagrams funext open import foundation.universe-levels ``` diff --git a/src/foundation/cartesian-product-types.lagda.md b/src/foundation/cartesian-product-types.lagda.md index 08740b0e83..70d77f7075 100644 --- a/src/foundation/cartesian-product-types.lagda.md +++ b/src/foundation/cartesian-product-types.lagda.md @@ -1,7 +1,13 @@ # Cartesian product types ```agda -module foundation.cartesian-product-types where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.cartesian-product-types + (funext : function-extensionality) + (univalence : univalence-axiom) + where open import foundation-core.cartesian-product-types public ``` @@ -10,7 +16,7 @@ open import foundation-core.cartesian-product-types public ```agda open import foundation.dependent-pair-types -open import foundation.subuniverses +open import foundation.subuniverses funext univalence open import foundation.universe-levels open import foundation-core.identity-types diff --git a/src/foundation/cartesian-products-set-quotients.lagda.md b/src/foundation/cartesian-products-set-quotients.lagda.md index 7c5319f8da..407385239b 100644 --- a/src/foundation/cartesian-products-set-quotients.lagda.md +++ b/src/foundation/cartesian-products-set-quotients.lagda.md @@ -1,7 +1,15 @@ # Cartesian products of set quotients ```agda -module foundation.cartesian-products-set-quotients where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.cartesian-products-set-quotients + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,18 +18,18 @@ module foundation.cartesian-products-set-quotients where open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types open import foundation.equality-cartesian-product-types -open import foundation.function-extensionality -open import foundation.products-equivalence-relations -open import foundation.reflecting-maps-equivalence-relations -open import foundation.set-quotients -open import foundation.sets -open import foundation.uniqueness-set-quotients -open import foundation.universal-property-set-quotients +open import foundation.function-extensionality funext +open import foundation.products-equivalence-relations funext univalence truncations +open import foundation.reflecting-maps-equivalence-relations funext univalence truncations +open import foundation.set-quotients funext univalence truncations +open import foundation.sets funext univalence +open import foundation.uniqueness-set-quotients funext univalence truncations +open import foundation.universal-property-set-quotients funext univalence truncations open import foundation.universe-levels open import foundation-core.cartesian-product-types open import foundation-core.equality-dependent-pair-types -open import foundation-core.equivalence-relations +open import foundation-core.equivalence-relations funext univalence truncations open import foundation-core.equivalences open import foundation-core.function-types open import foundation-core.homotopies diff --git a/src/foundation/category-of-families-of-sets.lagda.md b/src/foundation/category-of-families-of-sets.lagda.md index a5d7dff0ff..5fe42b647e 100644 --- a/src/foundation/category-of-families-of-sets.lagda.md +++ b/src/foundation/category-of-families-of-sets.lagda.md @@ -1,20 +1,28 @@ # The category of families of sets ```agda -module foundation.category-of-families-of-sets where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.category-of-families-of-sets + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.large-categories -open import category-theory.large-function-categories -open import category-theory.large-function-precategories -open import category-theory.large-precategories -open import category-theory.precategories - -open import foundation.category-of-sets +open import category-theory.categories funext univalence truncations +open import category-theory.large-categories funext univalence truncations +open import category-theory.large-function-categories funext univalence truncations +open import category-theory.large-function-precategories funext univalence truncations +open import category-theory.large-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations + +open import foundation.category-of-sets funext univalence truncations open import foundation.universe-levels ``` diff --git a/src/foundation/category-of-sets.lagda.md b/src/foundation/category-of-sets.lagda.md index 7089fccb08..e73cf409ab 100644 --- a/src/foundation/category-of-sets.lagda.md +++ b/src/foundation/category-of-sets.lagda.md @@ -1,47 +1,50 @@ # The category of sets ```agda -module foundation.category-of-sets where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.category-of-sets + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.complete-precategories -open import category-theory.cones-precategories -open import category-theory.constant-functors -open import category-theory.functors-precategories -open import category-theory.isomorphisms-in-large-precategories -open import category-theory.large-categories -open import category-theory.large-precategories -open import category-theory.limits-precategories -open import category-theory.natural-transformations-functors-precategories -open import category-theory.precategories -open import category-theory.right-extensions-precategories -open import category-theory.right-kan-extensions-precategories -open import category-theory.terminal-category - -open import foundation.action-on-identifications-functions +open import category-theory.categories funext univalence truncations +open import category-theory.complete-precategories funext univalence truncations +open import category-theory.cones-precategories funext univalence truncations +open import category-theory.constant-functors funext univalence truncations +open import category-theory.functors-precategories funext univalence truncations +open import category-theory.isomorphisms-in-large-precategories funext univalence truncations +open import category-theory.large-categories funext univalence truncations +open import category-theory.large-precategories funext univalence truncations +open import category-theory.limits-precategories funext univalence truncations +open import category-theory.natural-transformations-functors-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations + open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-types +open import foundation.equivalences funext +open import foundation.function-extensionality funext +open import foundation.function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types -open import foundation.isomorphisms-of-sets -open import foundation.multivariable-homotopies -open import foundation.raising-universe-levels -open import foundation.retractions -open import foundation.sections -open import foundation.sets -open import foundation.strictly-involutive-identity-types +open import foundation.identity-types funext +open import foundation.isomorphisms-of-sets funext univalence +open import foundation.raising-universe-levels-unit-type +open import foundation.retractions funext +open import foundation.sections funext +open import foundation.sets funext univalence +open import foundation.strictly-involutive-identity-types funext univalence open import foundation.unit-type open import foundation.universe-levels open import foundation-core.contractible-types open import foundation-core.functoriality-dependent-pair-types +open import foundation-core.raising-universe-levels ```
diff --git a/src/foundation/choice-of-representatives-equivalence-relation.lagda.md b/src/foundation/choice-of-representatives-equivalence-relation.lagda.md index 6ba3e69b75..bb70f6ad70 100644 --- a/src/foundation/choice-of-representatives-equivalence-relation.lagda.md +++ b/src/foundation/choice-of-representatives-equivalence-relation.lagda.md @@ -1,7 +1,15 @@ # Choice of representatives for an equivalence relation ```agda -module foundation.choice-of-representatives-equivalence-relation where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.choice-of-representatives-equivalence-relation + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,18 +17,18 @@ module foundation.choice-of-representatives-equivalence-relation where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalence-classes +open import foundation.equivalence-classes funext univalence truncations open import foundation.fundamental-theorem-of-identity-types -open import foundation.logical-equivalences -open import foundation.propositional-truncations -open import foundation.surjective-maps +open import foundation.logical-equivalences funext +open import foundation.propositional-truncations funext univalence +open import foundation.surjective-maps funext univalence truncations open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels open import foundation-core.cartesian-product-types open import foundation-core.contractible-types open import foundation-core.embeddings -open import foundation-core.equivalence-relations +open import foundation-core.equivalence-relations funext univalence truncations open import foundation-core.equivalences open import foundation-core.fibers-of-maps open import foundation-core.functoriality-dependent-pair-types diff --git a/src/foundation/coalgebras-maybe.lagda.md b/src/foundation/coalgebras-maybe.lagda.md index 855690a002..0a8043ba4c 100644 --- a/src/foundation/coalgebras-maybe.lagda.md +++ b/src/foundation/coalgebras-maybe.lagda.md @@ -1,17 +1,24 @@ # Coalgebras of the maybe monad ```agda -module foundation.coalgebras-maybe where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.coalgebras-maybe + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.maybe open import foundation.universe-levels -open import trees.polynomial-endofunctors +open import foundation-core.maybe + +open import trees.polynomial-endofunctors funext univalence ```
diff --git a/src/foundation/coherently-idempotent-maps.lagda.md b/src/foundation/coherently-idempotent-maps.lagda.md index d746a1ec6a..8bb32a7af9 100644 --- a/src/foundation/coherently-idempotent-maps.lagda.md +++ b/src/foundation/coherently-idempotent-maps.lagda.md @@ -1,7 +1,15 @@ # Coherently idempotent maps ```agda -module foundation.coherently-idempotent-maps where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.coherently-idempotent-maps + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -11,8 +19,8 @@ open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types open import foundation.homotopy-algebra -open import foundation.quasicoherently-idempotent-maps -open import foundation.split-idempotent-maps +open import foundation.quasicoherently-idempotent-maps funext univalence truncations +open import foundation.split-idempotent-maps funext univalence truncations open import foundation.universe-levels open import foundation.whiskering-homotopies-composition diff --git a/src/foundation/coherently-invertible-maps.lagda.md b/src/foundation/coherently-invertible-maps.lagda.md index 03f1ed4655..cbfbb4ee79 100644 --- a/src/foundation/coherently-invertible-maps.lagda.md +++ b/src/foundation/coherently-invertible-maps.lagda.md @@ -1,7 +1,11 @@ # Coherently invertible maps ```agda -module foundation.coherently-invertible-maps where +open import foundation.function-extensionality-axiom + +module foundation.coherently-invertible-maps + (funext : function-extensionality) + where open import foundation-core.coherently-invertible-maps public ``` @@ -10,9 +14,10 @@ open import foundation-core.coherently-invertible-maps public ```agda open import foundation.action-on-identifications-functions -open import foundation.equivalences -open import foundation.identity-types -open import foundation.logical-equivalences +open import foundation.dependent-products-contractible-types funext +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels diff --git a/src/foundation/coinhabited-pairs-of-types.lagda.md b/src/foundation/coinhabited-pairs-of-types.lagda.md index bb9be37fb9..1b56e8f421 100644 --- a/src/foundation/coinhabited-pairs-of-types.lagda.md +++ b/src/foundation/coinhabited-pairs-of-types.lagda.md @@ -1,15 +1,23 @@ # Coinhabited pairs of types ```agda -module foundation.coinhabited-pairs-of-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.coinhabited-pairs-of-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.inhabited-types -open import foundation.logical-equivalences -open import foundation.propositional-truncations +open import foundation.inhabited-types funext univalence truncations +open import foundation.logical-equivalences funext +open import foundation.propositional-truncations funext univalence open import foundation.universe-levels open import foundation-core.propositions diff --git a/src/foundation/commuting-cubes-of-maps.lagda.md b/src/foundation/commuting-cubes-of-maps.lagda.md index 0309bafe4b..edb4eada82 100644 --- a/src/foundation/commuting-cubes-of-maps.lagda.md +++ b/src/foundation/commuting-cubes-of-maps.lagda.md @@ -1,7 +1,13 @@ # Commuting cubes of maps ```agda -module foundation.commuting-cubes-of-maps where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.commuting-cubes-of-maps + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports @@ -9,15 +15,15 @@ module foundation.commuting-cubes-of-maps where ```agda open import foundation.action-on-identifications-functions open import foundation.commuting-hexagons-of-identifications -open import foundation.commuting-squares-of-homotopies -open import foundation.commuting-squares-of-maps -open import foundation.cones-over-cospan-diagrams +open import foundation.commuting-squares-of-homotopies funext +open import foundation.commuting-squares-of-maps funext univalence +open import foundation.cones-over-cospan-diagrams funext open import foundation.dependent-pair-types -open import foundation.function-extensionality -open import foundation.homotopies +open import foundation.function-extensionality funext +open import foundation.homotopies funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import foundation.whiskering-homotopies-concatenation +open import foundation.whiskering-homotopies-concatenation funext open import foundation-core.function-types open import foundation-core.identity-types diff --git a/src/foundation/commuting-prisms-of-maps.lagda.md b/src/foundation/commuting-prisms-of-maps.lagda.md index 1abe1edc03..b558889f49 100644 --- a/src/foundation/commuting-prisms-of-maps.lagda.md +++ b/src/foundation/commuting-prisms-of-maps.lagda.md @@ -1,29 +1,35 @@ # Commuting prisms of maps ```agda -module foundation.commuting-prisms-of-maps where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom -open import foundation-core.commuting-prisms-of-maps public +module foundation.commuting-prisms-of-maps + (funext : function-extensionality) + (univalence : univalence-axiom) + where + +open import foundation-core.commuting-prisms-of-maps funext public ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-maps -open import foundation.commuting-triangles-of-maps -open import foundation.composition-algebra -open import foundation.function-extensionality -open import foundation.identity-types -open import foundation.postcomposition-functions -open import foundation.precomposition-functions +open import foundation.commuting-squares-of-maps funext univalence +open import foundation.commuting-triangles-of-maps funext univalence +open import foundation.composition-algebra funext +open import foundation.function-extensionality funext +open import foundation.identity-types funext +open import foundation.postcomposition-functions funext +open import foundation.precomposition-functions funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition open import foundation-core.commuting-squares-of-homotopies open import foundation-core.equivalences open import foundation-core.function-types -open import foundation-core.functoriality-dependent-function-types +open import foundation-core.functoriality-dependent-function-types funext open import foundation-core.homotopies ``` diff --git a/src/foundation/commuting-squares-of-homotopies.lagda.md b/src/foundation/commuting-squares-of-homotopies.lagda.md index 102c3cee57..d1b069470a 100644 --- a/src/foundation/commuting-squares-of-homotopies.lagda.md +++ b/src/foundation/commuting-squares-of-homotopies.lagda.md @@ -1,7 +1,11 @@ # Commuting squares of homotopies ```agda -module foundation.commuting-squares-of-homotopies where +open import foundation.function-extensionality-axiom + +module foundation.commuting-squares-of-homotopies + (funext : function-extensionality) + where open import foundation-core.commuting-squares-of-homotopies public ``` @@ -9,13 +13,13 @@ open import foundation-core.commuting-squares-of-homotopies public
Imports ```agda -open import foundation.commuting-squares-of-identifications +open import foundation.commuting-squares-of-identifications funext open import foundation.dependent-pair-types -open import foundation.homotopies +open import foundation.homotopies funext open import foundation.universe-levels open import foundation-core.equivalences -open import foundation-core.functoriality-dependent-function-types +open import foundation-core.functoriality-dependent-function-types funext ```
diff --git a/src/foundation/commuting-squares-of-identifications.lagda.md b/src/foundation/commuting-squares-of-identifications.lagda.md index d0b7caf8b4..ecfaceec8e 100644 --- a/src/foundation/commuting-squares-of-identifications.lagda.md +++ b/src/foundation/commuting-squares-of-identifications.lagda.md @@ -1,7 +1,11 @@ # Commuting squares of identifications ```agda -module foundation.commuting-squares-of-identifications where +open import foundation.function-extensionality-axiom + +module foundation.commuting-squares-of-identifications + (funext : function-extensionality) + where open import foundation-core.commuting-squares-of-identifications public ``` @@ -10,7 +14,7 @@ open import foundation-core.commuting-squares-of-identifications public ```agda open import foundation.dependent-pair-types -open import foundation.path-algebra +open import foundation.path-algebra funext open import foundation.universe-levels open import foundation-core.equivalences diff --git a/src/foundation/commuting-squares-of-maps.lagda.md b/src/foundation/commuting-squares-of-maps.lagda.md index 347bb16120..dc23e1b1a4 100644 --- a/src/foundation/commuting-squares-of-maps.lagda.md +++ b/src/foundation/commuting-squares-of-maps.lagda.md @@ -1,9 +1,15 @@ # Commuting squares of maps ```agda -module foundation.commuting-squares-of-maps where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom -open import foundation-core.commuting-squares-of-maps public +module foundation.commuting-squares-of-maps + (funext : function-extensionality) + (univalence : univalence-axiom) + where + +open import foundation-core.commuting-squares-of-maps funext public ```
Imports @@ -11,18 +17,18 @@ open import foundation-core.commuting-squares-of-maps public ```agda open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.commuting-triangles-of-homotopies -open import foundation.commuting-triangles-of-maps -open import foundation.function-extensionality +open import foundation.commuting-triangles-of-homotopies funext +open import foundation.commuting-triangles-of-maps funext univalence +open import foundation.function-extensionality funext open import foundation.homotopy-algebra -open import foundation.postcomposition-functions -open import foundation.precomposition-functions -open import foundation.transposition-identifications-along-equivalences +open import foundation.postcomposition-functions funext +open import foundation.precomposition-functions funext +open import foundation.transposition-identifications-along-equivalences funext open import foundation.universe-levels open import foundation.whiskering-higher-homotopies-composition open import foundation.whiskering-homotopies-composition -open import foundation-core.commuting-prisms-of-maps +open import foundation-core.commuting-prisms-of-maps funext open import foundation-core.commuting-squares-of-homotopies open import foundation-core.commuting-squares-of-identifications open import foundation-core.equivalences diff --git a/src/foundation/commuting-tetrahedra-of-homotopies.lagda.md b/src/foundation/commuting-tetrahedra-of-homotopies.lagda.md index 2aa6902f83..805de7b350 100644 --- a/src/foundation/commuting-tetrahedra-of-homotopies.lagda.md +++ b/src/foundation/commuting-tetrahedra-of-homotopies.lagda.md @@ -1,13 +1,17 @@ # Commuting tetrahedra of homotopies ```agda -module foundation.commuting-tetrahedra-of-homotopies where +open import foundation.function-extensionality-axiom + +module foundation.commuting-tetrahedra-of-homotopies + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.commuting-triangles-of-homotopies +open import foundation.commuting-triangles-of-homotopies funext open import foundation.universe-levels open import foundation-core.homotopies diff --git a/src/foundation/commuting-triangles-of-homotopies.lagda.md b/src/foundation/commuting-triangles-of-homotopies.lagda.md index a9a57c0d7e..67d602fe40 100644 --- a/src/foundation/commuting-triangles-of-homotopies.lagda.md +++ b/src/foundation/commuting-triangles-of-homotopies.lagda.md @@ -1,13 +1,17 @@ # Commuting triangles of homotopies ```agda -module foundation.commuting-triangles-of-homotopies where +open import foundation.function-extensionality-axiom + +module foundation.commuting-triangles-of-homotopies + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.commuting-triangles-of-identifications +open import foundation.commuting-triangles-of-identifications funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition diff --git a/src/foundation/commuting-triangles-of-identifications.lagda.md b/src/foundation/commuting-triangles-of-identifications.lagda.md index ab6e12a82d..bda882e7b9 100644 --- a/src/foundation/commuting-triangles-of-identifications.lagda.md +++ b/src/foundation/commuting-triangles-of-identifications.lagda.md @@ -1,7 +1,11 @@ # Commuting triangles of identifications ```agda -module foundation.commuting-triangles-of-identifications where +open import foundation.function-extensionality-axiom + +module foundation.commuting-triangles-of-identifications + (funext : function-extensionality) + where ```
Imports @@ -10,9 +14,9 @@ module foundation.commuting-triangles-of-identifications where open import foundation.action-on-identifications-functions open import foundation.binary-equivalences open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import foundation.whiskering-identifications-concatenation +open import foundation.whiskering-identifications-concatenation funext open import foundation-core.commuting-squares-of-identifications open import foundation-core.equivalences diff --git a/src/foundation/commuting-triangles-of-maps.lagda.md b/src/foundation/commuting-triangles-of-maps.lagda.md index ef0e081b0a..cb466bb0ee 100644 --- a/src/foundation/commuting-triangles-of-maps.lagda.md +++ b/src/foundation/commuting-triangles-of-maps.lagda.md @@ -1,7 +1,13 @@ # Commuting triangles of maps ```agda -module foundation.commuting-triangles-of-maps where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.commuting-triangles-of-maps + (funext : function-extensionality) + (univalence : univalence-axiom) + where open import foundation-core.commuting-triangles-of-maps public ``` @@ -10,16 +16,16 @@ open import foundation-core.commuting-triangles-of-maps public ```agda open import foundation.action-on-identifications-functions -open import foundation.functoriality-dependent-function-types -open import foundation.homotopies +open import foundation.functoriality-dependent-function-types funext univalence +open import foundation.homotopies funext open import foundation.homotopy-algebra -open import foundation.identity-types -open import foundation.postcomposition-functions -open import foundation.precomposition-functions +open import foundation.identity-types funext +open import foundation.postcomposition-functions funext +open import foundation.precomposition-functions funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import foundation-core.commuting-squares-of-maps +open import foundation-core.commuting-squares-of-maps funext open import foundation-core.equivalences open import foundation-core.function-types open import foundation-core.whiskering-identifications-concatenation diff --git a/src/foundation/commuting-triangles-of-morphisms-arrows.lagda.md b/src/foundation/commuting-triangles-of-morphisms-arrows.lagda.md index 2e375cefa7..c68a7cfaf6 100644 --- a/src/foundation/commuting-triangles-of-morphisms-arrows.lagda.md +++ b/src/foundation/commuting-triangles-of-morphisms-arrows.lagda.md @@ -1,14 +1,18 @@ # Commuting triangles of morphisms of arrows ```agda -module foundation.commuting-triangles-of-morphisms-arrows where +open import foundation.function-extensionality-axiom + +module foundation.commuting-triangles-of-morphisms-arrows + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.homotopies-morphisms-arrows -open import foundation.morphisms-arrows +open import foundation.homotopies-morphisms-arrows funext +open import foundation.morphisms-arrows funext open import foundation.universe-levels ``` diff --git a/src/foundation/complements-subtypes.lagda.md b/src/foundation/complements-subtypes.lagda.md index 3331a3455c..309805de7a 100644 --- a/src/foundation/complements-subtypes.lagda.md +++ b/src/foundation/complements-subtypes.lagda.md @@ -1,35 +1,43 @@ # Complements of subtypes ```agda -module foundation.complements-subtypes where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.complements-subtypes + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.decidable-propositions -open import foundation.decidable-subtypes -open import foundation.double-negation-stable-propositions -open import foundation.full-subtypes -open import foundation.negation -open import foundation.postcomposition-functions -open import foundation.powersets -open import foundation.propositional-truncations -open import foundation.unions-subtypes +open import foundation.decidable-propositions funext univalence truncations +open import foundation.decidable-subtypes funext univalence truncations +open import foundation.double-negation-stable-propositions funext univalence truncations +open import foundation.full-subtypes funext univalence truncations +open import foundation.negation funext +open import foundation.postcomposition-functions funext +open import foundation.powersets funext univalence truncations +open import foundation.propositional-truncations funext univalence +open import foundation.unions-subtypes funext univalence truncations open import foundation.universe-levels open import foundation-core.function-types -open import foundation-core.subtypes +open import foundation-core.subtypes funext -open import logic.double-negation-stable-subtypes +open import logic.double-negation-stable-subtypes funext univalence truncations -open import order-theory.large-posets -open import order-theory.opposite-large-posets -open import order-theory.order-preserving-maps-large-posets -open import order-theory.order-preserving-maps-large-preorders -open import order-theory.order-preserving-maps-posets -open import order-theory.order-preserving-maps-preorders -open import order-theory.posets +open import order-theory.large-posets funext univalence truncations +open import order-theory.opposite-large-posets funext univalence truncations +open import order-theory.order-preserving-maps-large-posets funext univalence truncations +open import order-theory.order-preserving-maps-large-preorders funext univalence truncations +open import order-theory.order-preserving-maps-posets funext univalence truncations +open import order-theory.order-preserving-maps-preorders funext univalence truncations +open import order-theory.posets funext univalence truncations ```
diff --git a/src/foundation/composite-maps-in-inverse-sequential-diagrams.lagda.md b/src/foundation/composite-maps-in-inverse-sequential-diagrams.lagda.md index 78c23727e3..c40f6e0a90 100644 --- a/src/foundation/composite-maps-in-inverse-sequential-diagrams.lagda.md +++ b/src/foundation/composite-maps-in-inverse-sequential-diagrams.lagda.md @@ -1,7 +1,15 @@ # Composite maps in inverse sequential diagrams ```agda -module foundation.composite-maps-in-inverse-sequential-diagrams where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.composite-maps-in-inverse-sequential-diagrams + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,8 +18,8 @@ module foundation.composite-maps-in-inverse-sequential-diagrams where open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.natural-numbers -open import foundation.dependent-inverse-sequential-diagrams -open import foundation.inverse-sequential-diagrams +open import foundation.dependent-inverse-sequential-diagrams funext univalence truncations +open import foundation.inverse-sequential-diagrams funext univalence truncations open import foundation.universe-levels open import foundation-core.function-types diff --git a/src/foundation/composition-algebra.lagda.md b/src/foundation/composition-algebra.lagda.md index d78d99cfee..1d767b41c7 100644 --- a/src/foundation/composition-algebra.lagda.md +++ b/src/foundation/composition-algebra.lagda.md @@ -1,17 +1,21 @@ # Composition algebra ```agda -module foundation.composition-algebra where +open import foundation.function-extensionality-axiom + +module foundation.composition-algebra + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.function-extensionality -open import foundation.homotopy-induction -open import foundation.postcomposition-functions -open import foundation.precomposition-functions +open import foundation.function-extensionality funext +open import foundation.homotopy-induction funext +open import foundation.postcomposition-functions funext +open import foundation.precomposition-functions funext open import foundation.universe-levels open import foundation.whiskering-higher-homotopies-composition open import foundation.whiskering-homotopies-composition diff --git a/src/foundation/composition-spans.lagda.md b/src/foundation/composition-spans.lagda.md index 2611cdf5b1..715531ef31 100644 --- a/src/foundation/composition-spans.lagda.md +++ b/src/foundation/composition-spans.lagda.md @@ -1,25 +1,33 @@ # Composition of spans ```agda -module foundation.composition-spans where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.composition-spans + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.commuting-triangles-of-maps +open import foundation.commuting-triangles-of-maps funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.equivalences-arrows -open import foundation.equivalences-spans -open import foundation.homotopies -open import foundation.identity-types -open import foundation.morphisms-arrows +open import foundation.equivalences funext +open import foundation.equivalences-arrows funext univalence truncations +open import foundation.equivalences-spans funext univalence +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.morphisms-arrows funext open import foundation.morphisms-spans -open import foundation.pullbacks +open import foundation.pullbacks funext univalence truncations open import foundation.spans -open import foundation.standard-pullbacks -open import foundation.type-arithmetic-standard-pullbacks +open import foundation.standard-pullbacks funext +open import foundation.type-arithmetic-standard-pullbacks funext open import foundation.universe-levels open import foundation-core.function-types diff --git a/src/foundation/computational-identity-types.lagda.md b/src/foundation/computational-identity-types.lagda.md index dd7b53ac80..d477f08f80 100644 --- a/src/foundation/computational-identity-types.lagda.md +++ b/src/foundation/computational-identity-types.lagda.md @@ -1,7 +1,13 @@ # Computational identity types ```agda -module foundation.computational-identity-types where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.computational-identity-types + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports @@ -11,13 +17,13 @@ open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types open import foundation.equality-cartesian-product-types -open import foundation.function-extensionality +open import foundation.function-extensionality funext open import foundation.strictly-right-unital-concatenation-identifications open import foundation.transport-along-identifications -open import foundation.univalence -open import foundation.universal-property-identity-systems +open import foundation.univalence funext univalence +open import foundation.universal-property-identity-systems funext open import foundation.universe-levels -open import foundation.yoneda-identity-types +open import foundation.yoneda-identity-types funext univalence open import foundation-core.cartesian-product-types open import foundation-core.contractible-types diff --git a/src/foundation/cones-over-cospan-diagrams.lagda.md b/src/foundation/cones-over-cospan-diagrams.lagda.md index 56fa968cec..bc15f7f8f7 100644 --- a/src/foundation/cones-over-cospan-diagrams.lagda.md +++ b/src/foundation/cones-over-cospan-diagrams.lagda.md @@ -1,7 +1,11 @@ # Cones over cospan diagrams ```agda -module foundation.cones-over-cospan-diagrams where +open import foundation.function-extensionality-axiom + +module foundation.cones-over-cospan-diagrams + (funext : function-extensionality) + where ```
Imports @@ -9,18 +13,19 @@ module foundation.cones-over-cospan-diagrams where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.dependent-universal-property-equivalences -open import foundation.function-extensionality +open import foundation.dependent-universal-property-equivalences funext +open import foundation.function-extensionality funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types -open import foundation.multivariable-homotopies +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext +open import foundation.multivariable-homotopies funext open import foundation.structure-identity-principle +open import foundation.telescopes open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import foundation-core.commuting-squares-of-maps +open import foundation-core.commuting-squares-of-maps funext open import foundation-core.contractible-types open import foundation-core.equivalences open import foundation-core.function-types diff --git a/src/foundation/cones-over-inverse-sequential-diagrams.lagda.md b/src/foundation/cones-over-inverse-sequential-diagrams.lagda.md index a062c7b9d4..a20dc477a2 100644 --- a/src/foundation/cones-over-inverse-sequential-diagrams.lagda.md +++ b/src/foundation/cones-over-inverse-sequential-diagrams.lagda.md @@ -1,7 +1,15 @@ # Cones over inverse sequential diagrams ```agda -module foundation.cones-over-inverse-sequential-diagrams where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.cones-over-inverse-sequential-diagrams + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,13 +17,13 @@ module foundation.cones-over-inverse-sequential-diagrams where ```agda open import elementary-number-theory.natural-numbers -open import foundation.binary-homotopies +open import foundation.binary-homotopies funext open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types -open import foundation.function-extensionality +open import foundation.equality-dependent-function-types funext +open import foundation.function-extensionality funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopy-induction -open import foundation.inverse-sequential-diagrams +open import foundation.homotopy-induction funext +open import foundation.inverse-sequential-diagrams funext univalence truncations open import foundation.structure-identity-principle open import foundation.universe-levels open import foundation.whiskering-homotopies-composition diff --git a/src/foundation/conjunction.lagda.md b/src/foundation/conjunction.lagda.md index 54c4cc00c9..42f9630650 100644 --- a/src/foundation/conjunction.lagda.md +++ b/src/foundation/conjunction.lagda.md @@ -1,21 +1,30 @@ # Conjunction ```agda -module foundation.conjunction where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.conjunction + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.decidable-types +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.logical-equivalences -open import foundation.propositional-truncations -open import foundation.universal-property-cartesian-product-types +open import foundation.dependent-products-propositions funext +open import foundation.logical-equivalences funext +open import foundation.propositional-truncations funext univalence +open import foundation.universal-property-cartesian-product-types funext open import foundation.universe-levels open import foundation-core.cartesian-product-types -open import foundation-core.decidable-propositions +open import foundation-core.decidable-propositions funext univalence truncations open import foundation-core.equivalences open import foundation-core.function-types open import foundation-core.propositions diff --git a/src/foundation/connected-components-universes.lagda.md b/src/foundation/connected-components-universes.lagda.md index 6e4a87e413..3a65d9a36e 100644 --- a/src/foundation/connected-components-universes.lagda.md +++ b/src/foundation/connected-components-universes.lagda.md @@ -1,29 +1,37 @@ # Connected components of universes ```agda -module foundation.connected-components-universes where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.connected-components-universes + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.0-connected-types +open import foundation.0-connected-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.functoriality-propositional-truncation +open import foundation.empty-types funext univalence truncations +open import foundation.functoriality-propositional-truncation funext univalence truncations open import foundation.fundamental-theorem-of-identity-types -open import foundation.mere-equivalences -open import foundation.propositional-truncations -open import foundation.raising-universe-levels +open import foundation.mere-equivalences funext univalence truncations +open import foundation.propositional-truncations funext univalence open import foundation.subtype-identity-principle -open import foundation.subuniverses -open import foundation.univalence +open import foundation.subuniverses funext univalence +open import foundation.univalence funext univalence open import foundation.universe-levels open import foundation-core.contractible-types open import foundation-core.equivalences open import foundation-core.identity-types -open import foundation-core.subtypes +open import foundation-core.raising-universe-levels +open import foundation-core.subtypes funext open import foundation-core.torsorial-type-families ``` diff --git a/src/foundation/connected-components.lagda.md b/src/foundation/connected-components.lagda.md index 9de3f80bbc..929b5ef8ae 100644 --- a/src/foundation/connected-components.lagda.md +++ b/src/foundation/connected-components.lagda.md @@ -1,27 +1,36 @@ # Connected components of types ```agda -module foundation.connected-components where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.connected-components + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.0-connected-types +open import foundation.0-connected-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.logical-equivalences -open import foundation.mere-equality -open import foundation.propositional-truncations -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.logical-equivalences funext +open import foundation.mere-equality funext univalence truncations +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence open import foundation.universe-levels open import foundation-core.equality-dependent-pair-types open import foundation-core.identity-types -open import foundation-core.subtypes +open import foundation-core.subtypes funext open import foundation-core.truncated-types open import foundation-core.truncation-levels -open import higher-group-theory.higher-groups +open import higher-group-theory.higher-groups funext univalence truncations open import structured-types.pointed-types ``` diff --git a/src/foundation/connected-maps.lagda.md b/src/foundation/connected-maps.lagda.md index d893f11646..633408101c 100644 --- a/src/foundation/connected-maps.lagda.md +++ b/src/foundation/connected-maps.lagda.md @@ -1,25 +1,34 @@ # Connected maps ```agda -module foundation.connected-maps where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.connected-maps + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.connected-types +open import foundation.connected-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.function-extensionality +open import foundation.dependent-products-propositions funext +open import foundation.dependent-products-truncated-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopy-induction -open import foundation.precomposition-dependent-functions +open import foundation.homotopy-induction funext +open import foundation.precomposition-dependent-functions funext open import foundation.structure-identity-principle open import foundation.subtype-identity-principle -open import foundation.truncated-types +open import foundation.truncated-types funext univalence open import foundation.truncation-levels -open import foundation.truncations -open import foundation.univalence -open import foundation.universal-property-family-of-fibers-of-maps +open import foundation.truncations funext univalence truncations +open import foundation.univalence funext univalence +open import foundation.universal-property-family-of-fibers-of-maps funext open import foundation.universe-levels open import foundation-core.contractible-maps @@ -31,9 +40,9 @@ open import foundation-core.functoriality-dependent-pair-types open import foundation-core.homotopies open import foundation-core.identity-types open import foundation-core.propositions -open import foundation-core.subtypes +open import foundation-core.subtypes funext open import foundation-core.torsorial-type-families -open import foundation-core.truncated-maps +open import foundation-core.truncated-maps funext ```
diff --git a/src/foundation/connected-types.lagda.md b/src/foundation/connected-types.lagda.md index e7a26ab34e..b455aa0270 100644 --- a/src/foundation/connected-types.lagda.md +++ b/src/foundation/connected-types.lagda.md @@ -1,26 +1,34 @@ # Connected types ```agda -module foundation.connected-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.connected-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.contractible-types +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.diagonal-maps-of-types -open import foundation.function-extensionality -open import foundation.functoriality-truncation -open import foundation.inhabited-types -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.truncations +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.functoriality-truncation funext univalence truncations +open import foundation.inhabited-types funext univalence truncations +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence +open import foundation.truncations funext univalence truncations open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels -open import foundation-core.constant-maps open import foundation-core.contractible-maps +open import foundation-core.diagonal-maps-of-types open import foundation-core.equivalences open import foundation-core.functoriality-dependent-pair-types open import foundation-core.identity-types diff --git a/src/foundation/constant-maps.lagda.md b/src/foundation/constant-maps.lagda.md index ec686e7417..7eca4b3852 100644 --- a/src/foundation/constant-maps.lagda.md +++ b/src/foundation/constant-maps.lagda.md @@ -1,7 +1,15 @@ # Constant maps ```agda -module foundation.constant-maps where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.constant-maps + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where open import foundation-core.constant-maps public ``` @@ -9,28 +17,28 @@ open import foundation-core.constant-maps public
Imports ```agda -open import foundation.0-maps -open import foundation.action-on-homotopies-functions +open import foundation.0-maps funext +open import foundation.action-on-homotopies-functions funext open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.faithful-maps -open import foundation.function-extensionality -open import foundation.functoriality-dependent-pair-types -open import foundation.images -open import foundation.morphisms-arrows -open import foundation.postcomposition-functions -open import foundation.propositional-truncations -open import foundation.retracts-of-maps -open import foundation.retracts-of-types -open import foundation.transposition-identifications-along-equivalences -open import foundation.type-arithmetic-unit-type -open import foundation.type-theoretic-principle-of-choice +open import foundation.faithful-maps funext +open import foundation.function-extensionality funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.images funext univalence truncations +open import foundation.morphisms-arrows funext +open import foundation.postcomposition-functions funext +open import foundation.propositional-truncations funext univalence +open import foundation.retracts-of-maps funext univalence +open import foundation.retracts-of-types funext univalence +open import foundation.transposition-identifications-along-equivalences funext +open import foundation.type-arithmetic-unit-type funext +open import foundation.type-theoretic-principle-of-choice funext open import foundation.unit-type open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import foundation-core.1-types -open import foundation-core.commuting-squares-of-maps +open import foundation-core.1-types funext univalence +open import foundation-core.commuting-squares-of-maps funext open import foundation-core.contractible-maps open import foundation-core.contractible-types open import foundation-core.embeddings @@ -43,7 +51,7 @@ open import foundation-core.injective-maps open import foundation-core.propositional-maps open import foundation-core.propositions open import foundation-core.sets -open import foundation-core.truncated-maps +open import foundation-core.truncated-maps funext open import foundation-core.truncated-types open import foundation-core.truncation-levels ``` diff --git a/src/foundation/constant-span-diagrams.lagda.md b/src/foundation/constant-span-diagrams.lagda.md index eb2e81061d..8aee9a570c 100644 --- a/src/foundation/constant-span-diagrams.lagda.md +++ b/src/foundation/constant-span-diagrams.lagda.md @@ -1,15 +1,21 @@ # Constant span diagrams ```agda -module foundation.constant-span-diagrams where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.constant-span-diagrams + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.span-diagrams +open import foundation.span-diagrams funext open import foundation.spans open import foundation.universe-levels diff --git a/src/foundation/constant-type-families.lagda.md b/src/foundation/constant-type-families.lagda.md index 15db228460..84df872a9f 100644 --- a/src/foundation/constant-type-families.lagda.md +++ b/src/foundation/constant-type-families.lagda.md @@ -1,7 +1,11 @@ # Constant type families ```agda -module foundation.constant-type-families where +open import foundation.function-extensionality-axiom + +module foundation.constant-type-families + (funext : function-extensionality) + where ```
Imports @@ -10,13 +14,13 @@ module foundation.constant-type-families where open import foundation.action-on-identifications-dependent-functions open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.transport-along-identifications +open import foundation.identity-types funext open import foundation.universe-levels open import foundation-core.commuting-squares-of-identifications open import foundation-core.dependent-identifications open import foundation-core.equivalences +open import foundation-core.transport-along-identifications ```
diff --git a/src/foundation/continuations.lagda.md b/src/foundation/continuations.lagda.md index 3c7d65926e..b23205da5a 100644 --- a/src/foundation/continuations.lagda.md +++ b/src/foundation/continuations.lagda.md @@ -1,43 +1,37 @@ # The continuation monad ```agda -module foundation.continuations where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.continuations + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.equality-cartesian-product-types +open import foundation.dependent-products-propositions funext +open import foundation.empty-types funext univalence truncations open import foundation.evaluation-functions -open import foundation.function-extensionality -open import foundation.logical-equivalences -open import foundation.type-arithmetic-cartesian-product-types -open import foundation.type-arithmetic-dependent-function-types -open import foundation.type-arithmetic-empty-type -open import foundation.type-arithmetic-unit-type +open import foundation.type-arithmetic-dependent-function-types funext univalence +open import foundation.type-arithmetic-unit-type funext open import foundation.unit-type -open import foundation.universal-property-cartesian-product-types -open import foundation.universal-property-empty-type -open import foundation.universal-property-equivalences +open import foundation.universal-property-empty-type funext +open import foundation.universal-property-equivalences funext open import foundation.universe-levels -open import foundation-core.cartesian-product-types open import foundation-core.equivalences open import foundation-core.function-types open import foundation-core.homotopies -open import foundation-core.identity-types open import foundation-core.propositions -open import foundation-core.retractions -open import foundation-core.sections -open import foundation-core.transport-along-identifications - -open import orthogonal-factorization-systems.extensions-maps -open import orthogonal-factorization-systems.modal-operators -open import orthogonal-factorization-systems.types-local-at-maps -open import orthogonal-factorization-systems.uniquely-eliminating-modalities + +open import orthogonal-factorization-systems.extensions-maps funext univalence ```
diff --git a/src/foundation/contractible-maps.lagda.md b/src/foundation/contractible-maps.lagda.md index 15c5bb6786..c156b78646 100644 --- a/src/foundation/contractible-maps.lagda.md +++ b/src/foundation/contractible-maps.lagda.md @@ -1,7 +1,11 @@ # Contractible maps ```agda -module foundation.contractible-maps where +open import foundation.function-extensionality-axiom + +module foundation.contractible-maps + (funext : function-extensionality) + where open import foundation-core.contractible-maps public ``` @@ -10,9 +14,9 @@ open import foundation-core.contractible-maps public ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.logical-equivalences -open import foundation.truncated-maps +open import foundation.equivalences funext +open import foundation.logical-equivalences funext +open import foundation.truncated-maps funext open import foundation.universe-levels open import foundation-core.function-types diff --git a/src/foundation/contractible-types.lagda.md b/src/foundation/contractible-types.lagda.md index bfb117148d..13e59be474 100644 --- a/src/foundation/contractible-types.lagda.md +++ b/src/foundation/contractible-types.lagda.md @@ -1,7 +1,13 @@ # Contractible types ```agda -module foundation.contractible-types where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.contractible-types + (funext : function-extensionality) + (univalence : univalence-axiom) + where open import foundation-core.contractible-types public ``` @@ -11,21 +17,22 @@ open import foundation-core.contractible-types public ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.diagonal-maps-of-types -open import foundation.function-extensionality -open import foundation.logical-equivalences -open import foundation.subuniverses +open import foundation.dependent-products-contractible-types funext +open import foundation.function-extensionality funext +open import foundation.logical-equivalences funext +open import foundation.raising-universe-levels-unit-type +open import foundation.subuniverses funext univalence open import foundation.unit-type open import foundation.universe-levels -open import foundation-core.constant-maps open import foundation-core.contractible-maps +open import foundation-core.diagonal-maps-of-types open import foundation-core.equivalences open import foundation-core.function-types open import foundation-core.functoriality-dependent-pair-types open import foundation-core.identity-types open import foundation-core.propositions -open import foundation-core.subtypes +open import foundation-core.subtypes funext open import foundation-core.truncated-types open import foundation-core.truncation-levels ``` diff --git a/src/foundation/copartial-elements.lagda.md b/src/foundation/copartial-elements.lagda.md index 857e423d5b..86c95b8036 100644 --- a/src/foundation/copartial-elements.lagda.md +++ b/src/foundation/copartial-elements.lagda.md @@ -1,23 +1,31 @@ # Copartial elements ```agda -module foundation.copartial-elements where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.copartial-elements + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.negation +open import foundation.empty-types funext univalence truncations +open import foundation.negation funext open import foundation.partial-elements open import foundation.universe-levels open import foundation-core.propositions -open import orthogonal-factorization-systems.closed-modalities +open import orthogonal-factorization-systems.closed-modalities funext univalence truncations -open import synthetic-homotopy-theory.joins-of-types +open import synthetic-homotopy-theory.joins-of-types funext univalence truncations ```
diff --git a/src/foundation/copartial-functions.lagda.md b/src/foundation/copartial-functions.lagda.md index 6b5c611c47..ac1173c89a 100644 --- a/src/foundation/copartial-functions.lagda.md +++ b/src/foundation/copartial-functions.lagda.md @@ -1,15 +1,24 @@ # Copartial functions ```agda -module foundation.copartial-functions where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.copartial-functions + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.copartial-elements +open import foundation.copartial-elements funext univalence truncations +open import foundation.dependent-products-propositions funext open import foundation.partial-functions -open import foundation.propositions +open import foundation.propositions funext univalence open import foundation.universe-levels ``` diff --git a/src/foundation/coproduct-decompositions-subuniverse.lagda.md b/src/foundation/coproduct-decompositions-subuniverse.lagda.md index 3d8495b9a1..6f03ff043e 100644 --- a/src/foundation/coproduct-decompositions-subuniverse.lagda.md +++ b/src/foundation/coproduct-decompositions-subuniverse.lagda.md @@ -1,26 +1,34 @@ # Coproduct decompositions in a subuniverse ```agda -module foundation.coproduct-decompositions-subuniverse where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.coproduct-decompositions-subuniverse + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.coproduct-types +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.equivalence-extensionality -open import foundation.equivalences -open import foundation.functoriality-coproduct-types +open import foundation.empty-types funext univalence truncations +open import foundation.equivalence-extensionality funext +open import foundation.equivalences funext +open import foundation.functoriality-coproduct-types funext univalence truncations open import foundation.fundamental-theorem-of-identity-types open import foundation.structure-identity-principle -open import foundation.subuniverses +open import foundation.subuniverses funext univalence open import foundation.type-arithmetic-cartesian-product-types -open import foundation.type-arithmetic-coproduct-types +open import foundation.type-arithmetic-coproduct-types funext univalence truncations open import foundation.type-arithmetic-dependent-pair-types -open import foundation.type-arithmetic-empty-type -open import foundation.univalence +open import foundation.type-arithmetic-empty-type funext univalence truncations +open import foundation.univalence funext univalence open import foundation.universe-levels open import foundation-core.cartesian-product-types diff --git a/src/foundation/coproduct-decompositions.lagda.md b/src/foundation/coproduct-decompositions.lagda.md index 4f8dfd14be..29e2b94c55 100644 --- a/src/foundation/coproduct-decompositions.lagda.md +++ b/src/foundation/coproduct-decompositions.lagda.md @@ -1,26 +1,34 @@ # Coproduct decompositions ```agda -module foundation.coproduct-decompositions where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.coproduct-decompositions + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.coproduct-decompositions-subuniverse +open import foundation.coproduct-decompositions-subuniverse funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalence-extensionality -open import foundation.function-extensionality -open import foundation.functoriality-coproduct-types +open import foundation.equivalence-extensionality funext +open import foundation.function-extensionality funext +open import foundation.functoriality-coproduct-types funext univalence truncations open import foundation.fundamental-theorem-of-identity-types open import foundation.structure-identity-principle -open import foundation.transposition-identifications-along-equivalences -open import foundation.type-arithmetic-coproduct-types +open import foundation.transposition-identifications-along-equivalences funext +open import foundation.type-arithmetic-coproduct-types funext univalence truncations open import foundation.type-arithmetic-dependent-pair-types -open import foundation.type-arithmetic-empty-type +open import foundation.type-arithmetic-empty-type funext univalence truncations open import foundation.unit-type -open import foundation.univalence +open import foundation.univalence funext univalence open import foundation.universe-levels open import foundation.whiskering-homotopies-composition @@ -37,8 +45,8 @@ open import foundation-core.propositions open import foundation-core.torsorial-type-families open import foundation-core.transport-along-identifications -open import univalent-combinatorics.equality-standard-finite-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.equality-standard-finite-types funext univalence truncations +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/foundation/coproduct-types.lagda.md b/src/foundation/coproduct-types.lagda.md index aaadc73d63..9d9d28dfc5 100644 --- a/src/foundation/coproduct-types.lagda.md +++ b/src/foundation/coproduct-types.lagda.md @@ -1,7 +1,15 @@ # Coproduct types ```agda -module foundation.coproduct-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.coproduct-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where open import foundation-core.coproduct-types public ``` @@ -11,9 +19,9 @@ open import foundation-core.coproduct-types public ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.negated-equality -open import foundation.noncontractible-types -open import foundation.subuniverses +open import foundation.negated-equality funext univalence truncations +open import foundation.noncontractible-types funext univalence truncations +open import foundation.subuniverses funext univalence open import foundation.unit-type open import foundation.universe-levels diff --git a/src/foundation/coproducts-pullbacks.lagda.md b/src/foundation/coproducts-pullbacks.lagda.md index 780fecc445..ce12f15067 100644 --- a/src/foundation/coproducts-pullbacks.lagda.md +++ b/src/foundation/coproducts-pullbacks.lagda.md @@ -1,20 +1,28 @@ # Coproducts of pullbacks ```agda -module foundation.coproducts-pullbacks where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.coproducts-pullbacks + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cones-over-cospan-diagrams -open import foundation.coproduct-types +open import foundation.cones-over-cospan-diagrams funext +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equality-coproduct-types -open import foundation.functoriality-coproduct-types -open import foundation.identity-types -open import foundation.standard-pullbacks +open import foundation.equality-coproduct-types funext univalence truncations +open import foundation.functoriality-coproduct-types funext univalence truncations +open import foundation.identity-types funext +open import foundation.standard-pullbacks funext open import foundation.universe-levels open import foundation-core.commuting-triangles-of-maps @@ -22,10 +30,10 @@ open import foundation-core.equality-dependent-pair-types open import foundation-core.equivalences open import foundation-core.function-types open import foundation-core.homotopies -open import foundation-core.pullbacks +open import foundation-core.pullbacks funext open import foundation-core.retractions open import foundation-core.sections -open import foundation-core.universal-property-pullbacks +open import foundation-core.universal-property-pullbacks funext ```
diff --git a/src/foundation/coslice.lagda.md b/src/foundation/coslice.lagda.md index 20e4829866..91958c8dc3 100644 --- a/src/foundation/coslice.lagda.md +++ b/src/foundation/coslice.lagda.md @@ -1,15 +1,19 @@ # Morphisms in the coslice category of types ```agda -module foundation.coslice where +open import foundation.function-extensionality-axiom + +module foundation.coslice + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.commuting-triangles-of-homotopies +open import foundation.commuting-triangles-of-homotopies funext open import foundation.dependent-pair-types -open import foundation.function-extensionality +open import foundation.function-extensionality funext open import foundation.structure-identity-principle open import foundation.universe-levels open import foundation.whiskering-homotopies-composition diff --git a/src/foundation/cospans.lagda.md b/src/foundation/cospans.lagda.md index 41f0b583d6..ac8a374d21 100644 --- a/src/foundation/cospans.lagda.md +++ b/src/foundation/cospans.lagda.md @@ -8,10 +8,7 @@ module foundation.cospans where ```agda open import foundation.dependent-pair-types -open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopy-induction open import foundation.structure-identity-principle -open import foundation.univalence open import foundation.universe-levels open import foundation-core.cartesian-product-types diff --git a/src/foundation/decidable-dependent-function-types.lagda.md b/src/foundation/decidable-dependent-function-types.lagda.md index c63c6ddeea..ec9ed084b0 100644 --- a/src/foundation/decidable-dependent-function-types.lagda.md +++ b/src/foundation/decidable-dependent-function-types.lagda.md @@ -1,24 +1,32 @@ # Decidability of dependent function types ```agda -module foundation.decidable-dependent-function-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.decidable-dependent-function-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.decidable-types -open import foundation.functoriality-dependent-function-types -open import foundation.maybe -open import foundation.uniformly-decidable-type-families -open import foundation.universal-property-coproduct-types -open import foundation.universal-property-maybe +open import foundation.decidable-types funext univalence truncations +open import foundation.functoriality-dependent-function-types funext univalence +open import foundation.uniformly-decidable-type-families funext univalence truncations +open import foundation.universal-property-coproduct-types funext +open import foundation.universal-property-maybe funext open import foundation.universe-levels open import foundation-core.coproduct-types open import foundation-core.empty-types open import foundation-core.equivalences open import foundation-core.function-types +open import foundation-core.maybe open import foundation-core.negation ``` diff --git a/src/foundation/decidable-dependent-pair-types.lagda.md b/src/foundation/decidable-dependent-pair-types.lagda.md index 4af4b5e568..0f9a338ea2 100644 --- a/src/foundation/decidable-dependent-pair-types.lagda.md +++ b/src/foundation/decidable-dependent-pair-types.lagda.md @@ -1,24 +1,32 @@ # Decidability of dependent pair types ```agda -module foundation.decidable-dependent-pair-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.decidable-dependent-pair-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.decidable-types +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.maybe -open import foundation.type-arithmetic-coproduct-types -open import foundation.type-arithmetic-unit-type -open import foundation.uniformly-decidable-type-families +open import foundation.type-arithmetic-coproduct-types funext univalence truncations +open import foundation.type-arithmetic-unit-type funext +open import foundation.uniformly-decidable-type-families funext univalence truncations open import foundation.universe-levels open import foundation-core.coproduct-types open import foundation-core.equivalences open import foundation-core.function-types open import foundation-core.functoriality-dependent-pair-types +open import foundation-core.maybe open import foundation-core.negation ``` diff --git a/src/foundation/decidable-embeddings.lagda.md b/src/foundation/decidable-embeddings.lagda.md index f4780285bd..eaf3120815 100644 --- a/src/foundation/decidable-embeddings.lagda.md +++ b/src/foundation/decidable-embeddings.lagda.md @@ -1,33 +1,42 @@ # Decidable embeddings ```agda -module foundation.decidable-embeddings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.decidable-embeddings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cartesian-morphisms-arrows -open import foundation.decidable-maps -open import foundation.decidable-propositions -open import foundation.decidable-types +open import foundation.cartesian-morphisms-arrows funext univalence truncations +open import foundation.decidable-maps funext univalence truncations +open import foundation.decidable-propositions funext univalence truncations +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.fibers-of-maps -open import foundation.functoriality-cartesian-product-types -open import foundation.functoriality-coproduct-types +open import foundation.dependent-products-propositions funext +open import foundation.embeddings funext +open import foundation.fibers-of-maps funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.functoriality-coproduct-types funext univalence truncations open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopy-induction -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.propositional-maps -open import foundation.propositions -open import foundation.retracts-of-maps +open import foundation.homotopy-induction funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.propositional-maps funext +open import foundation.propositions funext univalence +open import foundation.retracts-of-maps funext univalence open import foundation.subtype-identity-principle open import foundation.type-arithmetic-dependent-pair-types open import foundation.unit-type -open import foundation.universal-property-equivalences +open import foundation.universal-property-equivalences funext open import foundation.universe-levels open import foundation-core.cartesian-product-types diff --git a/src/foundation/decidable-equality.lagda.md b/src/foundation/decidable-equality.lagda.md index 05a5b5b201..e51e88cc45 100644 --- a/src/foundation/decidable-equality.lagda.md +++ b/src/foundation/decidable-equality.lagda.md @@ -1,21 +1,30 @@ # Decidable equality ```agda -module foundation.decidable-equality where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.decidable-equality + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.coproduct-types -open import foundation.decidable-types +open import foundation.coproduct-types funext univalence truncations +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.double-negation -open import foundation.injective-maps -open import foundation.negation -open import foundation.sections -open import foundation.sets +open import foundation.dependent-products-propositions funext +open import foundation.double-negation funext univalence truncations +open import foundation.injective-maps funext +open import foundation.negation funext +open import foundation.sections funext +open import foundation.sets funext univalence open import foundation.type-arithmetic-dependent-pair-types open import foundation.unit-type open import foundation.universe-levels diff --git a/src/foundation/decidable-equivalence-relations.lagda.md b/src/foundation/decidable-equivalence-relations.lagda.md index 149af1b5ca..80fcae72ad 100644 --- a/src/foundation/decidable-equivalence-relations.lagda.md +++ b/src/foundation/decidable-equivalence-relations.lagda.md @@ -1,36 +1,45 @@ # Decidable equivalence relations ```agda -module foundation.decidable-equivalence-relations where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.decidable-equivalence-relations + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.binary-relations -open import foundation.decidable-equality -open import foundation.decidable-propositions -open import foundation.decidable-relations -open import foundation.decidable-subtypes -open import foundation.decidable-types +open import foundation.binary-relations funext univalence truncations +open import foundation.decidable-equality funext univalence truncations +open import foundation.decidable-propositions funext univalence truncations +open import foundation.decidable-relations funext univalence truncations +open import foundation.decidable-subtypes funext univalence truncations +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.effective-maps-equivalence-relations -open import foundation.equivalence-classes -open import foundation.equivalence-relations -open import foundation.existential-quantification -open import foundation.function-extensionality -open import foundation.functoriality-cartesian-product-types +open import foundation.dependent-products-propositions funext +open import foundation.effective-maps-equivalence-relations funext univalence truncations +open import foundation.equivalence-classes funext univalence truncations +open import foundation.equivalence-relations funext univalence truncations +open import foundation.existential-quantification funext univalence truncations +open import foundation.function-extensionality funext +open import foundation.functoriality-cartesian-product-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.images -open import foundation.logical-equivalences -open import foundation.propositional-truncations -open import foundation.reflecting-maps-equivalence-relations -open import foundation.sets -open import foundation.slice -open import foundation.surjective-maps +open import foundation.images funext univalence truncations +open import foundation.logical-equivalences funext +open import foundation.propositional-truncations funext univalence +open import foundation.reflecting-maps-equivalence-relations funext univalence truncations +open import foundation.sets funext univalence +open import foundation.slice funext univalence +open import foundation.surjective-maps funext univalence truncations open import foundation.type-arithmetic-cartesian-product-types open import foundation.type-arithmetic-dependent-pair-types -open import foundation.universal-property-image +open import foundation.universal-property-image funext univalence truncations open import foundation.universe-levels open import foundation-core.cartesian-product-types @@ -43,7 +52,7 @@ open import foundation-core.functoriality-dependent-pair-types open import foundation-core.homotopies open import foundation-core.identity-types open import foundation-core.propositions -open import foundation-core.subtypes +open import foundation-core.subtypes funext open import foundation-core.torsorial-type-families open import foundation-core.transport-along-identifications ``` diff --git a/src/foundation/decidable-maps.lagda.md b/src/foundation/decidable-maps.lagda.md index 926253c0dc..bc2b03f065 100644 --- a/src/foundation/decidable-maps.lagda.md +++ b/src/foundation/decidable-maps.lagda.md @@ -1,22 +1,30 @@ # Decidable maps ```agda -module foundation.decidable-maps where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.decidable-maps + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cartesian-morphisms-arrows -open import foundation.coproduct-types -open import foundation.decidable-equality -open import foundation.decidable-types +open import foundation.cartesian-morphisms-arrows funext univalence truncations +open import foundation.coproduct-types funext univalence truncations +open import foundation.decidable-equality funext univalence truncations +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.functoriality-cartesian-product-types -open import foundation.functoriality-coproduct-types -open import foundation.identity-types -open import foundation.retracts-of-maps +open import foundation.functoriality-cartesian-product-types funext +open import foundation.functoriality-coproduct-types funext univalence truncations +open import foundation.identity-types funext +open import foundation.retracts-of-maps funext univalence open import foundation.universe-levels open import foundation-core.contractible-maps diff --git a/src/foundation/decidable-propositions.lagda.md b/src/foundation/decidable-propositions.lagda.md index ef885f24e7..ce15ecc165 100644 --- a/src/foundation/decidable-propositions.lagda.md +++ b/src/foundation/decidable-propositions.lagda.md @@ -1,28 +1,37 @@ # Decidable propositions ```agda -module foundation.decidable-propositions where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.decidable-propositions + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where -open import foundation-core.decidable-propositions public +open import foundation-core.decidable-propositions funext univalence truncations public ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.booleans -open import foundation.decidable-types +open import foundation.booleans funext univalence truncations +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.empty-types -open import foundation.equivalences -open import foundation.logical-equivalences -open import foundation.negation -open import foundation.propositional-extensionality -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.raising-universe-levels -open import foundation.type-arithmetic-coproduct-types +open import foundation.dependent-products-propositions funext +open import foundation.embeddings funext +open import foundation.empty-types funext univalence truncations +open import foundation.equivalences funext +open import foundation.logical-equivalences funext +open import foundation.negation funext +open import foundation.propositional-extensionality funext univalence truncations +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence +open import foundation.raising-universe-levels-unit-type +open import foundation.type-arithmetic-coproduct-types funext univalence truncations open import foundation.type-arithmetic-dependent-pair-types open import foundation.unit-type open import foundation.universe-levels @@ -32,14 +41,15 @@ open import foundation-core.coproduct-types open import foundation-core.function-types open import foundation-core.homotopies open import foundation-core.identity-types +open import foundation-core.raising-universe-levels open import foundation-core.retracts-of-types open import foundation-core.sets -open import foundation-core.small-types -open import foundation-core.subtypes +open import foundation-core.small-types funext univalence truncations +open import foundation-core.subtypes funext open import foundation-core.transport-along-identifications -open import univalent-combinatorics.counting -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.counting funext univalence truncations +open import univalent-combinatorics.finite-types funext univalence truncations ```
diff --git a/src/foundation/decidable-relations.lagda.md b/src/foundation/decidable-relations.lagda.md index 770d4b5f81..1cc74b33c4 100644 --- a/src/foundation/decidable-relations.lagda.md +++ b/src/foundation/decidable-relations.lagda.md @@ -1,18 +1,26 @@ # Decidable relations on types ```agda -module foundation.decidable-relations where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.decidable-relations + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.binary-relations -open import foundation.decidable-types +open import foundation.binary-relations funext univalence truncations +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types open import foundation.universe-levels -open import foundation-core.decidable-propositions +open import foundation-core.decidable-propositions funext univalence truncations open import foundation-core.equivalences open import foundation-core.homotopies open import foundation-core.propositions diff --git a/src/foundation/decidable-subtypes.lagda.md b/src/foundation/decidable-subtypes.lagda.md index 0bd5ecec7f..92d88e52b7 100644 --- a/src/foundation/decidable-subtypes.lagda.md +++ b/src/foundation/decidable-subtypes.lagda.md @@ -1,29 +1,38 @@ # Decidable subtypes ```agda -module foundation.decidable-subtypes where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.decidable-subtypes + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.1-types -open import foundation.coproduct-types -open import foundation.decidable-embeddings -open import foundation.decidable-maps -open import foundation.decidable-propositions -open import foundation.decidable-types +open import foundation.1-types funext univalence +open import foundation.coproduct-types funext univalence truncations +open import foundation.decidable-embeddings funext univalence truncations +open import foundation.decidable-maps funext univalence truncations +open import foundation.decidable-propositions funext univalence truncations +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types -open import foundation.functoriality-cartesian-product-types -open import foundation.functoriality-dependent-function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.logical-equivalences -open import foundation.propositional-maps -open import foundation.sets -open import foundation.structured-type-duality -open import foundation.subtypes -open import foundation.type-theoretic-principle-of-choice +open import foundation.dependent-products-propositions funext +open import foundation.equality-dependent-function-types funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.functoriality-dependent-function-types funext univalence +open import foundation.functoriality-dependent-pair-types funext +open import foundation.logical-equivalences funext +open import foundation.propositional-maps funext +open import foundation.sets funext univalence +open import foundation.structured-type-duality funext univalence truncations +open import foundation.subtypes funext univalence truncations +open import foundation.type-theoretic-principle-of-choice funext open import foundation.universe-levels open import foundation-core.embeddings @@ -37,7 +46,7 @@ open import foundation-core.transport-along-identifications open import foundation-core.truncated-types open import foundation-core.truncation-levels -open import logic.double-negation-stable-subtypes +open import logic.double-negation-stable-subtypes funext univalence truncations ```
diff --git a/src/foundation/decidable-types.lagda.md b/src/foundation/decidable-types.lagda.md index 93bdd1707e..b09bc5f084 100644 --- a/src/foundation/decidable-types.lagda.md +++ b/src/foundation/decidable-types.lagda.md @@ -1,31 +1,39 @@ # Decidable types ```agda -module foundation.decidable-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.decidable-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.coproduct-types +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.double-negation -open import foundation.empty-types -open import foundation.equivalences -open import foundation.hilberts-epsilon-operators -open import foundation.logical-equivalences -open import foundation.negation -open import foundation.propositional-truncations -open import foundation.raising-universe-levels -open import foundation.retracts-of-types -open import foundation.type-arithmetic-empty-type +open import foundation.double-negation funext univalence truncations +open import foundation.empty-types funext univalence truncations +open import foundation.equivalences funext +open import foundation.hilberts-epsilon-operators funext univalence truncations +open import foundation.logical-equivalences funext +open import foundation.negation funext +open import foundation.propositional-truncations funext univalence +open import foundation.retracts-of-types funext univalence +open import foundation.type-arithmetic-empty-type funext univalence truncations open import foundation.unit-type open import foundation.universe-levels open import foundation-core.cartesian-product-types open import foundation-core.function-types open import foundation-core.propositions +open import foundation-core.raising-universe-levels open import foundation-core.retractions open import foundation-core.sections ``` diff --git a/src/foundation/dependent-binary-homotopies.lagda.md b/src/foundation/dependent-binary-homotopies.lagda.md index affccfbaf5..6d1c68daf8 100644 --- a/src/foundation/dependent-binary-homotopies.lagda.md +++ b/src/foundation/dependent-binary-homotopies.lagda.md @@ -1,13 +1,17 @@ # Dependent binary homotopies ```agda -module foundation.dependent-binary-homotopies where +open import foundation.function-extensionality-axiom + +module foundation.dependent-binary-homotopies + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.binary-homotopies +open import foundation.binary-homotopies funext open import foundation.universe-levels open import foundation-core.dependent-identifications diff --git a/src/foundation/dependent-binomial-theorem.lagda.md b/src/foundation/dependent-binomial-theorem.lagda.md index d86a4ac378..4eecd5ac43 100644 --- a/src/foundation/dependent-binomial-theorem.lagda.md +++ b/src/foundation/dependent-binomial-theorem.lagda.md @@ -1,23 +1,31 @@ # The dependent binomial theorem for types (distributivity of dependent function types over coproduct types) ```agda -module foundation.dependent-binomial-theorem where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.dependent-binomial-theorem + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.contractible-types -open import foundation.coproduct-decompositions +open import foundation.contractible-types funext univalence +open import foundation.coproduct-decompositions funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types -open import foundation.functoriality-cartesian-product-types -open import foundation.functoriality-dependent-function-types -open import foundation.raising-universe-levels +open import foundation.dependent-products-contractible-types funext +open import foundation.equality-dependent-pair-types funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.functoriality-dependent-function-types funext univalence open import foundation.transport-along-identifications -open import foundation.universal-property-coproduct-types -open import foundation.universal-property-dependent-pair-types +open import foundation.universal-property-coproduct-types funext +open import foundation.universal-property-dependent-pair-types funext open import foundation.universe-levels open import foundation-core.cartesian-product-types @@ -26,11 +34,10 @@ open import foundation-core.equivalences open import foundation-core.function-types open import foundation-core.functoriality-dependent-pair-types open import foundation-core.homotopies +open import foundation-core.raising-universe-levels open import foundation-core.type-theoretic-principle-of-choice -open import foundation-core.univalence - -open import univalent-combinatorics.equality-standard-finite-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.equality-standard-finite-types funext univalence truncations +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/foundation/dependent-epimorphisms-with-respect-to-truncated-types.lagda.md b/src/foundation/dependent-epimorphisms-with-respect-to-truncated-types.lagda.md index 7e107654bd..eadb15e829 100644 --- a/src/foundation/dependent-epimorphisms-with-respect-to-truncated-types.lagda.md +++ b/src/foundation/dependent-epimorphisms-with-respect-to-truncated-types.lagda.md @@ -1,13 +1,21 @@ # Dependent epimorphisms with respect to truncated types ```agda -module foundation.dependent-epimorphisms-with-respect-to-truncated-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.dependent-epimorphisms-with-respect-to-truncated-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.epimorphisms-with-respect-to-truncated-types +open import foundation.epimorphisms-with-respect-to-truncated-types funext univalence truncations open import foundation.universe-levels open import foundation-core.embeddings diff --git a/src/foundation/dependent-epimorphisms.lagda.md b/src/foundation/dependent-epimorphisms.lagda.md index d4da0dd5e6..50839d3444 100644 --- a/src/foundation/dependent-epimorphisms.lagda.md +++ b/src/foundation/dependent-epimorphisms.lagda.md @@ -1,13 +1,21 @@ # Dependent epimorphisms ```agda -module foundation.dependent-epimorphisms where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.dependent-epimorphisms + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.epimorphisms +open import foundation.epimorphisms funext univalence truncations open import foundation.universe-levels open import foundation-core.embeddings diff --git a/src/foundation/dependent-function-types.lagda.md b/src/foundation/dependent-function-types.lagda.md index 9ac456c7c7..d0632d57c1 100644 --- a/src/foundation/dependent-function-types.lagda.md +++ b/src/foundation/dependent-function-types.lagda.md @@ -1,7 +1,13 @@ # Dependent function types ```agda -module foundation.dependent-function-types where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.dependent-function-types + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports @@ -9,9 +15,9 @@ module foundation.dependent-function-types where ```agda open import foundation.dependent-pair-types open import foundation.spans-families-of-types -open import foundation.terminal-spans-families-of-types -open import foundation.type-arithmetic-dependent-function-types -open import foundation.universal-property-dependent-function-types +open import foundation.terminal-spans-families-of-types funext +open import foundation.type-arithmetic-dependent-function-types funext univalence +open import foundation.universal-property-dependent-function-types funext open import foundation.universe-levels ``` diff --git a/src/foundation/dependent-identifications.lagda.md b/src/foundation/dependent-identifications.lagda.md index 4a1da7c967..760afef419 100644 --- a/src/foundation/dependent-identifications.lagda.md +++ b/src/foundation/dependent-identifications.lagda.md @@ -1,7 +1,11 @@ # Dependent identifications ```agda -module foundation.dependent-identifications where +open import foundation.function-extensionality-axiom + +module foundation.dependent-identifications + (funext : function-extensionality) + where open import foundation-core.dependent-identifications public ``` @@ -13,7 +17,7 @@ open import foundation.action-on-identifications-dependent-functions open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types open import foundation.strictly-right-unital-concatenation-identifications -open import foundation.transport-along-higher-identifications +open import foundation.transport-along-higher-identifications funext open import foundation.universe-levels open import foundation-core.equivalences diff --git a/src/foundation/dependent-inverse-sequential-diagrams.lagda.md b/src/foundation/dependent-inverse-sequential-diagrams.lagda.md index f48ea9d065..ac106f9830 100644 --- a/src/foundation/dependent-inverse-sequential-diagrams.lagda.md +++ b/src/foundation/dependent-inverse-sequential-diagrams.lagda.md @@ -1,7 +1,15 @@ # Dependent inverse sequential diagrams of types ```agda -module foundation.dependent-inverse-sequential-diagrams where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.dependent-inverse-sequential-diagrams + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,8 +18,9 @@ module foundation.dependent-inverse-sequential-diagrams where open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.inverse-sequential-diagrams -open import foundation.iterating-families-of-maps +open import foundation.inverse-sequential-diagrams funext univalence truncations +open import foundation.iterating-families-of-maps funext univalence truncations +open import foundation.raising-universe-levels-unit-type open import foundation.unit-type open import foundation.universe-levels diff --git a/src/foundation/dependent-products-contractible-types.lagda.md b/src/foundation/dependent-products-contractible-types.lagda.md new file mode 100644 index 0000000000..db512ddf27 --- /dev/null +++ b/src/foundation/dependent-products-contractible-types.lagda.md @@ -0,0 +1,103 @@ +# Dependent products of contractible types + +```agda +open import foundation.function-extensionality-axiom + +module foundation.dependent-products-contractible-types + (funext : function-extensionality) + where +``` + +
Imports + +```agda +open import foundation.dependent-pair-types +open import foundation.function-extensionality funext +open import foundation.implicit-function-types +open import foundation.universe-levels + +open import foundation-core.contractible-types +open import foundation-core.equivalences +open import foundation-core.identity-types +``` + +
+ +## Idea + +Given a family of [contractible types](foundation-core.contractible-types.md) +`B : A → 𝒰`, then the dependent product `Π A B` is again contractible. + +## Properties + +### Products of families of contractible types are contractible + +```agda +abstract + is-contr-Π : + {l1 l2 : Level} {A : UU l1} {B : A → UU l2} → + ((x : A) → is-contr (B x)) → is-contr ((x : A) → B x) + pr1 (is-contr-Π {A = A} {B = B} H) x = center (H x) + pr2 (is-contr-Π {A = A} {B = B} H) f = + eq-htpy (λ x → contraction (H x) (f x)) + +abstract + is-contr-implicit-Π : + {l1 l2 : Level} {A : UU l1} {B : A → UU l2} → + ((x : A) → is-contr (B x)) → is-contr ({x : A} → B x) + is-contr-implicit-Π H = + is-contr-equiv _ equiv-explicit-implicit-Π (is-contr-Π H) +``` + +### The type of functions into a contractible type is contractible + +```agda +is-contr-function-type : + {l1 l2 : Level} {A : UU l1} {B : UU l2} → + is-contr B → is-contr (A → B) +is-contr-function-type is-contr-B = is-contr-Π (λ _ → is-contr-B) +``` + +### The type of equivalences between contractible types is contractible + +```agda +module _ + {l1 l2 : Level} {A : UU l1} {B : UU l2} + where + + is-contr-equiv-is-contr : + is-contr A → is-contr B → is-contr (A ≃ B) + is-contr-equiv-is-contr (pair a α) (pair b β) = + is-contr-Σ + ( is-contr-function-type (pair b β)) + ( λ x → b) + ( is-contr-product + ( is-contr-Σ + ( is-contr-function-type (pair a α)) + ( λ y → a) + ( is-contr-Π (is-prop-is-contr (pair b β) b))) + ( is-contr-Σ + ( is-contr-function-type (pair a α)) + ( λ y → a) + ( is-contr-Π (is-prop-is-contr (pair a α) a)))) +``` + +### Being contractible is a proposition + +```agda +module _ + {l : Level} {A : UU l} + where + + abstract + is-contr-is-contr : is-contr A → is-contr (is-contr A) + is-contr-is-contr (pair a α) = + is-contr-Σ + ( pair a α) + ( a) + ( is-contr-Π (is-prop-is-contr (pair a α) a)) + + abstract + is-property-is-contr : (H K : is-contr A) → is-contr (H ＝ K) + is-property-is-contr H = is-prop-is-contr (is-contr-is-contr H) H +``` diff --git a/src/foundation/dependent-products-propositions.lagda.md b/src/foundation/dependent-products-propositions.lagda.md new file mode 100644 index 0000000000..5b6b7c2145 --- /dev/null +++ b/src/foundation/dependent-products-propositions.lagda.md @@ -0,0 +1,247 @@ +# Dependent products of propositions + +```agda +open import foundation.function-extensionality-axiom + +module foundation.dependent-products-propositions + (funext : function-extensionality) + where +``` + +
Imports + +```agda +open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types funext +open import foundation.universe-levels + +open import foundation-core.contractible-types +open import foundation-core.equivalences +open import foundation-core.function-types +open import foundation-core.homotopies +open import foundation-core.propositions +``` + +
+ +## Idea + +Given a family of [propositions](foundation-core.propositions.md) `B : A → 𝒰`, +then the dependent product `Π A B` is again a proposition. + +## Definitions + +### Products of families of propositions are propositions + +```agda +abstract + is-prop-Π : + {l1 l2 : Level} {A : UU l1} {B : A → UU l2} → + ((x : A) → is-prop (B x)) → is-prop ((x : A) → B x) + is-prop-Π H = + is-prop-is-proof-irrelevant + ( λ f → is-contr-Π (λ x → is-proof-irrelevant-is-prop (H x) (f x))) + +module _ + {l1 l2 : Level} (A : UU l1) (P : A → Prop l2) + where + + type-Π-Prop : UU (l1 ⊔ l2) + type-Π-Prop = (x : A) → type-Prop (P x) + + is-prop-Π-Prop : is-prop type-Π-Prop + is-prop-Π-Prop = is-prop-Π (λ x → is-prop-type-Prop (P x)) + + Π-Prop : Prop (l1 ⊔ l2) + pr1 Π-Prop = type-Π-Prop + pr2 Π-Prop = is-prop-Π-Prop +``` + +We now repeat the above for implicit Π-types. + +```agda +abstract + is-prop-implicit-Π : + {l1 l2 : Level} {A : UU l1} {B : A → UU l2} → + ((x : A) → is-prop (B x)) → is-prop ({x : A} → B x) + is-prop-implicit-Π H = + is-prop-equiv + ( ( λ f x → f {x}) , + ( is-equiv-is-invertible (λ g {x} → g x) (refl-htpy) (refl-htpy))) + ( is-prop-Π H) + +module _ + {l1 l2 : Level} (A : UU l1) (P : A → Prop l2) + where + + type-implicit-Π-Prop : UU (l1 ⊔ l2) + type-implicit-Π-Prop = {x : A} → type-Prop (P x) + + is-prop-implicit-Π-Prop : is-prop type-implicit-Π-Prop + is-prop-implicit-Π-Prop = + is-prop-implicit-Π (λ x → is-prop-type-Prop (P x)) + + implicit-Π-Prop : Prop (l1 ⊔ l2) + pr1 implicit-Π-Prop = type-implicit-Π-Prop + pr2 implicit-Π-Prop = is-prop-implicit-Π-Prop +``` + +### The type of functions into a proposition is a proposition + +```agda +abstract + is-prop-function-type : + {l1 l2 : Level} {A : UU l1} {B : UU l2} → + is-prop B → is-prop (A → B) + is-prop-function-type H = is-prop-Π (λ _ → H) + +type-function-Prop : + {l1 l2 : Level} → UU l1 → Prop l2 → UU (l1 ⊔ l2) +type-function-Prop A P = A → type-Prop P + +is-prop-function-Prop : + {l1 l2 : Level} {A : UU l1} (P : Prop l2) → + is-prop (type-function-Prop A P) +is-prop-function-Prop P = + is-prop-function-type (is-prop-type-Prop P) + +function-Prop : + {l1 l2 : Level} → UU l1 → Prop l2 → Prop (l1 ⊔ l2) +pr1 (function-Prop A P) = type-function-Prop A P +pr2 (function-Prop A P) = is-prop-function-Prop P + +type-hom-Prop : + {l1 l2 : Level} (P : Prop l1) (Q : Prop l2) → UU (l1 ⊔ l2) +type-hom-Prop P = type-function-Prop (type-Prop P) + +is-prop-hom-Prop : + {l1 l2 : Level} (P : Prop l1) (Q : Prop l2) → + is-prop (type-hom-Prop P Q) +is-prop-hom-Prop P = is-prop-function-Prop + +hom-Prop : + {l1 l2 : Level} → Prop l1 → Prop l2 → Prop (l1 ⊔ l2) +pr1 (hom-Prop P Q) = type-hom-Prop P Q +pr2 (hom-Prop P Q) = is-prop-hom-Prop P Q + +infixr 5 _⇒_ +_⇒_ = hom-Prop +``` + +### The type of equivalences between two propositions is a proposition + +```agda +module _ + {l1 l2 : Level} {A : UU l1} {B : UU l2} + where + + is-prop-equiv-is-prop : is-prop A → is-prop B → is-prop (A ≃ B) + is-prop-equiv-is-prop H K = + is-prop-Σ + ( is-prop-function-type K) + ( λ f → + is-prop-product + ( is-prop-Σ + ( is-prop-function-type H) + ( λ g → is-prop-is-contr (is-contr-Π (λ y → K (f (g y)) y)))) + ( is-prop-Σ + ( is-prop-function-type H) + ( λ h → is-prop-is-contr (is-contr-Π (λ x → H (h (f x)) x))))) + +type-equiv-Prop : + { l1 l2 : Level} (P : Prop l1) (Q : Prop l2) → UU (l1 ⊔ l2) +type-equiv-Prop P Q = (type-Prop P) ≃ (type-Prop Q) + +abstract + is-prop-type-equiv-Prop : + {l1 l2 : Level} (P : Prop l1) (Q : Prop l2) → + is-prop (type-equiv-Prop P Q) + is-prop-type-equiv-Prop P Q = + is-prop-equiv-is-prop (is-prop-type-Prop P) (is-prop-type-Prop Q) + +equiv-Prop : + { l1 l2 : Level} → Prop l1 → Prop l2 → Prop (l1 ⊔ l2) +pr1 (equiv-Prop P Q) = type-equiv-Prop P Q +pr2 (equiv-Prop P Q) = is-prop-type-equiv-Prop P Q +``` + +### A type is a proposition if and only if the type of its endomaps is contractible + +```agda +abstract + is-contr-endomaps-is-prop : + {l : Level} (P : UU l) → is-prop P → is-contr (P → P) + is-contr-endomaps-is-prop P is-prop-P = + is-proof-irrelevant-is-prop (is-prop-function-type is-prop-P) id +``` + +### Being a proposition is a proposition + +```agda +abstract + is-prop-is-prop : + {l : Level} (A : UU l) → is-prop (is-prop A) + is-prop-is-prop A = is-prop-Π (λ x → is-prop-Π (λ y → is-property-is-contr)) + +is-prop-Prop : {l : Level} (A : UU l) → Prop l +pr1 (is-prop-Prop A) = is-prop A +pr2 (is-prop-Prop A) = is-prop-is-prop A +``` + +## See also + +### Operations on propositions + +There is a wide range of operations on propositions due to the rich structure of +intuitionistic logic. Below we give a structured overview of a notable selection +of such operations and their notation in the library. + +The list is split into two sections, the first consists of operations that +generalize to arbitrary types and even sufficiently nice +[subuniverses](foundation.subuniverses.md), such as +$n$-[types](foundation-core.truncated-types.md). + +| Name | Operator on types | Operator on propositions/subtypes | +| ----------------------------------------------------------- | ----------------- | --------------------------------- | +| [Dependent sum](foundation.dependent-pair-types.md) | `Σ` | `Σ-Prop` | +| [Dependent product](foundation.dependent-function-types.md) | `Π` | `Π-Prop` | +| [Functions](foundation-core.function-types.md) | `→` | `⇒` | +| [Logical equivalence](foundation.logical-equivalences.md) | `↔` | `⇔` | +| [Product](foundation-core.cartesian-product-types.md) | `×` | `product-Prop` | +| [Join](synthetic-homotopy-theory.joins-of-types.md) | `*` | `join-Prop` | +| [Exclusive sum](foundation.exclusive-sum.md) | `exclusive-sum` | `exclusive-sum-Prop` | +| [Coproduct](foundation-core.coproduct-types.md) | `+` | _N/A_ | + +Note that for many operations in the second section, there is an equivalent +operation on propositions in the first. + +| Name | Operator on types | Operator on propositions/subtypes | +| ---------------------------------------------------------------------------- | --------------------------- | ---------------------------------------- | +| [Initial object](foundation-core.empty-types.md) | `empty` | `empty-Prop` | +| [Terminal object](foundation.unit-type.md) | `unit` | `unit-Prop` | +| [Existential quantification](foundation.existential-quantification.md) | `exists-structure` | `∃` | +| [Unique existential quantification](foundation.uniqueness-quantification.md) | `uniquely-exists-structure` | `∃!` | +| [Universal quantification](foundation.universal-quantification.md) | | `∀'` (equivalent to `Π-Prop`) | +| [Conjunction](foundation.conjunction.md) | | `∧` (equivalent to `product-Prop`) | +| [Disjunction](foundation.disjunction.md) | `disjunction-type` | `∨` (equivalent to `join-Prop`) | +| [Exclusive disjunction](foundation.exclusive-disjunction.md) | `xor-type` | `⊻` (equivalent to `exclusive-sum-Prop`) | +| [Negation](foundation.negation.md) | `¬` | `¬'` | +| [Double negation](foundation.double-negation.md) | `¬¬` | `¬¬'` | + +We can also organize these operations by indexed and binary variants, giving us +the following table: + +| Name | Binary | Indexed | +| ---------------------- | ------ | ------- | +| Product | `×` | `Π` | +| Conjunction | `∧` | `∀'` | +| Constructive existence | `+` | `Σ` | +| Existence | `∨` | `∃` | +| Unique existence | `⊻` | `∃!` | + +### Table of files about propositional logic + +The following table gives an overview of basic constructions in propositional +logic and related considerations. + +{{#include tables/propositional-logic.md}} diff --git a/src/foundation/dependent-products-pullbacks.lagda.md b/src/foundation/dependent-products-pullbacks.lagda.md index 7c429ce124..b74f931063 100644 --- a/src/foundation/dependent-products-pullbacks.lagda.md +++ b/src/foundation/dependent-products-pullbacks.lagda.md @@ -1,27 +1,33 @@ # Dependent products of pullbacks ```agda -module foundation.dependent-products-pullbacks where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.dependent-products-pullbacks + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda -open import foundation.cones-over-cospan-diagrams +open import foundation.cones-over-cospan-diagrams funext open import foundation.dependent-pair-types -open import foundation.function-extensionality -open import foundation.functoriality-dependent-function-types -open import foundation.identity-types -open import foundation.standard-pullbacks +open import foundation.function-extensionality funext +open import foundation.functoriality-dependent-function-types funext univalence +open import foundation.identity-types funext +open import foundation.standard-pullbacks funext open import foundation.universe-levels open import foundation-core.equivalences open import foundation-core.function-types open import foundation-core.homotopies -open import foundation-core.pullbacks +open import foundation-core.pullbacks funext open import foundation-core.retractions open import foundation-core.sections -open import foundation-core.universal-property-pullbacks +open import foundation-core.universal-property-pullbacks funext ```
diff --git a/src/foundation/dependent-products-truncated-types.lagda.md b/src/foundation/dependent-products-truncated-types.lagda.md new file mode 100644 index 0000000000..ec2bcb4371 --- /dev/null +++ b/src/foundation/dependent-products-truncated-types.lagda.md @@ -0,0 +1,193 @@ +# Dependent products truncated types + +```agda +open import foundation.function-extensionality-axiom + +module foundation.dependent-products-truncated-types + (funext : function-extensionality) + where +``` + +
Imports + +```agda +open import foundation.action-on-identifications-dependent-functions +open import foundation.action-on-identifications-functions +open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types funext +open import foundation.equality-cartesian-product-types +open import foundation.function-extensionality funext +open import foundation.universe-levels + +open import foundation-core.cartesian-product-types +open import foundation-core.contractible-types +open import foundation-core.embeddings +open import foundation-core.equality-dependent-pair-types +open import foundation-core.equivalences +open import foundation-core.homotopies +open import foundation-core.identity-types +open import foundation-core.propositions +open import foundation-core.retracts-of-types +open import foundation-core.transport-along-identifications +open import foundation-core.truncated-types +open import foundation-core.truncation-levels +``` + +
+ +## Idea + +Given a family of $n$-[truncated](foundation-core.truncated-types.md) +`B : A → 𝒰`, then the dependent product `Π A B` is again $n$-truncated. + +## Properties + +### Products of families of truncated types are truncated + +```agda +abstract + is-trunc-Π : + {l1 l2 : Level} (k : 𝕋) {A : UU l1} {B : A → UU l2} → + ((x : A) → is-trunc k (B x)) → is-trunc k ((x : A) → B x) + is-trunc-Π neg-two-𝕋 is-trunc-B = is-contr-Π is-trunc-B + is-trunc-Π (succ-𝕋 k) is-trunc-B f g = + is-trunc-is-equiv k (f ~ g) htpy-eq + ( funext f g) + ( is-trunc-Π k (λ x → is-trunc-B x (f x) (g x))) + +type-Π-Truncated-Type' : + (k : 𝕋) {l1 l2 : Level} (A : UU l1) (B : A → Truncated-Type l2 k) → + UU (l1 ⊔ l2) +type-Π-Truncated-Type' k A B = (x : A) → type-Truncated-Type (B x) + +is-trunc-type-Π-Truncated-Type' : + (k : 𝕋) {l1 l2 : Level} (A : UU l1) (B : A → Truncated-Type l2 k) → + is-trunc k (type-Π-Truncated-Type' k A B) +is-trunc-type-Π-Truncated-Type' k A B = + is-trunc-Π k (λ x → is-trunc-type-Truncated-Type (B x)) + +Π-Truncated-Type' : + (k : 𝕋) {l1 l2 : Level} (A : UU l1) (B : A → Truncated-Type l2 k) → + Truncated-Type (l1 ⊔ l2) k +pr1 (Π-Truncated-Type' k A B) = type-Π-Truncated-Type' k A B +pr2 (Π-Truncated-Type' k A B) = is-trunc-type-Π-Truncated-Type' k A B + +type-Π-Truncated-Type : + (k : 𝕋) {l1 l2 : Level} (A : Truncated-Type l1 k) + (B : type-Truncated-Type A → Truncated-Type l2 k) → + UU (l1 ⊔ l2) +type-Π-Truncated-Type k A B = + type-Π-Truncated-Type' k (type-Truncated-Type A) B + +is-trunc-type-Π-Truncated-Type : + (k : 𝕋) {l1 l2 : Level} (A : Truncated-Type l1 k) + (B : type-Truncated-Type A → Truncated-Type l2 k) → + is-trunc k (type-Π-Truncated-Type k A B) +is-trunc-type-Π-Truncated-Type k A B = + is-trunc-type-Π-Truncated-Type' k (type-Truncated-Type A) B + +Π-Truncated-Type : + (k : 𝕋) {l1 l2 : Level} (A : Truncated-Type l1 k) + (B : type-Truncated-Type A → Truncated-Type l2 k) → + Truncated-Type (l1 ⊔ l2) k +Π-Truncated-Type k A B = + Π-Truncated-Type' k (type-Truncated-Type A) B +``` + +### The type of functions into a truncated type is truncated + +```agda +abstract + is-trunc-function-type : + {l1 l2 : Level} (k : 𝕋) {A : UU l1} {B : UU l2} → + is-trunc k B → is-trunc k (A → B) + is-trunc-function-type k {A} {B} is-trunc-B = + is-trunc-Π k {B = λ (x : A) → B} (λ x → is-trunc-B) + +function-type-Truncated-Type : + {l1 l2 : Level} {k : 𝕋} (A : UU l1) (B : Truncated-Type l2 k) → + Truncated-Type (l1 ⊔ l2) k +pr1 (function-type-Truncated-Type A B) = A → type-Truncated-Type B +pr2 (function-type-Truncated-Type A B) = + is-trunc-function-type _ (is-trunc-type-Truncated-Type B) + +type-hom-Truncated-Type : + (k : 𝕋) {l1 l2 : Level} (A : Truncated-Type l1 k) + (B : Truncated-Type l2 k) → UU (l1 ⊔ l2) +type-hom-Truncated-Type k A B = + type-Truncated-Type A → type-Truncated-Type B + +is-trunc-type-hom-Truncated-Type : + (k : 𝕋) {l1 l2 : Level} (A : Truncated-Type l1 k) + (B : Truncated-Type l2 k) → + is-trunc k (type-hom-Truncated-Type k A B) +is-trunc-type-hom-Truncated-Type k A B = + is-trunc-function-type k (is-trunc-type-Truncated-Type B) + +hom-Truncated-Type : + (k : 𝕋) {l1 l2 : Level} (A : Truncated-Type l1 k) + (B : Truncated-Type l2 k) → Truncated-Type (l1 ⊔ l2) k +pr1 (hom-Truncated-Type k A B) = type-hom-Truncated-Type k A B +pr2 (hom-Truncated-Type k A B) = is-trunc-type-hom-Truncated-Type k A B +``` + +### Being truncated is a property + +```agda +abstract + is-prop-is-trunc : + {l : Level} (k : 𝕋) (A : UU l) → is-prop (is-trunc k A) + is-prop-is-trunc neg-two-𝕋 A = is-property-is-contr + is-prop-is-trunc (succ-𝕋 k) A = + is-trunc-Π neg-one-𝕋 + ( λ x → is-trunc-Π neg-one-𝕋 (λ y → is-prop-is-trunc k (x ＝ y))) + +is-trunc-Prop : {l : Level} (k : 𝕋) (A : UU l) → Σ (UU l) (is-trunc neg-one-𝕋) +pr1 (is-trunc-Prop k A) = is-trunc k A +pr2 (is-trunc-Prop k A) = is-prop-is-trunc k A +``` + +### The type of equivalences between truncated types is truncated + +```agda +module _ + {l1 l2 : Level} {A : UU l1} {B : UU l2} + where + + is-trunc-equiv-is-trunc : + (k : 𝕋) → is-trunc k A → is-trunc k B → is-trunc k (A ≃ B) + is-trunc-equiv-is-trunc k H K = + is-trunc-Σ + ( is-trunc-function-type k K) + ( λ f → + is-trunc-Σ + ( is-trunc-Σ + ( is-trunc-function-type k H) + ( λ g → + is-trunc-Π k (λ y → is-trunc-Id K (f (g y)) y))) + ( λ _ → + is-trunc-Σ + ( is-trunc-function-type k H) + ( λ h → + is-trunc-Π k (λ x → is-trunc-Id H (h (f x)) x)))) + +type-equiv-Truncated-Type : + {l1 l2 : Level} {k : 𝕋} (A : Truncated-Type l1 k) (B : Truncated-Type l2 k) → + UU (l1 ⊔ l2) +type-equiv-Truncated-Type A B = + type-Truncated-Type A ≃ type-Truncated-Type B + +is-trunc-type-equiv-Truncated-Type : + {l1 l2 : Level} {k : 𝕋} (A : Truncated-Type l1 k) (B : Truncated-Type l2 k) → + is-trunc k (type-equiv-Truncated-Type A B) +is-trunc-type-equiv-Truncated-Type A B = + is-trunc-equiv-is-trunc _ + ( is-trunc-type-Truncated-Type A) + ( is-trunc-type-Truncated-Type B) + +equiv-Truncated-Type : + {l1 l2 : Level} {k : 𝕋} (A : Truncated-Type l1 k) (B : Truncated-Type l2 k) → + Truncated-Type (l1 ⊔ l2) k +pr1 (equiv-Truncated-Type A B) = type-equiv-Truncated-Type A B +pr2 (equiv-Truncated-Type A B) = is-trunc-type-equiv-Truncated-Type A B +``` diff --git a/src/foundation/dependent-sums-pullbacks.lagda.md b/src/foundation/dependent-sums-pullbacks.lagda.md index c1f09588ee..77a8756c05 100644 --- a/src/foundation/dependent-sums-pullbacks.lagda.md +++ b/src/foundation/dependent-sums-pullbacks.lagda.md @@ -1,17 +1,21 @@ # Dependent sums of pullbacks ```agda -module foundation.dependent-sums-pullbacks where +open import foundation.function-extensionality-axiom + +module foundation.dependent-sums-pullbacks + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cones-over-cospan-diagrams +open import foundation.cones-over-cospan-diagrams funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.identity-types -open import foundation.standard-pullbacks +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.standard-pullbacks funext open import foundation.transport-along-identifications open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels @@ -21,10 +25,10 @@ open import foundation-core.families-of-equivalences open import foundation-core.function-types open import foundation-core.functoriality-dependent-pair-types open import foundation-core.homotopies -open import foundation-core.pullbacks +open import foundation-core.pullbacks funext open import foundation-core.retractions open import foundation-core.sections -open import foundation-core.universal-property-pullbacks +open import foundation-core.universal-property-pullbacks funext ```
diff --git a/src/foundation/dependent-universal-property-equivalences.lagda.md b/src/foundation/dependent-universal-property-equivalences.lagda.md index f9a041351b..b5e64b90fd 100644 --- a/src/foundation/dependent-universal-property-equivalences.lagda.md +++ b/src/foundation/dependent-universal-property-equivalences.lagda.md @@ -1,7 +1,11 @@ # The dependent universal property of equivalences ```agda -module foundation.dependent-universal-property-equivalences where +open import foundation.function-extensionality-axiom + +module foundation.dependent-universal-property-equivalences + (funext : function-extensionality) + where ```
Imports @@ -10,7 +14,7 @@ module foundation.dependent-universal-property-equivalences where open import foundation.action-on-identifications-dependent-functions open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-extensionality +open import foundation.function-extensionality funext open import foundation.universe-levels open import foundation-core.coherently-invertible-maps diff --git a/src/foundation/descent-coproduct-types.lagda.md b/src/foundation/descent-coproduct-types.lagda.md index 03c1a582ba..a195c3bb42 100644 --- a/src/foundation/descent-coproduct-types.lagda.md +++ b/src/foundation/descent-coproduct-types.lagda.md @@ -2,20 +2,27 @@ ```agda {-# OPTIONS --lossy-unification #-} +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom -module foundation.descent-coproduct-types where +module foundation.descent-coproduct-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cones-over-cospan-diagrams +open import foundation.cones-over-cospan-diagrams funext open import foundation.dependent-pair-types -open import foundation.functoriality-coproduct-types -open import foundation.functoriality-fibers-of-maps +open import foundation.functoriality-coproduct-types funext univalence truncations +open import foundation.functoriality-fibers-of-maps funext open import foundation.universe-levels -open import foundation.whiskering-identifications-concatenation +open import foundation.whiskering-identifications-concatenation funext open import foundation-core.coproduct-types open import foundation-core.equality-dependent-pair-types @@ -24,7 +31,7 @@ open import foundation-core.families-of-equivalences open import foundation-core.function-types open import foundation-core.homotopies open import foundation-core.identity-types -open import foundation-core.pullbacks +open import foundation-core.pullbacks funext ```
diff --git a/src/foundation/descent-dependent-pair-types.lagda.md b/src/foundation/descent-dependent-pair-types.lagda.md index 9f3cdfc133..989df65f19 100644 --- a/src/foundation/descent-dependent-pair-types.lagda.md +++ b/src/foundation/descent-dependent-pair-types.lagda.md @@ -1,15 +1,19 @@ # Descent for dependent pair types ```agda -module foundation.descent-dependent-pair-types where +open import foundation.function-extensionality-axiom + +module foundation.descent-dependent-pair-types + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cones-over-cospan-diagrams +open import foundation.cones-over-cospan-diagrams funext open import foundation.dependent-pair-types -open import foundation.functoriality-fibers-of-maps +open import foundation.functoriality-fibers-of-maps funext open import foundation.universe-levels open import foundation-core.equivalences @@ -17,7 +21,7 @@ open import foundation-core.function-types open import foundation-core.functoriality-dependent-pair-types open import foundation-core.homotopies open import foundation-core.identity-types -open import foundation-core.pullbacks +open import foundation-core.pullbacks funext ```
diff --git a/src/foundation/descent-empty-types.lagda.md b/src/foundation/descent-empty-types.lagda.md index ca408517a6..4491b99492 100644 --- a/src/foundation/descent-empty-types.lagda.md +++ b/src/foundation/descent-empty-types.lagda.md @@ -1,18 +1,22 @@ # Descent for the empty type ```agda -module foundation.descent-empty-types where +open import foundation.function-extensionality-axiom + +module foundation.descent-empty-types + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cones-over-cospan-diagrams +open import foundation.cones-over-cospan-diagrams funext open import foundation.dependent-pair-types open import foundation.universe-levels open import foundation-core.empty-types -open import foundation-core.pullbacks +open import foundation-core.pullbacks funext ```
diff --git a/src/foundation/descent-equivalences.lagda.md b/src/foundation/descent-equivalences.lagda.md index 2a2da46991..56c3fca5d4 100644 --- a/src/foundation/descent-equivalences.lagda.md +++ b/src/foundation/descent-equivalences.lagda.md @@ -1,20 +1,24 @@ # Descent for equivalences ```agda -module foundation.descent-equivalences where +open import foundation.function-extensionality-axiom + +module foundation.descent-equivalences + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cones-over-cospan-diagrams -open import foundation.dependent-universal-property-equivalences -open import foundation.equivalences -open import foundation.functoriality-fibers-of-maps +open import foundation.cones-over-cospan-diagrams funext +open import foundation.dependent-universal-property-equivalences funext +open import foundation.equivalences funext +open import foundation.functoriality-fibers-of-maps funext open import foundation.universe-levels open import foundation-core.function-types -open import foundation-core.pullbacks +open import foundation-core.pullbacks funext ```
diff --git a/src/foundation/diaconescus-theorem.lagda.md b/src/foundation/diaconescus-theorem.lagda.md index adcacce8cc..e31f0b767f 100644 --- a/src/foundation/diaconescus-theorem.lagda.md +++ b/src/foundation/diaconescus-theorem.lagda.md @@ -1,30 +1,39 @@ # Diaconescu's theorem ```agda -module foundation.diaconescus-theorem where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.diaconescus-theorem + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.axiom-of-choice -open import foundation.booleans -open import foundation.decidable-propositions -open import foundation.decidable-types +open import foundation.axiom-of-choice funext univalence truncations +open import foundation.booleans funext univalence truncations +open import foundation.decidable-propositions funext univalence truncations +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.law-of-excluded-middle -open import foundation.logical-equivalences -open import foundation.propositional-truncations -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.law-of-excluded-middle funext univalence truncations +open import foundation.logical-equivalences funext +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence open import foundation.universe-levels open import foundation-core.fibers-of-maps open import foundation-core.function-types open import foundation-core.identity-types -open import synthetic-homotopy-theory.suspensions-of-propositions -open import synthetic-homotopy-theory.suspensions-of-types +open import synthetic-homotopy-theory.suspensions-of-propositions funext univalence truncations +open import synthetic-homotopy-theory.suspensions-of-types funext univalence truncations ```
@@ -44,8 +53,8 @@ We follow the proof given under Theorem 10.1.14 in {{#cite UF13}}. [suspension](synthetic-homotopy-theory.suspensions-of-propositions.md) `ΣP` is a [set](foundation-core.sets.md) with the property that `(N ＝ S) ≃ ΣP`, where `N` and `S` are the _poles_ of `ΣP`. There is a surjection from the -[booleans](foundation.booleans.md) onto the suspension `f : bool ↠ ΣP` such that -`f true ≐ N` and `f false ≐ S`. Its +[booleans](foundation-core.booleans.md) onto the suspension `f : bool ↠ ΣP` such +that `f true ≐ N` and `f false ≐ S`. Its [fiber family](foundation-core.fibers-of-maps.md) is in other words an [inhabited](foundation.inhabited-types.md) family over `ΣP`. Applying the axiom of choice to this family, we obtain a diff --git a/src/foundation/diagonal-maps-cartesian-products-of-types.lagda.md b/src/foundation/diagonal-maps-cartesian-products-of-types.lagda.md index 06fe26c051..8dee3f4574 100644 --- a/src/foundation/diagonal-maps-cartesian-products-of-types.lagda.md +++ b/src/foundation/diagonal-maps-cartesian-products-of-types.lagda.md @@ -1,7 +1,13 @@ # Diagonal maps into cartesian products of types ```agda -module foundation.diagonal-maps-cartesian-products-of-types where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.diagonal-maps-cartesian-products-of-types + (funext : function-extensionality) + (univalence : univalence-axiom) + where open import foundation-core.diagonal-maps-cartesian-products-of-types public ``` @@ -9,12 +15,12 @@ open import foundation-core.diagonal-maps-cartesian-products-of-types public
Imports ```agda -open import foundation.0-maps +open import foundation.0-maps funext open import foundation.dependent-pair-types -open import foundation.faithful-maps +open import foundation.faithful-maps funext open import foundation.universe-levels -open import foundation-core.1-types +open import foundation-core.1-types funext univalence open import foundation-core.cartesian-product-types open import foundation-core.contractible-maps open import foundation-core.embeddings @@ -23,7 +29,7 @@ open import foundation-core.identity-types open import foundation-core.propositional-maps open import foundation-core.propositions open import foundation-core.sets -open import foundation-core.truncated-maps +open import foundation-core.truncated-maps funext open import foundation-core.truncated-types open import foundation-core.truncation-levels ``` diff --git a/src/foundation/diagonal-maps-of-types.lagda.md b/src/foundation/diagonal-maps-of-types.lagda.md index b4a0135888..ca694fab0f 100644 --- a/src/foundation/diagonal-maps-of-types.lagda.md +++ b/src/foundation/diagonal-maps-of-types.lagda.md @@ -1,7 +1,13 @@ # Diagonal maps of types ```agda -module foundation.diagonal-maps-of-types where +open import foundation.function-extensionality-axiom + +module foundation.diagonal-maps-of-types + (funext : function-extensionality) + where + +open import foundation-core.diagonal-maps-of-types public ```
Imports @@ -9,26 +15,18 @@ module foundation.diagonal-maps-of-types where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equality-cartesian-product-types -open import foundation.function-extensionality -open import foundation.functoriality-dependent-pair-types -open import foundation.morphisms-arrows -open import foundation.postcomposition-functions -open import foundation.retracts-of-types -open import foundation.transposition-identifications-along-equivalences +open import foundation.function-extensionality funext +open import foundation.transposition-identifications-along-equivalences funext open import foundation.universe-levels -open import foundation-core.cartesian-product-types open import foundation-core.constant-maps open import foundation-core.equivalences open import foundation-core.fibers-of-maps open import foundation-core.function-types +open import foundation-core.functoriality-dependent-pair-types open import foundation-core.homotopies open import foundation-core.identity-types open import foundation-core.injective-maps -open import foundation-core.propositions -open import foundation-core.retractions -open import foundation-core.sections ```
@@ -40,52 +38,8 @@ The of a type `A` is the map that includes the points of `A` into the exponential `X → A`. -## Definitions - -```agda -module _ - {l1 l2 : Level} (A : UU l1) (X : UU l2) - where - - diagonal-exponential : A → X → A - diagonal-exponential = const X -``` - ## Properties -### The action on identifications of a diagonal map is another diagonal map - -```agda -module _ - {l1 l2 : Level} {A : UU l1} (x y : A) (B : UU l2) - where - - htpy-diagonal-exponential-Id-ap-diagonal-exponential-htpy-eq : - htpy-eq ∘ ap (diagonal-exponential A B) ~ diagonal-exponential (x ＝ y) B - htpy-diagonal-exponential-Id-ap-diagonal-exponential-htpy-eq refl = refl - - htpy-ap-diagonal-exponential-htpy-eq-diagonal-exponential-Id : - diagonal-exponential (x ＝ y) B ~ htpy-eq ∘ ap (diagonal-exponential A B) - htpy-ap-diagonal-exponential-htpy-eq-diagonal-exponential-Id = - inv-htpy htpy-diagonal-exponential-Id-ap-diagonal-exponential-htpy-eq -``` - -### Given an element of the exponent the diagonal map is injective - -```agda -module _ - {l1 l2 : Level} (A : UU l1) (B : UU l2) (b : B) - where - - is-injective-diagonal-exponential : - is-injective (diagonal-exponential A B) - is-injective-diagonal-exponential p = htpy-eq p b - - diagonal-exponential-injection : injection A (B → A) - pr1 diagonal-exponential-injection = diagonal-exponential A B - pr2 diagonal-exponential-injection = is-injective-diagonal-exponential -``` - ### The action on identifications of an (exponential) diagonal is a diagonal ```agda @@ -93,21 +47,12 @@ module _ {l1 l2 : Level} (A : UU l1) {B : UU l2} (x y : B) where - compute-htpy-eq-ap-diagonal-exponential : - htpy-eq ∘ ap (diagonal-exponential B A) ~ diagonal-exponential (x ＝ y) A - compute-htpy-eq-ap-diagonal-exponential refl = refl - - inv-compute-htpy-eq-ap-diagonal-exponential : - diagonal-exponential (x ＝ y) A ~ htpy-eq ∘ ap (diagonal-exponential B A) - inv-compute-htpy-eq-ap-diagonal-exponential = - inv-htpy compute-htpy-eq-ap-diagonal-exponential - compute-eq-htpy-ap-diagonal-exponential : ap (diagonal-exponential B A) ~ eq-htpy ∘ diagonal-exponential (x ＝ y) A compute-eq-htpy-ap-diagonal-exponential p = map-eq-transpose-equiv ( equiv-funext) - ( compute-htpy-eq-ap-diagonal-exponential p) + ( compute-htpy-eq-ap-diagonal-exponential A x y p) ``` ### Computing the fibers of diagonal maps diff --git a/src/foundation/diagonal-span-diagrams.lagda.md b/src/foundation/diagonal-span-diagrams.lagda.md index bde07d12e9..d333772cbc 100644 --- a/src/foundation/diagonal-span-diagrams.lagda.md +++ b/src/foundation/diagonal-span-diagrams.lagda.md @@ -1,13 +1,17 @@ # Diagonal span diagrams ```agda -module foundation.diagonal-span-diagrams where +open import foundation.function-extensionality-axiom + +module foundation.diagonal-span-diagrams + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.span-diagrams +open import foundation.span-diagrams funext open import foundation.universe-levels ``` diff --git a/src/foundation/diagonals-of-maps.lagda.md b/src/foundation/diagonals-of-maps.lagda.md index a965e62bc4..c9c0313c21 100644 --- a/src/foundation/diagonals-of-maps.lagda.md +++ b/src/foundation/diagonals-of-maps.lagda.md @@ -1,7 +1,11 @@ # Diagonals of maps ```agda -module foundation.diagonals-of-maps where +open import foundation.function-extensionality-axiom + +module foundation.diagonals-of-maps + (funext : function-extensionality) + where ```
Imports @@ -9,8 +13,8 @@ module foundation.diagonals-of-maps where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equality-fibers-of-maps -open import foundation.standard-pullbacks +open import foundation.equality-fibers-of-maps funext +open import foundation.standard-pullbacks funext open import foundation.universe-levels open import foundation-core.contractible-maps @@ -23,7 +27,7 @@ open import foundation-core.identity-types open import foundation-core.propositional-maps open import foundation-core.retractions open import foundation-core.sections -open import foundation-core.truncated-maps +open import foundation-core.truncated-maps funext open import foundation-core.truncated-types open import foundation-core.truncation-levels ``` diff --git a/src/foundation/discrete-binary-relations.lagda.md b/src/foundation/discrete-binary-relations.lagda.md index 9edf7ffd3f..21d7a9d8b8 100644 --- a/src/foundation/discrete-binary-relations.lagda.md +++ b/src/foundation/discrete-binary-relations.lagda.md @@ -1,15 +1,24 @@ # Discrete binary relations ```agda -module foundation.discrete-binary-relations where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.discrete-binary-relations + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.binary-relations -open import foundation.empty-types -open import foundation.propositions +open import foundation.binary-relations funext univalence truncations +open import foundation.dependent-products-propositions funext +open import foundation.empty-types funext univalence truncations +open import foundation.propositions funext univalence open import foundation.universe-levels ``` diff --git a/src/foundation/discrete-reflexive-relations.lagda.md b/src/foundation/discrete-reflexive-relations.lagda.md index 236e380874..e84c32d4d6 100644 --- a/src/foundation/discrete-reflexive-relations.lagda.md +++ b/src/foundation/discrete-reflexive-relations.lagda.md @@ -1,17 +1,27 @@ # Discrete reflexive relations ```agda -module foundation.discrete-reflexive-relations where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.discrete-reflexive-relations + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.binary-relations -open import foundation.contractible-types +open import foundation.binary-relations funext univalence truncations +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.reflexive-relations -open import foundation.torsorial-type-families +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.reflexive-relations funext univalence truncations +open import foundation.torsorial-type-families funext univalence truncations open import foundation.universe-levels open import foundation-core.identity-types diff --git a/src/foundation/discrete-relaxed-sigma-decompositions.lagda.md b/src/foundation/discrete-relaxed-sigma-decompositions.lagda.md index 76cdac43a7..901ec6d697 100644 --- a/src/foundation/discrete-relaxed-sigma-decompositions.lagda.md +++ b/src/foundation/discrete-relaxed-sigma-decompositions.lagda.md @@ -1,17 +1,26 @@ # Discrete relaxed Σ-decompositions ```agda -module foundation.discrete-relaxed-sigma-decompositions where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.discrete-relaxed-sigma-decompositions + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.contractible-types +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.relaxed-sigma-decompositions +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.raising-universe-levels-unit-type +open import foundation.relaxed-sigma-decompositions funext univalence open import foundation.type-arithmetic-dependent-pair-types open import foundation.unit-type open import foundation.universe-levels @@ -20,7 +29,7 @@ open import foundation-core.equality-dependent-pair-types open import foundation-core.function-types open import foundation-core.identity-types open import foundation-core.propositions -open import foundation-core.subtypes +open import foundation-core.subtypes funext ```
diff --git a/src/foundation/discrete-sigma-decompositions.lagda.md b/src/foundation/discrete-sigma-decompositions.lagda.md index 3ed376b244..e464b8522e 100644 --- a/src/foundation/discrete-sigma-decompositions.lagda.md +++ b/src/foundation/discrete-sigma-decompositions.lagda.md @@ -1,18 +1,29 @@ # Discrete Σ-decompositions ```agda -module foundation.discrete-sigma-decompositions where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.discrete-sigma-decompositions + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.contractible-types +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.propositional-truncations -open import foundation.sigma-decompositions +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.propositional-truncations funext univalence +open import foundation.raising-universe-levels-unit-type +open import foundation.sigma-decompositions funext univalence truncations open import foundation.type-arithmetic-dependent-pair-types open import foundation.unit-type open import foundation.universe-levels @@ -21,7 +32,7 @@ open import foundation-core.equality-dependent-pair-types open import foundation-core.function-types open import foundation-core.identity-types open import foundation-core.propositions -open import foundation-core.subtypes +open import foundation-core.subtypes funext ```
diff --git a/src/foundation/discrete-types.lagda.md b/src/foundation/discrete-types.lagda.md index 9f52a992b4..682995c154 100644 --- a/src/foundation/discrete-types.lagda.md +++ b/src/foundation/discrete-types.lagda.md @@ -1,21 +1,29 @@ # Discrete types ```agda -module foundation.discrete-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.discrete-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where -open import foundation-core.discrete-types public +open import foundation-core.discrete-types funext univalence truncations public ```
Imports ```agda -open import foundation.apartness-relations -open import foundation.binary-relations -open import foundation.decidable-types +open import foundation.apartness-relations funext univalence truncations +open import foundation.binary-relations funext univalence truncations +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.negation -open import foundation.propositional-truncations -open import foundation.tight-apartness-relations +open import foundation.negation funext +open import foundation.propositional-truncations funext univalence +open import foundation.tight-apartness-relations funext univalence truncations open import foundation.universe-levels open import foundation-core.coproduct-types diff --git a/src/foundation/disjoint-subtypes.lagda.md b/src/foundation/disjoint-subtypes.lagda.md index e21739bbd5..513bab84e9 100644 --- a/src/foundation/disjoint-subtypes.lagda.md +++ b/src/foundation/disjoint-subtypes.lagda.md @@ -1,18 +1,26 @@ # Disjoint subtypes ```agda -module foundation.disjoint-subtypes where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.disjoint-subtypes + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.intersections-subtypes -open import foundation.propositions -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.empty-types funext univalence truncations +open import foundation.propositions funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels ``` diff --git a/src/foundation/disjunction.lagda.md b/src/foundation/disjunction.lagda.md index 21a764be49..73c12b69d3 100644 --- a/src/foundation/disjunction.lagda.md +++ b/src/foundation/disjunction.lagda.md @@ -1,23 +1,31 @@ # Disjunction ```agda -module foundation.disjunction where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.disjunction + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.decidable-types +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.functoriality-coproduct-types -open import foundation.inhabited-types -open import foundation.logical-equivalences -open import foundation.propositional-truncations +open import foundation.functoriality-coproduct-types funext univalence truncations +open import foundation.inhabited-types funext univalence truncations +open import foundation.logical-equivalences funext +open import foundation.propositional-truncations funext univalence open import foundation.universe-levels open import foundation-core.cartesian-product-types open import foundation-core.coproduct-types -open import foundation-core.decidable-propositions +open import foundation-core.decidable-propositions funext univalence truncations open import foundation-core.empty-types open import foundation-core.equivalences open import foundation-core.function-types diff --git a/src/foundation/double-arrows.lagda.md b/src/foundation/double-arrows.lagda.md index aac5db2de6..a6c2d5afe3 100644 --- a/src/foundation/double-arrows.lagda.md +++ b/src/foundation/double-arrows.lagda.md @@ -7,9 +7,10 @@ module foundation.double-arrows where
Imports ```agda -open import foundation.cartesian-product-types open import foundation.dependent-pair-types open import foundation.universe-levels + +open import foundation-core.cartesian-product-types ```
diff --git a/src/foundation/double-negation-modality.lagda.md b/src/foundation/double-negation-modality.lagda.md index 89f91c3ee0..718999685d 100644 --- a/src/foundation/double-negation-modality.lagda.md +++ b/src/foundation/double-negation-modality.lagda.md @@ -1,32 +1,41 @@ # The double negation modality ```agda -module foundation.double-negation-modality where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.double-negation-modality + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.double-negation -open import foundation.empty-types -open import foundation.logical-equivalences -open import foundation.negation -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.double-negation funext univalence truncations +open import foundation.empty-types funext univalence truncations +open import foundation.logical-equivalences funext +open import foundation.negation funext +open import foundation.propositions funext univalence open import foundation.unit-type open import foundation.universe-levels open import foundation-core.function-types open import foundation-core.transport-along-identifications -open import logic.double-negation-elimination +open import logic.double-negation-elimination funext univalence truncations -open import orthogonal-factorization-systems.continuation-modalities -open import orthogonal-factorization-systems.large-lawvere-tierney-topologies -open import orthogonal-factorization-systems.lawvere-tierney-topologies -open import orthogonal-factorization-systems.modal-operators -open import orthogonal-factorization-systems.types-local-at-maps -open import orthogonal-factorization-systems.uniquely-eliminating-modalities +open import orthogonal-factorization-systems.continuation-modalities funext univalence truncations +open import orthogonal-factorization-systems.large-lawvere-tierney-topologies funext univalence truncations +open import orthogonal-factorization-systems.lawvere-tierney-topologies funext univalence truncations +open import orthogonal-factorization-systems.modal-operators funext univalence truncations +open import orthogonal-factorization-systems.types-local-at-maps funext univalence truncations +open import orthogonal-factorization-systems.uniquely-eliminating-modalities funext univalence truncations ```
diff --git a/src/foundation/double-negation-stable-equality.lagda.md b/src/foundation/double-negation-stable-equality.lagda.md index 8917c7da41..4b2575d3d4 100644 --- a/src/foundation/double-negation-stable-equality.lagda.md +++ b/src/foundation/double-negation-stable-equality.lagda.md @@ -1,7 +1,15 @@ # Double negation stable equality ```agda -module foundation.double-negation-stable-equality where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.double-negation-stable-equality + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,16 +17,17 @@ module foundation.double-negation-stable-equality where ```agda open import foundation.action-on-identifications-dependent-functions open import foundation.action-on-identifications-functions -open import foundation.coproduct-types +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.double-negation +open import foundation.dependent-products-propositions funext +open import foundation.double-negation funext univalence truncations open import foundation.equality-cartesian-product-types -open import foundation.equality-dependent-pair-types -open import foundation.equivalences -open import foundation.injective-maps -open import foundation.negated-equality -open import foundation.negation -open import foundation.sets +open import foundation.equality-dependent-pair-types funext +open import foundation.equivalences funext +open import foundation.injective-maps funext +open import foundation.negated-equality funext univalence truncations +open import foundation.negation funext +open import foundation.sets funext univalence open import foundation.transport-along-identifications open import foundation.unit-type open import foundation.universe-levels @@ -30,7 +39,7 @@ open import foundation-core.propositions open import foundation-core.retractions open import foundation-core.retracts-of-types -open import logic.double-negation-elimination +open import logic.double-negation-elimination funext univalence truncations ```
diff --git a/src/foundation/double-negation-stable-propositions.lagda.md b/src/foundation/double-negation-stable-propositions.lagda.md index 0ba325bf24..3c3d8d5815 100644 --- a/src/foundation/double-negation-stable-propositions.lagda.md +++ b/src/foundation/double-negation-stable-propositions.lagda.md @@ -1,34 +1,43 @@ # Double negation stable propositions ```agda -module foundation.double-negation-stable-propositions where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.double-negation-stable-propositions + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.cartesian-product-types -open import foundation.conjunction -open import foundation.coproduct-types -open import foundation.decidable-propositions -open import foundation.decidable-types +open import foundation.cartesian-product-types funext univalence +open import foundation.conjunction funext univalence truncations +open import foundation.coproduct-types funext univalence truncations +open import foundation.decidable-propositions funext univalence truncations +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.disjunction -open import foundation.double-negation -open import foundation.embeddings -open import foundation.empty-types -open import foundation.equivalences -open import foundation.existential-quantification -open import foundation.logical-equivalences -open import foundation.negation -open import foundation.propositional-extensionality -open import foundation.propositions -open import foundation.sets -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.disjunction funext univalence truncations +open import foundation.double-negation funext univalence truncations +open import foundation.embeddings funext +open import foundation.empty-types funext univalence truncations +open import foundation.equivalences funext +open import foundation.existential-quantification funext univalence truncations +open import foundation.logical-equivalences funext +open import foundation.negation funext +open import foundation.propositional-extensionality funext univalence truncations +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.transport-along-identifications open import foundation.type-arithmetic-dependent-pair-types open import foundation.unit-type -open import foundation.universal-quantification +open import foundation.universal-quantification funext univalence truncations open import foundation.universe-levels open import foundation-core.contractible-types @@ -36,7 +45,7 @@ open import foundation-core.function-types open import foundation-core.identity-types open import foundation-core.retracts-of-types -open import logic.double-negation-elimination +open import logic.double-negation-elimination funext univalence truncations ```
diff --git a/src/foundation/double-negation.lagda.md b/src/foundation/double-negation.lagda.md index ee813f6384..2d6986adb8 100644 --- a/src/foundation/double-negation.lagda.md +++ b/src/foundation/double-negation.lagda.md @@ -1,14 +1,22 @@ # Double negation ```agda -module foundation.double-negation where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.double-negation + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.negation -open import foundation.propositional-truncations +open import foundation.negation funext +open import foundation.propositional-truncations funext univalence open import foundation.universe-levels open import foundation-core.coproduct-types diff --git a/src/foundation/double-powersets.lagda.md b/src/foundation/double-powersets.lagda.md index 45d84375c0..923aa68008 100644 --- a/src/foundation/double-powersets.lagda.md +++ b/src/foundation/double-powersets.lagda.md @@ -1,23 +1,32 @@ # Double powersets ```agda -module foundation.double-powersets where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.double-powersets + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.existential-quantification -open import foundation.powersets -open import foundation.propositional-truncations +open import foundation.dependent-products-propositions funext +open import foundation.existential-quantification funext univalence truncations +open import foundation.powersets funext univalence truncations +open import foundation.propositional-truncations funext univalence open import foundation.universe-levels open import foundation-core.propositions -open import foundation-core.subtypes +open import foundation-core.subtypes funext -open import order-theory.large-posets -open import order-theory.posets +open import order-theory.large-posets funext univalence truncations +open import order-theory.posets funext univalence truncations ```
diff --git a/src/foundation/dubuc-penon-compact-types.lagda.md b/src/foundation/dubuc-penon-compact-types.lagda.md index 7a80fcc588..02304d19fc 100644 --- a/src/foundation/dubuc-penon-compact-types.lagda.md +++ b/src/foundation/dubuc-penon-compact-types.lagda.md @@ -1,18 +1,27 @@ # Dubuc-Penon compact types ```agda -module foundation.dubuc-penon-compact-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.dubuc-penon-compact-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.disjunction -open import foundation.universal-quantification +open import foundation.dependent-products-propositions funext +open import foundation.disjunction funext univalence truncations +open import foundation.universal-quantification funext univalence truncations open import foundation.universe-levels open import foundation-core.propositions -open import foundation-core.subtypes +open import foundation-core.subtypes funext ```
diff --git a/src/foundation/effective-maps-equivalence-relations.lagda.md b/src/foundation/effective-maps-equivalence-relations.lagda.md index 2e7cb51d1b..aad9ebfe0d 100644 --- a/src/foundation/effective-maps-equivalence-relations.lagda.md +++ b/src/foundation/effective-maps-equivalence-relations.lagda.md @@ -1,17 +1,25 @@ # Effective maps for equivalence relations ```agda -module foundation.effective-maps-equivalence-relations where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.effective-maps-equivalence-relations + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.surjective-maps +open import foundation.surjective-maps funext univalence truncations open import foundation.universe-levels open import foundation-core.cartesian-product-types -open import foundation-core.equivalence-relations +open import foundation-core.equivalence-relations funext univalence truncations open import foundation-core.equivalences open import foundation-core.identity-types ``` diff --git a/src/foundation/embeddings.lagda.md b/src/foundation/embeddings.lagda.md index 6631d6bead..2bc17c2d0b 100644 --- a/src/foundation/embeddings.lagda.md +++ b/src/foundation/embeddings.lagda.md @@ -1,7 +1,11 @@ # Embeddings ```agda -module foundation.embeddings where +open import foundation.function-extensionality-axiom + +module foundation.embeddings + (funext : function-extensionality) + where open import foundation-core.embeddings public ``` @@ -10,19 +14,20 @@ open import foundation-core.embeddings public ```agda open import foundation.action-on-identifications-functions -open import foundation.cones-over-cospan-diagrams +open import foundation.cones-over-cospan-diagrams funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.functoriality-cartesian-product-types -open import foundation.functoriality-dependent-pair-types +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.transport-along-identifications -open import foundation.truncated-maps +open import foundation.truncated-maps funext open import foundation.universe-levels open import foundation-core.cartesian-product-types -open import foundation-core.commuting-squares-of-maps +open import foundation-core.commuting-squares-of-maps funext open import foundation-core.commuting-triangles-of-maps open import foundation-core.contractible-types open import foundation-core.fibers-of-maps @@ -30,7 +35,7 @@ open import foundation-core.function-types open import foundation-core.homotopies open import foundation-core.propositional-maps open import foundation-core.propositions -open import foundation-core.pullbacks +open import foundation-core.pullbacks funext open import foundation-core.retractions open import foundation-core.sections open import foundation-core.torsorial-type-families diff --git a/src/foundation/empty-types.lagda.md b/src/foundation/empty-types.lagda.md index 67cfc187b9..eb6d3afcbb 100644 --- a/src/foundation/empty-types.lagda.md +++ b/src/foundation/empty-types.lagda.md @@ -1,7 +1,15 @@ # Empty types ```agda -module foundation.empty-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.empty-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where open import foundation-core.empty-types public ``` @@ -10,18 +18,19 @@ open import foundation-core.empty-types public ```agda open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalences -open import foundation.propositional-truncations -open import foundation.raising-universe-levels -open import foundation.subuniverses -open import foundation.univalence +open import foundation.dependent-products-propositions funext +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.propositional-truncations funext univalence +open import foundation.subuniverses funext univalence +open import foundation.univalence funext univalence open import foundation.universe-levels open import foundation-core.contractible-types open import foundation-core.equality-dependent-pair-types open import foundation-core.function-types open import foundation-core.propositions +open import foundation-core.raising-universe-levels open import foundation-core.sets open import foundation-core.truncated-types open import foundation-core.truncation-levels diff --git a/src/foundation/endomorphisms.lagda.md b/src/foundation/endomorphisms.lagda.md index 178d2f3786..4b208c4d96 100644 --- a/src/foundation/endomorphisms.lagda.md +++ b/src/foundation/endomorphisms.lagda.md @@ -1,9 +1,17 @@ # Endomorphisms ```agda -module foundation.endomorphisms where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom -open import foundation-core.endomorphisms public +module foundation.endomorphisms + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where + +open import foundation-core.endomorphisms funext univalence public ```
Imports @@ -17,10 +25,10 @@ open import foundation-core.function-types open import foundation-core.identity-types open import foundation-core.sets -open import group-theory.monoids -open import group-theory.semigroups +open import group-theory.monoids funext univalence truncations +open import group-theory.semigroups funext univalence -open import structured-types.wild-monoids +open import structured-types.wild-monoids funext univalence truncations ```
diff --git a/src/foundation/epimorphisms-with-respect-to-sets.lagda.md b/src/foundation/epimorphisms-with-respect-to-sets.lagda.md index f34760598e..5c0b08e0b9 100644 --- a/src/foundation/epimorphisms-with-respect-to-sets.lagda.md +++ b/src/foundation/epimorphisms-with-respect-to-sets.lagda.md @@ -1,7 +1,15 @@ # Epimorphisms with respect to maps into sets ```agda -module foundation.epimorphisms-with-respect-to-sets where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.epimorphisms-with-respect-to-sets + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,14 +17,15 @@ module foundation.epimorphisms-with-respect-to-sets where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.existential-quantification -open import foundation.function-extensionality -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.propositional-extensionality -open import foundation.propositional-truncations -open import foundation.sets -open import foundation.surjective-maps +open import foundation.existential-quantification funext univalence truncations +open import foundation.function-extensionality funext +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.propositional-extensionality funext univalence truncations +open import foundation.propositional-truncations funext univalence +open import foundation.raising-universe-levels-unit-type +open import foundation.sets funext univalence +open import foundation.surjective-maps funext univalence truncations open import foundation.unit-type open import foundation.universe-levels @@ -28,7 +37,6 @@ open import foundation-core.homotopies open import foundation-core.precomposition-functions open import foundation-core.propositional-maps open import foundation-core.propositions -open import foundation-core.univalence ```
diff --git a/src/foundation/epimorphisms-with-respect-to-truncated-types.lagda.md b/src/foundation/epimorphisms-with-respect-to-truncated-types.lagda.md index e5ff5b16a5..1e1f374856 100644 --- a/src/foundation/epimorphisms-with-respect-to-truncated-types.lagda.md +++ b/src/foundation/epimorphisms-with-respect-to-truncated-types.lagda.md @@ -1,23 +1,32 @@ # Epimorphisms with respect to truncated types ```agda -module foundation.epimorphisms-with-respect-to-truncated-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.epimorphisms-with-respect-to-truncated-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-maps -open import foundation.connected-maps +open import foundation.commuting-squares-of-maps funext univalence +open import foundation.connected-maps funext univalence truncations open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.function-extensionality -open import foundation.functoriality-truncation -open import foundation.precomposition-functions -open import foundation.sections -open import foundation.truncation-equivalences -open import foundation.truncations +open import foundation.dependent-products-propositions funext +open import foundation.embeddings funext +open import foundation.function-extensionality funext +open import foundation.functoriality-truncation funext univalence truncations +open import foundation.precomposition-functions funext +open import foundation.sections funext +open import foundation.truncation-equivalences funext univalence truncations +open import foundation.truncations funext univalence truncations open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels @@ -31,9 +40,9 @@ open import foundation-core.propositions open import foundation-core.truncated-types open import foundation-core.truncation-levels -open import synthetic-homotopy-theory.cocones-under-spans -open import synthetic-homotopy-theory.codiagonals-of-maps -open import synthetic-homotopy-theory.pushouts +open import synthetic-homotopy-theory.cocones-under-spans funext +open import synthetic-homotopy-theory.codiagonals-of-maps funext univalence truncations +open import synthetic-homotopy-theory.pushouts funext univalence truncations ```
diff --git a/src/foundation/epimorphisms.lagda.md b/src/foundation/epimorphisms.lagda.md index b7c5bb9ab4..1f2817f4df 100644 --- a/src/foundation/epimorphisms.lagda.md +++ b/src/foundation/epimorphisms.lagda.md @@ -1,19 +1,27 @@ # Epimorphisms ```agda -module foundation.epimorphisms where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.epimorphisms + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.precomposition-functions -open import foundation.sections +open import foundation.embeddings funext +open import foundation.precomposition-functions funext +open import foundation.sections funext open import foundation.universe-levels -open import foundation-core.commuting-squares-of-maps +open import foundation-core.commuting-squares-of-maps funext open import foundation-core.contractible-types open import foundation-core.equivalences open import foundation-core.function-types @@ -21,10 +29,10 @@ open import foundation-core.identity-types open import foundation-core.propositional-maps open import foundation-core.propositions -open import synthetic-homotopy-theory.cocones-under-spans -open import synthetic-homotopy-theory.codiagonals-of-maps -open import synthetic-homotopy-theory.pushouts -open import synthetic-homotopy-theory.universal-property-pushouts +open import synthetic-homotopy-theory.cocones-under-spans funext +open import synthetic-homotopy-theory.codiagonals-of-maps funext univalence truncations +open import synthetic-homotopy-theory.pushouts funext univalence truncations +open import synthetic-homotopy-theory.universal-property-pushouts funext univalence truncations ```
diff --git a/src/foundation/equality-cartesian-product-types.lagda.md b/src/foundation/equality-cartesian-product-types.lagda.md index b500eb9d43..068c6de89a 100644 --- a/src/foundation/equality-cartesian-product-types.lagda.md +++ b/src/foundation/equality-cartesian-product-types.lagda.md @@ -13,7 +13,6 @@ open import foundation.dependent-pair-types open import foundation.universe-levels open import foundation-core.cartesian-product-types -open import foundation-core.equality-dependent-pair-types open import foundation-core.equivalences open import foundation-core.function-types open import foundation-core.homotopies diff --git a/src/foundation/equality-coproduct-types.lagda.md b/src/foundation/equality-coproduct-types.lagda.md index 83776f0ce3..43e4983105 100644 --- a/src/foundation/equality-coproduct-types.lagda.md +++ b/src/foundation/equality-coproduct-types.lagda.md @@ -1,17 +1,25 @@ # Equality of coproduct types ```agda -module foundation.equality-coproduct-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.equality-coproduct-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.coproduct-types +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.negated-equality +open import foundation.negated-equality funext univalence truncations open import foundation.universe-levels open import foundation-core.contractible-types diff --git a/src/foundation/equality-dependent-function-types.lagda.md b/src/foundation/equality-dependent-function-types.lagda.md index 04e62574f7..6481792f81 100644 --- a/src/foundation/equality-dependent-function-types.lagda.md +++ b/src/foundation/equality-dependent-function-types.lagda.md @@ -1,13 +1,18 @@ # Equality on dependent function types ```agda -module foundation.equality-dependent-function-types where +open import foundation.function-extensionality-axiom + +module foundation.equality-dependent-function-types + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types funext open import foundation.fundamental-theorem-of-identity-types open import foundation.implicit-function-types open import foundation.universe-levels diff --git a/src/foundation/equality-dependent-pair-types.lagda.md b/src/foundation/equality-dependent-pair-types.lagda.md index 6ab7a7bbb3..177ffce439 100644 --- a/src/foundation/equality-dependent-pair-types.lagda.md +++ b/src/foundation/equality-dependent-pair-types.lagda.md @@ -1,7 +1,11 @@ # Equality of dependent pair types ```agda -module foundation.equality-dependent-pair-types where +open import foundation.function-extensionality-axiom + +module foundation.equality-dependent-pair-types + (funext : function-extensionality) + where open import foundation-core.equality-dependent-pair-types public ``` @@ -11,7 +15,7 @@ open import foundation-core.equality-dependent-pair-types public ```agda open import foundation.action-on-identifications-dependent-functions open import foundation.action-on-identifications-functions -open import foundation.dependent-identifications +open import foundation.dependent-identifications funext open import foundation.dependent-pair-types open import foundation.transport-along-identifications open import foundation.type-arithmetic-dependent-pair-types diff --git a/src/foundation/equality-fibers-of-maps.lagda.md b/src/foundation/equality-fibers-of-maps.lagda.md index e5fa8e6684..16e3c2654e 100644 --- a/src/foundation/equality-fibers-of-maps.lagda.md +++ b/src/foundation/equality-fibers-of-maps.lagda.md @@ -1,7 +1,11 @@ # Equality in the fibers of a map ```agda -module foundation.equality-fibers-of-maps where +open import foundation.function-extensionality-axiom + +module foundation.equality-fibers-of-maps + (funext : function-extensionality) + where ```
Imports @@ -9,7 +13,7 @@ module foundation.equality-fibers-of-maps where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.transport-along-identifications open import foundation.universe-levels diff --git a/src/foundation/equivalence-classes.lagda.md b/src/foundation/equivalence-classes.lagda.md index 71954bae57..5d8bccb662 100644 --- a/src/foundation/equivalence-classes.lagda.md +++ b/src/foundation/equivalence-classes.lagda.md @@ -1,34 +1,42 @@ # Equivalence classes ```agda -module foundation.equivalence-classes where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.equivalence-classes + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.conjunction +open import foundation.conjunction funext univalence truncations open import foundation.dependent-pair-types -open import foundation.effective-maps-equivalence-relations -open import foundation.existential-quantification -open import foundation.functoriality-propositional-truncation +open import foundation.effective-maps-equivalence-relations funext univalence truncations +open import foundation.existential-quantification funext univalence truncations +open import foundation.functoriality-propositional-truncation funext univalence truncations open import foundation.fundamental-theorem-of-identity-types -open import foundation.inhabited-subtypes -open import foundation.locally-small-types -open import foundation.logical-equivalences -open import foundation.propositional-truncations -open import foundation.reflecting-maps-equivalence-relations -open import foundation.slice -open import foundation.small-types +open import foundation.inhabited-subtypes funext univalence truncations +open import foundation.locally-small-types funext univalence truncations +open import foundation.logical-equivalences funext +open import foundation.propositional-truncations funext univalence +open import foundation.reflecting-maps-equivalence-relations funext univalence truncations +open import foundation.slice funext univalence +open import foundation.small-types funext univalence truncations open import foundation.subtype-identity-principle -open import foundation.subtypes -open import foundation.surjective-maps -open import foundation.universal-property-image +open import foundation.subtypes funext univalence truncations +open import foundation.surjective-maps funext univalence truncations +open import foundation.universal-property-image funext univalence truncations open import foundation.universe-levels open import foundation-core.cartesian-product-types open import foundation-core.embeddings -open import foundation-core.equivalence-relations +open import foundation-core.equivalence-relations funext univalence truncations open import foundation-core.equivalences open import foundation-core.functoriality-dependent-pair-types open import foundation-core.identity-types diff --git a/src/foundation/equivalence-extensionality.lagda.md b/src/foundation/equivalence-extensionality.lagda.md index 54aad95056..5f4dabea37 100644 --- a/src/foundation/equivalence-extensionality.lagda.md +++ b/src/foundation/equivalence-extensionality.lagda.md @@ -1,15 +1,20 @@ # Equivalence extensionality ```agda -module foundation.equivalence-extensionality where +open import foundation.function-extensionality-axiom + +module foundation.equivalence-extensionality + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.dependent-universal-property-equivalences -open import foundation.function-extensionality +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-universal-property-equivalences funext +open import foundation.function-extensionality funext open import foundation.fundamental-theorem-of-identity-types open import foundation.identity-systems open import foundation.subtype-identity-principle diff --git a/src/foundation/equivalence-induction.lagda.md b/src/foundation/equivalence-induction.lagda.md index a4b437a51f..b3df8ab62f 100644 --- a/src/foundation/equivalence-induction.lagda.md +++ b/src/foundation/equivalence-induction.lagda.md @@ -1,7 +1,13 @@ # Equivalence induction ```agda -module foundation.equivalence-induction where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.equivalence-induction + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports @@ -9,9 +15,9 @@ module foundation.equivalence-induction where ```agda open import foundation.dependent-pair-types open import foundation.identity-systems -open import foundation.subuniverses -open import foundation.univalence -open import foundation.universal-property-identity-systems +open import foundation.subuniverses funext univalence +open import foundation.univalence funext univalence +open import foundation.universal-property-identity-systems funext open import foundation.universe-levels open import foundation-core.commuting-triangles-of-maps diff --git a/src/foundation/equivalence-injective-type-families.lagda.md b/src/foundation/equivalence-injective-type-families.lagda.md index 5b1ea1cb5f..6aac274249 100644 --- a/src/foundation/equivalence-injective-type-families.lagda.md +++ b/src/foundation/equivalence-injective-type-families.lagda.md @@ -1,17 +1,25 @@ # Equivalence injective type families ```agda -module foundation.equivalence-injective-type-families where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.equivalence-injective-type-families + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.functoriality-dependent-function-types -open import foundation.iterated-dependent-product-types -open import foundation.univalence -open import foundation.universal-property-equivalences +open import foundation.dependent-products-propositions funext +open import foundation.functoriality-dependent-function-types funext univalence +open import foundation.iterated-dependent-product-types funext +open import foundation.telescopes +open import foundation.univalence funext univalence +open import foundation.universal-property-equivalences funext open import foundation.universe-levels open import foundation-core.equivalences diff --git a/src/foundation/equivalence-relations.lagda.md b/src/foundation/equivalence-relations.lagda.md index 931f0e8264..45ebc24d7f 100644 --- a/src/foundation/equivalence-relations.lagda.md +++ b/src/foundation/equivalence-relations.lagda.md @@ -1,27 +1,35 @@ # Equivalence relations ```agda -module foundation.equivalence-relations where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.equivalence-relations + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where -open import foundation-core.equivalence-relations public +open import foundation-core.equivalence-relations funext univalence truncations public ```
Imports ```agda -open import foundation.binary-relations +open import foundation.binary-relations funext univalence truncations open import foundation.dependent-pair-types -open import foundation.effective-maps-equivalence-relations -open import foundation.fundamental-theorem-of-equivalence-relations -open import foundation.logical-equivalences -open import foundation.partitions -open import foundation.propositional-truncations -open import foundation.reflecting-maps-equivalence-relations -open import foundation.set-quotients -open import foundation.sigma-decompositions -open import foundation.surjective-maps -open import foundation.uniqueness-set-quotients -open import foundation.universal-property-set-quotients +open import foundation.effective-maps-equivalence-relations funext univalence truncations +open import foundation.fundamental-theorem-of-equivalence-relations funext univalence truncations +open import foundation.logical-equivalences funext +open import foundation.partitions funext univalence truncations +open import foundation.propositional-truncations funext univalence +open import foundation.reflecting-maps-equivalence-relations funext univalence truncations +open import foundation.set-quotients funext univalence truncations +open import foundation.sigma-decompositions funext univalence truncations +open import foundation.surjective-maps funext univalence truncations +open import foundation.uniqueness-set-quotients funext univalence truncations +open import foundation.universal-property-set-quotients funext univalence truncations open import foundation.universe-levels open import foundation-core.contractible-types diff --git a/src/foundation/equivalences-arrows.lagda.md b/src/foundation/equivalences-arrows.lagda.md index 23e82b5948..0ab063e72e 100644 --- a/src/foundation/equivalences-arrows.lagda.md +++ b/src/foundation/equivalences-arrows.lagda.md @@ -1,22 +1,30 @@ # Equivalences of arrows ```agda -module foundation.equivalences-arrows where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.equivalences-arrows + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.cartesian-morphisms-arrows -open import foundation.commuting-squares-of-maps +open import foundation.cartesian-morphisms-arrows funext univalence truncations +open import foundation.commuting-squares-of-maps funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.homotopies -open import foundation.morphisms-arrows -open import foundation.retractions -open import foundation.retracts-of-maps -open import foundation.sections -open import foundation.span-diagrams +open import foundation.equivalences funext +open import foundation.homotopies funext +open import foundation.morphisms-arrows funext +open import foundation.retractions funext +open import foundation.retracts-of-maps funext univalence +open import foundation.sections funext +open import foundation.span-diagrams funext open import foundation.spans open import foundation.universe-levels diff --git a/src/foundation/equivalences-cospans.lagda.md b/src/foundation/equivalences-cospans.lagda.md index a44b7e3b11..41231d3bfe 100644 --- a/src/foundation/equivalences-cospans.lagda.md +++ b/src/foundation/equivalences-cospans.lagda.md @@ -1,7 +1,13 @@ # Equivalences of cospans ```agda -module foundation.equivalences-cospans where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.equivalences-cospans + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports @@ -10,10 +16,10 @@ module foundation.equivalences-cospans where open import foundation.cospans open import foundation.dependent-pair-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopy-induction +open import foundation.homotopy-induction funext open import foundation.morphisms-cospans open import foundation.structure-identity-principle -open import foundation.univalence +open import foundation.univalence funext univalence open import foundation.universe-levels open import foundation-core.equivalences diff --git a/src/foundation/equivalences-double-arrows.lagda.md b/src/foundation/equivalences-double-arrows.lagda.md index 54c7f508e0..f5657b8645 100644 --- a/src/foundation/equivalences-double-arrows.lagda.md +++ b/src/foundation/equivalences-double-arrows.lagda.md @@ -1,20 +1,28 @@ # Equivalences of double arrows ```agda -module foundation.equivalences-double-arrows where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.equivalences-double-arrows + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.cartesian-product-types -open import foundation.commuting-squares-of-maps +open import foundation.cartesian-product-types funext univalence +open import foundation.commuting-squares-of-maps funext univalence open import foundation.dependent-pair-types open import foundation.double-arrows -open import foundation.equivalences -open import foundation.equivalences-arrows -open import foundation.homotopies -open import foundation.morphisms-double-arrows +open import foundation.equivalences funext +open import foundation.equivalences-arrows funext univalence truncations +open import foundation.homotopies funext +open import foundation.morphisms-double-arrows funext univalence open import foundation.universe-levels ``` diff --git a/src/foundation/equivalences-inverse-sequential-diagrams.lagda.md b/src/foundation/equivalences-inverse-sequential-diagrams.lagda.md index 3653847a20..1a819e1c1e 100644 --- a/src/foundation/equivalences-inverse-sequential-diagrams.lagda.md +++ b/src/foundation/equivalences-inverse-sequential-diagrams.lagda.md @@ -1,7 +1,15 @@ # Equivalences of inverse sequential diagrams of types ```agda -module foundation.equivalences-inverse-sequential-diagrams where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.equivalences-inverse-sequential-diagrams + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,15 +17,15 @@ module foundation.equivalences-inverse-sequential-diagrams where ```agda open import elementary-number-theory.natural-numbers -open import foundation.binary-homotopies +open import foundation.binary-homotopies funext open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types +open import foundation.equality-dependent-function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopy-induction -open import foundation.inverse-sequential-diagrams -open import foundation.morphisms-inverse-sequential-diagrams +open import foundation.homotopy-induction funext +open import foundation.inverse-sequential-diagrams funext univalence truncations +open import foundation.morphisms-inverse-sequential-diagrams funext univalence truncations open import foundation.structure-identity-principle -open import foundation.univalence +open import foundation.univalence funext univalence open import foundation.universe-levels open import foundation-core.equivalences diff --git a/src/foundation/equivalences-maybe.lagda.md b/src/foundation/equivalences-maybe.lagda.md index c656a2d528..56f2fc4a8d 100644 --- a/src/foundation/equivalences-maybe.lagda.md +++ b/src/foundation/equivalences-maybe.lagda.md @@ -1,7 +1,15 @@ # Equivalences on `Maybe` ```agda -module foundation.equivalences-maybe where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.equivalences-maybe + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,13 +17,13 @@ module foundation.equivalences-maybe where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equality-coproduct-types -open import foundation.equivalence-extensionality -open import foundation.equivalences -open import foundation.functoriality-coproduct-types -open import foundation.maybe +open import foundation.equality-coproduct-types funext univalence truncations +open import foundation.equivalence-extensionality funext +open import foundation.equivalences funext +open import foundation.functoriality-coproduct-types funext univalence truncations +open import foundation.maybe funext univalence truncations open import foundation.unit-type -open import foundation.universal-property-maybe +open import foundation.universal-property-maybe funext open import foundation.universe-levels open import foundation-core.coproduct-types diff --git a/src/foundation/equivalences-span-diagrams-families-of-types.lagda.md b/src/foundation/equivalences-span-diagrams-families-of-types.lagda.md index 05c24bbdad..3381bbc8db 100644 --- a/src/foundation/equivalences-span-diagrams-families-of-types.lagda.md +++ b/src/foundation/equivalences-span-diagrams-families-of-types.lagda.md @@ -1,17 +1,23 @@ # Equivalences of span diagrams on families of types ```agda -module foundation.equivalences-span-diagrams-families-of-types where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.equivalences-span-diagrams-families-of-types + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda -open import foundation.commuting-squares-of-maps +open import foundation.commuting-squares-of-maps funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.equivalences-spans-families-of-types -open import foundation.homotopies +open import foundation.equivalences funext +open import foundation.equivalences-spans-families-of-types funext univalence +open import foundation.homotopies funext open import foundation.operations-spans-families-of-types open import foundation.span-diagrams-families-of-types open import foundation.universe-levels diff --git a/src/foundation/equivalences-span-diagrams.lagda.md b/src/foundation/equivalences-span-diagrams.lagda.md index 92238d6cff..864e8a9d44 100644 --- a/src/foundation/equivalences-span-diagrams.lagda.md +++ b/src/foundation/equivalences-span-diagrams.lagda.md @@ -1,29 +1,38 @@ # Equivalences of span diagrams ```agda -module foundation.equivalences-span-diagrams where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.equivalences-span-diagrams + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.equivalences-arrows -open import foundation.equivalences-spans +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.equivalences-arrows funext univalence truncations +open import foundation.equivalences-spans funext univalence open import foundation.fundamental-theorem-of-identity-types -open import foundation.morphisms-span-diagrams +open import foundation.morphisms-span-diagrams funext univalence truncations open import foundation.morphisms-spans -open import foundation.operations-spans -open import foundation.propositions -open import foundation.span-diagrams +open import foundation.operations-spans funext univalence truncations +open import foundation.propositions funext univalence +open import foundation.span-diagrams funext open import foundation.structure-identity-principle open import foundation.type-arithmetic-dependent-pair-types -open import foundation.univalence +open import foundation.univalence funext univalence open import foundation.universe-levels -open import foundation-core.commuting-squares-of-maps +open import foundation-core.commuting-squares-of-maps funext open import foundation-core.functoriality-dependent-pair-types open import foundation-core.identity-types open import foundation-core.torsorial-type-families diff --git a/src/foundation/equivalences-spans-families-of-types.lagda.md b/src/foundation/equivalences-spans-families-of-types.lagda.md index f76bbf5f10..043d204abf 100644 --- a/src/foundation/equivalences-spans-families-of-types.lagda.md +++ b/src/foundation/equivalences-spans-families-of-types.lagda.md @@ -1,22 +1,28 @@ # Equivalences of spans of families of types ```agda -module foundation.equivalences-spans-families-of-types where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.equivalences-spans-families-of-types + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types +open import foundation.equality-dependent-function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types -open import foundation.morphisms-spans-families-of-types +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext +open import foundation.morphisms-spans-families-of-types funext open import foundation.spans-families-of-types open import foundation.structure-identity-principle -open import foundation.univalence +open import foundation.univalence funext univalence open import foundation.universe-levels open import foundation-core.commuting-triangles-of-maps diff --git a/src/foundation/equivalences-spans.lagda.md b/src/foundation/equivalences-spans.lagda.md index 4e804c318a..022b7cae69 100644 --- a/src/foundation/equivalences-spans.lagda.md +++ b/src/foundation/equivalences-spans.lagda.md @@ -1,23 +1,29 @@ # Equivalences of spans ```agda -module foundation.equivalences-spans where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.equivalences-spans + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda -open import foundation.cartesian-product-types -open import foundation.commuting-squares-of-maps +open import foundation.cartesian-product-types funext univalence +open import foundation.commuting-squares-of-maps funext univalence open import foundation.dependent-pair-types -open import foundation.functoriality-dependent-pair-types +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopy-induction +open import foundation.homotopy-induction funext open import foundation.morphisms-spans open import foundation.spans open import foundation.structure-identity-principle open import foundation.type-arithmetic-dependent-pair-types -open import foundation.univalence +open import foundation.univalence funext univalence open import foundation.universe-levels open import foundation-core.commuting-triangles-of-maps @@ -25,7 +31,7 @@ open import foundation-core.equivalences open import foundation-core.function-types open import foundation-core.homotopies open import foundation-core.identity-types -open import foundation-core.operations-spans +open import foundation-core.operations-spans funext open import foundation-core.torsorial-type-families ``` diff --git a/src/foundation/equivalences.lagda.md b/src/foundation/equivalences.lagda.md index 14919d3b92..ece8cf8bce 100644 --- a/src/foundation/equivalences.lagda.md +++ b/src/foundation/equivalences.lagda.md @@ -1,7 +1,11 @@ # Equivalences ```agda -module foundation.equivalences where +open import foundation.function-extensionality-axiom + +module foundation.equivalences + (funext : function-extensionality) + where open import foundation-core.equivalences public ``` @@ -10,16 +14,17 @@ open import foundation-core.equivalences public ```agda open import foundation.action-on-identifications-functions -open import foundation.cones-over-cospan-diagrams +open import foundation.cones-over-cospan-diagrams funext open import foundation.dependent-pair-types -open import foundation.equivalence-extensionality -open import foundation.function-extensionality -open import foundation.functoriality-fibers-of-maps -open import foundation.logical-equivalences +open import foundation.dependent-products-contractible-types funext +open import foundation.equivalence-extensionality funext +open import foundation.function-extensionality funext +open import foundation.functoriality-fibers-of-maps funext +open import foundation.logical-equivalences funext open import foundation.transport-along-identifications -open import foundation.transposition-identifications-along-equivalences -open import foundation.truncated-maps -open import foundation.universal-property-equivalences +open import foundation.transposition-identifications-along-equivalences funext +open import foundation.truncated-maps funext +open import foundation.universal-property-equivalences funext open import foundation.universe-levels open import foundation-core.commuting-triangles-of-maps @@ -33,11 +38,11 @@ open import foundation-core.homotopies open import foundation-core.identity-types open import foundation-core.injective-maps open import foundation-core.propositions -open import foundation-core.pullbacks +open import foundation-core.pullbacks funext open import foundation-core.retractions open import foundation-core.retracts-of-types open import foundation-core.sections -open import foundation-core.subtypes +open import foundation-core.subtypes funext open import foundation-core.truncation-levels open import foundation-core.type-theoretic-principle-of-choice ``` diff --git a/src/foundation/evaluation-functions.lagda.md b/src/foundation/evaluation-functions.lagda.md index 45faaf7850..9503610877 100644 --- a/src/foundation/evaluation-functions.lagda.md +++ b/src/foundation/evaluation-functions.lagda.md @@ -7,10 +7,7 @@ module foundation.evaluation-functions where
Imports ```agda -open import foundation.action-on-identifications-functions open import foundation.universe-levels - -open import foundation-core.identity-types ```
diff --git a/src/foundation/exclusive-disjunction.lagda.md b/src/foundation/exclusive-disjunction.lagda.md index 92407933be..0a4e9af46f 100644 --- a/src/foundation/exclusive-disjunction.lagda.md +++ b/src/foundation/exclusive-disjunction.lagda.md @@ -1,27 +1,36 @@ # Exclusive disjunctions ```agda -module foundation.exclusive-disjunction where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.exclusive-disjunction + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.contractible-types -open import foundation.coproduct-types +open import foundation.contractible-types funext univalence +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equality-coproduct-types -open import foundation.exclusive-sum -open import foundation.functoriality-coproduct-types -open import foundation.propositional-truncations +open import foundation.dependent-products-contractible-types funext +open import foundation.equality-coproduct-types funext univalence truncations +open import foundation.exclusive-sum funext univalence truncations +open import foundation.functoriality-coproduct-types funext univalence truncations +open import foundation.propositional-truncations funext univalence open import foundation.type-arithmetic-cartesian-product-types -open import foundation.type-arithmetic-coproduct-types -open import foundation.universal-property-coproduct-types +open import foundation.type-arithmetic-coproduct-types funext univalence truncations +open import foundation.universal-property-coproduct-types funext open import foundation.universe-levels open import foundation-core.embeddings open import foundation-core.equivalences -open import foundation-core.functoriality-dependent-function-types +open import foundation-core.functoriality-dependent-function-types funext open import foundation-core.functoriality-dependent-pair-types open import foundation-core.identity-types open import foundation-core.propositions diff --git a/src/foundation/exclusive-sum.lagda.md b/src/foundation/exclusive-sum.lagda.md index 7282c9e05d..82a8333860 100644 --- a/src/foundation/exclusive-sum.lagda.md +++ b/src/foundation/exclusive-sum.lagda.md @@ -1,36 +1,43 @@ # Exclusive sums ```agda -module foundation.exclusive-sum where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.exclusive-sum + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.conjunction -open import foundation.coproduct-types -open import foundation.decidable-types +open import foundation.conjunction funext univalence truncations +open import foundation.coproduct-types funext univalence truncations +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.negation -open import foundation.propositional-extensionality -open import foundation.symmetric-operations -open import foundation.universal-quantification +open import foundation.dependent-products-propositions funext +open import foundation.negation funext +open import foundation.propositional-extensionality funext univalence truncations +open import foundation.symmetric-operations funext univalence truncations open import foundation.universe-levels -open import foundation.unordered-pairs +open import foundation.unordered-pairs funext univalence truncations open import foundation-core.cartesian-product-types -open import foundation-core.decidable-propositions -open import foundation-core.embeddings +open import foundation-core.decidable-propositions funext univalence truncations open import foundation-core.empty-types open import foundation-core.equality-dependent-pair-types open import foundation-core.identity-types open import foundation-core.propositions open import foundation-core.transport-along-identifications -open import univalent-combinatorics.2-element-types -open import univalent-combinatorics.equality-finite-types -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.2-element-types funext univalence truncations +open import univalent-combinatorics.equality-finite-types funext univalence truncations +open import univalent-combinatorics.finite-types funext univalence truncations +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/foundation/existential-quantification.lagda.md b/src/foundation/existential-quantification.lagda.md index 13a376ea80..60b07a6569 100644 --- a/src/foundation/existential-quantification.lagda.md +++ b/src/foundation/existential-quantification.lagda.md @@ -1,24 +1,31 @@ # Existential quantification ```agda -module foundation.existential-quantification where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.existential-quantification + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.conjunction +open import foundation.conjunction funext univalence truncations open import foundation.dependent-pair-types -open import foundation.functoriality-propositional-truncation -open import foundation.logical-equivalences -open import foundation.propositional-extensionality -open import foundation.propositional-truncations +open import foundation.dependent-products-propositions funext +open import foundation.logical-equivalences funext +open import foundation.propositional-extensionality funext univalence truncations +open import foundation.propositional-truncations funext univalence open import foundation.universe-levels open import foundation-core.cartesian-product-types open import foundation-core.equivalences open import foundation-core.function-types -open import foundation-core.functoriality-dependent-pair-types open import foundation-core.identity-types open import foundation-core.propositions ``` diff --git a/src/foundation/exponents-set-quotients.lagda.md b/src/foundation/exponents-set-quotients.lagda.md index bfc9888f3c..1b1d03114b 100644 --- a/src/foundation/exponents-set-quotients.lagda.md +++ b/src/foundation/exponents-set-quotients.lagda.md @@ -2,28 +2,36 @@ ```agda {-# OPTIONS --lossy-unification #-} - -module foundation.exponents-set-quotients where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.exponents-set-quotients + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.binary-relations +open import foundation.binary-relations funext univalence truncations open import foundation.dependent-pair-types -open import foundation.function-extensionality -open import foundation.functoriality-set-quotients -open import foundation.postcomposition-functions -open import foundation.reflecting-maps-equivalence-relations -open import foundation.set-quotients -open import foundation.sets -open import foundation.universal-property-set-quotients +open import foundation.dependent-products-propositions funext +open import foundation.function-extensionality funext +open import foundation.functoriality-set-quotients funext univalence truncations +open import foundation.postcomposition-functions funext +open import foundation.reflecting-maps-equivalence-relations funext univalence truncations +open import foundation.set-quotients funext univalence truncations +open import foundation.sets funext univalence +open import foundation.universal-property-set-quotients funext univalence truncations open import foundation.universe-levels open import foundation.whiskering-homotopies-composition open import foundation-core.contractible-types open import foundation-core.embeddings -open import foundation-core.equivalence-relations +open import foundation-core.equivalence-relations funext univalence truncations open import foundation-core.function-types open import foundation-core.homotopies open import foundation-core.identity-types diff --git a/src/foundation/extensions-types-global-subuniverses.lagda.md b/src/foundation/extensions-types-global-subuniverses.lagda.md index a75184e2aa..7e98b03f26 100644 --- a/src/foundation/extensions-types-global-subuniverses.lagda.md +++ b/src/foundation/extensions-types-global-subuniverses.lagda.md @@ -1,32 +1,42 @@ # Extensions of types in a global subuniverse ```agda -module foundation.extensions-types-global-subuniverses where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.extensions-types-global-subuniverses + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-triangles-of-maps -open import foundation.contractible-types +open import foundation.commuting-triangles-of-maps funext univalence +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalences -open import foundation.extensions-types -open import foundation.fibers-of-maps -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.extensions-types funext univalence truncations +open import foundation.fibers-of-maps funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.global-subuniverses -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types -open import foundation.propositional-maps -open import foundation.propositions -open import foundation.torsorial-type-families +open import foundation.global-subuniverses funext univalence +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext +open import foundation.propositional-maps funext +open import foundation.propositions funext univalence +open import foundation.torsorial-type-families funext univalence truncations open import foundation.type-arithmetic-dependent-pair-types -open import foundation.univalence +open import foundation.univalence funext univalence open import foundation.universe-levels ``` diff --git a/src/foundation/extensions-types-subuniverses.lagda.md b/src/foundation/extensions-types-subuniverses.lagda.md index b76a1afee1..352d8fc1c2 100644 --- a/src/foundation/extensions-types-subuniverses.lagda.md +++ b/src/foundation/extensions-types-subuniverses.lagda.md @@ -1,34 +1,44 @@ # Extensions of types in a subuniverse ```agda -module foundation.extensions-types-subuniverses where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.extensions-types-subuniverses + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-triangles-of-maps -open import foundation.contractible-types +open import foundation.commuting-triangles-of-maps funext univalence +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalences -open import foundation.extensions-types -open import foundation.fibers-of-maps -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.extensions-types funext univalence truncations +open import foundation.fibers-of-maps funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types -open import foundation.propositional-maps -open import foundation.propositions +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext +open import foundation.propositional-maps funext +open import foundation.propositions funext univalence open import foundation.structure-identity-principle open import foundation.subtype-identity-principle -open import foundation.subuniverses -open import foundation.torsorial-type-families +open import foundation.subuniverses funext univalence +open import foundation.torsorial-type-families funext univalence truncations open import foundation.type-arithmetic-dependent-pair-types -open import foundation.univalence +open import foundation.univalence funext univalence open import foundation.universe-levels ``` diff --git a/src/foundation/extensions-types.lagda.md b/src/foundation/extensions-types.lagda.md index 7d78a32bdd..e5e9293352 100644 --- a/src/foundation/extensions-types.lagda.md +++ b/src/foundation/extensions-types.lagda.md @@ -1,22 +1,30 @@ # Extensions of types ```agda -module foundation.extensions-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.extensions-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.commuting-triangles-of-maps +open import foundation.commuting-triangles-of-maps funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences +open import foundation.equivalences funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext open import foundation.structure-identity-principle -open import foundation.torsorial-type-families -open import foundation.univalence +open import foundation.torsorial-type-families funext univalence truncations +open import foundation.univalence funext univalence open import foundation.universe-levels ``` diff --git a/src/foundation/faithful-maps.lagda.md b/src/foundation/faithful-maps.lagda.md index 0e523f08b3..845d2d1d1e 100644 --- a/src/foundation/faithful-maps.lagda.md +++ b/src/foundation/faithful-maps.lagda.md @@ -1,13 +1,17 @@ # Faithful maps ```agda -module foundation.faithful-maps where +open import foundation.function-extensionality-axiom + +module foundation.faithful-maps + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.0-maps +open import foundation.0-maps funext open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types open import foundation.universe-levels @@ -20,7 +24,7 @@ open import foundation-core.homotopies open import foundation-core.identity-types open import foundation-core.propositional-maps open import foundation-core.sets -open import foundation-core.truncated-maps +open import foundation-core.truncated-maps funext open import foundation-core.truncation-levels ``` diff --git a/src/foundation/families-of-equivalences.lagda.md b/src/foundation/families-of-equivalences.lagda.md index 3cfded46ff..1f41557710 100644 --- a/src/foundation/families-of-equivalences.lagda.md +++ b/src/foundation/families-of-equivalences.lagda.md @@ -1,7 +1,11 @@ # Families of equivalences ```agda -module foundation.families-of-equivalences where +open import foundation.function-extensionality-axiom + +module foundation.families-of-equivalences + (funext : function-extensionality) + where open import foundation-core.families-of-equivalences public ``` @@ -9,7 +13,8 @@ open import foundation-core.families-of-equivalences public
Imports ```agda -open import foundation.equivalences +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext open import foundation.universe-levels open import foundation-core.propositions diff --git a/src/foundation/families-of-maps.lagda.md b/src/foundation/families-of-maps.lagda.md index be752e98b8..fdbd63398d 100644 --- a/src/foundation/families-of-maps.lagda.md +++ b/src/foundation/families-of-maps.lagda.md @@ -1,27 +1,32 @@ # Families of maps ```agda -module foundation.families-of-maps where +open import foundation.function-extensionality-axiom + +module foundation.families-of-maps + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext open import foundation.type-arithmetic-dependent-pair-types -open import foundation.universal-property-dependent-pair-types +open import foundation.universal-property-dependent-pair-types funext open import foundation.universe-levels open import foundation-core.contractible-types open import foundation-core.families-of-equivalences open import foundation-core.function-types -open import foundation-core.functoriality-dependent-function-types +open import foundation-core.functoriality-dependent-function-types funext open import foundation-core.functoriality-dependent-pair-types open import foundation-core.homotopies open import foundation-core.identity-types open import foundation-core.propositions -open import foundation-core.subtypes +open import foundation-core.subtypes funext open import foundation-core.torsorial-type-families open import foundation-core.type-theoretic-principle-of-choice ``` diff --git a/src/foundation/families-over-telescopes.lagda.md b/src/foundation/families-over-telescopes.lagda.md index a6a2844f56..7e36e446f0 100644 --- a/src/foundation/families-over-telescopes.lagda.md +++ b/src/foundation/families-over-telescopes.lagda.md @@ -9,9 +9,10 @@ module foundation.families-over-telescopes where ```agda open import elementary-number-theory.natural-numbers -open import foundation.raising-universe-levels open import foundation.telescopes open import foundation.universe-levels + +open import foundation-core.raising-universe-levels ```
diff --git a/src/foundation/fiber-inclusions.lagda.md b/src/foundation/fiber-inclusions.lagda.md index fb33d403c9..08740090c2 100644 --- a/src/foundation/fiber-inclusions.lagda.md +++ b/src/foundation/fiber-inclusions.lagda.md @@ -1,24 +1,31 @@ # Fiber inclusions ```agda -module foundation.fiber-inclusions where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.fiber-inclusions + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda -open import foundation.0-maps -open import foundation.cones-over-cospan-diagrams +open import foundation.0-maps funext +open import foundation.cones-over-cospan-diagrams funext open import foundation.dependent-pair-types -open import foundation.faithful-maps -open import foundation.fibers-of-maps -open import foundation.standard-pullbacks +open import foundation.faithful-maps funext +open import foundation.fibers-of-maps funext +open import foundation.raising-universe-levels-unit-type +open import foundation.standard-pullbacks funext open import foundation.transport-along-identifications open import foundation.type-arithmetic-dependent-pair-types open import foundation.unit-type open import foundation.universe-levels -open import foundation-core.1-types +open import foundation-core.1-types funext univalence open import foundation-core.contractible-maps open import foundation-core.embeddings open import foundation-core.equality-dependent-pair-types @@ -28,9 +35,9 @@ open import foundation-core.homotopies open import foundation-core.identity-types open import foundation-core.propositional-maps open import foundation-core.propositions -open import foundation-core.pullbacks +open import foundation-core.pullbacks funext open import foundation-core.sets -open import foundation-core.truncated-maps +open import foundation-core.truncated-maps funext open import foundation-core.truncated-types open import foundation-core.truncation-levels ``` diff --git a/src/foundation/fibered-equivalences.lagda.md b/src/foundation/fibered-equivalences.lagda.md index 3d899df149..7544535c91 100644 --- a/src/foundation/fibered-equivalences.lagda.md +++ b/src/foundation/fibered-equivalences.lagda.md @@ -1,19 +1,27 @@ # Fibered equivalences ```agda -module foundation.fibered-equivalences where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.fibered-equivalences + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalences -open import foundation.fibered-maps -open import foundation.logical-equivalences -open import foundation.pullbacks -open import foundation.slice +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.fibered-maps funext univalence truncations +open import foundation.logical-equivalences funext +open import foundation.pullbacks funext univalence truncations +open import foundation.slice funext univalence open import foundation.universe-levels open import foundation-core.cartesian-product-types @@ -23,7 +31,7 @@ open import foundation-core.function-types open import foundation-core.homotopies open import foundation-core.identity-types open import foundation-core.propositions -open import foundation-core.subtypes +open import foundation-core.subtypes funext ```
diff --git a/src/foundation/fibered-involutions.lagda.md b/src/foundation/fibered-involutions.lagda.md index e00fab4ca6..55681381ff 100644 --- a/src/foundation/fibered-involutions.lagda.md +++ b/src/foundation/fibered-involutions.lagda.md @@ -1,15 +1,23 @@ # Fibered involutions ```agda -module foundation.fibered-involutions where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.fibered-involutions + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.fibered-maps -open import foundation.involutions +open import foundation.fibered-maps funext univalence truncations +open import foundation.involutions funext univalence open import foundation.universe-levels open import foundation-core.cartesian-product-types diff --git a/src/foundation/fibered-maps.lagda.md b/src/foundation/fibered-maps.lagda.md index 686a7b601f..4a8f71e6e1 100644 --- a/src/foundation/fibered-maps.lagda.md +++ b/src/foundation/fibered-maps.lagda.md @@ -1,26 +1,36 @@ # Maps fibered over a map ```agda -module foundation.fibered-maps where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.fibered-maps + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.cones-over-cospan-diagrams +open import foundation.cones-over-cospan-diagrams funext open import foundation.dependent-pair-types -open import foundation.function-extensionality +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-truncated-types funext +open import foundation.function-extensionality funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopy-induction -open import foundation.slice +open import foundation.homotopy-induction funext +open import foundation.slice funext univalence open import foundation.structure-identity-principle open import foundation.type-arithmetic-dependent-pair-types open import foundation.unit-type -open import foundation.universal-property-empty-type +open import foundation.universal-property-empty-type funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import foundation-core.commuting-squares-of-maps +open import foundation-core.commuting-squares-of-maps funext open import foundation-core.contractible-types open import foundation-core.empty-types open import foundation-core.equality-dependent-pair-types @@ -29,7 +39,7 @@ open import foundation-core.fibers-of-maps open import foundation-core.function-types open import foundation-core.homotopies open import foundation-core.identity-types -open import foundation-core.small-types +open import foundation-core.small-types funext univalence truncations open import foundation-core.torsorial-type-families open import foundation-core.truncated-types open import foundation-core.truncation-levels diff --git a/src/foundation/fibers-of-maps.lagda.md b/src/foundation/fibers-of-maps.lagda.md index 01e4a3f77b..4b2d3acb54 100644 --- a/src/foundation/fibers-of-maps.lagda.md +++ b/src/foundation/fibers-of-maps.lagda.md @@ -1,7 +1,11 @@ # Fibers of maps ```agda -module foundation.fibers-of-maps where +open import foundation.function-extensionality-axiom + +module foundation.fibers-of-maps + (funext : function-extensionality) + where open import foundation-core.fibers-of-maps public ``` @@ -10,24 +14,24 @@ open import foundation-core.fibers-of-maps public ```agda open import foundation.action-on-identifications-functions -open import foundation.cones-over-cospan-diagrams +open import foundation.cones-over-cospan-diagrams funext open import foundation.dependent-pair-types -open import foundation.postcomposition-functions +open import foundation.postcomposition-functions funext open import foundation.type-arithmetic-dependent-pair-types -open import foundation.type-arithmetic-unit-type +open import foundation.type-arithmetic-unit-type funext open import foundation.unit-type open import foundation.universe-levels open import foundation-core.contractible-types open import foundation-core.equivalences open import foundation-core.function-types -open import foundation-core.functoriality-dependent-function-types +open import foundation-core.functoriality-dependent-function-types funext open import foundation-core.functoriality-dependent-pair-types open import foundation-core.homotopies open import foundation-core.identity-types -open import foundation-core.pullbacks +open import foundation-core.pullbacks funext open import foundation-core.transport-along-identifications -open import foundation-core.universal-property-pullbacks +open import foundation-core.universal-property-pullbacks funext ```
diff --git a/src/foundation/finitely-coherent-equivalences.lagda.md b/src/foundation/finitely-coherent-equivalences.lagda.md index ad8dcd5167..3f1dcf80b0 100644 --- a/src/foundation/finitely-coherent-equivalences.lagda.md +++ b/src/foundation/finitely-coherent-equivalences.lagda.md @@ -1,7 +1,11 @@ # Finitely coherent equivalences ```agda -module foundation.finitely-coherent-equivalences where +open import foundation.function-extensionality-axiom + +module foundation.finitely-coherent-equivalences + (funext : function-extensionality) + where ```
Imports @@ -9,7 +13,7 @@ module foundation.finitely-coherent-equivalences where ```agda open import elementary-number-theory.natural-numbers -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.unit-type open import foundation.universe-levels ``` diff --git a/src/foundation/finitely-coherently-invertible-maps.lagda.md b/src/foundation/finitely-coherently-invertible-maps.lagda.md index a48d827c1e..14d8d7516f 100644 --- a/src/foundation/finitely-coherently-invertible-maps.lagda.md +++ b/src/foundation/finitely-coherently-invertible-maps.lagda.md @@ -1,7 +1,11 @@ # Finitely coherently invertible maps ```agda -module foundation.finitely-coherently-invertible-maps where +open import foundation.function-extensionality-axiom + +module foundation.finitely-coherently-invertible-maps + (funext : function-extensionality) + where ```
Imports @@ -9,7 +13,7 @@ module foundation.finitely-coherently-invertible-maps where ```agda open import elementary-number-theory.natural-numbers -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.unit-type open import foundation.universe-levels ``` diff --git a/src/foundation/full-subtypes.lagda.md b/src/foundation/full-subtypes.lagda.md index 57a9714080..4efd50df1d 100644 --- a/src/foundation/full-subtypes.lagda.md +++ b/src/foundation/full-subtypes.lagda.md @@ -1,21 +1,31 @@ # Full subtypes of types ```agda -module foundation.full-subtypes where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.full-subtypes + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.decidable-subtypes +open import foundation.decidable-subtypes funext univalence truncations open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions funext +open import foundation.raising-universe-levels-unit-type open import foundation.type-arithmetic-dependent-pair-types open import foundation.unit-type open import foundation.universe-levels open import foundation-core.equivalences open import foundation-core.propositions -open import foundation-core.subtypes +open import foundation-core.subtypes funext open import foundation-core.transport-along-identifications ``` diff --git a/src/foundation/function-extensionality-axiom.lagda.md b/src/foundation/function-extensionality-axiom.lagda.md new file mode 100644 index 0000000000..064197ecd1 --- /dev/null +++ b/src/foundation/function-extensionality-axiom.lagda.md @@ -0,0 +1,166 @@ +# The function extensionality axiom + +```agda +module foundation.function-extensionality-axiom where +``` + +
Imports + +```agda +open import foundation.action-on-identifications-functions +open import foundation.evaluation-functions +open import foundation.universe-levels + +open import foundation-core.equivalences +open import foundation-core.function-types +open import foundation-core.homotopies +open import foundation-core.identity-types +``` + +
+ +## Idea + +The +{{#concept "function extensionality axiom" Agda=function-extensionality Agda=funext}} +asserts that [identifications](foundation-core.identity-types.md) of (dependent) +functions are [equivalently](foundation-core.equivalences.md) described as +[homotopies](foundation-core.homotopies.md) between them. In other words, a +function is completely determined by its values. + +Function extensionality is postulated by stating that the canonical map + +```text + htpy-eq : f ＝ g → f ~ g +``` + +from identifications between two functions to homotopies between them is an +equivalence. The map `htpy-eq` is the unique map that fits in a +[commuting triangle](foundation-core.commuting-triangles-of-maps.md) + +```text + htpy-eq + (f ＝ g) ----------> (f ~ g) + \ / + ap (ev x) \ / ev x + ∨ ∨ + (f x ＝ g x) +``` + +In other words, we define + +```text + htpy-eq p x := ap (ev x) p. +``` + +It follows from this definition that `htpy-eq refl ≐ refl-htpy`, as expected. + +## Definitions + +### Equalities induce homotopies + +```agda +module _ + {l1 l2 : Level} {A : UU l1} {B : A → UU l2} + where + + htpy-eq : {f g : (x : A) → B x} → f ＝ g → f ~ g + htpy-eq p a = ap (ev a) p + + compute-htpy-eq-refl : {f : (x : A) → B x} → htpy-eq refl ＝ refl-htpy' f + compute-htpy-eq-refl = refl +``` + +### An instance of function extensionality + +This property asserts that, _given_ two functions `f` and `g`, the map + +```text + htpy-eq : f ＝ g → f ~ g +``` + +is an equivalence. + +```agda +module _ + {l1 l2 : Level} {A : UU l1} {B : A → UU l2} + where + + instance-function-extensionality : (f g : (x : A) → B x) → UU (l1 ⊔ l2) + instance-function-extensionality f g = is-equiv (htpy-eq {f = f} {g}) +``` + +### Based function extensionality + +This property asserts that, _given_ a function `f`, the map + +```text + htpy-eq : f ＝ g → f ~ g +``` + +is an equivalence for any function `g` of the same type. + +```agda +module _ + {l1 l2 : Level} {A : UU l1} {B : A → UU l2} + where + + based-function-extensionality : (f : (x : A) → B x) → UU (l1 ⊔ l2) + based-function-extensionality f = + (g : (x : A) → B x) → instance-function-extensionality f g +``` + +### The function extensionality principle with respect to a universe level + +```agda +function-extensionality-Level : (l1 l2 : Level) → UU (lsuc l1 ⊔ lsuc l2) +function-extensionality-Level l1 l2 = + {A : UU l1} {B : A → UU l2} + (f : (x : A) → B x) → based-function-extensionality f +``` + +### The function extensionality axiom + +```agda +function-extensionality : UUω +function-extensionality = {l1 l2 : Level} → function-extensionality-Level l1 l2 +``` + +## Properties + +### `htpy-eq` preserves inverses + +For any two functions `f g : (x : A) → B x` we have a +[commuting square](foundation-core.commuting-squares-of-maps.md) + +```text + inv + (f = g) ---------> (g = f) + | | + htpy-eq | | htpy-eq + ∨ ∨ + (f ~ g) ---------> (g ~ f). + inv-htpy +``` + +```agda +module _ + {l1 l2 : Level} {A : UU l1} {B : A → UU l2} {f g : (x : A) → B x} + where + + compute-htpy-eq-inv : inv-htpy {f = f} {g} ∘ htpy-eq ~ htpy-eq ∘ inv + compute-htpy-eq-inv refl = refl + + compute-inv-htpy-htpy-eq : htpy-eq ∘ inv ~ inv-htpy {f = f} {g} ∘ htpy-eq + compute-inv-htpy-htpy-eq = inv-htpy compute-htpy-eq-inv +``` + +## See also + +- The fact that the univalence axiom implies function extensionality is proven + in + [`foundation.univalence-implies-function-extensionality`](foundation.univalence-implies-function-extensionality.md). +- Weak function extensionality is defined in + [`foundation.weak-function-extensionality`](foundation.weak-function-extensionality.md). +- Transporting along homotopies is defined in + [`foundation.transport-along-homotopies`](foundation.transport-along-homotopies.md). diff --git a/src/foundation/function-extensionality.lagda.md b/src/foundation/function-extensionality.lagda.md index 5633842ad1..d26c3c48c8 100644 --- a/src/foundation/function-extensionality.lagda.md +++ b/src/foundation/function-extensionality.lagda.md @@ -1,6 +1,8 @@ # Function extensionality ```agda +open import foundation.function-extensionality-axiom + module foundation.function-extensionality where ``` @@ -10,7 +12,6 @@ module foundation.function-extensionality where open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.evaluation-functions open import foundation.implicit-function-types open import foundation.universe-levels @@ -63,75 +64,8 @@ It follows from this definition that `htpy-eq refl ≐ refl-htpy`, as expected. ## Definitions -### Equalities induce homotopies - -```agda -module _ - {l1 l2 : Level} {A : UU l1} {B : A → UU l2} - where - - htpy-eq : {f g : (x : A) → B x} → f ＝ g → f ~ g - htpy-eq p a = ap (ev a) p - - compute-htpy-eq-refl : {f : (x : A) → B x} → htpy-eq refl ＝ refl-htpy' f - compute-htpy-eq-refl = refl -``` - -### An instance of function extensionality - -This property asserts that, _given_ two functions `f` and `g`, the map - -```text - htpy-eq : f ＝ g → f ~ g -``` - -is an equivalence. - -```agda -module _ - {l1 l2 : Level} {A : UU l1} {B : A → UU l2} - where - - instance-function-extensionality : (f g : (x : A) → B x) → UU (l1 ⊔ l2) - instance-function-extensionality f g = is-equiv (htpy-eq {f = f} {g}) -``` - -### Based function extensionality - -This property asserts that, _given_ a function `f`, the map - -```text - htpy-eq : f ＝ g → f ~ g -``` - -is an equivalence for any function `g` of the same type. - -```agda -module _ - {l1 l2 : Level} {A : UU l1} {B : A → UU l2} - where - - based-function-extensionality : (f : (x : A) → B x) → UU (l1 ⊔ l2) - based-function-extensionality f = - (g : (x : A) → B x) → instance-function-extensionality f g -``` - -### The function extensionality principle with respect to a universe level - -```agda -function-extensionality-Level : (l1 l2 : Level) → UU (lsuc l1 ⊔ lsuc l2) -function-extensionality-Level l1 l2 = - {A : UU l1} {B : A → UU l2} - (f : (x : A) → B x) → based-function-extensionality f -``` - ### The function extensionality axiom -```agda -function-extensionality : UUω -function-extensionality = {l1 l2 : Level} → function-extensionality-Level l1 l2 -``` - Rather than postulating a witness of `function-extensionality` directly, we postulate the constituents of a coherent two-sided inverse to `htpy-eq`. The benefits are that we end up with a single converse map to `htpy-eq`, rather than @@ -244,33 +178,6 @@ module _ ( is-retraction-eq-htpy (eq-htpy H ∙ eq-htpy K)) ``` -### `htpy-eq` preserves inverses - -For any two functions `f g : (x : A) → B x` we have a -[commuting square](foundation-core.commuting-squares-of-maps.md) - -```text - inv - (f = g) ---------> (g = f) - | | - htpy-eq | | htpy-eq - ∨ ∨ - (f ~ g) ---------> (g ~ f). - inv-htpy -``` - -```agda -module _ - {l1 l2 : Level} {A : UU l1} {B : A → UU l2} {f g : (x : A) → B x} - where - - compute-htpy-eq-inv : inv-htpy {f = f} {g} ∘ htpy-eq ~ htpy-eq ∘ inv - compute-htpy-eq-inv refl = refl - - compute-inv-htpy-htpy-eq : htpy-eq ∘ inv ~ inv-htpy {f = f} {g} ∘ htpy-eq - compute-inv-htpy-htpy-eq = inv-htpy compute-htpy-eq-inv -``` - ### `eq-htpy` preserves inverses For any two functions `f g : (x : A) → B x` we have a commuting square diff --git a/src/foundation/function-types.lagda.md b/src/foundation/function-types.lagda.md index d6fb4ed16f..c37c181954 100644 --- a/src/foundation/function-types.lagda.md +++ b/src/foundation/function-types.lagda.md @@ -1,7 +1,11 @@ # Function types ```agda -module foundation.function-types where +open import foundation.function-extensionality-axiom + +module foundation.function-types + (funext : function-extensionality) + where open import foundation-core.function-types public ``` @@ -13,8 +17,8 @@ open import foundation.action-on-identifications-dependent-functions open import foundation.action-on-identifications-functions open import foundation.commuting-pentagons-of-identifications open import foundation.dependent-pair-types -open import foundation.function-extensionality -open import foundation.homotopy-induction +open import foundation.function-extensionality funext +open import foundation.homotopy-induction funext open import foundation.universe-levels open import foundation-core.dependent-identifications diff --git a/src/foundation/functional-correspondences.lagda.md b/src/foundation/functional-correspondences.lagda.md index ed5998a661..1f8dc28e36 100644 --- a/src/foundation/functional-correspondences.lagda.md +++ b/src/foundation/functional-correspondences.lagda.md @@ -1,27 +1,37 @@ # Functional correspondences ```agda -module foundation.functional-correspondences where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.functional-correspondences + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.contractible-types +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types -open import foundation.function-extensionality +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.equality-dependent-function-types funext +open import foundation.function-extensionality funext open import foundation.fundamental-theorem-of-identity-types open import foundation.subtype-identity-principle -open import foundation.torsorial-type-families -open import foundation.univalence +open import foundation.torsorial-type-families funext univalence truncations +open import foundation.univalence funext univalence open import foundation.universe-levels open import foundation-core.equivalences open import foundation-core.identity-types open import foundation-core.propositions -open import foundation-core.subtypes +open import foundation-core.subtypes funext ```
diff --git a/src/foundation/functoriality-action-on-identifications-functions.lagda.md b/src/foundation/functoriality-action-on-identifications-functions.lagda.md index 987e964955..dfbbb82aaa 100644 --- a/src/foundation/functoriality-action-on-identifications-functions.lagda.md +++ b/src/foundation/functoriality-action-on-identifications-functions.lagda.md @@ -1,26 +1,30 @@ # Functoriality of the action on identifications of functions ```agda -module foundation.functoriality-action-on-identifications-functions where +open import foundation.function-extensionality-axiom + +module foundation.functoriality-action-on-identifications-functions + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.action-on-higher-identifications-functions +open import foundation.action-on-higher-identifications-functions funext open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.commuting-triangles-of-morphisms-arrows -open import foundation.cones-over-cospan-diagrams +open import foundation.commuting-triangles-of-morphisms-arrows funext +open import foundation.cones-over-cospan-diagrams funext open import foundation.dependent-pair-types -open import foundation.homotopies-morphisms-arrows -open import foundation.morphisms-arrows -open import foundation.path-algebra +open import foundation.homotopies-morphisms-arrows funext +open import foundation.morphisms-arrows funext +open import foundation.path-algebra funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition open import foundation-core.commuting-squares-of-homotopies -open import foundation-core.commuting-squares-of-maps +open import foundation-core.commuting-squares-of-maps funext open import foundation-core.equality-dependent-pair-types open import foundation-core.fibers-of-maps open import foundation-core.function-types diff --git a/src/foundation/functoriality-cartesian-product-types.lagda.md b/src/foundation/functoriality-cartesian-product-types.lagda.md index 08be06910b..499cf07dd3 100644 --- a/src/foundation/functoriality-cartesian-product-types.lagda.md +++ b/src/foundation/functoriality-cartesian-product-types.lagda.md @@ -1,7 +1,11 @@ # Functoriality of cartesian product types ```agda -module foundation.functoriality-cartesian-product-types where +open import foundation.function-extensionality-axiom + +module foundation.functoriality-cartesian-product-types + (funext : function-extensionality) + where ```
Imports @@ -10,11 +14,11 @@ module foundation.functoriality-cartesian-product-types where open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types open import foundation.equality-cartesian-product-types -open import foundation.morphisms-arrows +open import foundation.morphisms-arrows funext open import foundation.universe-levels open import foundation-core.cartesian-product-types -open import foundation-core.commuting-squares-of-maps +open import foundation-core.commuting-squares-of-maps funext open import foundation-core.contractible-maps open import foundation-core.contractible-types open import foundation-core.equivalences diff --git a/src/foundation/functoriality-coproduct-types.lagda.md b/src/foundation/functoriality-coproduct-types.lagda.md index 1c629f6117..e97cba60f4 100644 --- a/src/foundation/functoriality-coproduct-types.lagda.md +++ b/src/foundation/functoriality-coproduct-types.lagda.md @@ -1,30 +1,38 @@ # Functoriality of coproduct types ```agda -module foundation.functoriality-coproduct-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.functoriality-coproduct-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.coproduct-types +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types open import foundation.equality-cartesian-product-types -open import foundation.equality-coproduct-types -open import foundation.equivalence-extensionality -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.functoriality-cartesian-product-types -open import foundation.homotopy-induction -open import foundation.morphisms-arrows -open import foundation.negated-equality -open import foundation.propositional-truncations -open import foundation.retractions +open import foundation.equality-coproduct-types funext univalence truncations +open import foundation.equivalence-extensionality funext +open import foundation.equivalences funext +open import foundation.function-extensionality funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.homotopy-induction funext +open import foundation.morphisms-arrows funext +open import foundation.negated-equality funext univalence truncations +open import foundation.propositional-truncations funext univalence +open import foundation.retractions funext open import foundation.structure-identity-principle -open import foundation.surjective-maps +open import foundation.surjective-maps funext univalence truncations open import foundation.unit-type -open import foundation.universal-property-coproduct-types +open import foundation.universal-property-coproduct-types funext open import foundation.universe-levels open import foundation-core.cartesian-product-types @@ -33,7 +41,7 @@ open import foundation-core.embeddings open import foundation-core.empty-types open import foundation-core.fibers-of-maps open import foundation-core.function-types -open import foundation-core.functoriality-dependent-function-types +open import foundation-core.functoriality-dependent-function-types funext open import foundation-core.functoriality-dependent-pair-types open import foundation-core.homotopies open import foundation-core.identity-types diff --git a/src/foundation/functoriality-dependent-function-types.lagda.md b/src/foundation/functoriality-dependent-function-types.lagda.md index 9fc8e6c98c..62bcbdbac3 100644 --- a/src/foundation/functoriality-dependent-function-types.lagda.md +++ b/src/foundation/functoriality-dependent-function-types.lagda.md @@ -1,9 +1,15 @@ # Functoriality of dependent function types ```agda -module foundation.functoriality-dependent-function-types where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom -open import foundation-core.functoriality-dependent-function-types public +module foundation.functoriality-dependent-function-types + (funext : function-extensionality) + (univalence : univalence-axiom) + where + +open import foundation-core.functoriality-dependent-function-types funext public ```
Imports @@ -11,13 +17,14 @@ open import foundation-core.functoriality-dependent-function-types public ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.dependent-universal-property-equivalences -open import foundation.equivalence-extensionality -open import foundation.function-extensionality -open import foundation.retracts-of-types +open import foundation.dependent-products-truncated-types funext +open import foundation.dependent-universal-property-equivalences funext +open import foundation.equivalence-extensionality funext +open import foundation.function-extensionality funext +open import foundation.retracts-of-types funext univalence open import foundation.transport-along-identifications open import foundation.unit-type -open import foundation.universal-property-unit-type +open import foundation.universal-property-unit-type funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition @@ -31,7 +38,7 @@ open import foundation-core.homotopies open import foundation-core.identity-types open import foundation-core.precomposition-dependent-functions open import foundation-core.propositional-maps -open import foundation-core.truncated-maps +open import foundation-core.truncated-maps funext open import foundation-core.truncated-types open import foundation-core.truncation-levels ``` diff --git a/src/foundation/functoriality-dependent-pair-types.lagda.md b/src/foundation/functoriality-dependent-pair-types.lagda.md index beffdd38f2..c84ccb6c26 100644 --- a/src/foundation/functoriality-dependent-pair-types.lagda.md +++ b/src/foundation/functoriality-dependent-pair-types.lagda.md @@ -1,7 +1,11 @@ # Functoriality of dependent pair types ```agda -module foundation.functoriality-dependent-pair-types where +open import foundation.function-extensionality-axiom + +module foundation.functoriality-dependent-pair-types + (funext : function-extensionality) + where open import foundation-core.functoriality-dependent-pair-types public ``` @@ -12,10 +16,10 @@ open import foundation-core.functoriality-dependent-pair-types public open import foundation.action-on-identifications-functions open import foundation.dependent-homotopies open import foundation.dependent-pair-types -open import foundation.morphisms-arrows +open import foundation.morphisms-arrows funext open import foundation.universe-levels -open import foundation-core.commuting-squares-of-maps +open import foundation-core.commuting-squares-of-maps funext open import foundation-core.commuting-triangles-of-maps open import foundation-core.contractible-maps open import foundation-core.dependent-identifications @@ -28,7 +32,7 @@ open import foundation-core.identity-types open import foundation-core.injective-maps open import foundation-core.propositional-maps open import foundation-core.transport-along-identifications -open import foundation-core.truncated-maps +open import foundation-core.truncated-maps funext open import foundation-core.truncated-types open import foundation-core.truncation-levels ``` diff --git a/src/foundation/functoriality-fibers-of-maps.lagda.md b/src/foundation/functoriality-fibers-of-maps.lagda.md index 5beb6de9e9..c040e172f1 100644 --- a/src/foundation/functoriality-fibers-of-maps.lagda.md +++ b/src/foundation/functoriality-fibers-of-maps.lagda.md @@ -1,23 +1,27 @@ # Functoriality of fibers of maps ```agda -module foundation.functoriality-fibers-of-maps where +open import foundation.function-extensionality-axiom + +module foundation.functoriality-fibers-of-maps + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.action-on-higher-identifications-functions +open import foundation.action-on-higher-identifications-functions funext open import foundation.action-on-identifications-functions -open import foundation.cones-over-cospan-diagrams +open import foundation.cones-over-cospan-diagrams funext open import foundation.dependent-pair-types -open import foundation.homotopies-morphisms-arrows -open import foundation.morphisms-arrows +open import foundation.homotopies-morphisms-arrows funext +open import foundation.morphisms-arrows funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition open import foundation-core.commuting-squares-of-homotopies -open import foundation-core.commuting-squares-of-maps +open import foundation-core.commuting-squares-of-maps funext open import foundation-core.equality-dependent-pair-types open import foundation-core.fibers-of-maps open import foundation-core.function-types diff --git a/src/foundation/functoriality-function-types.lagda.md b/src/foundation/functoriality-function-types.lagda.md index a86808a6d2..0d05d84c70 100644 --- a/src/foundation/functoriality-function-types.lagda.md +++ b/src/foundation/functoriality-function-types.lagda.md @@ -1,7 +1,13 @@ # Functoriality of function types ```agda -module foundation.functoriality-function-types where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.functoriality-function-types + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports @@ -9,10 +15,10 @@ module foundation.functoriality-function-types where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.functoriality-dependent-function-types -open import foundation.postcomposition-functions +open import foundation.functoriality-dependent-function-types funext univalence +open import foundation.postcomposition-functions funext open import foundation.unit-type -open import foundation.universal-property-equivalences +open import foundation.universal-property-equivalences funext open import foundation.universe-levels open import foundation-core.embeddings @@ -21,7 +27,7 @@ open import foundation-core.function-types open import foundation-core.identity-types open import foundation-core.precomposition-functions open import foundation-core.propositional-maps -open import foundation-core.truncated-maps +open import foundation-core.truncated-maps funext open import foundation-core.truncation-levels ``` diff --git a/src/foundation/functoriality-morphisms-arrows.lagda.md b/src/foundation/functoriality-morphisms-arrows.lagda.md index a8cdd6b387..790fa38dba 100644 --- a/src/foundation/functoriality-morphisms-arrows.lagda.md +++ b/src/foundation/functoriality-morphisms-arrows.lagda.md @@ -1,7 +1,15 @@ # Functoriality of morphisms of arrows ```agda -module foundation.functoriality-morphisms-arrows where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.functoriality-morphisms-arrows + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,31 +17,31 @@ module foundation.functoriality-morphisms-arrows where ```agda open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.bicomposition-functions -open import foundation.commuting-squares-of-maps -open import foundation.composition-algebra -open import foundation.cones-over-cospan-diagrams +open import foundation.bicomposition-functions funext +open import foundation.commuting-squares-of-maps funext univalence +open import foundation.composition-algebra funext +open import foundation.cones-over-cospan-diagrams funext open import foundation.cospan-diagrams open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.functoriality-pullbacks -open import foundation.homotopies -open import foundation.homotopies-morphisms-arrows -open import foundation.homotopies-morphisms-cospan-diagrams -open import foundation.identity-types -open import foundation.morphisms-arrows +open import foundation.dependent-products-propositions funext +open import foundation.equality-dependent-pair-types funext +open import foundation.equivalences funext +open import foundation.function-extensionality funext +open import foundation.function-types funext +open import foundation.functoriality-pullbacks funext univalence truncations +open import foundation.homotopies funext +open import foundation.homotopies-morphisms-arrows funext +open import foundation.homotopies-morphisms-cospan-diagrams funext univalence truncations +open import foundation.identity-types funext +open import foundation.morphisms-arrows funext open import foundation.morphisms-cospan-diagrams -open import foundation.postcomposition-functions -open import foundation.precomposition-functions -open import foundation.pullback-cones -open import foundation.pullbacks -open import foundation.retractions -open import foundation.retracts-of-maps -open import foundation.sections -open import foundation.standard-pullbacks +open import foundation.postcomposition-functions funext +open import foundation.precomposition-functions funext +open import foundation.pullback-cones funext univalence truncations +open import foundation.pullbacks funext univalence truncations +open import foundation.retractions funext +open import foundation.sections funext +open import foundation.standard-pullbacks funext open import foundation.universe-levels open import foundation.whiskering-higher-homotopies-composition open import foundation.whiskering-homotopies-composition diff --git a/src/foundation/functoriality-propositional-truncation.lagda.md b/src/foundation/functoriality-propositional-truncation.lagda.md index 1c895736c6..5fde866adc 100644 --- a/src/foundation/functoriality-propositional-truncation.lagda.md +++ b/src/foundation/functoriality-propositional-truncation.lagda.md @@ -1,7 +1,15 @@ # Functoriality of propositional truncations ```agda -module foundation.functoriality-propositional-truncation where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.functoriality-propositional-truncation + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,9 +17,9 @@ module foundation.functoriality-propositional-truncation where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-extensionality -open import foundation.logical-equivalences -open import foundation.propositional-truncations +open import foundation.dependent-products-propositions funext +open import foundation.logical-equivalences funext +open import foundation.propositional-truncations funext univalence open import foundation.universe-levels open import foundation.whiskering-homotopies-composition diff --git a/src/foundation/functoriality-pullbacks.lagda.md b/src/foundation/functoriality-pullbacks.lagda.md index 60e01bf16e..fbb40789a5 100644 --- a/src/foundation/functoriality-pullbacks.lagda.md +++ b/src/foundation/functoriality-pullbacks.lagda.md @@ -1,29 +1,37 @@ # Functorialty of pullbacks ```agda -module foundation.functoriality-pullbacks where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.functoriality-pullbacks + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cones-over-cospan-diagrams +open import foundation.cones-over-cospan-diagrams funext open import foundation.cospan-diagrams open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types -open import foundation.function-types -open import foundation.homotopies -open import foundation.homotopies-morphisms-cospan-diagrams +open import foundation.equality-dependent-pair-types funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.homotopies-morphisms-cospan-diagrams funext univalence truncations open import foundation.morphisms-cospan-diagrams -open import foundation.pullback-cones -open import foundation.standard-pullbacks +open import foundation.pullback-cones funext univalence truncations +open import foundation.standard-pullbacks funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition open import foundation-core.equivalences open import foundation-core.identity-types -open import foundation-core.pullbacks +open import foundation-core.pullbacks funext ```
diff --git a/src/foundation/functoriality-sequential-limits.lagda.md b/src/foundation/functoriality-sequential-limits.lagda.md index 32979a1d7b..7ef162b87b 100644 --- a/src/foundation/functoriality-sequential-limits.lagda.md +++ b/src/foundation/functoriality-sequential-limits.lagda.md @@ -1,7 +1,15 @@ # Functoriality of sequential limits ```agda -module foundation.functoriality-sequential-limits where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.functoriality-sequential-limits + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,11 +18,11 @@ module foundation.functoriality-sequential-limits where open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.cones-over-inverse-sequential-diagrams +open import foundation.cones-over-inverse-sequential-diagrams funext univalence truncations open import foundation.dependent-pair-types -open import foundation.inverse-sequential-diagrams -open import foundation.morphisms-inverse-sequential-diagrams -open import foundation.sequential-limits +open import foundation.inverse-sequential-diagrams funext univalence truncations +open import foundation.morphisms-inverse-sequential-diagrams funext univalence truncations +open import foundation.sequential-limits funext univalence truncations open import foundation.universe-levels open import foundation-core.equivalences diff --git a/src/foundation/functoriality-set-quotients.lagda.md b/src/foundation/functoriality-set-quotients.lagda.md index 556c6b19c2..3a6e53b407 100644 --- a/src/foundation/functoriality-set-quotients.lagda.md +++ b/src/foundation/functoriality-set-quotients.lagda.md @@ -2,8 +2,15 @@ ```agda {-# OPTIONS --lossy-unification #-} - -module foundation.functoriality-set-quotients where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.functoriality-set-quotients + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -11,28 +18,29 @@ module foundation.functoriality-set-quotients where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalence-extensionality +open import foundation.dependent-products-propositions funext +open import foundation.equivalence-extensionality funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopy-induction -open import foundation.logical-equivalences -open import foundation.reflecting-maps-equivalence-relations -open import foundation.set-quotients +open import foundation.homotopy-induction funext +open import foundation.logical-equivalences funext +open import foundation.reflecting-maps-equivalence-relations funext univalence truncations +open import foundation.set-quotients funext univalence truncations open import foundation.subtype-identity-principle -open import foundation.surjective-maps -open import foundation.uniqueness-set-quotients -open import foundation.universal-property-set-quotients +open import foundation.surjective-maps funext univalence truncations +open import foundation.uniqueness-set-quotients funext univalence truncations +open import foundation.universal-property-set-quotients funext univalence truncations open import foundation.universe-levels -open import foundation-core.commuting-squares-of-maps +open import foundation-core.commuting-squares-of-maps funext open import foundation-core.contractible-types -open import foundation-core.equivalence-relations +open import foundation-core.equivalence-relations funext univalence truncations open import foundation-core.equivalences open import foundation-core.function-types open import foundation-core.homotopies open import foundation-core.identity-types open import foundation-core.propositions open import foundation-core.sets -open import foundation-core.subtypes +open import foundation-core.subtypes funext open import foundation-core.torsorial-type-families ``` diff --git a/src/foundation/functoriality-set-truncation.lagda.md b/src/foundation/functoriality-set-truncation.lagda.md index 6e1fb2db8d..67f3f8aa01 100644 --- a/src/foundation/functoriality-set-truncation.lagda.md +++ b/src/foundation/functoriality-set-truncation.lagda.md @@ -1,7 +1,15 @@ # Functoriality of set truncation ```agda -module foundation.functoriality-set-truncation where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.functoriality-set-truncation + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,19 +17,20 @@ module foundation.functoriality-set-truncation where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.functoriality-truncation -open import foundation.images -open import foundation.injective-maps -open import foundation.propositional-truncations -open import foundation.retracts-of-types -open import foundation.set-truncations -open import foundation.sets -open import foundation.slice -open import foundation.surjective-maps -open import foundation.uniqueness-image -open import foundation.uniqueness-set-truncations -open import foundation.universal-property-image -open import foundation.universal-property-set-truncation +open import foundation.dependent-products-propositions funext +open import foundation.functoriality-truncation funext univalence truncations +open import foundation.images funext univalence truncations +open import foundation.injective-maps funext +open import foundation.propositional-truncations funext univalence +open import foundation.retracts-of-types funext univalence +open import foundation.set-truncations funext univalence +open import foundation.sets funext univalence +open import foundation.slice funext univalence +open import foundation.surjective-maps funext univalence truncations +open import foundation.uniqueness-image funext univalence truncations +open import foundation.uniqueness-set-truncations funext univalence +open import foundation.universal-property-image funext univalence truncations +open import foundation.universal-property-set-truncation funext univalence truncations open import foundation.universe-levels open import foundation.whiskering-homotopies-composition diff --git a/src/foundation/functoriality-truncation.lagda.md b/src/foundation/functoriality-truncation.lagda.md index 92e1760616..5da44c62f3 100644 --- a/src/foundation/functoriality-truncation.lagda.md +++ b/src/foundation/functoriality-truncation.lagda.md @@ -1,7 +1,15 @@ # Functoriality of truncations ```agda -module foundation.functoriality-truncation where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.functoriality-truncation + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,12 +17,12 @@ module foundation.functoriality-truncation where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-extensionality -open import foundation.truncations +open import foundation.function-extensionality funext +open import foundation.truncations funext univalence truncations open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import foundation-core.commuting-squares-of-maps +open import foundation-core.commuting-squares-of-maps funext open import foundation-core.contractible-types open import foundation-core.equivalences open import foundation-core.function-types diff --git a/src/foundation/fundamental-theorem-of-equivalence-relations.lagda.md b/src/foundation/fundamental-theorem-of-equivalence-relations.lagda.md index 8bd7600e74..f1217a374a 100644 --- a/src/foundation/fundamental-theorem-of-equivalence-relations.lagda.md +++ b/src/foundation/fundamental-theorem-of-equivalence-relations.lagda.md @@ -1,28 +1,36 @@ # Fundamental theorem of equivalence relations ```agda -module foundation.fundamental-theorem-of-equivalence-relations where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.fundamental-theorem-of-equivalence-relations + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.binary-relations +open import foundation.binary-relations funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalence-classes -open import foundation.full-subtypes -open import foundation.inhabited-subtypes -open import foundation.logical-equivalences -open import foundation.partitions -open import foundation.propositional-truncations -open import foundation.subtypes +open import foundation.equivalence-classes funext univalence truncations +open import foundation.full-subtypes funext univalence truncations +open import foundation.inhabited-subtypes funext univalence truncations +open import foundation.logical-equivalences funext +open import foundation.partitions funext univalence truncations +open import foundation.propositional-truncations funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels open import foundation-core.cartesian-product-types open import foundation-core.contractible-types -open import foundation-core.equivalence-relations +open import foundation-core.equivalence-relations funext univalence truncations open import foundation-core.equivalences open import foundation-core.function-types open import foundation-core.functoriality-dependent-pair-types diff --git a/src/foundation/global-choice.lagda.md b/src/foundation/global-choice.lagda.md index dde44fdbc8..461d20b1c5 100644 --- a/src/foundation/global-choice.lagda.md +++ b/src/foundation/global-choice.lagda.md @@ -1,22 +1,30 @@ # Global choice ```agda -module foundation.global-choice where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.global-choice + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.functoriality-propositional-truncation -open import foundation.hilberts-epsilon-operators +open import foundation.functoriality-propositional-truncation funext univalence truncations +open import foundation.hilberts-epsilon-operators funext univalence truncations open import foundation.universe-levels open import foundation-core.equivalences open import foundation-core.negation -open import univalent-combinatorics.2-element-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.2-element-types funext univalence truncations +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/foundation/global-subuniverses.lagda.md b/src/foundation/global-subuniverses.lagda.md index fffb54617f..93aa6fa639 100644 --- a/src/foundation/global-subuniverses.lagda.md +++ b/src/foundation/global-subuniverses.lagda.md @@ -1,15 +1,22 @@ # Global subuniverses ```agda -module foundation.global-subuniverses where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.global-subuniverses + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.iterated-dependent-product-types -open import foundation.subuniverses +open import foundation.iterated-dependent-product-types funext +open import foundation.subuniverses funext univalence +open import foundation.telescopes open import foundation.universe-levels open import foundation-core.equivalences diff --git a/src/foundation/globular-type-of-dependent-functions.lagda.md b/src/foundation/globular-type-of-dependent-functions.lagda.md index c620d17ec1..dafb45a114 100644 --- a/src/foundation/globular-type-of-dependent-functions.lagda.md +++ b/src/foundation/globular-type-of-dependent-functions.lagda.md @@ -2,8 +2,15 @@ ```agda {-# OPTIONS --guardedness #-} - -module foundation.globular-type-of-dependent-functions where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.globular-type-of-dependent-functions + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -14,8 +21,8 @@ open import foundation.universe-levels open import foundation-core.homotopies open import globular-types.globular-types -open import globular-types.reflexive-globular-types -open import globular-types.transitive-globular-types +open import globular-types.reflexive-globular-types funext univalence truncations +open import globular-types.transitive-globular-types funext univalence truncations ```
diff --git a/src/foundation/globular-type-of-functions.lagda.md b/src/foundation/globular-type-of-functions.lagda.md index 41533c9aee..62003eb957 100644 --- a/src/foundation/globular-type-of-functions.lagda.md +++ b/src/foundation/globular-type-of-functions.lagda.md @@ -2,21 +2,28 @@ ```agda {-# OPTIONS --guardedness #-} - -module foundation.globular-type-of-functions where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.globular-type-of-functions + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.globular-type-of-dependent-functions +open import foundation.globular-type-of-dependent-functions funext univalence truncations open import foundation.universe-levels open import foundation-core.homotopies open import globular-types.globular-types -open import globular-types.reflexive-globular-types -open import globular-types.transitive-globular-types +open import globular-types.reflexive-globular-types funext univalence truncations +open import globular-types.transitive-globular-types funext univalence truncations ```
diff --git a/src/foundation/higher-homotopies-morphisms-arrows.lagda.md b/src/foundation/higher-homotopies-morphisms-arrows.lagda.md index 842b83be66..ed76f499f2 100644 --- a/src/foundation/higher-homotopies-morphisms-arrows.lagda.md +++ b/src/foundation/higher-homotopies-morphisms-arrows.lagda.md @@ -1,27 +1,35 @@ # Higher homotopies of morphisms of arrows ```agda -module foundation.higher-homotopies-morphisms-arrows where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.higher-homotopies-morphisms-arrows + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-homotopies -open import foundation.commuting-squares-of-identifications +open import foundation.commuting-squares-of-homotopies funext +open import foundation.commuting-squares-of-identifications funext open import foundation.dependent-pair-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies-morphisms-arrows -open import foundation.homotopy-induction -open import foundation.morphisms-arrows -open import foundation.path-algebra +open import foundation.homotopies-morphisms-arrows funext +open import foundation.homotopy-induction funext +open import foundation.morphisms-arrows funext +open import foundation.path-algebra funext open import foundation.structure-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext univalence truncations open import foundation.universe-levels open import foundation.whiskering-higher-homotopies-composition -open import foundation.whiskering-homotopies-concatenation -open import foundation.whiskering-identifications-concatenation +open import foundation.whiskering-homotopies-concatenation funext +open import foundation.whiskering-identifications-concatenation funext open import foundation-core.equivalences open import foundation-core.homotopies diff --git a/src/foundation/hilberts-epsilon-operators.lagda.md b/src/foundation/hilberts-epsilon-operators.lagda.md index 1c23904a8b..812028ae3c 100644 --- a/src/foundation/hilberts-epsilon-operators.lagda.md +++ b/src/foundation/hilberts-epsilon-operators.lagda.md @@ -1,14 +1,22 @@ # Hilbert's `ε`-operators ```agda -module foundation.hilberts-epsilon-operators where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.hilberts-epsilon-operators + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.functoriality-propositional-truncation -open import foundation.propositional-truncations +open import foundation.functoriality-propositional-truncation funext univalence truncations +open import foundation.propositional-truncations funext univalence open import foundation.universe-levels open import foundation-core.equivalences diff --git a/src/foundation/homotopies-morphisms-arrows.lagda.md b/src/foundation/homotopies-morphisms-arrows.lagda.md index 4eb4eeead5..dd8f4b5254 100644 --- a/src/foundation/homotopies-morphisms-arrows.lagda.md +++ b/src/foundation/homotopies-morphisms-arrows.lagda.md @@ -1,29 +1,33 @@ # Homotopies of morphisms of arrows ```agda -module foundation.homotopies-morphisms-arrows where +open import foundation.function-extensionality-axiom + +module foundation.homotopies-morphisms-arrows + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-identifications -open import foundation.commuting-triangles-of-identifications -open import foundation.cones-over-cospan-diagrams +open import foundation.commuting-squares-of-identifications funext +open import foundation.commuting-triangles-of-identifications funext +open import foundation.cones-over-cospan-diagrams funext open import foundation.dependent-pair-types -open import foundation.function-extensionality +open import foundation.function-extensionality funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopy-induction -open import foundation.morphisms-arrows -open import foundation.postcomposition-functions +open import foundation.homotopy-induction funext +open import foundation.morphisms-arrows funext +open import foundation.postcomposition-functions funext open import foundation.structure-identity-principle open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import foundation.whiskering-identifications-concatenation +open import foundation.whiskering-identifications-concatenation funext open import foundation-core.commuting-squares-of-homotopies -open import foundation-core.commuting-squares-of-maps +open import foundation-core.commuting-squares-of-maps funext open import foundation-core.equivalences open import foundation-core.function-types open import foundation-core.homotopies diff --git a/src/foundation/homotopies-morphisms-cospan-diagrams.lagda.md b/src/foundation/homotopies-morphisms-cospan-diagrams.lagda.md index 0b4e7d6bb5..49c888a90a 100644 --- a/src/foundation/homotopies-morphisms-cospan-diagrams.lagda.md +++ b/src/foundation/homotopies-morphisms-cospan-diagrams.lagda.md @@ -1,22 +1,30 @@ # Homotopies of morphisms of cospan diagrams ```agda -module foundation.homotopies-morphisms-cospan-diagrams where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.homotopies-morphisms-cospan-diagrams + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.commuting-squares-of-homotopies +open import foundation.commuting-squares-of-homotopies funext open import foundation.cospan-diagrams open import foundation.dependent-pair-types -open import foundation.function-extensionality +open import foundation.function-extensionality funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopy-induction -open import foundation.identity-types +open import foundation.homotopy-induction funext +open import foundation.identity-types funext open import foundation.morphisms-cospan-diagrams open import foundation.structure-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext univalence truncations open import foundation.universe-levels open import foundation.whiskering-homotopies-composition diff --git a/src/foundation/homotopies.lagda.md b/src/foundation/homotopies.lagda.md index 54f138533e..c212cdb047 100644 --- a/src/foundation/homotopies.lagda.md +++ b/src/foundation/homotopies.lagda.md @@ -1,7 +1,11 @@ # Homotopies ```agda -module foundation.homotopies where +open import foundation.function-extensionality-axiom + +module foundation.homotopies + (funext : function-extensionality) + where open import foundation-core.homotopies public ``` @@ -9,22 +13,22 @@ open import foundation-core.homotopies public
Imports ```agda -open import foundation.action-on-higher-identifications-functions +open import foundation.action-on-higher-identifications-functions funext open import foundation.action-on-identifications-dependent-functions open import foundation.action-on-identifications-functions open import foundation.binary-equivalences open import foundation.dependent-pair-types -open import foundation.function-extensionality -open import foundation.homotopy-induction -open import foundation.identity-types -open import foundation.path-algebra +open import foundation.function-extensionality funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext +open import foundation.path-algebra funext open import foundation.universe-levels open import foundation-core.commuting-squares-of-identifications open import foundation-core.dependent-identifications open import foundation-core.equivalences open import foundation-core.function-types -open import foundation-core.functoriality-dependent-function-types +open import foundation-core.functoriality-dependent-function-types funext open import foundation-core.transport-along-identifications open import foundation-core.whiskering-homotopies-concatenation ``` diff --git a/src/foundation/homotopy-induction.lagda.md b/src/foundation/homotopy-induction.lagda.md index 325ffb7e9c..7d45067d65 100644 --- a/src/foundation/homotopy-induction.lagda.md +++ b/src/foundation/homotopy-induction.lagda.md @@ -1,17 +1,20 @@ # Homotopy induction ```agda -module foundation.homotopy-induction where +open import foundation.function-extensionality-axiom + +module foundation.homotopy-induction + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-extensionality +open import foundation.function-extensionality funext open import foundation.identity-systems -open import foundation.universal-property-dependent-pair-types -open import foundation.universal-property-identity-systems +open import foundation.universal-property-identity-systems funext open import foundation.universe-levels open import foundation-core.commuting-triangles-of-maps diff --git a/src/foundation/homotopy-preorder-of-types.lagda.md b/src/foundation/homotopy-preorder-of-types.lagda.md index c6c1e1902e..66aaaa7eab 100644 --- a/src/foundation/homotopy-preorder-of-types.lagda.md +++ b/src/foundation/homotopy-preorder-of-types.lagda.md @@ -10,17 +10,18 @@ module ```agda open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.identity-types -open import foundation.mere-functions -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.sets +open import foundation.dependent-products-propositions funext +open import foundation.empty-types funext univalence truncations +open import foundation.identity-types funext +open import foundation.mere-functions funext univalence truncations +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence +open import foundation.sets funext univalence open import foundation.universe-levels -open import order-theory.large-preorders -open import order-theory.posets -open import order-theory.preorders +open import order-theory.large-preorders funext univalence truncations +open import order-theory.posets funext univalence truncations +open import order-theory.preorders funext univalence truncations ```
diff --git a/src/foundation/horizontal-composition-spans-of-spans.lagda.md b/src/foundation/horizontal-composition-spans-of-spans.lagda.md index eed1567115..5e0260ff66 100644 --- a/src/foundation/horizontal-composition-spans-of-spans.lagda.md +++ b/src/foundation/horizontal-composition-spans-of-spans.lagda.md @@ -1,28 +1,36 @@ # Horizontal composition of spans of spans ```agda -module foundation.horizontal-composition-spans-of-spans where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.horizontal-composition-spans-of-spans + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.commuting-triangles-of-maps -open import foundation.composition-spans -open import foundation.cones-over-cospan-diagrams +open import foundation.commuting-triangles-of-maps funext univalence +open import foundation.composition-spans funext univalence truncations +open import foundation.cones-over-cospan-diagrams funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.equivalences-arrows -open import foundation.equivalences-spans -open import foundation.homotopies -open import foundation.identity-types -open import foundation.morphisms-arrows +open import foundation.equivalences funext +open import foundation.equivalences-arrows funext univalence truncations +open import foundation.equivalences-spans funext univalence +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.morphisms-arrows funext open import foundation.morphisms-spans -open import foundation.pullbacks +open import foundation.pullbacks funext univalence truncations open import foundation.spans -open import foundation.spans-of-spans -open import foundation.standard-pullbacks -open import foundation.type-arithmetic-standard-pullbacks +open import foundation.spans-of-spans funext univalence +open import foundation.standard-pullbacks funext +open import foundation.type-arithmetic-standard-pullbacks funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition diff --git a/src/foundation/idempotent-maps.lagda.md b/src/foundation/idempotent-maps.lagda.md index 791fca96fa..01bca09df3 100644 --- a/src/foundation/idempotent-maps.lagda.md +++ b/src/foundation/idempotent-maps.lagda.md @@ -1,13 +1,18 @@ # Idempotent maps ```agda -module foundation.idempotent-maps where +open import foundation.function-extensionality-axiom + +module foundation.idempotent-maps + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions funext open import foundation.homotopy-algebra open import foundation.universe-levels open import foundation.whiskering-homotopies-composition diff --git a/src/foundation/identity-systems.lagda.md b/src/foundation/identity-systems.lagda.md index 9f1f3c9ff0..f36c1352dd 100644 --- a/src/foundation/identity-systems.lagda.md +++ b/src/foundation/identity-systems.lagda.md @@ -9,17 +9,12 @@ module foundation.identity-systems where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-extensionality open import foundation.fundamental-theorem-of-identity-types open import foundation.universe-levels open import foundation-core.contractible-types open import foundation-core.families-of-equivalences -open import foundation-core.function-types -open import foundation-core.functoriality-dependent-pair-types open import foundation-core.identity-types -open import foundation-core.propositions -open import foundation-core.retractions open import foundation-core.sections open import foundation-core.torsorial-type-families open import foundation-core.transport-along-identifications diff --git a/src/foundation/identity-truncated-types.lagda.md b/src/foundation/identity-truncated-types.lagda.md index 3da3145597..a719f43730 100644 --- a/src/foundation/identity-truncated-types.lagda.md +++ b/src/foundation/identity-truncated-types.lagda.md @@ -1,13 +1,20 @@ # Identity types of truncated types ```agda -module foundation.identity-truncated-types where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.identity-truncated-types + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda -open import foundation.univalence +open import foundation.dependent-products-truncated-types funext +open import foundation.univalence funext univalence open import foundation.universe-levels open import foundation-core.equivalences diff --git a/src/foundation/identity-types.lagda.md b/src/foundation/identity-types.lagda.md index 2f517ddffe..d0d6f33eb3 100644 --- a/src/foundation/identity-types.lagda.md +++ b/src/foundation/identity-types.lagda.md @@ -1,7 +1,11 @@ # Identity types ```agda -module foundation.identity-types where +open import foundation.function-extensionality-axiom + +module foundation.identity-types + (funext : function-extensionality) + where open import foundation-core.identity-types public ``` @@ -13,8 +17,8 @@ open import foundation.action-on-identifications-functions open import foundation.binary-equivalences open import foundation.commuting-pentagons-of-identifications open import foundation.dependent-pair-types -open import foundation.equivalence-extensionality -open import foundation.function-extensionality +open import foundation.equivalence-extensionality funext +open import foundation.function-extensionality funext open import foundation.universe-levels open import foundation-core.equivalences diff --git a/src/foundation/images-subtypes.lagda.md b/src/foundation/images-subtypes.lagda.md index f2959311bd..8dbd6a7fb2 100644 --- a/src/foundation/images-subtypes.lagda.md +++ b/src/foundation/images-subtypes.lagda.md @@ -1,21 +1,29 @@ # Images of subtypes ```agda -module foundation.images-subtypes where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.images-subtypes + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.full-subtypes -open import foundation.functoriality-propositional-truncation -open import foundation.images -open import foundation.logical-equivalences -open import foundation.powersets -open import foundation.propositional-truncations -open import foundation.pullbacks-subtypes -open import foundation.subtypes +open import foundation.full-subtypes funext univalence truncations +open import foundation.functoriality-propositional-truncation funext univalence truncations +open import foundation.images funext univalence truncations +open import foundation.logical-equivalences funext +open import foundation.powersets funext univalence truncations +open import foundation.propositional-truncations funext univalence +open import foundation.pullbacks-subtypes funext univalence truncations +open import foundation.subtypes funext univalence truncations open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels @@ -25,10 +33,10 @@ open import foundation-core.fibers-of-maps open import foundation-core.function-types open import foundation-core.identity-types -open import order-theory.galois-connections-large-posets -open import order-theory.order-preserving-maps-large-posets -open import order-theory.order-preserving-maps-large-preorders -open import order-theory.similarity-of-order-preserving-maps-large-posets +open import order-theory.galois-connections-large-posets funext univalence truncations +open import order-theory.order-preserving-maps-large-posets funext univalence truncations +open import order-theory.order-preserving-maps-large-preorders funext univalence truncations +open import order-theory.similarity-of-order-preserving-maps-large-posets funext univalence truncations ```
diff --git a/src/foundation/images.lagda.md b/src/foundation/images.lagda.md index 4ffd596c45..a6170fc136 100644 --- a/src/foundation/images.lagda.md +++ b/src/foundation/images.lagda.md @@ -1,7 +1,15 @@ # The image of a map ```agda -module foundation.images where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.images + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,13 +17,13 @@ module foundation.images where ```agda open import foundation.dependent-pair-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.propositional-truncations -open import foundation.slice +open import foundation.propositional-truncations funext univalence +open import foundation.slice funext univalence open import foundation.subtype-identity-principle -open import foundation.surjective-maps +open import foundation.surjective-maps funext univalence truncations open import foundation.universe-levels -open import foundation-core.1-types +open import foundation-core.1-types funext univalence open import foundation-core.commuting-triangles-of-maps open import foundation-core.contractible-types open import foundation-core.embeddings @@ -26,7 +34,7 @@ open import foundation-core.identity-types open import foundation-core.injective-maps open import foundation-core.propositions open import foundation-core.sets -open import foundation-core.subtypes +open import foundation-core.subtypes funext open import foundation-core.torsorial-type-families open import foundation-core.truncated-types open import foundation-core.truncation-levels diff --git a/src/foundation/impredicative-encodings.lagda.md b/src/foundation/impredicative-encodings.lagda.md index dbf1136729..ad6ba6bf65 100644 --- a/src/foundation/impredicative-encodings.lagda.md +++ b/src/foundation/impredicative-encodings.lagda.md @@ -1,22 +1,31 @@ # Impredicative encodings of the logical operations ```agda -module foundation.impredicative-encodings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.impredicative-encodings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.conjunction +open import foundation.conjunction funext univalence truncations open import foundation.dependent-pair-types -open import foundation.disjunction -open import foundation.empty-types -open import foundation.existential-quantification -open import foundation.homotopies -open import foundation.logical-equivalences -open import foundation.negation -open import foundation.propositional-truncations -open import foundation.universal-quantification +open import foundation.dependent-products-propositions funext +open import foundation.disjunction funext univalence truncations +open import foundation.empty-types funext univalence truncations +open import foundation.existential-quantification funext univalence truncations +open import foundation.homotopies funext +open import foundation.logical-equivalences funext +open import foundation.negation funext +open import foundation.propositional-truncations funext univalence +open import foundation.universal-quantification funext univalence truncations open import foundation.universe-levels open import foundation-core.coproduct-types diff --git a/src/foundation/impredicative-universes.lagda.md b/src/foundation/impredicative-universes.lagda.md index c1f2ed3f59..b9c61f0a05 100644 --- a/src/foundation/impredicative-universes.lagda.md +++ b/src/foundation/impredicative-universes.lagda.md @@ -1,7 +1,15 @@ # Impredicative universes ```agda -module foundation.impredicative-universes where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.impredicative-universes + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,7 +18,7 @@ module foundation.impredicative-universes where open import foundation.universe-levels open import foundation-core.propositions -open import foundation-core.small-types +open import foundation-core.small-types funext univalence truncations ```
diff --git a/src/foundation/infinitely-coherent-equivalences.lagda.md b/src/foundation/infinitely-coherent-equivalences.lagda.md index a650beffa9..999f0a9fcf 100644 --- a/src/foundation/infinitely-coherent-equivalences.lagda.md +++ b/src/foundation/infinitely-coherent-equivalences.lagda.md @@ -2,23 +2,29 @@ ```agda {-# OPTIONS --guardedness --lossy-unification #-} +open import foundation-core.univalence +open import foundation.function-extensionality-axiom -module foundation.infinitely-coherent-equivalences where +module foundation.infinitely-coherent-equivalences + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda -open import foundation.commuting-triangles-of-maps +open import foundation.commuting-triangles-of-maps funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.propositions -open import foundation.retractions -open import foundation.sections -open import foundation.transposition-identifications-along-equivalences +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.retractions funext +open import foundation.sections funext +open import foundation.transposition-identifications-along-equivalences funext open import foundation.universe-levels ``` diff --git a/src/foundation/inhabited-subtypes.lagda.md b/src/foundation/inhabited-subtypes.lagda.md index 5a4a67c0b3..38998b972a 100644 --- a/src/foundation/inhabited-subtypes.lagda.md +++ b/src/foundation/inhabited-subtypes.lagda.md @@ -1,17 +1,25 @@ # Inhabited subtypes ```agda -module foundation.inhabited-subtypes where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.inhabited-subtypes + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.inhabited-types -open import foundation.propositional-truncations +open import foundation.inhabited-types funext univalence truncations +open import foundation.propositional-truncations funext univalence open import foundation.subtype-identity-principle -open import foundation.subtypes +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels open import foundation-core.equivalences diff --git a/src/foundation/inhabited-types.lagda.md b/src/foundation/inhabited-types.lagda.md index 93682e4ba5..6c5e679b94 100644 --- a/src/foundation/inhabited-types.lagda.md +++ b/src/foundation/inhabited-types.lagda.md @@ -1,26 +1,32 @@ # Inhabited types ```agda -module foundation.inhabited-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.inhabited-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.action-on-identifications-functions -open import foundation.contractible-types +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types -open import foundation.function-extensionality -open import foundation.functoriality-propositional-truncation +open import foundation.dependent-products-contractible-types funext +open import foundation.equality-dependent-function-types funext +open import foundation.functoriality-propositional-truncation funext univalence truncations open import foundation.fundamental-theorem-of-identity-types -open import foundation.propositional-truncations +open import foundation.propositional-truncations funext univalence open import foundation.subtype-identity-principle -open import foundation.univalence +open import foundation.univalence funext univalence open import foundation.universe-levels open import foundation-core.equivalences -open import foundation-core.homotopies open import foundation-core.identity-types open import foundation-core.propositions open import foundation-core.torsorial-type-families diff --git a/src/foundation/injective-maps.lagda.md b/src/foundation/injective-maps.lagda.md index 8ab3913353..6ee4b737cb 100644 --- a/src/foundation/injective-maps.lagda.md +++ b/src/foundation/injective-maps.lagda.md @@ -1,7 +1,11 @@ # Injective maps ```agda -module foundation.injective-maps where +open import foundation.function-extensionality-axiom + +module foundation.injective-maps + (funext : function-extensionality) + where open import foundation-core.injective-maps public ``` @@ -9,11 +13,11 @@ open import foundation-core.injective-maps public
Imports ```agda -open import foundation.action-on-identifications-dependent-functions open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-extensionality -open import foundation.logical-equivalences +open import foundation.dependent-products-propositions funext +open import foundation.function-extensionality funext +open import foundation.logical-equivalences funext open import foundation.transport-along-identifications open import foundation.universe-levels diff --git a/src/foundation/intersections-subtypes.lagda.md b/src/foundation/intersections-subtypes.lagda.md index 3ff9cc3f3b..e870bbb679 100644 --- a/src/foundation/intersections-subtypes.lagda.md +++ b/src/foundation/intersections-subtypes.lagda.md @@ -1,24 +1,33 @@ # Intersections of subtypes ```agda -module foundation.intersections-subtypes where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.intersections-subtypes + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.conjunction -open import foundation.decidable-subtypes +open import foundation.conjunction funext univalence truncations +open import foundation.decidable-subtypes funext univalence truncations open import foundation.dependent-pair-types -open import foundation.large-locale-of-subtypes -open import foundation.powersets +open import foundation.dependent-products-propositions funext +open import foundation.large-locale-of-subtypes funext univalence truncations +open import foundation.powersets funext univalence truncations open import foundation.universe-levels -open import foundation-core.decidable-propositions +open import foundation-core.decidable-propositions funext univalence truncations open import foundation-core.propositions -open import foundation-core.subtypes +open import foundation-core.subtypes funext -open import order-theory.greatest-lower-bounds-large-posets +open import order-theory.greatest-lower-bounds-large-posets funext univalence truncations ```
diff --git a/src/foundation/inverse-sequential-diagrams.lagda.md b/src/foundation/inverse-sequential-diagrams.lagda.md index 28053d466e..12392cc670 100644 --- a/src/foundation/inverse-sequential-diagrams.lagda.md +++ b/src/foundation/inverse-sequential-diagrams.lagda.md @@ -1,7 +1,15 @@ # Inverse sequential diagrams of types ```agda -module foundation.inverse-sequential-diagrams where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.inverse-sequential-diagrams + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,7 +18,8 @@ module foundation.inverse-sequential-diagrams where open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.iterating-functions +open import foundation.iterating-functions funext univalence truncations +open import foundation.raising-universe-levels-unit-type open import foundation.unit-type open import foundation.universe-levels ``` diff --git a/src/foundation/invertible-maps.lagda.md b/src/foundation/invertible-maps.lagda.md index 47fb7cca31..f8c6b5a013 100644 --- a/src/foundation/invertible-maps.lagda.md +++ b/src/foundation/invertible-maps.lagda.md @@ -1,7 +1,15 @@ # Invertible maps ```agda -module foundation.invertible-maps where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.invertible-maps + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where open import foundation-core.invertible-maps public ``` @@ -10,21 +18,22 @@ open import foundation-core.invertible-maps public ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-triangles-of-homotopies +open import foundation.commuting-triangles-of-homotopies funext open import foundation.dependent-pair-types +open import foundation.dependent-products-truncated-types funext open import foundation.equality-cartesian-product-types -open import foundation.equivalence-extensionality -open import foundation.equivalences -open import foundation.full-subtypes -open import foundation.function-extensionality -open import foundation.functoriality-cartesian-product-types +open import foundation.equivalence-extensionality funext +open import foundation.equivalences funext +open import foundation.full-subtypes funext univalence truncations +open import foundation.function-extensionality funext +open import foundation.functoriality-cartesian-product-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies +open import foundation.homotopies funext open import foundation.homotopy-algebra -open import foundation.homotopy-induction -open import foundation.postcomposition-functions -open import foundation.retractions -open import foundation.sections +open import foundation.homotopy-induction funext +open import foundation.postcomposition-functions funext +open import foundation.retractions funext +open import foundation.sections funext open import foundation.structure-identity-principle open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels @@ -40,7 +49,7 @@ open import foundation-core.torsorial-type-families open import foundation-core.truncated-types open import foundation-core.truncation-levels -open import synthetic-homotopy-theory.free-loops +open import synthetic-homotopy-theory.free-loops funext univalence truncations ```
diff --git a/src/foundation/involutions.lagda.md b/src/foundation/involutions.lagda.md index df78de65a1..41141cab04 100644 --- a/src/foundation/involutions.lagda.md +++ b/src/foundation/involutions.lagda.md @@ -1,20 +1,27 @@ # Involutions ```agda -module foundation.involutions where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.involutions + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda -open import foundation.automorphisms +open import foundation.automorphisms funext univalence open import foundation.dependent-pair-types -open import foundation.equivalence-extensionality -open import foundation.equivalences -open import foundation.function-extensionality +open import foundation.dependent-products-truncated-types funext +open import foundation.equivalence-extensionality funext +open import foundation.equivalences funext +open import foundation.function-extensionality funext open import foundation.fundamental-theorem-of-identity-types open import foundation.homotopy-algebra -open import foundation.homotopy-induction +open import foundation.homotopy-induction funext open import foundation.structure-identity-principle open import foundation.universe-levels open import foundation.whiskering-homotopies-composition diff --git a/src/foundation/irrefutable-propositions.lagda.md b/src/foundation/irrefutable-propositions.lagda.md index a6a0d7fcde..eb54bc8be3 100644 --- a/src/foundation/irrefutable-propositions.lagda.md +++ b/src/foundation/irrefutable-propositions.lagda.md @@ -1,28 +1,38 @@ # Irrefutable propositions ```agda -module foundation.irrefutable-propositions where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.irrefutable-propositions + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.cartesian-product-types -open import foundation.contractible-types -open import foundation.coproduct-types -open import foundation.decidable-propositions -open import foundation.decidable-types +open import foundation.cartesian-product-types funext univalence +open import foundation.contractible-types funext univalence +open import foundation.coproduct-types funext univalence truncations +open import foundation.decidable-propositions funext univalence truncations +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.double-negation -open import foundation.empty-types -open import foundation.function-types -open import foundation.negation -open import foundation.propositions -open import foundation.subuniverses +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.double-negation funext univalence truncations +open import foundation.empty-types funext univalence truncations +open import foundation.function-types funext +open import foundation.negation funext +open import foundation.propositions funext univalence +open import foundation.subuniverses funext univalence open import foundation.unit-type open import foundation.universe-levels -open import logic.double-negation-elimination +open import logic.double-negation-elimination funext univalence truncations ```
diff --git a/src/foundation/isolated-elements.lagda.md b/src/foundation/isolated-elements.lagda.md index ebf38b94f7..e2bf3302b9 100644 --- a/src/foundation/isolated-elements.lagda.md +++ b/src/foundation/isolated-elements.lagda.md @@ -1,41 +1,50 @@ # Isolated elements ```agda -module foundation.isolated-elements where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.isolated-elements + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.constant-maps -open import foundation.decidable-embeddings -open import foundation.decidable-equality -open import foundation.decidable-maps -open import foundation.decidable-types +open import foundation.constant-maps funext univalence truncations +open import foundation.decidable-embeddings funext univalence truncations +open import foundation.decidable-equality funext univalence truncations +open import foundation.decidable-maps funext univalence truncations +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.embeddings +open import foundation.dependent-products-propositions funext +open import foundation.embeddings funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.maybe -open import foundation.negated-equality -open import foundation.negation -open import foundation.sets -open import foundation.type-arithmetic-unit-type +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.negated-equality funext univalence truncations +open import foundation.negation funext +open import foundation.sets funext univalence +open import foundation.type-arithmetic-unit-type funext open import foundation.unit-type open import foundation.universe-levels open import foundation-core.contractible-types open import foundation-core.coproduct-types -open import foundation-core.decidable-propositions +open import foundation-core.decidable-propositions funext univalence truncations open import foundation-core.empty-types open import foundation-core.equivalences open import foundation-core.function-types open import foundation-core.functoriality-dependent-pair-types open import foundation-core.homotopies +open import foundation-core.maybe open import foundation-core.propositions -open import foundation-core.subtypes +open import foundation-core.subtypes funext open import foundation-core.torsorial-type-families open import foundation-core.transport-along-identifications ``` diff --git a/src/foundation/isomorphisms-of-sets.lagda.md b/src/foundation/isomorphisms-of-sets.lagda.md index db721c44c7..c776132635 100644 --- a/src/foundation/isomorphisms-of-sets.lagda.md +++ b/src/foundation/isomorphisms-of-sets.lagda.md @@ -1,7 +1,13 @@ # Isomorphisms of sets ```agda -module foundation.isomorphisms-of-sets where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.isomorphisms-of-sets + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports @@ -9,16 +15,16 @@ module foundation.isomorphisms-of-sets where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.sets +open import foundation.equivalences funext +open import foundation.function-extensionality funext +open import foundation.sets funext univalence open import foundation.universe-levels open import foundation-core.cartesian-product-types open import foundation-core.function-types open import foundation-core.identity-types open import foundation-core.propositions -open import foundation-core.subtypes +open import foundation-core.subtypes funext ```
diff --git a/src/foundation/iterated-cartesian-product-types.lagda.md b/src/foundation/iterated-cartesian-product-types.lagda.md index ab1849056b..0b589fd58f 100644 --- a/src/foundation/iterated-cartesian-product-types.lagda.md +++ b/src/foundation/iterated-cartesian-product-types.lagda.md @@ -1,7 +1,15 @@ # Iterated cartesian product types ```agda -module foundation.iterated-cartesian-product-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.iterated-cartesian-product-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,18 +17,19 @@ module foundation.iterated-cartesian-product-types where ```agda open import elementary-number-theory.natural-numbers -open import finite-group-theory.permutations-standard-finite-types +open import finite-group-theory.permutations-standard-finite-types funext univalence truncations open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.functoriality-cartesian-product-types -open import foundation.functoriality-dependent-function-types +open import foundation.functoriality-cartesian-product-types funext +open import foundation.functoriality-dependent-function-types funext univalence +open import foundation.raising-universe-levels-unit-type open import foundation.type-arithmetic-cartesian-product-types -open import foundation.type-arithmetic-dependent-function-types +open import foundation.type-arithmetic-dependent-function-types funext univalence open import foundation.unit-type -open import foundation.univalence -open import foundation.universal-property-coproduct-types -open import foundation.universal-property-empty-type +open import foundation.univalence funext univalence +open import foundation.universal-property-coproduct-types funext +open import foundation.universal-property-empty-type funext open import foundation.universe-levels open import foundation-core.cartesian-product-types @@ -30,12 +39,12 @@ open import foundation-core.equivalences open import foundation-core.function-types open import foundation-core.identity-types -open import lists.arrays -open import lists.concatenation-lists +open import lists.arrays funext univalence truncations +open import lists.concatenation-lists funext univalence truncations open import lists.lists -open import lists.permutation-lists +open import lists.permutation-lists funext univalence truncations -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/foundation/iterated-dependent-pair-types.lagda.md b/src/foundation/iterated-dependent-pair-types.lagda.md index ee7b8b853f..cf0e985ca9 100644 --- a/src/foundation/iterated-dependent-pair-types.lagda.md +++ b/src/foundation/iterated-dependent-pair-types.lagda.md @@ -2,8 +2,6 @@ ```agda module foundation.iterated-dependent-pair-types where - -open import foundation.telescopes public ```
Imports @@ -12,6 +10,7 @@ open import foundation.telescopes public open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types +open import foundation.telescopes open import foundation.universe-levels open import foundation-core.cartesian-product-types diff --git a/src/foundation/iterated-dependent-product-types.lagda.md b/src/foundation/iterated-dependent-product-types.lagda.md index eb1217e03e..df2ea9b53b 100644 --- a/src/foundation/iterated-dependent-product-types.lagda.md +++ b/src/foundation/iterated-dependent-product-types.lagda.md @@ -1,9 +1,11 @@ # Iterated dependent product types ```agda -module foundation.iterated-dependent-product-types where +open import foundation.function-extensionality-axiom -open import foundation.telescopes public +module foundation.iterated-dependent-product-types + (funext : function-extensionality) + where ```
Imports @@ -11,12 +13,16 @@ open import foundation.telescopes public ```agda open import elementary-number-theory.natural-numbers +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.dependent-products-truncated-types funext open import foundation.implicit-function-types +open import foundation.telescopes open import foundation.universe-levels open import foundation-core.contractible-types open import foundation-core.equivalences -open import foundation-core.functoriality-dependent-function-types +open import foundation-core.functoriality-dependent-function-types funext open import foundation-core.propositions open import foundation-core.truncated-types open import foundation-core.truncation-levels diff --git a/src/foundation/iterating-automorphisms.lagda.md b/src/foundation/iterating-automorphisms.lagda.md index dfae65d2f3..ae68e26fa6 100644 --- a/src/foundation/iterating-automorphisms.lagda.md +++ b/src/foundation/iterating-automorphisms.lagda.md @@ -1,19 +1,27 @@ # Iterating automorphisms ```agda -module foundation.iterating-automorphisms where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.iterating-automorphisms + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.addition-integers +open import elementary-number-theory.addition-integers funext univalence truncations open import elementary-number-theory.integers open import elementary-number-theory.natural-numbers -open import foundation.automorphisms -open import foundation.equivalence-extensionality -open import foundation.iterating-functions +open import foundation.automorphisms funext univalence +open import foundation.equivalence-extensionality funext +open import foundation.iterating-functions funext univalence truncations open import foundation.universe-levels open import foundation.whiskering-homotopies-composition diff --git a/src/foundation/iterating-families-of-maps.lagda.md b/src/foundation/iterating-families-of-maps.lagda.md index 97b4fa1ce6..4c9b810970 100644 --- a/src/foundation/iterating-families-of-maps.lagda.md +++ b/src/foundation/iterating-families-of-maps.lagda.md @@ -1,36 +1,29 @@ # Iterating families of maps over a map ```agda -module foundation.iterating-families-of-maps where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.iterating-families-of-maps + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.exponentiation-natural-numbers -open import elementary-number-theory.multiplication-natural-numbers -open import elementary-number-theory.multiplicative-monoid-of-natural-numbers open import elementary-number-theory.natural-numbers -open import foundation.action-on-higher-identifications-functions -open import foundation.action-on-identifications-dependent-functions open import foundation.action-on-identifications-functions -open import foundation.dependent-homotopies -open import foundation.dependent-identifications -open import foundation.dependent-pair-types -open import foundation.function-extensionality -open import foundation.iterating-functions +open import foundation.dependent-identifications funext +open import foundation.iterating-functions funext univalence truncations open import foundation.transport-along-identifications open import foundation.universe-levels -open import foundation-core.commuting-squares-of-maps -open import foundation-core.endomorphisms -open import foundation-core.homotopies open import foundation-core.identity-types -open import foundation-core.sets - -open import group-theory.monoid-actions ```
diff --git a/src/foundation/iterating-functions.lagda.md b/src/foundation/iterating-functions.lagda.md index 60dafe2242..5aa4c02325 100644 --- a/src/foundation/iterating-functions.lagda.md +++ b/src/foundation/iterating-functions.lagda.md @@ -1,31 +1,39 @@ # Iterating functions ```agda -module foundation.iterating-functions where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.iterating-functions + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.exponentiation-natural-numbers +open import elementary-number-theory.exponentiation-natural-numbers funext univalence truncations open import elementary-number-theory.multiplication-natural-numbers -open import elementary-number-theory.multiplicative-monoid-of-natural-numbers +open import elementary-number-theory.multiplicative-monoid-of-natural-numbers funext univalence truncations open import elementary-number-theory.natural-numbers -open import foundation.action-on-higher-identifications-functions +open import foundation.action-on-higher-identifications-functions funext open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-extensionality +open import foundation.function-extensionality funext open import foundation.universe-levels -open import foundation-core.commuting-squares-of-maps -open import foundation-core.endomorphisms +open import foundation-core.commuting-squares-of-maps funext +open import foundation-core.endomorphisms funext univalence open import foundation-core.homotopies open import foundation-core.identity-types open import foundation-core.sets -open import group-theory.monoid-actions +open import group-theory.monoid-actions funext univalence truncations ```
diff --git a/src/foundation/iterating-involutions.lagda.md b/src/foundation/iterating-involutions.lagda.md index 06170f10fe..3361e10405 100644 --- a/src/foundation/iterating-involutions.lagda.md +++ b/src/foundation/iterating-involutions.lagda.md @@ -1,24 +1,32 @@ # Iterating involutions ```agda -module foundation.iterating-involutions where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.iterating-involutions + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.modular-arithmetic-standard-finite-types +open import elementary-number-theory.modular-arithmetic-standard-finite-types funext univalence truncations open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.involutions -open import foundation.iterating-functions +open import foundation.involutions funext univalence +open import foundation.iterating-functions funext univalence truncations open import foundation.universe-levels open import foundation-core.coproduct-types open import foundation-core.identity-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/foundation/kernel-span-diagrams-of-maps.lagda.md b/src/foundation/kernel-span-diagrams-of-maps.lagda.md index 37d56efd8d..b9814dd334 100644 --- a/src/foundation/kernel-span-diagrams-of-maps.lagda.md +++ b/src/foundation/kernel-span-diagrams-of-maps.lagda.md @@ -1,14 +1,18 @@ # Kernel span diagrams of maps ```agda -module foundation.kernel-span-diagrams-of-maps where +open import foundation.function-extensionality-axiom + +module foundation.kernel-span-diagrams-of-maps + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.span-diagrams +open import foundation.span-diagrams funext open import foundation.spans open import foundation.universe-levels diff --git a/src/foundation/large-apartness-relations.lagda.md b/src/foundation/large-apartness-relations.lagda.md index 49844edacb..87898ce12d 100644 --- a/src/foundation/large-apartness-relations.lagda.md +++ b/src/foundation/large-apartness-relations.lagda.md @@ -1,19 +1,26 @@ # Large apartness relations ```agda -module foundation.large-apartness-relations where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.large-apartness-relations + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.cartesian-product-types -open import foundation.disjunction -open import foundation.identity-types -open import foundation.large-binary-relations -open import foundation.negated-equality -open import foundation.negation -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.identity-types funext +open import foundation.large-binary-relations funext univalence truncations +open import foundation.negated-equality funext univalence truncations +open import foundation.negation funext +open import foundation.propositions funext univalence open import foundation.universe-levels ``` diff --git a/src/foundation/large-binary-relations.lagda.md b/src/foundation/large-binary-relations.lagda.md index 9077016804..4806d15b9f 100644 --- a/src/foundation/large-binary-relations.lagda.md +++ b/src/foundation/large-binary-relations.lagda.md @@ -1,16 +1,23 @@ # Large binary relations ```agda -module foundation.large-binary-relations where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.large-binary-relations + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.binary-relations -open import foundation.coproduct-types +open import foundation.binary-relations funext univalence truncations open import foundation.dependent-pair-types -open import foundation.disjunction +open import foundation.disjunction funext univalence truncations open import foundation.universe-levels open import foundation-core.cartesian-product-types diff --git a/src/foundation/large-locale-of-propositions.lagda.md b/src/foundation/large-locale-of-propositions.lagda.md index d5ef3ea50a..7ddcc6012b 100644 --- a/src/foundation/large-locale-of-propositions.lagda.md +++ b/src/foundation/large-locale-of-propositions.lagda.md @@ -1,33 +1,42 @@ # The large locale of propositions ```agda -module foundation.large-locale-of-propositions where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.large-locale-of-propositions + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.conjunction -open import foundation.empty-types -open import foundation.existential-quantification -open import foundation.logical-equivalences -open import foundation.propositional-extensionality +open import foundation.conjunction funext univalence truncations +open import foundation.dependent-products-propositions funext +open import foundation.empty-types funext univalence truncations +open import foundation.existential-quantification funext univalence truncations +open import foundation.logical-equivalences funext +open import foundation.propositional-extensionality funext univalence truncations open import foundation.unit-type -open import foundation.universal-property-cartesian-product-types +open import foundation.universal-property-cartesian-product-types funext open import foundation.universe-levels open import foundation-core.function-types open import foundation-core.propositions -open import order-theory.bottom-elements-large-posets -open import order-theory.large-frames -open import order-theory.large-locales -open import order-theory.large-meet-semilattices -open import order-theory.large-posets -open import order-theory.large-preorders -open import order-theory.large-suplattices -open import order-theory.least-upper-bounds-large-posets -open import order-theory.top-elements-large-posets +open import order-theory.bottom-elements-large-posets funext univalence truncations +open import order-theory.large-frames funext univalence truncations +open import order-theory.large-locales funext univalence truncations +open import order-theory.large-meet-semilattices funext univalence truncations +open import order-theory.large-posets funext univalence truncations +open import order-theory.large-preorders funext univalence truncations +open import order-theory.large-suplattices funext univalence truncations +open import order-theory.least-upper-bounds-large-posets funext univalence truncations +open import order-theory.top-elements-large-posets funext univalence truncations ```
diff --git a/src/foundation/large-locale-of-subtypes.lagda.md b/src/foundation/large-locale-of-subtypes.lagda.md index 2661d3c83d..faa5f0d9ca 100644 --- a/src/foundation/large-locale-of-subtypes.lagda.md +++ b/src/foundation/large-locale-of-subtypes.lagda.md @@ -1,29 +1,37 @@ # The large locale of subtypes ```agda -module foundation.large-locale-of-subtypes where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.large-locale-of-subtypes + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.large-binary-relations -open import foundation.large-locale-of-propositions +open import foundation.large-binary-relations funext univalence truncations +open import foundation.large-locale-of-propositions funext univalence truncations open import foundation.universe-levels open import foundation-core.identity-types open import foundation-core.sets -open import order-theory.bottom-elements-large-posets -open import order-theory.greatest-lower-bounds-large-posets -open import order-theory.large-locales -open import order-theory.large-meet-semilattices -open import order-theory.large-posets -open import order-theory.large-preorders -open import order-theory.large-suplattices -open import order-theory.least-upper-bounds-large-posets -open import order-theory.powers-of-large-locales -open import order-theory.top-elements-large-posets +open import order-theory.bottom-elements-large-posets funext univalence truncations +open import order-theory.greatest-lower-bounds-large-posets funext univalence truncations +open import order-theory.large-locales funext univalence truncations +open import order-theory.large-meet-semilattices funext univalence truncations +open import order-theory.large-posets funext univalence truncations +open import order-theory.large-preorders funext univalence truncations +open import order-theory.large-suplattices funext univalence truncations +open import order-theory.least-upper-bounds-large-posets funext univalence truncations +open import order-theory.powers-of-large-locales funext univalence truncations +open import order-theory.top-elements-large-posets funext univalence truncations ```
diff --git a/src/foundation/law-of-excluded-middle.lagda.md b/src/foundation/law-of-excluded-middle.lagda.md index a633ea32d6..3e50887ef6 100644 --- a/src/foundation/law-of-excluded-middle.lagda.md +++ b/src/foundation/law-of-excluded-middle.lagda.md @@ -1,21 +1,30 @@ # The law of excluded middle ```agda -module foundation.law-of-excluded-middle where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.law-of-excluded-middle + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.decidable-types +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions funext open import foundation.universe-levels -open import foundation-core.decidable-propositions +open import foundation-core.decidable-propositions funext univalence truncations open import foundation-core.negation open import foundation-core.propositions -open import univalent-combinatorics.2-element-types +open import univalent-combinatorics.2-element-types funext univalence truncations ```
diff --git a/src/foundation/lawveres-fixed-point-theorem.lagda.md b/src/foundation/lawveres-fixed-point-theorem.lagda.md index 5432486db4..5fa5f6fe4b 100644 --- a/src/foundation/lawveres-fixed-point-theorem.lagda.md +++ b/src/foundation/lawveres-fixed-point-theorem.lagda.md @@ -1,17 +1,24 @@ # Lawvere's fixed point theorem ```agda -module foundation.lawveres-fixed-point-theorem where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.lawveres-fixed-point-theorem + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.existential-quantification -open import foundation.function-extensionality -open import foundation.propositional-truncations -open import foundation.surjective-maps +open import foundation.existential-quantification funext univalence truncations +open import foundation.propositional-truncations funext univalence +open import foundation.surjective-maps funext univalence truncations open import foundation.universe-levels open import foundation-core.identity-types diff --git a/src/foundation/lesser-limited-principle-of-omniscience.lagda.md b/src/foundation/lesser-limited-principle-of-omniscience.lagda.md index 242c9b27b6..891f0000d4 100644 --- a/src/foundation/lesser-limited-principle-of-omniscience.lagda.md +++ b/src/foundation/lesser-limited-principle-of-omniscience.lagda.md @@ -1,21 +1,30 @@ # The lesser limited principle of omniscience ```agda -module foundation.lesser-limited-principle-of-omniscience where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.lesser-limited-principle-of-omniscience + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import elementary-number-theory.natural-numbers -open import elementary-number-theory.parity-natural-numbers +open import elementary-number-theory.parity-natural-numbers funext univalence truncations -open import foundation.booleans open import foundation.dependent-pair-types -open import foundation.disjunction -open import foundation.universal-quantification +open import foundation.dependent-products-propositions funext +open import foundation.disjunction funext univalence truncations +open import foundation.universal-quantification funext univalence truncations open import foundation.universe-levels +open import foundation-core.booleans open import foundation-core.fibers-of-maps open import foundation-core.propositions open import foundation-core.sets @@ -27,9 +36,9 @@ open import foundation-core.sets The {{#concept "lesser limited principle of omniscience" Agda=LLPO}} (LLPO) asserts that for any [sequence](foundation.sequences.md) of -[booleans](foundation.booleans.md) `f : ℕ → bool` such that `f n` is true for -[at most one](foundation-core.propositions.md) `n`, then either `f n` is false -for all even `n` or `f n` is false for all odd `n`. +[booleans](foundation-core.booleans.md) `f : ℕ → bool` such that `f n` is true +for [at most one](foundation-core.propositions.md) `n`, then either `f n` is +false for all even `n` or `f n` is false for all odd `n`. ```agda prop-LLPO : Prop lzero diff --git a/src/foundation/limited-principle-of-omniscience.lagda.md b/src/foundation/limited-principle-of-omniscience.lagda.md index e66cea9ad0..329759d515 100644 --- a/src/foundation/limited-principle-of-omniscience.lagda.md +++ b/src/foundation/limited-principle-of-omniscience.lagda.md @@ -1,7 +1,15 @@ # The limited principle of omniscience ```agda -module foundation.limited-principle-of-omniscience where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.limited-principle-of-omniscience + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,20 +17,21 @@ module foundation.limited-principle-of-omniscience where ```agda open import elementary-number-theory.natural-numbers -open import foundation.booleans -open import foundation.coproduct-types +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.disjunction -open import foundation.existential-quantification -open import foundation.negation -open import foundation.universal-quantification +open import foundation.dependent-products-propositions funext +open import foundation.disjunction funext univalence truncations +open import foundation.existential-quantification funext univalence truncations +open import foundation.negation funext +open import foundation.universal-quantification funext univalence truncations open import foundation.universe-levels +open import foundation-core.booleans open import foundation-core.identity-types open import foundation-core.propositions open import foundation-core.sets -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/foundation/locale-of-propositions.lagda.md b/src/foundation/locale-of-propositions.lagda.md index daef5de811..e72f3a78ea 100644 --- a/src/foundation/locale-of-propositions.lagda.md +++ b/src/foundation/locale-of-propositions.lagda.md @@ -1,32 +1,41 @@ # The locale of propositions ```agda -module foundation.locale-of-propositions where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.locale-of-propositions + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.conjunction +open import foundation.conjunction funext univalence truncations open import foundation.dependent-pair-types -open import foundation.existential-quantification -open import foundation.large-locale-of-propositions -open import foundation.logical-equivalences +open import foundation.existential-quantification funext univalence truncations +open import foundation.large-locale-of-propositions funext univalence truncations +open import foundation.logical-equivalences funext +open import foundation.raising-universe-levels-unit-type open import foundation.unit-type open import foundation.universe-levels open import foundation-core.function-types -open import order-theory.frames -open import order-theory.greatest-lower-bounds-posets -open import order-theory.large-posets -open import order-theory.large-preorders -open import order-theory.meet-semilattices -open import order-theory.meet-suplattices -open import order-theory.posets -open import order-theory.preorders -open import order-theory.suplattices -open import order-theory.top-elements-posets +open import order-theory.frames funext univalence truncations +open import order-theory.greatest-lower-bounds-posets funext univalence truncations +open import order-theory.large-posets funext univalence truncations +open import order-theory.large-preorders funext univalence truncations +open import order-theory.meet-semilattices funext univalence truncations +open import order-theory.meet-suplattices funext univalence truncations +open import order-theory.posets funext univalence truncations +open import order-theory.preorders funext univalence truncations +open import order-theory.suplattices funext univalence truncations +open import order-theory.top-elements-posets funext univalence truncations ```
diff --git a/src/foundation/locally-small-types.lagda.md b/src/foundation/locally-small-types.lagda.md index d46bd2d4bb..925461d399 100644 --- a/src/foundation/locally-small-types.lagda.md +++ b/src/foundation/locally-small-types.lagda.md @@ -1,18 +1,28 @@ # Locally small types ```agda -module foundation.locally-small-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.locally-small-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.inhabited-subtypes -open import foundation.subuniverses -open import foundation.univalence +open import foundation.dependent-products-propositions funext +open import foundation.dependent-products-truncated-types funext +open import foundation.equivalences funext +open import foundation.function-extensionality funext +open import foundation.inhabited-subtypes funext univalence truncations +open import foundation.subuniverses funext univalence +open import foundation.univalence funext univalence open import foundation.universe-levels open import foundation-core.embeddings @@ -21,8 +31,8 @@ open import foundation-core.function-types open import foundation-core.homotopies open import foundation-core.identity-types open import foundation-core.propositions -open import foundation-core.small-types -open import foundation-core.subtypes +open import foundation-core.small-types funext univalence truncations +open import foundation-core.subtypes funext open import foundation-core.transport-along-identifications open import foundation-core.truncated-types open import foundation-core.truncation-levels diff --git a/src/foundation/logical-equivalences.lagda.md b/src/foundation/logical-equivalences.lagda.md index d806e1ca3d..89aa08f6cc 100644 --- a/src/foundation/logical-equivalences.lagda.md +++ b/src/foundation/logical-equivalences.lagda.md @@ -1,17 +1,24 @@ # Logical equivalences ```agda -module foundation.logical-equivalences where +open import foundation.function-extensionality-axiom + +module foundation.logical-equivalences + (funext : function-extensionality) + where + +open import foundation-core.logical-equivalences public ```
Imports ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions funext open import foundation.equality-cartesian-product-types -open import foundation.equivalence-extensionality -open import foundation.function-extensionality -open import foundation.functoriality-cartesian-product-types +open import foundation.equivalence-extensionality funext +open import foundation.function-extensionality funext +open import foundation.functoriality-cartesian-product-types funext open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels @@ -32,9 +39,9 @@ open import foundation-core.torsorial-type-families ## Idea -{{#concept "Logical equivalences" Disambiguation="of types" Agda=iff}} between -two types `A` and `B` consist of a map `A → B` and a map `B → A`. The type of -logical equivalences between types is the +{{#concept "Logical equivalences" Disambiguation="of types"}} between two types +`A` and `B` consist of a map `A → B` and a map `B → A`. The type of logical +equivalences between types is the [Curry–Howard interpretation](https://en.wikipedia.org/wiki/Curry–Howard_correspondence) of logical equivalences between [propositions](foundation-core.propositions.md). @@ -43,16 +50,10 @@ of logical equivalences between [propositions](foundation-core.propositions.md). ### The structure on a map of being a logical equivalence ```agda -module _ - {l1 l2 : Level} {A : UU l1} {B : UU l2} - where - - has-converse : (A → B) → UU (l1 ⊔ l2) - has-converse f = B → A - - is-prop-has-converse : - is-prop A → (f : A → B) → is-prop (has-converse f) - is-prop-has-converse is-prop-A f = is-prop-function-type is-prop-A +is-prop-has-converse : + {l1 l2 : Level} {A : UU l1} {B : UU l2} → + is-prop A → (f : A → B) → is-prop (has-converse f) +is-prop-has-converse is-prop-A f = is-prop-function-type is-prop-A has-converse-Prop : {l1 l2 : Level} (A : Prop l1) {B : UU l2} → (type-Prop A → B) → Prop (l1 ⊔ l2) @@ -61,28 +62,6 @@ has-converse-Prop A f = is-prop-has-converse (is-prop-type-Prop A) f) ``` -### Logical equivalences between types - -```agda -iff : {l1 l2 : Level} → UU l1 → UU l2 → UU (l1 ⊔ l2) -iff A B = Σ (A → B) has-converse - -infix 6 _↔_ - -_↔_ : {l1 l2 : Level} → UU l1 → UU l2 → UU (l1 ⊔ l2) -_↔_ = iff - -module _ - {l1 l2 : Level} {A : UU l1} {B : UU l2} (H : A ↔ B) - where - - forward-implication : A → B - forward-implication = pr1 H - - backward-implication : B → A - backward-implication = pr2 H -``` - ### Logical equivalences between propositions ```agda @@ -109,34 +88,6 @@ module _ _⇔_ = iff-Prop ``` -### The identity logical equivalence - -```agda -id-iff : {l1 : Level} {A : UU l1} → A ↔ A -id-iff = (id , id) -``` - -### Composition of logical equivalences - -```agda -infixr 15 _∘iff_ - -_∘iff_ : - {l1 l2 l3 : Level} {A : UU l1} {B : UU l2} {C : UU l3} → - (B ↔ C) → (A ↔ B) → (A ↔ C) -pr1 ((g1 , g2) ∘iff (f1 , f2)) = g1 ∘ f1 -pr2 ((g1 , g2) ∘iff (f1 , f2)) = f2 ∘ g2 -``` - -### Inverting a logical equivalence - -```agda -inv-iff : - {l1 l2 : Level} {A : UU l1} {B : UU l2} → (A ↔ B) → (B ↔ A) -pr1 (inv-iff (f , g)) = g -pr2 (inv-iff (f , g)) = f -``` - ## Properties ### Characterizing equality of logical equivalences @@ -146,11 +97,6 @@ module _ {l1 l2 : Level} {A : UU l1} {B : UU l2} where - htpy-iff : (f g : A ↔ B) → UU (l1 ⊔ l2) - htpy-iff f g = - ( forward-implication f ~ forward-implication g) × - ( backward-implication f ~ backward-implication g) - ext-iff : (f g : A ↔ B) → (f ＝ g) ≃ htpy-iff f g ext-iff f g = equiv-product equiv-funext equiv-funext ∘e equiv-pair-eq f g @@ -165,89 +111,6 @@ module _ eq-htpy-iff f g = map-inv-equiv (ext-iff f g) ``` -### Logical equivalences between propositions induce equivalences - -```agda -module _ - {l1 l2 : Level} {A : UU l1} {B : UU l2} - where - - abstract - is-equiv-has-converse-is-prop : - is-prop A → is-prop B → {f : A → B} → (B → A) → is-equiv f - is-equiv-has-converse-is-prop is-prop-A is-prop-B {f} g = - is-equiv-is-invertible - ( g) - ( λ y → eq-is-prop is-prop-B) - ( λ x → eq-is-prop is-prop-A) - - abstract - equiv-iff-is-prop : is-prop A → is-prop B → (A → B) → (B → A) → A ≃ B - pr1 (equiv-iff-is-prop is-prop-A is-prop-B f g) = f - pr2 (equiv-iff-is-prop is-prop-A is-prop-B f g) = - is-equiv-has-converse-is-prop is-prop-A is-prop-B g - -module _ - {l1 l2 : Level} (P : Prop l1) (Q : Prop l2) - where - - abstract - is-equiv-has-converse : - {f : type-Prop P → type-Prop Q} → (type-Prop Q → type-Prop P) → is-equiv f - is-equiv-has-converse = - is-equiv-has-converse-is-prop - ( is-prop-type-Prop P) - ( is-prop-type-Prop Q) - - equiv-iff' : type-Prop (P ⇔ Q) → (type-Prop P ≃ type-Prop Q) - pr1 (equiv-iff' t) = forward-implication t - pr2 (equiv-iff' t) = - is-equiv-has-converse-is-prop - ( is-prop-type-Prop P) - ( is-prop-type-Prop Q) - ( backward-implication t) - - equiv-iff : - (type-Prop P → type-Prop Q) → (type-Prop Q → type-Prop P) → - type-Prop P ≃ type-Prop Q - equiv-iff f g = equiv-iff' (f , g) -``` - -### Equivalences are logical equivalences - -```agda -iff-equiv : {l1 l2 : Level} {A : UU l1} {B : UU l2} → (A ≃ B) → (A ↔ B) -pr1 (iff-equiv e) = map-equiv e -pr2 (iff-equiv e) = map-inv-equiv e - -iff-equiv' : {l1 l2 : Level} {A : UU l1} {B : UU l2} → (A ≃ B) → (B ↔ A) -pr1 (iff-equiv' e) = map-inv-equiv e -pr2 (iff-equiv' e) = map-equiv e - -is-injective-iff-equiv : - {l1 l2 : Level} {A : UU l1} {B : UU l2} → is-injective (iff-equiv {A = A} {B}) -is-injective-iff-equiv p = eq-htpy-equiv (pr1 (htpy-eq-iff p)) - -compute-fiber-iff-equiv : - {l1 l2 : Level} {A : UU l1} {B : UU l2} ((f , g) : A ↔ B) → - fiber (iff-equiv) (f , g) ≃ Σ (is-equiv f) (λ f' → map-inv-is-equiv f' ~ g) -compute-fiber-iff-equiv {A = A} {B} (f , g) = - ( equiv-tot (λ _ → equiv-funext)) ∘e - ( left-unit-law-Σ-is-contr (is-torsorial-Id' f) (f , refl)) ∘e - ( inv-associative-Σ (A → B) (_＝ f) _) ∘e - ( equiv-tot (λ _ → equiv-left-swap-Σ)) ∘e - ( associative-Σ (A → B) _ _) ∘e - ( equiv-tot (λ e → equiv-pair-eq (iff-equiv e) (f , g))) -``` - -### Two equal propositions are logically equivalent - -```agda -iff-eq : {l1 : Level} {P Q : Prop l1} → P ＝ Q → type-Prop (P ⇔ Q) -pr1 (iff-eq refl) = id -pr2 (iff-eq refl) = id -``` - ### Logical equivalence of propositions is equivalent to equivalence of propositions ```agda @@ -268,43 +131,12 @@ pr1 (equiv-equiv-iff P Q) = equiv-iff' P Q pr2 (equiv-equiv-iff P Q) = is-equiv-equiv-iff P Q ``` -## Logical equivalences between dependent function types - -```agda -module _ - {l1 l2 l3 : Level} {I : UU l1} {A : I → UU l2} {B : I → UU l3} - where - - iff-Π-iff-family : ((i : I) → A i ↔ B i) → ((i : I) → A i) ↔ ((i : I) → B i) - pr1 (iff-Π-iff-family e) a i = forward-implication (e i) (a i) - pr2 (iff-Π-iff-family e) b i = backward-implication (e i) (b i) -``` - -## Reasoning with logical equivalences - -Logical equivalences can be constructed by equational reasoning in the following -way: - -```text -logical-equivalence-reasoning - X ↔ Y by equiv-1 - ↔ Z by equiv-2 - ↔ V by equiv-3 -``` +### Equivalences are logical equivalences ```agda -infixl 1 logical-equivalence-reasoning_ -infixl 0 step-logical-equivalence-reasoning - -logical-equivalence-reasoning_ : - {l1 : Level} (X : UU l1) → X ↔ X -pr1 (logical-equivalence-reasoning X) = id -pr2 (logical-equivalence-reasoning X) = id - -step-logical-equivalence-reasoning : - {l1 l2 l3 : Level} {X : UU l1} {Y : UU l2} → - (X ↔ Y) → (Z : UU l3) → (Y ↔ Z) → (X ↔ Z) -step-logical-equivalence-reasoning e Z f = f ∘iff e - -syntax step-logical-equivalence-reasoning e Z f = e ↔ Z by f +compute-fiber-iff-equiv : + {l1 l2 : Level} {A : UU l1} {B : UU l2} ((f , g) : A ↔ B) → + fiber (iff-equiv) (f , g) ≃ Σ (is-equiv f) (λ f' → map-inv-is-equiv f' ~ g) +compute-fiber-iff-equiv {A = A} {B} e = + equiv-tot (λ _ → equiv-funext) ∘e compute-fiber-iff-equiv' e ``` diff --git a/src/foundation/maps-in-global-subuniverses.lagda.md b/src/foundation/maps-in-global-subuniverses.lagda.md index c3f263ac66..1ef87fa5c1 100644 --- a/src/foundation/maps-in-global-subuniverses.lagda.md +++ b/src/foundation/maps-in-global-subuniverses.lagda.md @@ -1,17 +1,26 @@ # Maps in global subuniverses ```agda -module foundation.maps-in-global-subuniverses where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.maps-in-global-subuniverses + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.cartesian-morphisms-arrows +open import foundation.cartesian-morphisms-arrows funext univalence truncations open import foundation.dependent-pair-types -open import foundation.fibers-of-maps -open import foundation.functoriality-fibers-of-maps -open import foundation.global-subuniverses +open import foundation.dependent-products-propositions funext +open import foundation.fibers-of-maps funext +open import foundation.functoriality-fibers-of-maps funext +open import foundation.global-subuniverses funext univalence open import foundation.unit-type open import foundation.universe-levels diff --git a/src/foundation/maps-in-subuniverses.lagda.md b/src/foundation/maps-in-subuniverses.lagda.md index 52c43cb7cc..8f1a21447e 100644 --- a/src/foundation/maps-in-subuniverses.lagda.md +++ b/src/foundation/maps-in-subuniverses.lagda.md @@ -1,14 +1,20 @@ # Maps in subuniverses ```agda -module foundation.maps-in-subuniverses where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.maps-in-subuniverses + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda -open import foundation.homotopies -open import foundation.subuniverses +open import foundation.homotopies funext +open import foundation.subuniverses funext univalence open import foundation.universe-levels open import foundation-core.fibers-of-maps diff --git a/src/foundation/maybe.lagda.md b/src/foundation/maybe.lagda.md index eb0267724d..be57573322 100644 --- a/src/foundation/maybe.lagda.md +++ b/src/foundation/maybe.lagda.md @@ -1,34 +1,40 @@ # The maybe monad ```agda -module foundation.maybe where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.maybe + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where + +open import foundation-core.maybe public ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types -open import foundation.coproduct-types -open import foundation.decidable-types +open import foundation.coproduct-types funext univalence truncations +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equality-coproduct-types -open import foundation.existential-quantification -open import foundation.propositional-truncations -open import foundation.surjective-maps -open import foundation.type-arithmetic-empty-type +open import foundation.equality-coproduct-types funext univalence truncations +open import foundation.existential-quantification funext univalence truncations +open import foundation.propositional-truncations funext univalence +open import foundation.surjective-maps funext univalence truncations +open import foundation.type-arithmetic-empty-type funext univalence truncations open import foundation.unit-type open import foundation.universe-levels open import foundation-core.embeddings open import foundation-core.empty-types -open import foundation-core.equivalences open import foundation-core.identity-types open import foundation-core.injective-maps open import foundation-core.negation open import foundation-core.propositions -open import foundation-core.retractions -open import foundation-core.sections ```
@@ -45,80 +51,6 @@ The maybe monad is an example of a monad that is not a [modality](orthogonal-factorization-systems.higher-modalities.md), since it is not [idempotent](foundation.idempotent-maps.md). -## Definitions - -### The maybe monad - -```agda -Maybe : {l : Level} → UU l → UU l -Maybe X = X + unit - -unit-Maybe : {l : Level} {X : UU l} → X → Maybe X -unit-Maybe = inl - -exception-Maybe : {l : Level} {X : UU l} → Maybe X -exception-Maybe = inr star - -extend-Maybe : - {l1 l2 : Level} {X : UU l1} {Y : UU l2} → (X → Maybe Y) → Maybe X → Maybe Y -extend-Maybe f (inl x) = f x -extend-Maybe f (inr *) = inr * - -map-Maybe : - {l1 l2 : Level} {X : UU l1} {Y : UU l2} → (X → Y) → Maybe X → Maybe Y -map-Maybe f (inl x) = inl (f x) -map-Maybe f (inr *) = inr * -``` - -### The inductive definition of the maybe monad - -```agda -data Maybe' {l : Level} (X : UU l) : UU l where - unit-Maybe' : X → Maybe' X - exception-Maybe' : Maybe' X - -{-# BUILTIN MAYBE Maybe' #-} -``` - -### The predicate of being an exception - -```agda -is-exception-Maybe : {l : Level} {X : UU l} → Maybe X → UU l -is-exception-Maybe {l} {X} x = (x ＝ exception-Maybe) - -is-not-exception-Maybe : {l : Level} {X : UU l} → Maybe X → UU l -is-not-exception-Maybe x = ¬ (is-exception-Maybe x) - -is-prop-is-exception-Maybe : - {l : Level} {X : UU l} (x : Maybe X) → is-prop (is-exception-Maybe x) -is-prop-is-exception-Maybe (inl x) () -is-prop-is-exception-Maybe (inr x) = - is-prop-equiv (compute-eq-coproduct-inr-inr x star) (is-set-unit x star) -``` - -### The predicate of being a value - -```agda -is-value-Maybe : {l : Level} {X : UU l} → Maybe X → UU l -is-value-Maybe {l} {X} x = Σ X (λ y → inl y ＝ x) - -value-is-value-Maybe : - {l : Level} {X : UU l} (x : Maybe X) → is-value-Maybe x → X -value-is-value-Maybe x = pr1 - -eq-is-value-Maybe : - {l : Level} {X : UU l} (x : Maybe X) (H : is-value-Maybe x) → - inl (value-is-value-Maybe x H) ＝ x -eq-is-value-Maybe x H = pr2 H -``` - -### Maybe structure on a type - -```agda -maybe-structure : {l1 : Level} (X : UU l1) → UU (lsuc l1) -maybe-structure {l1} X = Σ (UU l1) (λ Y → Maybe Y ≃ X) -``` - ## Properties ### The unit of `Maybe` is an embedding @@ -157,47 +89,6 @@ module _ is-decidable-neg (is-decidable-is-exception-Maybe x) ``` -### The values of the unit of the `Maybe` monad are not exceptions - -```agda -abstract - is-not-exception-unit-Maybe : - {l : Level} {X : UU l} (x : X) → is-not-exception-Maybe (unit-Maybe x) - is-not-exception-unit-Maybe x () -``` - -### The unit of `Maybe` is not surjective - -```agda -abstract - is-not-surjective-unit-Maybe : - {l : Level} {X : UU l} → ¬ (is-surjective (unit-Maybe {X = X})) - is-not-surjective-unit-Maybe H = - rec-trunc-Prop empty-Prop - ( λ p → is-not-exception-unit-Maybe (pr1 p) (pr2 p)) - ( H exception-Maybe) -``` - -### For any element of type `Maybe X` we can decide whether it is a value or an exception - -```agda -decide-Maybe : - {l : Level} {X : UU l} (x : Maybe X) → is-value-Maybe x + is-exception-Maybe x -decide-Maybe (inl x) = inl (x , refl) -decide-Maybe (inr star) = inr refl -``` - -### Values are not exceptions - -```agda -abstract - is-not-exception-is-value-Maybe : - {l1 : Level} {X : UU l1} (x : Maybe X) → - is-value-Maybe x → is-not-exception-Maybe x - is-not-exception-is-value-Maybe {l1} {X} .(inl x) (x , refl) = - is-not-exception-unit-Maybe x -``` - ### If a point is not an exception, then it is a value ```agda @@ -223,40 +114,16 @@ eq-is-not-exception-Maybe x H = eq-is-value-Maybe x (is-value-is-not-exception-Maybe x H) ``` -### The two definitions of `Maybe` are equivalent +### The unit of `Maybe` is not surjective ```agda -module _ - {l1 l2 : Level} {X : UU l1} - where - - map-Maybe-Maybe' : Maybe X → Maybe' X - map-Maybe-Maybe' (inl x) = unit-Maybe' x - map-Maybe-Maybe' (inr _) = exception-Maybe' - - map-inv-Maybe-Maybe' : Maybe' X → Maybe X - map-inv-Maybe-Maybe' (unit-Maybe' x) = inl x - map-inv-Maybe-Maybe' exception-Maybe' = inr star - - is-section-map-inv-Maybe-Maybe' : - is-section map-Maybe-Maybe' map-inv-Maybe-Maybe' - is-section-map-inv-Maybe-Maybe' (unit-Maybe' x) = refl - is-section-map-inv-Maybe-Maybe' exception-Maybe' = refl - - is-retraction-map-inv-Maybe-Maybe' : - is-retraction map-Maybe-Maybe' map-inv-Maybe-Maybe' - is-retraction-map-inv-Maybe-Maybe' (inl x) = refl - is-retraction-map-inv-Maybe-Maybe' (inr x) = refl - - is-equiv-map-Maybe-Maybe' : is-equiv map-Maybe-Maybe' - is-equiv-map-Maybe-Maybe' = - is-equiv-is-invertible - ( map-inv-Maybe-Maybe') - ( is-section-map-inv-Maybe-Maybe') - ( is-retraction-map-inv-Maybe-Maybe') - - equiv-Maybe-Maybe' : Maybe X ≃ Maybe' X - equiv-Maybe-Maybe' = (map-Maybe-Maybe' , is-equiv-map-Maybe-Maybe') +abstract + is-not-surjective-unit-Maybe : + {l : Level} {X : UU l} → ¬ (is-surjective (unit-Maybe {X = X})) + is-not-surjective-unit-Maybe H = + rec-trunc-Prop empty-Prop + ( λ p → is-not-exception-unit-Maybe (pr1 p) (pr2 p)) + ( H exception-Maybe) ``` ### The extension of surjective maps is surjective @@ -299,13 +166,8 @@ module _ {l1 l2 : Level} {A : UU l1} {B : UU l2} where - map-maybe-coproduct : Maybe A + Maybe B → Maybe (A + B) - map-maybe-coproduct (inl (inl x)) = inl (inl x) - map-maybe-coproduct (inl (inr star)) = inr star - map-maybe-coproduct (inr (inl x)) = inl (inr x) - map-maybe-coproduct (inr (inr star)) = inr star - - is-surjective-map-maybe-coproduct : is-surjective map-maybe-coproduct + is-surjective-map-maybe-coproduct : + is-surjective (map-maybe-coproduct {A = A} {B}) is-surjective-map-maybe-coproduct (inl (inl x)) = unit-trunc-Prop ((inl (inl x)) , refl) is-surjective-map-maybe-coproduct (inl (inr x)) = @@ -321,13 +183,8 @@ module _ {l1 l2 : Level} {A : UU l1} {B : UU l2} where - map-maybe-product : Maybe A × Maybe B → Maybe (A × B) - map-maybe-product (inl a , inl b) = inl (a , b) - map-maybe-product (inl a , inr star) = inr star - map-maybe-product (inr star , inl b) = inr star - map-maybe-product (inr star , inr star) = inr star - - is-surjective-map-maybe-product : is-surjective map-maybe-product + is-surjective-map-maybe-product : + is-surjective (map-maybe-product {A = A} {B}) is-surjective-map-maybe-product (inl (a , b)) = unit-trunc-Prop ((inl a , inl b) , refl) is-surjective-map-maybe-product (inr star) = diff --git a/src/foundation/mere-embeddings.lagda.md b/src/foundation/mere-embeddings.lagda.md index 4fbccc13d4..489a00dcea 100644 --- a/src/foundation/mere-embeddings.lagda.md +++ b/src/foundation/mere-embeddings.lagda.md @@ -1,22 +1,30 @@ # Mere embeddings ```agda -module foundation.mere-embeddings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.mere-embeddings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.cantor-schroder-bernstein-escardo -open import foundation.embeddings -open import foundation.law-of-excluded-middle -open import foundation.mere-equivalences -open import foundation.propositional-truncations +open import foundation.cantor-schroder-bernstein-escardo funext univalence truncations +open import foundation.embeddings funext +open import foundation.law-of-excluded-middle funext univalence truncations +open import foundation.mere-equivalences funext univalence truncations +open import foundation.propositional-truncations funext univalence open import foundation.universe-levels open import foundation-core.propositions -open import order-theory.large-preorders +open import order-theory.large-preorders funext univalence truncations ```
diff --git a/src/foundation/mere-equality.lagda.md b/src/foundation/mere-equality.lagda.md index d5319cae0a..525a441417 100644 --- a/src/foundation/mere-equality.lagda.md +++ b/src/foundation/mere-equality.lagda.md @@ -1,21 +1,29 @@ # Mere equality ```agda -module foundation.mere-equality where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.mere-equality + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.binary-relations +open import foundation.binary-relations funext univalence truncations open import foundation.dependent-pair-types -open import foundation.functoriality-propositional-truncation -open import foundation.propositional-truncations -open import foundation.reflecting-maps-equivalence-relations +open import foundation.functoriality-propositional-truncation funext univalence truncations +open import foundation.propositional-truncations funext univalence +open import foundation.reflecting-maps-equivalence-relations funext univalence truncations open import foundation.universe-levels -open import foundation-core.equivalence-relations +open import foundation-core.equivalence-relations funext univalence truncations open import foundation-core.identity-types open import foundation-core.propositions open import foundation-core.sets diff --git a/src/foundation/mere-equivalences.lagda.md b/src/foundation/mere-equivalences.lagda.md index 663c8f4d24..4d155f5e6c 100644 --- a/src/foundation/mere-equivalences.lagda.md +++ b/src/foundation/mere-equivalences.lagda.md @@ -1,18 +1,27 @@ # Mere equivalences ```agda -module foundation.mere-equivalences where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.mere-equivalences + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.binary-relations -open import foundation.decidable-equality -open import foundation.functoriality-propositional-truncation -open import foundation.mere-equality -open import foundation.propositional-truncations -open import foundation.univalence +open import foundation.binary-relations funext univalence truncations +open import foundation.decidable-equality funext univalence truncations +open import foundation.dependent-products-truncated-types funext +open import foundation.functoriality-propositional-truncation funext univalence truncations +open import foundation.mere-equality funext univalence truncations +open import foundation.propositional-truncations funext univalence +open import foundation.univalence funext univalence open import foundation.universe-levels open import foundation-core.equivalences diff --git a/src/foundation/mere-functions.lagda.md b/src/foundation/mere-functions.lagda.md index 4597357ccd..c2db0172ae 100644 --- a/src/foundation/mere-functions.lagda.md +++ b/src/foundation/mere-functions.lagda.md @@ -1,13 +1,21 @@ # Mere functions ```agda -module foundation.mere-functions where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.mere-functions + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.propositional-truncations +open import foundation.propositional-truncations funext univalence open import foundation.universe-levels open import foundation-core.function-types diff --git a/src/foundation/mere-logical-equivalences.lagda.md b/src/foundation/mere-logical-equivalences.lagda.md index 5bf9ebe781..38dd959e70 100644 --- a/src/foundation/mere-logical-equivalences.lagda.md +++ b/src/foundation/mere-logical-equivalences.lagda.md @@ -1,18 +1,26 @@ # Mere logical equivalences ```agda -module foundation.mere-logical-equivalences where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.mere-logical-equivalences + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.conjunction +open import foundation.conjunction funext univalence truncations open import foundation.dependent-pair-types -open import foundation.inhabited-types -open import foundation.logical-equivalences -open import foundation.mere-functions -open import foundation.propositional-truncations +open import foundation.inhabited-types funext univalence truncations +open import foundation.logical-equivalences funext +open import foundation.mere-functions funext univalence truncations +open import foundation.propositional-truncations funext univalence open import foundation.universe-levels open import foundation-core.cartesian-product-types diff --git a/src/foundation/mere-path-cosplit-maps.lagda.md b/src/foundation/mere-path-cosplit-maps.lagda.md index dd39c03112..c653adc451 100644 --- a/src/foundation/mere-path-cosplit-maps.lagda.md +++ b/src/foundation/mere-path-cosplit-maps.lagda.md @@ -1,7 +1,15 @@ # Mere path-cosplit maps ```agda -module foundation.mere-path-cosplit-maps where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.mere-path-cosplit-maps + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,12 +17,13 @@ module foundation.mere-path-cosplit-maps where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalences-arrows -open import foundation.inhabited-types -open import foundation.iterated-dependent-product-types -open import foundation.logical-equivalences -open import foundation.propositional-truncations -open import foundation.truncated-maps +open import foundation.dependent-products-propositions funext +open import foundation.equivalences-arrows funext univalence truncations +open import foundation.inhabited-types funext univalence truncations +open import foundation.iterated-dependent-product-types funext +open import foundation.logical-equivalences funext +open import foundation.propositional-truncations funext univalence +open import foundation.truncated-maps funext open import foundation.truncation-levels open import foundation.universe-levels diff --git a/src/foundation/monomorphisms.lagda.md b/src/foundation/monomorphisms.lagda.md index 1908560489..c0b99626a4 100644 --- a/src/foundation/monomorphisms.lagda.md +++ b/src/foundation/monomorphisms.lagda.md @@ -1,7 +1,13 @@ # Monomorphisms ```agda -module foundation.monomorphisms where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.monomorphisms + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports @@ -9,10 +15,11 @@ module foundation.monomorphisms where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.function-extensionality -open import foundation.functoriality-function-types -open import foundation.postcomposition-functions +open import foundation.dependent-products-propositions funext +open import foundation.embeddings funext +open import foundation.function-extensionality funext +open import foundation.functoriality-function-types funext univalence +open import foundation.postcomposition-functions funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition diff --git a/src/foundation/morphisms-arrows.lagda.md b/src/foundation/morphisms-arrows.lagda.md index b80513a416..db81612f4f 100644 --- a/src/foundation/morphisms-arrows.lagda.md +++ b/src/foundation/morphisms-arrows.lagda.md @@ -1,21 +1,25 @@ # Morphisms of arrows ```agda -module foundation.morphisms-arrows where +open import foundation.function-extensionality-axiom + +module foundation.morphisms-arrows + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cones-over-cospan-diagrams +open import foundation.cones-over-cospan-diagrams funext open import foundation.dependent-pair-types -open import foundation.function-extensionality +open import foundation.function-extensionality funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import foundation-core.commuting-squares-of-maps +open import foundation-core.commuting-squares-of-maps funext open import foundation-core.function-types -open import foundation-core.functoriality-dependent-function-types +open import foundation-core.functoriality-dependent-function-types funext open import foundation-core.functoriality-dependent-pair-types open import foundation-core.homotopies open import foundation-core.identity-types diff --git a/src/foundation/morphisms-binary-relations.lagda.md b/src/foundation/morphisms-binary-relations.lagda.md index 5e9c42e904..8c1a398b69 100644 --- a/src/foundation/morphisms-binary-relations.lagda.md +++ b/src/foundation/morphisms-binary-relations.lagda.md @@ -1,14 +1,22 @@ # Morphisms of binary relations ```agda -module foundation.morphisms-binary-relations where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.morphisms-binary-relations + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.binary-homotopies -open import foundation.binary-relations +open import foundation.binary-homotopies funext +open import foundation.binary-relations funext univalence truncations open import foundation.universe-levels open import foundation-core.equivalences diff --git a/src/foundation/morphisms-coalgebras-maybe.lagda.md b/src/foundation/morphisms-coalgebras-maybe.lagda.md index 356b8eba5b..aea13a97dc 100644 --- a/src/foundation/morphisms-coalgebras-maybe.lagda.md +++ b/src/foundation/morphisms-coalgebras-maybe.lagda.md @@ -1,19 +1,26 @@ # Morphisms of coalgebras of the maybe monad ```agda -module foundation.morphisms-coalgebras-maybe where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.morphisms-coalgebras-maybe + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda -open import foundation.coalgebras-maybe -open import foundation.commuting-squares-of-maps +open import foundation.coalgebras-maybe funext univalence +open import foundation.commuting-squares-of-maps funext univalence open import foundation.dependent-pair-types -open import foundation.maybe open import foundation.universe-levels -open import trees.polynomial-endofunctors +open import foundation-core.maybe + +open import trees.polynomial-endofunctors funext univalence ```
@@ -21,8 +28,8 @@ open import trees.polynomial-endofunctors ## Idea Given two [coalgebras](foundation.coalgebras-maybe.md) of the -[maybe monad](foundation.maybe.md) `η : X → Maybe X`, `η' : Y → Maybe Y`, then a -map `f : X → Y` is a +[maybe monad](foundation-core.maybe.md) `η : X → Maybe X`, `η' : Y → Maybe Y`, +then a map `f : X → Y` is a {{#concept "morphism of coalgebras" Disambiguation="of the maybe monad" Agda=hom-coalgebra-Maybe}} if the square diff --git a/src/foundation/morphisms-cospans.lagda.md b/src/foundation/morphisms-cospans.lagda.md index b3cdf33eb6..4eade956fa 100644 --- a/src/foundation/morphisms-cospans.lagda.md +++ b/src/foundation/morphisms-cospans.lagda.md @@ -7,11 +7,11 @@ module foundation.morphisms-cospans where
Imports ```agda -open import foundation.cartesian-product-types open import foundation.cospans open import foundation.dependent-pair-types open import foundation.universe-levels +open import foundation-core.cartesian-product-types open import foundation-core.commuting-triangles-of-maps ``` diff --git a/src/foundation/morphisms-double-arrows.lagda.md b/src/foundation/morphisms-double-arrows.lagda.md index 33810a5de8..043a2a37be 100644 --- a/src/foundation/morphisms-double-arrows.lagda.md +++ b/src/foundation/morphisms-double-arrows.lagda.md @@ -1,19 +1,25 @@ # Morphisms of double arrows ```agda -module foundation.morphisms-double-arrows where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.morphisms-double-arrows + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda -open import foundation.cartesian-product-types -open import foundation.commuting-squares-of-maps +open import foundation.cartesian-product-types funext univalence +open import foundation.commuting-squares-of-maps funext univalence open import foundation.dependent-pair-types open import foundation.double-arrows -open import foundation.function-types -open import foundation.homotopies -open import foundation.morphisms-arrows +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.morphisms-arrows funext open import foundation.universe-levels ``` diff --git a/src/foundation/morphisms-inverse-sequential-diagrams.lagda.md b/src/foundation/morphisms-inverse-sequential-diagrams.lagda.md index 515f06b8ce..c131b0a211 100644 --- a/src/foundation/morphisms-inverse-sequential-diagrams.lagda.md +++ b/src/foundation/morphisms-inverse-sequential-diagrams.lagda.md @@ -1,7 +1,15 @@ # Morphisms of inverse sequential diagrams of types ```agda -module foundation.morphisms-inverse-sequential-diagrams where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.morphisms-inverse-sequential-diagrams + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,13 +18,13 @@ module foundation.morphisms-inverse-sequential-diagrams where open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.binary-homotopies -open import foundation.dependent-inverse-sequential-diagrams +open import foundation.binary-homotopies funext +open import foundation.dependent-inverse-sequential-diagrams funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types +open import foundation.equality-dependent-function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopy-induction -open import foundation.inverse-sequential-diagrams +open import foundation.homotopy-induction funext +open import foundation.inverse-sequential-diagrams funext univalence truncations open import foundation.structure-identity-principle open import foundation.universe-levels open import foundation.whiskering-homotopies-composition diff --git a/src/foundation/morphisms-span-diagrams.lagda.md b/src/foundation/morphisms-span-diagrams.lagda.md index 604d0c6d6e..8b98dd11e1 100644 --- a/src/foundation/morphisms-span-diagrams.lagda.md +++ b/src/foundation/morphisms-span-diagrams.lagda.md @@ -1,20 +1,28 @@ # Morphisms of span diagrams ```agda -module foundation.morphisms-span-diagrams where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.morphisms-span-diagrams + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.morphisms-arrows +open import foundation.morphisms-arrows funext open import foundation.morphisms-spans -open import foundation.operations-spans -open import foundation.span-diagrams +open import foundation.operations-spans funext univalence truncations +open import foundation.span-diagrams funext open import foundation.universe-levels -open import foundation-core.commuting-squares-of-maps +open import foundation-core.commuting-squares-of-maps funext ```
diff --git a/src/foundation/morphisms-spans-families-of-types.lagda.md b/src/foundation/morphisms-spans-families-of-types.lagda.md index 8c372f1a61..cf0a4704ba 100644 --- a/src/foundation/morphisms-spans-families-of-types.lagda.md +++ b/src/foundation/morphisms-spans-families-of-types.lagda.md @@ -1,17 +1,21 @@ # Morphisms of spans on families of types ```agda -module foundation.morphisms-spans-families-of-types where +open import foundation.function-extensionality-axiom + +module foundation.morphisms-spans-families-of-types + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.commuting-triangles-of-homotopies +open import foundation.commuting-triangles-of-homotopies funext open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types +open import foundation.equality-dependent-function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopy-induction +open import foundation.homotopy-induction funext open import foundation.spans-families-of-types open import foundation.structure-identity-principle open import foundation.universe-levels diff --git a/src/foundation/morphisms-spans.lagda.md b/src/foundation/morphisms-spans.lagda.md index 0632d4ed00..10cddfab98 100644 --- a/src/foundation/morphisms-spans.lagda.md +++ b/src/foundation/morphisms-spans.lagda.md @@ -12,9 +12,7 @@ open import foundation.spans open import foundation.universe-levels open import foundation-core.cartesian-product-types -open import foundation-core.commuting-squares-of-maps open import foundation-core.commuting-triangles-of-maps -open import foundation-core.operations-spans ```
diff --git a/src/foundation/multisubsets.lagda.md b/src/foundation/multisubsets.lagda.md index 3819e8ba69..682b723507 100644 --- a/src/foundation/multisubsets.lagda.md +++ b/src/foundation/multisubsets.lagda.md @@ -1,7 +1,15 @@ # Multisubsets ```agda -module foundation.multisubsets where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.multisubsets + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,14 +18,14 @@ module foundation.multisubsets where open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.images -open import foundation.negated-equality +open import foundation.images funext univalence truncations +open import foundation.negated-equality funext univalence truncations open import foundation.universe-levels open import foundation-core.fibers-of-maps open import foundation-core.sets -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.finite-types funext univalence truncations ```
diff --git a/src/foundation/multivariable-correspondences.lagda.md b/src/foundation/multivariable-correspondences.lagda.md index 817901c593..09ddd4bd61 100644 --- a/src/foundation/multivariable-correspondences.lagda.md +++ b/src/foundation/multivariable-correspondences.lagda.md @@ -1,7 +1,15 @@ # Multivariable correspondences ```agda -module foundation.multivariable-correspondences where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.multivariable-correspondences + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -11,7 +19,7 @@ open import elementary-number-theory.natural-numbers open import foundation.universe-levels -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/foundation/multivariable-decidable-relations.lagda.md b/src/foundation/multivariable-decidable-relations.lagda.md index 9a5467028e..0aa8924613 100644 --- a/src/foundation/multivariable-decidable-relations.lagda.md +++ b/src/foundation/multivariable-decidable-relations.lagda.md @@ -1,7 +1,15 @@ # Multivariable decidable relations ```agda -module foundation.multivariable-decidable-relations where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.multivariable-decidable-relations + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,12 +17,12 @@ module foundation.multivariable-decidable-relations where ```agda open import elementary-number-theory.natural-numbers -open import foundation.decidable-subtypes -open import foundation.multivariable-correspondences -open import foundation.multivariable-relations +open import foundation.decidable-subtypes funext univalence truncations +open import foundation.multivariable-correspondences funext univalence truncations +open import foundation.multivariable-relations funext univalence truncations open import foundation.universe-levels -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/foundation/multivariable-functoriality-set-quotients.lagda.md b/src/foundation/multivariable-functoriality-set-quotients.lagda.md index 62cad9dc12..2087a6d910 100644 --- a/src/foundation/multivariable-functoriality-set-quotients.lagda.md +++ b/src/foundation/multivariable-functoriality-set-quotients.lagda.md @@ -1,7 +1,15 @@ # Multivariable functoriality of set quotients ```agda -module foundation.multivariable-functoriality-set-quotients where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.multivariable-functoriality-set-quotients + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,18 +17,18 @@ module foundation.multivariable-functoriality-set-quotients where ```agda open import elementary-number-theory.natural-numbers -open import foundation.functoriality-set-quotients -open import foundation.set-quotients +open import foundation.functoriality-set-quotients funext univalence truncations +open import foundation.set-quotients funext univalence truncations open import foundation.universe-levels -open import foundation.vectors-set-quotients +open import foundation.vectors-set-quotients funext univalence truncations -open import foundation-core.equivalence-relations +open import foundation-core.equivalence-relations funext univalence truncations open import foundation-core.function-types open import foundation-core.homotopies -open import linear-algebra.vectors +open import linear-algebra.vectors funext univalence truncations -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/foundation/multivariable-homotopies.lagda.md b/src/foundation/multivariable-homotopies.lagda.md index 01f1635bf5..fab06b21b8 100644 --- a/src/foundation/multivariable-homotopies.lagda.md +++ b/src/foundation/multivariable-homotopies.lagda.md @@ -1,9 +1,11 @@ # Multivariable homotopies ```agda -module foundation.multivariable-homotopies where +open import foundation.function-extensionality-axiom -open import foundation.telescopes public +module foundation.multivariable-homotopies + (funext : function-extensionality) + where ```
Imports @@ -12,15 +14,16 @@ open import foundation.telescopes public open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types -open import foundation.function-extensionality +open import foundation.equality-dependent-function-types funext +open import foundation.function-extensionality funext open import foundation.implicit-function-types -open import foundation.iterated-dependent-product-types +open import foundation.iterated-dependent-product-types funext +open import foundation.telescopes open import foundation.universe-levels open import foundation-core.contractible-types open import foundation-core.equivalences -open import foundation-core.functoriality-dependent-function-types +open import foundation-core.functoriality-dependent-function-types funext open import foundation-core.functoriality-dependent-pair-types open import foundation-core.identity-types open import foundation-core.torsorial-type-families diff --git a/src/foundation/multivariable-operations.lagda.md b/src/foundation/multivariable-operations.lagda.md index fe71b9e834..c1452fc5ce 100644 --- a/src/foundation/multivariable-operations.lagda.md +++ b/src/foundation/multivariable-operations.lagda.md @@ -1,7 +1,15 @@ # Multivariable operations ```agda -module foundation.multivariable-operations where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.multivariable-operations + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -12,7 +20,7 @@ open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types open import foundation.equality-cartesian-product-types -open import foundation.raising-universe-levels +open import foundation.raising-universe-levels-unit-type open import foundation.unit-type open import foundation.universe-levels @@ -22,8 +30,9 @@ open import foundation-core.equivalences open import foundation-core.function-types open import foundation-core.homotopies open import foundation-core.identity-types +open import foundation-core.raising-universe-levels -open import linear-algebra.vectors +open import linear-algebra.vectors funext univalence truncations ```
diff --git a/src/foundation/multivariable-relations.lagda.md b/src/foundation/multivariable-relations.lagda.md index 630c453e97..c927d9dcd4 100644 --- a/src/foundation/multivariable-relations.lagda.md +++ b/src/foundation/multivariable-relations.lagda.md @@ -1,7 +1,15 @@ # Multivariable relations ```agda -module foundation.multivariable-relations where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.multivariable-relations + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,12 +17,12 @@ module foundation.multivariable-relations where ```agda open import elementary-number-theory.natural-numbers -open import foundation.multivariable-correspondences +open import foundation.multivariable-correspondences funext univalence truncations open import foundation.universe-levels -open import foundation-core.subtypes +open import foundation-core.subtypes funext -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/foundation/multivariable-sections.lagda.md b/src/foundation/multivariable-sections.lagda.md index 08d12e5bd9..72e9fb76ae 100644 --- a/src/foundation/multivariable-sections.lagda.md +++ b/src/foundation/multivariable-sections.lagda.md @@ -1,9 +1,11 @@ # Multivariable sections ```agda -module foundation.multivariable-sections where +open import foundation.function-extensionality-axiom -open import foundation.telescopes public +module foundation.multivariable-sections + (funext : function-extensionality) + where ```
Imports @@ -12,8 +14,9 @@ open import foundation.telescopes public open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.iterated-dependent-product-types -open import foundation.multivariable-homotopies +open import foundation.iterated-dependent-product-types funext +open import foundation.multivariable-homotopies funext +open import foundation.telescopes open import foundation.universe-levels open import foundation-core.function-types diff --git a/src/foundation/negated-equality.lagda.md b/src/foundation/negated-equality.lagda.md index 96ad3cd6a1..f1c767f143 100644 --- a/src/foundation/negated-equality.lagda.md +++ b/src/foundation/negated-equality.lagda.md @@ -1,17 +1,24 @@ # Negated equality ```agda -module foundation.negated-equality where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.negated-equality + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.binary-relations +open import foundation.binary-relations funext univalence truncations open import foundation.dependent-pair-types -open import foundation.function-extensionality -open import foundation.negation +open import foundation.negation funext open import foundation.universe-levels open import foundation-core.cartesian-product-types diff --git a/src/foundation/negation.lagda.md b/src/foundation/negation.lagda.md index 273c37d133..ff5d812ba3 100644 --- a/src/foundation/negation.lagda.md +++ b/src/foundation/negation.lagda.md @@ -1,7 +1,11 @@ # Negation ```agda -module foundation.negation where +open import foundation.function-extensionality-axiom + +module foundation.negation + (funext : function-extensionality) + where open import foundation-core.negation public ``` @@ -10,7 +14,8 @@ open import foundation-core.negation public ```agda open import foundation.dependent-pair-types -open import foundation.logical-equivalences +open import foundation.dependent-products-propositions funext +open import foundation.logical-equivalences funext open import foundation.universe-levels open import foundation-core.empty-types @@ -55,13 +60,6 @@ eq-neg : {l : Level} {A : UU l} {p q : ¬ A} → p ＝ q eq-neg = eq-is-prop is-prop-neg ``` -### Reductio ad absurdum - -```agda -reductio-ad-absurdum : {l1 l2 : Level} {P : UU l1} {Q : UU l2} → P → ¬ P → Q -reductio-ad-absurdum p np = ex-falso (np p) -``` - ### Logically equivalent types have logically equivalent negations ```agda @@ -91,11 +89,6 @@ module _ ### Negation has no fixed points ```agda -no-fixed-points-neg : - {l : Level} (A : UU l) → ¬ (A ↔ ¬ A) -no-fixed-points-neg A (f , g) = - ( λ (h : ¬ A) → h (g h)) (λ (a : A) → f a a) - abstract no-fixed-points-neg-Prop : {l : Level} (P : Prop l) → ¬ (type-Prop P ↔ ¬ (type-Prop P)) diff --git a/src/foundation/noncontractible-types.lagda.md b/src/foundation/noncontractible-types.lagda.md index 98d2d49311..2df5dd6160 100644 --- a/src/foundation/noncontractible-types.lagda.md +++ b/src/foundation/noncontractible-types.lagda.md @@ -1,7 +1,15 @@ # Noncontractible types ```agda -module foundation.noncontractible-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.noncontractible-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,8 +18,8 @@ module foundation.noncontractible-types where open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.inhabited-types +open import foundation.empty-types funext univalence truncations +open import foundation.inhabited-types funext univalence truncations open import foundation.universe-levels open import foundation-core.contractible-types diff --git a/src/foundation/null-homotopic-maps.lagda.md b/src/foundation/null-homotopic-maps.lagda.md index 2500c019f4..ee02b5534f 100644 --- a/src/foundation/null-homotopic-maps.lagda.md +++ b/src/foundation/null-homotopic-maps.lagda.md @@ -1,33 +1,42 @@ # Null-homotopic maps ```agda -module foundation.null-homotopic-maps where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.null-homotopic-maps + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.commuting-triangles-of-identifications -open import foundation.constant-maps +open import foundation.commuting-triangles-of-identifications funext +open import foundation.constant-maps funext univalence truncations open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.functoriality-dependent-pair-types +open import foundation.dependent-products-propositions funext +open import foundation.empty-types funext univalence truncations +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopy-induction -open import foundation.identity-types -open import foundation.images -open import foundation.inhabited-types -open import foundation.negation -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.sets +open import foundation.homotopy-induction funext +open import foundation.identity-types funext +open import foundation.images funext univalence truncations +open import foundation.inhabited-types funext univalence truncations +open import foundation.negation funext +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence +open import foundation.sets funext univalence open import foundation.structure-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext univalence truncations open import foundation.type-arithmetic-dependent-pair-types open import foundation.unit-type -open import foundation.universal-property-empty-type +open import foundation.universal-property-empty-type funext open import foundation.universe-levels -open import foundation.weakly-constant-maps +open import foundation.weakly-constant-maps funext open import foundation-core.contractible-types open import foundation-core.equivalences diff --git a/src/foundation/operations-span-diagrams.lagda.md b/src/foundation/operations-span-diagrams.lagda.md index 9337e9f12a..ca519783d8 100644 --- a/src/foundation/operations-span-diagrams.lagda.md +++ b/src/foundation/operations-span-diagrams.lagda.md @@ -1,18 +1,26 @@ # Operations on span diagrams ```agda -module foundation.operations-span-diagrams where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.operations-span-diagrams + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where -open import foundation-core.operations-span-diagrams public +open import foundation-core.operations-span-diagrams funext univalence truncations public ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences-arrows -open import foundation.operations-spans -open import foundation.span-diagrams +open import foundation.equivalences-arrows funext univalence truncations +open import foundation.operations-spans funext univalence truncations +open import foundation.span-diagrams funext open import foundation.spans open import foundation.universe-levels ``` diff --git a/src/foundation/operations-spans.lagda.md b/src/foundation/operations-spans.lagda.md index 6562513941..f54fa49ba0 100644 --- a/src/foundation/operations-spans.lagda.md +++ b/src/foundation/operations-spans.lagda.md @@ -1,17 +1,25 @@ # Operations on spans ```agda -module foundation.operations-spans where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.operations-spans + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where -open import foundation-core.operations-spans public +open import foundation-core.operations-spans funext public ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences-arrows -open import foundation.morphisms-arrows +open import foundation.equivalences-arrows funext univalence truncations +open import foundation.morphisms-arrows funext open import foundation.spans open import foundation.universe-levels diff --git a/src/foundation/pairs-of-distinct-elements.lagda.md b/src/foundation/pairs-of-distinct-elements.lagda.md index 8b152f6408..2d45991581 100644 --- a/src/foundation/pairs-of-distinct-elements.lagda.md +++ b/src/foundation/pairs-of-distinct-elements.lagda.md @@ -1,18 +1,26 @@ # Pairs of distinct elements ```agda -module foundation.pairs-of-distinct-elements where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.pairs-of-distinct-elements + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalences +open import foundation.embeddings funext +open import foundation.equivalences funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.negated-equality -open import foundation.negation +open import foundation.negated-equality funext univalence truncations +open import foundation.negation funext open import foundation.structure-identity-principle open import foundation.subtype-identity-principle open import foundation.universe-levels diff --git a/src/foundation/partitions.lagda.md b/src/foundation/partitions.lagda.md index 11658b834b..9345e42d3a 100644 --- a/src/foundation/partitions.lagda.md +++ b/src/foundation/partitions.lagda.md @@ -1,31 +1,41 @@ # Partitions ```agda -module foundation.partitions where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.partitions + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.conjunction -open import foundation.contractible-types +open import foundation.conjunction funext univalence truncations +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalences -open import foundation.existential-quantification -open import foundation.fiber-inclusions +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.existential-quantification funext univalence truncations +open import foundation.fiber-inclusions funext univalence open import foundation.fundamental-theorem-of-identity-types -open import foundation.inhabited-subtypes -open import foundation.inhabited-types -open import foundation.locally-small-types -open import foundation.logical-equivalences -open import foundation.propositional-truncations -open import foundation.sigma-decompositions -open import foundation.small-types +open import foundation.inhabited-subtypes funext univalence truncations +open import foundation.inhabited-types funext univalence truncations +open import foundation.locally-small-types funext univalence truncations +open import foundation.logical-equivalences funext +open import foundation.propositional-truncations funext univalence +open import foundation.sigma-decompositions funext univalence truncations +open import foundation.small-types funext univalence truncations open import foundation.subtype-identity-principle -open import foundation.subtypes -open import foundation.surjective-maps +open import foundation.subtypes funext univalence truncations +open import foundation.surjective-maps funext univalence truncations open import foundation.transport-along-identifications open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels @@ -33,7 +43,7 @@ open import foundation.universe-levels open import foundation-core.cartesian-product-types open import foundation-core.fibers-of-maps open import foundation-core.function-types -open import foundation-core.functoriality-dependent-function-types +open import foundation-core.functoriality-dependent-function-types funext open import foundation-core.functoriality-dependent-pair-types open import foundation-core.homotopies open import foundation-core.identity-types diff --git a/src/foundation/path-algebra.lagda.md b/src/foundation/path-algebra.lagda.md index 471a4d85e1..d6d36cca42 100644 --- a/src/foundation/path-algebra.lagda.md +++ b/src/foundation/path-algebra.lagda.md @@ -1,7 +1,11 @@ # Path algebra ```agda -module foundation.path-algebra where +open import foundation.function-extensionality-axiom + +module foundation.path-algebra + (funext : function-extensionality) + where ```
Imports @@ -9,9 +13,9 @@ module foundation.path-algebra where ```agda open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.binary-embeddings +open import foundation.binary-embeddings funext open import foundation.binary-equivalences -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels open import foundation-core.commuting-squares-of-identifications diff --git a/src/foundation/path-cosplit-maps.lagda.md b/src/foundation/path-cosplit-maps.lagda.md index 6a4f96e2e3..9dac862460 100644 --- a/src/foundation/path-cosplit-maps.lagda.md +++ b/src/foundation/path-cosplit-maps.lagda.md @@ -1,7 +1,15 @@ # Path-cosplit maps ```agda -module foundation.path-cosplit-maps where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.path-cosplit-maps + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,35 +18,38 @@ module foundation.path-cosplit-maps where open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.commuting-triangles-of-maps -open import foundation.coproduct-types +open import foundation.commuting-triangles-of-maps funext univalence +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.empty-types +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.dependent-products-truncated-types funext +open import foundation.empty-types funext univalence truncations open import foundation.equality-cartesian-product-types -open import foundation.equality-coproduct-types -open import foundation.equality-dependent-pair-types -open import foundation.equivalences-arrows -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.functoriality-action-on-identifications-functions -open import foundation.functoriality-cartesian-product-types -open import foundation.functoriality-coproduct-types -open import foundation.functoriality-dependent-function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopy-induction -open import foundation.identity-types -open import foundation.inhabited-types -open import foundation.iterated-dependent-product-types -open import foundation.logical-equivalences -open import foundation.mere-path-cosplit-maps -open import foundation.morphisms-arrows -open import foundation.negated-equality -open import foundation.postcomposition-functions -open import foundation.precomposition-functions -open import foundation.propositional-truncations -open import foundation.retractions -open import foundation.retracts-of-maps -open import foundation.truncated-maps +open import foundation.equality-coproduct-types funext univalence truncations +open import foundation.equality-dependent-pair-types funext +open import foundation.equivalences-arrows funext univalence truncations +open import foundation.function-extensionality funext +open import foundation.function-types funext +open import foundation.functoriality-action-on-identifications-functions funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.functoriality-coproduct-types funext univalence truncations +open import foundation.functoriality-dependent-function-types funext univalence +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext +open import foundation.inhabited-types funext univalence truncations +open import foundation.iterated-dependent-product-types funext +open import foundation.logical-equivalences funext +open import foundation.mere-path-cosplit-maps funext univalence truncations +open import foundation.morphisms-arrows funext +open import foundation.negated-equality funext univalence truncations +open import foundation.postcomposition-functions funext +open import foundation.precomposition-functions funext +open import foundation.propositional-truncations funext univalence +open import foundation.retractions funext +open import foundation.retracts-of-maps funext univalence +open import foundation.truncated-maps funext open import foundation.truncation-levels open import foundation.universe-levels diff --git a/src/foundation/path-split-maps.lagda.md b/src/foundation/path-split-maps.lagda.md index 7c985434d4..f5ddf45849 100644 --- a/src/foundation/path-split-maps.lagda.md +++ b/src/foundation/path-split-maps.lagda.md @@ -1,7 +1,11 @@ # Path-split maps ```agda -module foundation.path-split-maps where +open import foundation.function-extensionality-axiom + +module foundation.path-split-maps + (funext : function-extensionality) + where open import foundation-core.path-split-maps public ``` @@ -10,9 +14,10 @@ open import foundation-core.path-split-maps public ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.iterated-dependent-product-types -open import foundation.logical-equivalences +open import foundation.equivalences funext +open import foundation.iterated-dependent-product-types funext +open import foundation.logical-equivalences funext +open import foundation.telescopes open import foundation.universe-levels open import foundation-core.contractible-types diff --git a/src/foundation/path-split-type-families.lagda.md b/src/foundation/path-split-type-families.lagda.md index 690d6d1a74..ca076b71a5 100644 --- a/src/foundation/path-split-type-families.lagda.md +++ b/src/foundation/path-split-type-families.lagda.md @@ -1,7 +1,11 @@ # Path-split type families ```agda -module foundation.path-split-type-families where +open import foundation.function-extensionality-axiom + +module foundation.path-split-type-families + (funext : function-extensionality) + where ```
Imports @@ -9,7 +13,8 @@ module foundation.path-split-type-families where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.embeddings +open import foundation.dependent-products-contractible-types funext +open import foundation.embeddings funext open import foundation.transport-along-identifications open import foundation.universe-levels @@ -20,7 +25,7 @@ open import foundation-core.identity-types open import foundation-core.injective-maps open import foundation-core.propositions open import foundation-core.sections -open import foundation-core.subtypes +open import foundation-core.subtypes funext ```
diff --git a/src/foundation/perfect-images.lagda.md b/src/foundation/perfect-images.lagda.md index 73b8c53e54..4f5a4afd5e 100644 --- a/src/foundation/perfect-images.lagda.md +++ b/src/foundation/perfect-images.lagda.md @@ -1,7 +1,15 @@ # Perfect images ```agda -module foundation.perfect-images where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.perfect-images + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,14 +18,15 @@ module foundation.perfect-images where open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.decidable-types +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.double-negation -open import foundation.iterated-dependent-product-types -open import foundation.iterating-functions -open import foundation.law-of-excluded-middle -open import foundation.negated-equality -open import foundation.negation +open import foundation.double-negation funext univalence truncations +open import foundation.iterated-dependent-product-types funext +open import foundation.iterating-functions funext univalence truncations +open import foundation.law-of-excluded-middle funext univalence truncations +open import foundation.negated-equality funext univalence truncations +open import foundation.negation funext +open import foundation.telescopes open import foundation.universe-levels open import foundation-core.cartesian-product-types diff --git a/src/foundation/pi-decompositions-subuniverse.lagda.md b/src/foundation/pi-decompositions-subuniverse.lagda.md index 940decfffb..950fde6571 100644 --- a/src/foundation/pi-decompositions-subuniverse.lagda.md +++ b/src/foundation/pi-decompositions-subuniverse.lagda.md @@ -1,15 +1,21 @@ # Π-decompositions of types into types in a subuniverse ```agda -module foundation.pi-decompositions-subuniverse where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.pi-decompositions-subuniverse + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.pi-decompositions -open import foundation.subuniverses +open import foundation.pi-decompositions funext univalence +open import foundation.subuniverses funext univalence open import foundation.universe-levels open import foundation-core.cartesian-product-types diff --git a/src/foundation/pi-decompositions.lagda.md b/src/foundation/pi-decompositions.lagda.md index 1d57a83088..949600addb 100644 --- a/src/foundation/pi-decompositions.lagda.md +++ b/src/foundation/pi-decompositions.lagda.md @@ -2,20 +2,26 @@ ```agda {-# OPTIONS --lossy-unification #-} +open import foundation-core.univalence +open import foundation.function-extensionality-axiom -module foundation.pi-decompositions where +module foundation.pi-decompositions + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalence-extensionality -open import foundation.equivalences -open import foundation.functoriality-dependent-function-types +open import foundation.dependent-products-contractible-types funext +open import foundation.equivalence-extensionality funext +open import foundation.equivalences funext +open import foundation.functoriality-dependent-function-types funext univalence open import foundation.fundamental-theorem-of-identity-types open import foundation.structure-identity-principle -open import foundation.univalence +open import foundation.univalence funext univalence open import foundation.universe-levels open import foundation.whiskering-homotopies-composition diff --git a/src/foundation/pointed-torsorial-type-families.lagda.md b/src/foundation/pointed-torsorial-type-families.lagda.md index 247b60ec3a..76c5b1cda3 100644 --- a/src/foundation/pointed-torsorial-type-families.lagda.md +++ b/src/foundation/pointed-torsorial-type-families.lagda.md @@ -1,22 +1,31 @@ # Pointed torsorial type families ```agda -module foundation.pointed-torsorial-type-families where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.pointed-torsorial-type-families + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.0-connected-types +open import foundation.0-connected-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalences +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.locally-small-types -open import foundation.logical-equivalences -open import foundation.propositional-truncations +open import foundation.locally-small-types funext univalence truncations +open import foundation.logical-equivalences funext +open import foundation.propositional-truncations funext univalence open import foundation.sorial-type-families open import foundation.transport-along-identifications -open import foundation.type-theoretic-principle-of-choice +open import foundation.type-theoretic-principle-of-choice funext open import foundation.universe-levels open import foundation-core.cartesian-product-types @@ -24,7 +33,7 @@ open import foundation-core.contractible-types open import foundation-core.functoriality-dependent-pair-types open import foundation-core.identity-types open import foundation-core.propositions -open import foundation-core.small-types +open import foundation-core.small-types funext univalence truncations open import foundation-core.torsorial-type-families open import structured-types.pointed-types diff --git a/src/foundation/postcomposition-dependent-functions.lagda.md b/src/foundation/postcomposition-dependent-functions.lagda.md index af9cd90fde..afc1807812 100644 --- a/src/foundation/postcomposition-dependent-functions.lagda.md +++ b/src/foundation/postcomposition-dependent-functions.lagda.md @@ -1,7 +1,11 @@ # Postcomposition of dependent functions ```agda -module foundation.postcomposition-dependent-functions where +open import foundation.function-extensionality-axiom + +module foundation.postcomposition-dependent-functions + (funext : function-extensionality) + where open import foundation-core.postcomposition-dependent-functions public ``` @@ -10,12 +14,11 @@ open import foundation-core.postcomposition-dependent-functions public ```agda open import foundation.action-on-identifications-functions -open import foundation.function-extensionality +open import foundation.function-extensionality funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import foundation-core.commuting-squares-of-maps -open import foundation-core.function-types +open import foundation-core.commuting-squares-of-maps funext open import foundation-core.identity-types ``` diff --git a/src/foundation/postcomposition-functions.lagda.md b/src/foundation/postcomposition-functions.lagda.md index 2799d76ae4..d6f7eff276 100644 --- a/src/foundation/postcomposition-functions.lagda.md +++ b/src/foundation/postcomposition-functions.lagda.md @@ -1,7 +1,11 @@ # Postcomposition of functions ```agda -module foundation.postcomposition-functions where +open import foundation.function-extensionality-axiom + +module foundation.postcomposition-functions + (funext : function-extensionality) + where open import foundation-core.postcomposition-functions public ``` @@ -11,19 +15,19 @@ open import foundation-core.postcomposition-functions public ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-extensionality -open import foundation.postcomposition-dependent-functions +open import foundation.function-extensionality funext +open import foundation.postcomposition-dependent-functions funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import foundation-core.commuting-squares-of-maps +open import foundation-core.commuting-squares-of-maps funext open import foundation-core.commuting-triangles-of-maps open import foundation-core.contractible-maps open import foundation-core.contractible-types open import foundation-core.equivalences open import foundation-core.fibers-of-maps open import foundation-core.function-types -open import foundation-core.functoriality-dependent-function-types +open import foundation-core.functoriality-dependent-function-types funext open import foundation-core.functoriality-dependent-pair-types open import foundation-core.homotopies open import foundation-core.identity-types diff --git a/src/foundation/postcomposition-pullbacks.lagda.md b/src/foundation/postcomposition-pullbacks.lagda.md index b24c28bb74..3aa3bed817 100644 --- a/src/foundation/postcomposition-pullbacks.lagda.md +++ b/src/foundation/postcomposition-pullbacks.lagda.md @@ -1,17 +1,21 @@ # Postcomposition of pullbacks ```agda -module foundation.postcomposition-pullbacks where +open import foundation.function-extensionality-axiom + +module foundation.postcomposition-pullbacks + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cones-over-cospan-diagrams +open import foundation.cones-over-cospan-diagrams funext open import foundation.dependent-pair-types -open import foundation.function-extensionality -open import foundation.identity-types -open import foundation.standard-pullbacks +open import foundation.function-extensionality funext +open import foundation.identity-types funext +open import foundation.standard-pullbacks funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition @@ -20,10 +24,9 @@ open import foundation-core.equality-dependent-pair-types open import foundation-core.equivalences open import foundation-core.function-types open import foundation-core.functoriality-dependent-pair-types -open import foundation-core.homotopies open import foundation-core.postcomposition-functions -open import foundation-core.pullbacks -open import foundation-core.universal-property-pullbacks +open import foundation-core.pullbacks funext +open import foundation-core.universal-property-pullbacks funext ```
diff --git a/src/foundation/powersets.lagda.md b/src/foundation/powersets.lagda.md index b375489232..087631dfb3 100644 --- a/src/foundation/powersets.lagda.md +++ b/src/foundation/powersets.lagda.md @@ -1,44 +1,50 @@ # Powersets ```agda -module foundation.powersets where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.powersets + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.empty-types -open import foundation.identity-types -open import foundation.large-locale-of-propositions -open import foundation.logical-equivalences -open import foundation.propositions -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.empty-types funext univalence truncations +open import foundation.identity-types funext +open import foundation.large-locale-of-propositions funext univalence truncations +open import foundation.logical-equivalences funext +open import foundation.propositions funext univalence +open import foundation.raising-universe-levels-unit-type +open import foundation.subtypes funext univalence truncations open import foundation.unit-type open import foundation.universe-levels open import foundation-core.sets -open import order-theory.bottom-elements-large-posets -open import order-theory.bottom-elements-posets -open import order-theory.dependent-products-large-meet-semilattices -open import order-theory.dependent-products-large-posets -open import order-theory.dependent-products-large-preorders -open import order-theory.dependent-products-large-suplattices -open import order-theory.large-meet-semilattices -open import order-theory.large-posets -open import order-theory.large-preorders -open import order-theory.large-suplattices -open import order-theory.meet-semilattices -open import order-theory.order-preserving-maps-large-posets -open import order-theory.order-preserving-maps-large-preorders -open import order-theory.posets -open import order-theory.preorders -open import order-theory.similarity-of-elements-large-posets -open import order-theory.suplattices -open import order-theory.top-elements-large-posets -open import order-theory.top-elements-posets +open import order-theory.bottom-elements-large-posets funext univalence truncations +open import order-theory.bottom-elements-posets funext univalence truncations +open import order-theory.dependent-products-large-meet-semilattices funext univalence truncations +open import order-theory.dependent-products-large-posets funext univalence truncations +open import order-theory.dependent-products-large-preorders funext univalence truncations +open import order-theory.dependent-products-large-suplattices funext univalence truncations +open import order-theory.large-meet-semilattices funext univalence truncations +open import order-theory.large-posets funext univalence truncations +open import order-theory.large-preorders funext univalence truncations +open import order-theory.large-suplattices funext univalence truncations +open import order-theory.posets funext univalence truncations +open import order-theory.preorders funext univalence truncations +open import order-theory.similarity-of-elements-large-posets funext univalence truncations +open import order-theory.suplattices funext univalence truncations +open import order-theory.top-elements-large-posets funext univalence truncations +open import order-theory.top-elements-posets funext univalence truncations ```
diff --git a/src/foundation/precomposition-dependent-functions.lagda.md b/src/foundation/precomposition-dependent-functions.lagda.md index fef97c901d..0540179de8 100644 --- a/src/foundation/precomposition-dependent-functions.lagda.md +++ b/src/foundation/precomposition-dependent-functions.lagda.md @@ -1,7 +1,11 @@ # Precomposition of dependent functions ```agda -module foundation.precomposition-dependent-functions where +open import foundation.function-extensionality-axiom + +module foundation.precomposition-dependent-functions + (funext : function-extensionality) + where open import foundation-core.precomposition-dependent-functions public ``` @@ -11,17 +15,17 @@ open import foundation-core.precomposition-dependent-functions public ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.dependent-universal-property-equivalences -open import foundation.function-extensionality +open import foundation.dependent-universal-property-equivalences funext +open import foundation.function-extensionality funext open import foundation.universe-levels -open import foundation-core.commuting-squares-of-maps +open import foundation-core.commuting-squares-of-maps funext open import foundation-core.equivalences open import foundation-core.function-types open import foundation-core.functoriality-dependent-pair-types open import foundation-core.homotopies open import foundation-core.identity-types -open import foundation-core.truncated-maps +open import foundation-core.truncated-maps funext open import foundation-core.truncation-levels open import foundation-core.type-theoretic-principle-of-choice ``` diff --git a/src/foundation/precomposition-functions-into-subuniverses.lagda.md b/src/foundation/precomposition-functions-into-subuniverses.lagda.md index 8e0a567f55..c14638f188 100644 --- a/src/foundation/precomposition-functions-into-subuniverses.lagda.md +++ b/src/foundation/precomposition-functions-into-subuniverses.lagda.md @@ -1,7 +1,11 @@ # Precomposition of functions into subuniverses ```agda -module foundation.precomposition-functions-into-subuniverses where +open import foundation.function-extensionality-axiom + +module foundation.precomposition-functions-into-subuniverses + (funext : function-extensionality) + where ```
Imports @@ -9,15 +13,13 @@ module foundation.precomposition-functions-into-subuniverses where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-extensionality -open import foundation.precomposition-functions +open import foundation.precomposition-functions funext open import foundation.universe-levels open import foundation-core.contractible-maps open import foundation-core.contractible-types open import foundation-core.equivalences open import foundation-core.function-types -open import foundation-core.homotopies open import foundation-core.identity-types open import foundation-core.propositions open import foundation-core.retractions diff --git a/src/foundation/precomposition-functions.lagda.md b/src/foundation/precomposition-functions.lagda.md index 9e48f70cfd..97f38758fa 100644 --- a/src/foundation/precomposition-functions.lagda.md +++ b/src/foundation/precomposition-functions.lagda.md @@ -1,7 +1,11 @@ # Precomposition of functions ```agda -module foundation.precomposition-functions where +open import foundation.function-extensionality-axiom + +module foundation.precomposition-functions + (funext : function-extensionality) + where open import foundation-core.precomposition-functions public ``` @@ -11,13 +15,13 @@ open import foundation-core.precomposition-functions public ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-extensionality -open import foundation.precomposition-dependent-functions -open import foundation.sections +open import foundation.function-extensionality funext +open import foundation.precomposition-dependent-functions funext +open import foundation.sections funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import foundation-core.commuting-squares-of-maps +open import foundation-core.commuting-squares-of-maps funext open import foundation-core.commuting-triangles-of-maps open import foundation-core.equivalences open import foundation-core.fibers-of-maps diff --git a/src/foundation/precomposition-type-families.lagda.md b/src/foundation/precomposition-type-families.lagda.md index 0d86dd8b97..ec2ba78f60 100644 --- a/src/foundation/precomposition-type-families.lagda.md +++ b/src/foundation/precomposition-type-families.lagda.md @@ -1,14 +1,18 @@ # Precomposition of type families ```agda -module foundation.precomposition-type-families where +open import foundation.function-extensionality-axiom + +module foundation.precomposition-type-families + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.homotopy-induction -open import foundation.transport-along-homotopies +open import foundation.homotopy-induction funext +open import foundation.transport-along-homotopies funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition diff --git a/src/foundation/preunivalence.lagda.md b/src/foundation/preunivalence.lagda.md index 9fe3c4409c..88b5f3dd52 100644 --- a/src/foundation/preunivalence.lagda.md +++ b/src/foundation/preunivalence.lagda.md @@ -1,21 +1,27 @@ # The preunivalence axiom ```agda -module foundation.preunivalence where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.preunivalence + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalences -open import foundation.sets -open import foundation.univalence +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.sets funext univalence +open import foundation.univalence funext univalence open import foundation.universe-levels open import foundation-core.identity-types -open import foundation-core.subtypes +open import foundation-core.subtypes funext ```
diff --git a/src/foundation/preunivalent-type-families.lagda.md b/src/foundation/preunivalent-type-families.lagda.md index 933a182ad5..8b38eca85a 100644 --- a/src/foundation/preunivalent-type-families.lagda.md +++ b/src/foundation/preunivalent-type-families.lagda.md @@ -1,30 +1,35 @@ # Preunivalent type families ```agda -module foundation.preunivalent-type-families where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.preunivalent-type-families + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda -open import foundation.0-maps +open import foundation.0-maps funext open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalence-injective-type-families -open import foundation.faithful-maps -open import foundation.function-types -open import foundation.injective-maps -open import foundation.preunivalence -open import foundation.retractions -open import foundation.sets -open import foundation.subuniverses +open import foundation.embeddings funext +open import foundation.equivalence-injective-type-families funext univalence +open import foundation.faithful-maps funext +open import foundation.function-types funext +open import foundation.injective-maps funext +open import foundation.preunivalence funext univalence +open import foundation.retractions funext +open import foundation.sets funext univalence +open import foundation.subuniverses funext univalence open import foundation.transport-along-identifications open import foundation.universe-levels open import foundation-core.equivalences open import foundation-core.identity-types -open import foundation-core.univalence ```
diff --git a/src/foundation/principle-of-omniscience.lagda.md b/src/foundation/principle-of-omniscience.lagda.md index cf03f741b2..bcb9d8d629 100644 --- a/src/foundation/principle-of-omniscience.lagda.md +++ b/src/foundation/principle-of-omniscience.lagda.md @@ -1,17 +1,26 @@ # The principle of omniscience ```agda -module foundation.principle-of-omniscience where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.principle-of-omniscience + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.decidable-subtypes -open import foundation.propositional-truncations +open import foundation.decidable-subtypes funext univalence truncations +open import foundation.dependent-products-propositions funext +open import foundation.propositional-truncations funext univalence open import foundation.universe-levels -open import foundation-core.decidable-propositions +open import foundation-core.decidable-propositions funext univalence truncations open import foundation-core.propositions ``` diff --git a/src/foundation/product-decompositions-subuniverse.lagda.md b/src/foundation/product-decompositions-subuniverse.lagda.md index 8b340ce9dd..6209529b8d 100644 --- a/src/foundation/product-decompositions-subuniverse.lagda.md +++ b/src/foundation/product-decompositions-subuniverse.lagda.md @@ -1,20 +1,29 @@ # Product decompositions of types in a subuniverse ```agda -module foundation.product-decompositions-subuniverse where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.product-decompositions-subuniverse + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.subuniverses +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.raising-universe-levels-unit-type +open import foundation.subuniverses funext univalence open import foundation.type-arithmetic-cartesian-product-types open import foundation.type-arithmetic-dependent-pair-types open import foundation.unit-type -open import foundation.univalence +open import foundation.univalence funext univalence open import foundation.universe-levels open import foundation-core.contractible-types diff --git a/src/foundation/products-binary-relations.lagda.md b/src/foundation/products-binary-relations.lagda.md index 93f4ce0c07..b6134ac125 100644 --- a/src/foundation/products-binary-relations.lagda.md +++ b/src/foundation/products-binary-relations.lagda.md @@ -1,13 +1,21 @@ # Products of binary relations ```agda -module foundation.products-binary-relations where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.products-binary-relations + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.binary-relations +open import foundation.binary-relations funext univalence truncations open import foundation.dependent-pair-types open import foundation.universe-levels diff --git a/src/foundation/products-equivalence-relations.lagda.md b/src/foundation/products-equivalence-relations.lagda.md index 37e2364b6d..5dee6524a9 100644 --- a/src/foundation/products-equivalence-relations.lagda.md +++ b/src/foundation/products-equivalence-relations.lagda.md @@ -1,19 +1,27 @@ # Products of equivalence relataions ```agda -module foundation.products-equivalence-relations where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.products-equivalence-relations + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.binary-relations +open import foundation.binary-relations funext univalence truncations open import foundation.dependent-pair-types -open import foundation.products-binary-relations +open import foundation.products-binary-relations funext univalence truncations open import foundation.universe-levels open import foundation-core.cartesian-product-types -open import foundation-core.equivalence-relations +open import foundation-core.equivalence-relations funext univalence truncations ```
diff --git a/src/foundation/products-of-tuples-of-types.lagda.md b/src/foundation/products-of-tuples-of-types.lagda.md index 0fc4d95508..b2bb6af29e 100644 --- a/src/foundation/products-of-tuples-of-types.lagda.md +++ b/src/foundation/products-of-tuples-of-types.lagda.md @@ -1,7 +1,15 @@ # Products of tuples of types ```agda -module foundation.products-of-tuples-of-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.products-of-tuples-of-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,10 +17,10 @@ module foundation.products-of-tuples-of-types where ```agda open import elementary-number-theory.natural-numbers -open import foundation.tuples-of-types +open import foundation.tuples-of-types funext univalence truncations open import foundation.universe-levels -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/foundation/products-pullbacks.lagda.md b/src/foundation/products-pullbacks.lagda.md index acd174310d..d8879d8d23 100644 --- a/src/foundation/products-pullbacks.lagda.md +++ b/src/foundation/products-pullbacks.lagda.md @@ -1,20 +1,28 @@ # Products of pullbacks ```agda -module foundation.products-pullbacks where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.products-pullbacks + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.cones-over-cospan-diagrams +open import foundation.cones-over-cospan-diagrams funext open import foundation.dependent-pair-types open import foundation.equality-cartesian-product-types -open import foundation.functoriality-cartesian-product-types -open import foundation.inhabited-types -open import foundation.propositional-truncations -open import foundation.pullbacks -open import foundation.standard-pullbacks +open import foundation.functoriality-cartesian-product-types funext +open import foundation.inhabited-types funext univalence truncations +open import foundation.propositional-truncations funext univalence +open import foundation.pullbacks funext univalence truncations +open import foundation.standard-pullbacks funext open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels @@ -24,7 +32,7 @@ open import foundation-core.function-types open import foundation-core.functoriality-dependent-pair-types open import foundation-core.homotopies open import foundation-core.identity-types -open import foundation-core.universal-property-pullbacks +open import foundation-core.universal-property-pullbacks funext ```
diff --git a/src/foundation/products-unordered-pairs-of-types.lagda.md b/src/foundation/products-unordered-pairs-of-types.lagda.md index 73d194ded8..fa43e518b5 100644 --- a/src/foundation/products-unordered-pairs-of-types.lagda.md +++ b/src/foundation/products-unordered-pairs-of-types.lagda.md @@ -1,28 +1,36 @@ # Products of unordered pairs of types ```agda -module foundation.products-unordered-pairs-of-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.products-unordered-pairs-of-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.dependent-universal-property-equivalences -open import foundation.functoriality-cartesian-product-types -open import foundation.functoriality-dependent-function-types -open import foundation.symmetric-operations +open import foundation.dependent-universal-property-equivalences funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.functoriality-dependent-function-types funext univalence +open import foundation.symmetric-operations funext univalence truncations open import foundation.transport-along-identifications open import foundation.universe-levels -open import foundation.unordered-pairs -open import foundation.unordered-pairs-of-types +open import foundation.unordered-pairs funext univalence truncations +open import foundation.unordered-pairs-of-types funext univalence truncations open import foundation-core.cartesian-product-types open import foundation-core.equivalences open import foundation-core.function-types -open import univalent-combinatorics.2-element-types -open import univalent-combinatorics.universal-property-standard-finite-types +open import univalent-combinatorics.2-element-types funext univalence truncations +open import univalent-combinatorics.universal-property-standard-finite-types funext univalence truncations ```
diff --git a/src/foundation/products-unordered-tuples-of-types.lagda.md b/src/foundation/products-unordered-tuples-of-types.lagda.md index c33e6374ef..cb8ebd1101 100644 --- a/src/foundation/products-unordered-tuples-of-types.lagda.md +++ b/src/foundation/products-unordered-tuples-of-types.lagda.md @@ -1,7 +1,15 @@ # Products of unordered tuples of types ```agda -module foundation.products-unordered-tuples-of-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.products-unordered-tuples-of-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,16 +18,16 @@ module foundation.products-unordered-tuples-of-types where open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.functoriality-dependent-function-types -open import foundation.universal-property-maybe +open import foundation.functoriality-dependent-function-types funext univalence +open import foundation.universal-property-maybe funext open import foundation.universe-levels -open import foundation.unordered-tuples -open import foundation.unordered-tuples-of-types +open import foundation.unordered-tuples funext univalence truncations +open import foundation.unordered-tuples-of-types funext univalence truncations open import foundation-core.cartesian-product-types open import foundation-core.equivalences -open import univalent-combinatorics.complements-isolated-elements +open import univalent-combinatorics.complements-isolated-elements funext univalence truncations ```
diff --git a/src/foundation/projective-types.lagda.md b/src/foundation/projective-types.lagda.md index f537366853..6a6e4fd97e 100644 --- a/src/foundation/projective-types.lagda.md +++ b/src/foundation/projective-types.lagda.md @@ -1,7 +1,15 @@ # Projective types ```agda -module foundation.projective-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.projective-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,9 +17,9 @@ module foundation.projective-types where ```agda open import elementary-number-theory.natural-numbers -open import foundation.connected-maps -open import foundation.postcomposition-functions -open import foundation.surjective-maps +open import foundation.connected-maps funext univalence truncations +open import foundation.postcomposition-functions funext +open import foundation.surjective-maps funext univalence truncations open import foundation.truncation-levels open import foundation.universe-levels diff --git a/src/foundation/proper-subtypes.lagda.md b/src/foundation/proper-subtypes.lagda.md index 2ca5864332..d648d27941 100644 --- a/src/foundation/proper-subtypes.lagda.md +++ b/src/foundation/proper-subtypes.lagda.md @@ -1,18 +1,26 @@ # Proper subsets ```agda -module foundation.proper-subtypes where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.proper-subtypes + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.complements-subtypes -open import foundation.inhabited-subtypes +open import foundation.complements-subtypes funext univalence truncations +open import foundation.inhabited-subtypes funext univalence truncations open import foundation.universe-levels open import foundation-core.propositions -open import foundation-core.subtypes +open import foundation-core.subtypes funext ```
diff --git a/src/foundation/propositional-extensionality.lagda.md b/src/foundation/propositional-extensionality.lagda.md index a92f6d6176..c5ad1bb502 100644 --- a/src/foundation/propositional-extensionality.lagda.md +++ b/src/foundation/propositional-extensionality.lagda.md @@ -1,27 +1,37 @@ # Propositional extensionality ```agda -module foundation.propositional-extensionality where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.propositional-extensionality + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.empty-types +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.empty-types funext univalence truncations open import foundation.fundamental-theorem-of-identity-types -open import foundation.logical-equivalences -open import foundation.negation -open import foundation.postcomposition-functions -open import foundation.raising-universe-levels +open import foundation.logical-equivalences funext +open import foundation.negation funext +open import foundation.postcomposition-functions funext +open import foundation.raising-universe-levels-unit-type open import foundation.subtype-identity-principle open import foundation.transport-along-identifications open import foundation.type-arithmetic-cartesian-product-types open import foundation.unit-type -open import foundation.univalence -open import foundation.univalent-type-families -open import foundation.universal-property-contractible-types -open import foundation.universal-property-empty-type +open import foundation.univalence funext univalence +open import foundation.univalent-type-families funext univalence +open import foundation.universal-property-contractible-types funext +open import foundation.universal-property-empty-type funext open import foundation.universe-levels open import foundation-core.contractible-types @@ -29,6 +39,7 @@ open import foundation-core.equivalences open import foundation-core.functoriality-dependent-pair-types open import foundation-core.identity-types open import foundation-core.propositions +open import foundation-core.raising-universe-levels open import foundation-core.sets open import foundation-core.torsorial-type-families ``` diff --git a/src/foundation/propositional-maps.lagda.md b/src/foundation/propositional-maps.lagda.md index 39115738b7..f4fec3ce09 100644 --- a/src/foundation/propositional-maps.lagda.md +++ b/src/foundation/propositional-maps.lagda.md @@ -1,7 +1,11 @@ # Propositional maps ```agda -module foundation.propositional-maps where +open import foundation.function-extensionality-axiom + +module foundation.propositional-maps + (funext : function-extensionality) + where open import foundation-core.propositional-maps public ``` @@ -10,9 +14,10 @@ open import foundation-core.propositional-maps public ```agda open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.logical-equivalences -open import foundation.truncated-maps +open import foundation.dependent-products-propositions funext +open import foundation.embeddings funext +open import foundation.logical-equivalences funext +open import foundation.truncated-maps funext open import foundation.universe-levels open import foundation-core.equivalences diff --git a/src/foundation/propositional-resizing.lagda.md b/src/foundation/propositional-resizing.lagda.md index 4abe732a36..6fa2d840bd 100644 --- a/src/foundation/propositional-resizing.lagda.md +++ b/src/foundation/propositional-resizing.lagda.md @@ -1,19 +1,28 @@ # Propositional resizing ```agda -module foundation.propositional-resizing where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.propositional-resizing + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions funext open import foundation.universe-levels open import foundation-core.equivalences open import foundation-core.propositions -open import foundation-core.small-types -open import foundation-core.subtypes +open import foundation-core.small-types funext univalence truncations +open import foundation-core.subtypes funext ```
diff --git a/src/foundation/propositional-truncations.lagda.md b/src/foundation/propositional-truncations.lagda.md index 2ae3713137..8969ae7c7f 100644 --- a/src/foundation/propositional-truncations.lagda.md +++ b/src/foundation/propositional-truncations.lagda.md @@ -1,7 +1,14 @@ # Propositional truncations ```agda -module foundation.propositional-truncations where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.propositional-truncations + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports @@ -9,11 +16,12 @@ module foundation.propositional-truncations where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.functoriality-cartesian-product-types -open import foundation.logical-equivalences -open import foundation.propositions -open import foundation.truncations -open import foundation.universal-property-propositional-truncation +open import foundation.dependent-products-propositions funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.logical-equivalences funext +open import foundation.propositions funext univalence +open import foundation.truncations funext univalence truncations +open import foundation.universal-property-propositional-truncation funext open import foundation.universe-levels open import foundation-core.cartesian-product-types diff --git a/src/foundation/propositions.lagda.md b/src/foundation/propositions.lagda.md index e4bf1eb773..78b599e7bb 100644 --- a/src/foundation/propositions.lagda.md +++ b/src/foundation/propositions.lagda.md @@ -1,7 +1,13 @@ # Propositions ```agda -module foundation.propositions where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.propositions + (funext : function-extensionality) + (univalence : univalence-axiom) + where open import foundation-core.propositions public ``` @@ -9,11 +15,13 @@ open import foundation-core.propositions public
Imports ```agda -open import foundation.contractible-types +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.fibers-of-maps -open import foundation.logical-equivalences -open import foundation.retracts-of-types +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.fibers-of-maps funext +open import foundation.logical-equivalences funext +open import foundation.retracts-of-types funext univalence open import foundation.unit-type open import foundation.universe-levels diff --git a/src/foundation/pullback-cones.lagda.md b/src/foundation/pullback-cones.lagda.md index f35b29848d..7b0e4da909 100644 --- a/src/foundation/pullback-cones.lagda.md +++ b/src/foundation/pullback-cones.lagda.md @@ -1,43 +1,37 @@ # Pullback cones ```agda -module foundation.pullback-cones where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.pullback-cones + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types -open import foundation.cones-over-cospan-diagrams +open import foundation.cartesian-product-types funext univalence +open import foundation.cones-over-cospan-diagrams funext open import foundation.cospan-diagrams open import foundation.dependent-pair-types -open import foundation.dependent-universal-property-equivalences -open import foundation.function-extensionality -open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types -open import foundation.multivariable-homotopies -open import foundation.pullbacks -open import foundation.standard-pullbacks -open import foundation.structure-identity-principle +open import foundation.identity-types funext +open import foundation.pullbacks funext univalence truncations +open import foundation.standard-pullbacks funext open import foundation.unit-type -open import foundation.universal-property-cartesian-product-types +open import foundation.universal-property-cartesian-product-types funext open import foundation.universe-levels -open import foundation.whiskering-homotopies-composition -open import foundation-core.commuting-squares-of-maps -open import foundation-core.contractible-types +open import foundation-core.commuting-squares-of-maps funext open import foundation-core.equivalences open import foundation-core.function-types -open import foundation-core.functoriality-dependent-pair-types open import foundation-core.retractions open import foundation-core.sections -open import foundation-core.torsorial-type-families -open import foundation-core.transport-along-identifications -open import foundation-core.universal-property-pullbacks -open import foundation-core.whiskering-identifications-concatenation +open import foundation-core.universal-property-pullbacks funext ```
diff --git a/src/foundation/pullbacks-subtypes.lagda.md b/src/foundation/pullbacks-subtypes.lagda.md index f2f6b26b72..dda33a1333 100644 --- a/src/foundation/pullbacks-subtypes.lagda.md +++ b/src/foundation/pullbacks-subtypes.lagda.md @@ -1,22 +1,30 @@ # Pullbacks of subtypes ```agda -module foundation.pullbacks-subtypes where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.pullbacks-subtypes + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.logical-equivalences -open import foundation.powersets +open import foundation.logical-equivalences funext +open import foundation.powersets funext univalence truncations open import foundation.universe-levels open import foundation-core.function-types open import foundation-core.propositions -open import foundation-core.subtypes +open import foundation-core.subtypes funext -open import order-theory.order-preserving-maps-large-posets -open import order-theory.order-preserving-maps-large-preorders +open import order-theory.order-preserving-maps-large-posets funext univalence truncations +open import order-theory.order-preserving-maps-large-preorders funext univalence truncations ```
diff --git a/src/foundation/pullbacks.lagda.md b/src/foundation/pullbacks.lagda.md index aa710ea8cd..c8b59c7ad6 100644 --- a/src/foundation/pullbacks.lagda.md +++ b/src/foundation/pullbacks.lagda.md @@ -1,9 +1,17 @@ # Pullbacks ```agda -module foundation.pullbacks where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.pullbacks + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where -open import foundation-core.pullbacks public +open import foundation-core.pullbacks funext public ```
Imports @@ -11,37 +19,27 @@ open import foundation-core.pullbacks public ```agda open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.commuting-cubes-of-maps -open import foundation.cones-over-cospan-diagrams +open import foundation.commuting-cubes-of-maps funext univalence +open import foundation.cones-over-cospan-diagrams funext open import foundation.dependent-pair-types -open import foundation.dependent-sums-pullbacks -open import foundation.descent-equivalences +open import foundation.dependent-sums-pullbacks funext +open import foundation.descent-equivalences funext open import foundation.equality-cartesian-product-types -open import foundation.equivalence-extensionality -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.functoriality-coproduct-types -open import foundation.functoriality-function-types -open import foundation.standard-pullbacks -open import foundation.subtypes +open import foundation.equivalences funext +open import foundation.function-extensionality funext +open import foundation.standard-pullbacks funext +open import foundation.subtypes funext univalence truncations open import foundation.unit-type open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import foundation-core.cartesian-product-types -open import foundation-core.constant-maps open import foundation-core.contractible-types -open import foundation-core.diagonal-maps-cartesian-products-of-types open import foundation-core.equality-dependent-pair-types open import foundation-core.function-types -open import foundation-core.functoriality-dependent-function-types open import foundation-core.functoriality-dependent-pair-types open import foundation-core.homotopies open import foundation-core.identity-types -open import foundation-core.postcomposition-functions open import foundation-core.propositions -open import foundation-core.retractions -open import foundation-core.sections open import foundation-core.torsorial-type-families open import foundation-core.transport-along-identifications open import foundation-core.whiskering-identifications-concatenation diff --git a/src/foundation/quasicoherently-idempotent-maps.lagda.md b/src/foundation/quasicoherently-idempotent-maps.lagda.md index bec945c76a..8df088cb16 100644 --- a/src/foundation/quasicoherently-idempotent-maps.lagda.md +++ b/src/foundation/quasicoherently-idempotent-maps.lagda.md @@ -1,26 +1,35 @@ # Quasicoherently idempotent maps ```agda -module foundation.quasicoherently-idempotent-maps where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.quasicoherently-idempotent-maps + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.1-types +open import foundation.1-types funext univalence open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-homotopies +open import foundation.commuting-squares-of-homotopies funext open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types +open import foundation.dependent-products-propositions funext +open import foundation.equality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types open import foundation.homotopy-algebra -open import foundation.homotopy-induction -open import foundation.idempotent-maps -open import foundation.identity-types -open import foundation.negated-equality -open import foundation.negation +open import foundation.homotopy-induction funext +open import foundation.idempotent-maps funext +open import foundation.identity-types funext +open import foundation.negated-equality funext univalence truncations +open import foundation.negation funext open import foundation.structure-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext univalence truncations open import foundation.transport-along-identifications open import foundation.universe-levels open import foundation.whiskering-higher-homotopies-composition @@ -33,8 +42,8 @@ open import foundation-core.propositions open import foundation-core.retractions open import foundation-core.sets -open import synthetic-homotopy-theory.circle -open import synthetic-homotopy-theory.loop-homotopy-circle +open import synthetic-homotopy-theory.circle funext univalence truncations +open import synthetic-homotopy-theory.loop-homotopy-circle funext univalence truncations ```
diff --git a/src/foundation/raising-universe-levels-booleans.lagda.md b/src/foundation/raising-universe-levels-booleans.lagda.md new file mode 100644 index 0000000000..3b47e71463 --- /dev/null +++ b/src/foundation/raising-universe-levels-booleans.lagda.md @@ -0,0 +1,41 @@ +# Raising universe levels of the booleans + +```agda +module foundation.raising-universe-levels-booleans where +``` + +
Imports + +```agda +open import foundation.universe-levels + +open import foundation-core.booleans +open import foundation-core.equivalences +open import foundation-core.raising-universe-levels +``` + +
+ +## Idea + +We can [raise](foundation.raising-universe-levels.md) the type of +[booleans](foundation-core.booleans.md) to any +[universe](foundation.universe-levels.md). + +## Definition + +### Raising universe levels of the booleans + +```agda +raise-bool : (l : Level) → UU l +raise-bool l = raise l bool + +raise-true : (l : Level) → raise-bool l +raise-true l = map-raise true + +raise-false : (l : Level) → raise-bool l +raise-false l = map-raise false + +compute-raise-bool : (l : Level) → bool ≃ raise-bool l +compute-raise-bool l = compute-raise l bool +``` diff --git a/src/foundation/raising-universe-levels-unit-type.lagda.md b/src/foundation/raising-universe-levels-unit-type.lagda.md new file mode 100644 index 0000000000..403eb843ca --- /dev/null +++ b/src/foundation/raising-universe-levels-unit-type.lagda.md @@ -0,0 +1,123 @@ +# Raising universe levels for the unit type + +```agda +module foundation.raising-universe-levels-unit-type where +``` + +
Imports + +```agda +open import foundation.action-on-identifications-functions +open import foundation.dependent-pair-types +open import foundation.unit-type +open import foundation.universe-levels + +open import foundation-core.constant-maps +open import foundation-core.contractible-types +open import foundation-core.equivalences +open import foundation-core.identity-types +open import foundation-core.propositions +open import foundation-core.raising-universe-levels +open import foundation-core.retractions +open import foundation-core.sets +open import foundation-core.truncated-types +open import foundation-core.truncation-levels +``` + +
+ +## Idea + +We can [raise](foundation.raising-universe-levels.md) the type of +[booleans](foundation-core.booleans.md) to any +[universe](foundation.universe-levels.md). + +## Definition + +### Raising the universe level of the unit type + +```agda +raise-unit : (l : Level) → UU l +raise-unit l = raise l unit + +raise-star : {l : Level} → raise l unit +raise-star = map-raise star + +raise-terminal-map : {l1 l2 : Level} (A : UU l1) → A → raise-unit l2 +raise-terminal-map {l2 = l2} A = const A raise-star + +compute-raise-unit : (l : Level) → unit ≃ raise-unit l +compute-raise-unit l = compute-raise l unit + +inv-compute-raise-unit : (l : Level) → raise-unit l ≃ unit +inv-compute-raise-unit l = inv-compute-raise l unit +``` + +## Properties + +### The raised unit type is contractible + +```agda +abstract + is-contr-raise-unit : {l1 : Level} → is-contr (raise-unit l1) + is-contr-raise-unit {l1} = + is-contr-equiv' unit (compute-raise l1 unit) is-contr-unit +``` + +### Any contractible type is equivalent to the raised unit type + +```agda +module _ + {l1 l2 : Level} {A : UU l1} + where + + is-equiv-raise-terminal-map-is-contr : + is-contr A → is-equiv (raise-terminal-map {l2 = l2} A) + is-equiv-raise-terminal-map-is-contr H = + is-equiv-is-invertible + ( λ _ → center H) + ( λ where (map-raise x) → refl) + ( contraction H) + + equiv-raise-unit-is-contr : is-contr A → A ≃ raise-unit l2 + equiv-raise-unit-is-contr H = + raise-terminal-map A , is-equiv-raise-terminal-map-is-contr H + + is-contr-retraction-raise-terminal-map : + retraction (raise-terminal-map {l2 = l2} A) → is-contr A + is-contr-retraction-raise-terminal-map (h , H) = h raise-star , H + + is-contr-is-equiv-raise-terminal-map : + is-equiv (raise-terminal-map {l2 = l2} A) → is-contr A + is-contr-is-equiv-raise-terminal-map H = + is-contr-retraction-raise-terminal-map (retraction-is-equiv H) + + is-contr-equiv-raise-unit : A ≃ raise-unit l2 → is-contr A + is-contr-equiv-raise-unit e = + ( map-inv-equiv e raise-star) , + ( λ x → + ap (map-inv-equiv e) (eq-is-contr is-contr-raise-unit) ∙ + is-retraction-map-inv-equiv e x) +``` + +### The raised unit type is a proposition + +```agda +abstract + is-prop-raise-unit : {l1 : Level} → is-prop (raise-unit l1) + is-prop-raise-unit {l1} = is-prop-equiv' (compute-raise l1 unit) is-prop-unit + +raise-unit-Prop : (l1 : Level) → Prop l1 +raise-unit-Prop l1 = raise-unit l1 , is-prop-raise-unit +``` + +### The raised unit type is a set + +```agda +abstract + is-set-raise-unit : {l1 : Level} → is-set (raise-unit l1) + is-set-raise-unit = is-trunc-succ-is-trunc neg-one-𝕋 is-prop-raise-unit + +raise-unit-Set : (l1 : Level) → Set l1 +raise-unit-Set l1 = raise-unit l1 , is-set-raise-unit +``` diff --git a/src/foundation/raising-universe-levels.lagda.md b/src/foundation/raising-universe-levels.lagda.md index 81c3676716..53b08bed6a 100644 --- a/src/foundation/raising-universe-levels.lagda.md +++ b/src/foundation/raising-universe-levels.lagda.md @@ -1,7 +1,15 @@ # Raising universe levels ```agda -module foundation.raising-universe-levels where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.raising-universe-levels + (funext : function-extensionality) + (univalence : univalence-axiom) + where + +open import foundation-core.raising-universe-levels public ```
Imports @@ -9,9 +17,9 @@ module foundation.raising-universe-levels where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.identity-types -open import foundation.univalence +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.univalence funext univalence open import foundation.universe-levels open import foundation-core.contractible-types @@ -22,7 +30,7 @@ open import foundation-core.homotopies open import foundation-core.propositional-maps open import foundation-core.propositions open import foundation-core.sets -open import foundation-core.subtypes +open import foundation-core.subtypes funext ```
@@ -33,118 +41,17 @@ In Agda, types have a designated universe levels, and universes in Agda don't overlap. Using `data` types we can construct for any type `A` of universe level `l` an equivalent type in any higher universe. -## Definition - -```agda -data raise (l : Level) {l1 : Level} (A : UU l1) : UU (l1 ⊔ l) where - map-raise : A → raise l A - -data raiseω {l1 : Level} (A : UU l1) : UUω where - map-raiseω : A → raiseω A -``` - ## Properties -### Types are equivalent to their raised equivalents - -```agda -module _ - {l l1 : Level} {A : UU l1} - where - - map-inv-raise : raise l A → A - map-inv-raise (map-raise x) = x - - is-section-map-inv-raise : (map-raise ∘ map-inv-raise) ~ id - is-section-map-inv-raise (map-raise x) = refl - - is-retraction-map-inv-raise : (map-inv-raise ∘ map-raise) ~ id - is-retraction-map-inv-raise x = refl - - is-equiv-map-raise : is-equiv (map-raise {l} {l1} {A}) - is-equiv-map-raise = - is-equiv-is-invertible - map-inv-raise - is-section-map-inv-raise - is-retraction-map-inv-raise - -compute-raise : (l : Level) {l1 : Level} (A : UU l1) → A ≃ raise l A -pr1 (compute-raise l A) = map-raise -pr2 (compute-raise l A) = is-equiv-map-raise - -inv-compute-raise : (l : Level) {l1 : Level} (A : UU l1) → raise l A ≃ A -inv-compute-raise l A = inv-equiv (compute-raise l A) - -Raise : (l : Level) {l1 : Level} (A : UU l1) → Σ (UU (l1 ⊔ l)) (λ X → A ≃ X) -pr1 (Raise l A) = raise l A -pr2 (Raise l A) = compute-raise l A -``` - -### Raising universe levels of propositions - -```agda -raise-Prop : (l : Level) {l1 : Level} → Prop l1 → Prop (l ⊔ l1) -pr1 (raise-Prop l P) = raise l (type-Prop P) -pr2 (raise-Prop l P) = - is-prop-equiv' (compute-raise l (type-Prop P)) (is-prop-type-Prop P) -``` - -### Raising universe levels of sets - -```agda -raise-Set : (l : Level) {l1 : Level} → Set l1 → Set (l ⊔ l1) -pr1 (raise-Set l A) = raise l (type-Set A) -pr2 (raise-Set l A) = - is-set-equiv' (type-Set A) (compute-raise l (type-Set A)) (is-set-type-Set A) -``` - ### Raising universe levels of subtypes ```agda raise-subtype : - (l : Level) → - {l1 l2 : Level} → - {A : UU l1} → - subtype l2 A → - subtype (l2 ⊔ l) A + (l : Level) {l1 l2 : Level} {A : UU l1} → + subtype l2 A → subtype (l2 ⊔ l) A raise-subtype l B x = raise-Prop l (B x) ``` -### Raising equivalent types - -```agda -module _ - {l1 l2 : Level} (l3 l4 : Level) {A : UU l1} {B : UU l2} (e : A ≃ B) - where - - map-equiv-raise : raise l3 A → raise l4 B - map-equiv-raise (map-raise x) = map-raise (map-equiv e x) - - map-inv-equiv-raise : raise l4 B → raise l3 A - map-inv-equiv-raise (map-raise y) = map-raise (map-inv-equiv e y) - - is-section-map-inv-equiv-raise : - ( map-equiv-raise ∘ map-inv-equiv-raise) ~ id - is-section-map-inv-equiv-raise (map-raise y) = - ap map-raise (is-section-map-inv-equiv e y) - - is-retraction-map-inv-equiv-raise : - ( map-inv-equiv-raise ∘ map-equiv-raise) ~ id - is-retraction-map-inv-equiv-raise (map-raise x) = - ap map-raise (is-retraction-map-inv-equiv e x) - - is-equiv-map-equiv-raise : is-equiv map-equiv-raise - is-equiv-map-equiv-raise = - is-equiv-is-invertible - map-inv-equiv-raise - is-section-map-inv-equiv-raise - is-retraction-map-inv-equiv-raise - - equiv-raise : raise l3 A ≃ raise l4 B - pr1 equiv-raise = map-equiv-raise - pr2 equiv-raise = is-equiv-map-equiv-raise -``` - ### Raising universe levels from `l1` to `l ⊔ l1` is an embedding from `UU l1` to `UU (l ⊔ l1)` ```agda diff --git a/src/foundation/reflecting-maps-equivalence-relations.lagda.md b/src/foundation/reflecting-maps-equivalence-relations.lagda.md index e3ff095700..31c89e9b86 100644 --- a/src/foundation/reflecting-maps-equivalence-relations.lagda.md +++ b/src/foundation/reflecting-maps-equivalence-relations.lagda.md @@ -1,20 +1,29 @@ # Reflecting maps for equivalence relations ```agda -module foundation.reflecting-maps-equivalence-relations where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.reflecting-maps-equivalence-relations + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.effective-maps-equivalence-relations +open import foundation.dependent-products-propositions funext +open import foundation.effective-maps-equivalence-relations funext univalence truncations open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopy-induction +open import foundation.homotopy-induction funext open import foundation.subtype-identity-principle open import foundation.universe-levels -open import foundation-core.equivalence-relations +open import foundation-core.equivalence-relations funext univalence truncations open import foundation-core.equivalences open import foundation-core.homotopies open import foundation-core.identity-types diff --git a/src/foundation/reflexive-relations.lagda.md b/src/foundation/reflexive-relations.lagda.md index 0953b7c3f4..a9aa5a1aa7 100644 --- a/src/foundation/reflexive-relations.lagda.md +++ b/src/foundation/reflexive-relations.lagda.md @@ -1,14 +1,22 @@ # Reflexive relations ```agda -module foundation.reflexive-relations where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.reflexive-relations + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.binary-dependent-identifications -open import foundation.binary-relations +open import foundation.binary-relations funext univalence truncations open import foundation.dependent-pair-types open import foundation.universe-levels diff --git a/src/foundation/regensburg-extension-fundamental-theorem-of-identity-types.lagda.md b/src/foundation/regensburg-extension-fundamental-theorem-of-identity-types.lagda.md index c830446ce5..42ca5cc7a5 100644 --- a/src/foundation/regensburg-extension-fundamental-theorem-of-identity-types.lagda.md +++ b/src/foundation/regensburg-extension-fundamental-theorem-of-identity-types.lagda.md @@ -9,30 +9,31 @@ module
Imports ```agda -open import foundation.0-connected-types -open import foundation.connected-maps -open import foundation.connected-types +open import foundation.0-connected-types funext univalence truncations +open import foundation.connected-maps funext univalence truncations +open import foundation.connected-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.fiber-inclusions -open import foundation.fibers-of-maps -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.functoriality-propositional-truncation -open import foundation.functoriality-truncation -open import foundation.homotopies -open import foundation.identity-types -open import foundation.inhabited-types -open import foundation.logical-equivalences -open import foundation.maps-in-subuniverses -open import foundation.mere-equality -open import foundation.propositional-truncations -open import foundation.separated-types-subuniverses -open import foundation.structured-equality-duality -open import foundation.subuniverses -open import foundation.surjective-maps -open import foundation.truncated-maps -open import foundation.truncated-types +open import foundation.dependent-products-truncated-types funext +open import foundation.equivalences funext +open import foundation.fiber-inclusions funext univalence +open import foundation.fibers-of-maps funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.functoriality-propositional-truncation funext univalence truncations +open import foundation.functoriality-truncation funext univalence truncations +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.inhabited-types funext univalence truncations +open import foundation.logical-equivalences funext +open import foundation.maps-in-subuniverses funext univalence +open import foundation.mere-equality funext univalence truncations +open import foundation.propositional-truncations funext univalence +open import foundation.separated-types-subuniverses funext univalence +open import foundation.structured-equality-duality funext univalence +open import foundation.subuniverses funext univalence +open import foundation.surjective-maps funext univalence truncations +open import foundation.truncated-maps funext +open import foundation.truncated-types funext univalence open import foundation.truncation-levels open import foundation.universe-levels ``` @@ -89,7 +90,14 @@ agda-unimath. ### The extended fundamental theorem of identity types ```agda +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + module _ + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) {l1 l2 l3 : Level} (𝒫 : subuniverse (l1 ⊔ l2) l3) {A : UU l1} (a : A) {B : A → UU l2} where diff --git a/src/foundation/relaxed-sigma-decompositions.lagda.md b/src/foundation/relaxed-sigma-decompositions.lagda.md index 521c531132..425bccceaf 100644 --- a/src/foundation/relaxed-sigma-decompositions.lagda.md +++ b/src/foundation/relaxed-sigma-decompositions.lagda.md @@ -2,8 +2,13 @@ ```agda {-# OPTIONS --lossy-unification #-} +open import foundation-core.univalence +open import foundation.function-extensionality-axiom -module foundation.relaxed-sigma-decompositions where +module foundation.relaxed-sigma-decompositions + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports @@ -11,13 +16,14 @@ module foundation.relaxed-sigma-decompositions where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalence-extensionality -open import foundation.equivalences +open import foundation.dependent-products-contractible-types funext +open import foundation.equivalence-extensionality funext +open import foundation.equivalences funext open import foundation.fundamental-theorem-of-identity-types open import foundation.structure-identity-principle -open import foundation.transposition-identifications-along-equivalences +open import foundation.transposition-identifications-along-equivalences funext open import foundation.type-arithmetic-dependent-pair-types -open import foundation.univalence +open import foundation.univalence funext univalence open import foundation.universe-levels open import foundation-core.contractible-types diff --git a/src/foundation/repetitions-of-values.lagda.md b/src/foundation/repetitions-of-values.lagda.md index cbecce73b5..e86fb07851 100644 --- a/src/foundation/repetitions-of-values.lagda.md +++ b/src/foundation/repetitions-of-values.lagda.md @@ -1,7 +1,15 @@ # Repetitions of values of maps ```agda -module foundation.repetitions-of-values where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.repetitions-of-values + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,14 +17,14 @@ module foundation.repetitions-of-values where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalences -open import foundation.identity-types -open import foundation.negated-equality -open import foundation.pairs-of-distinct-elements +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.negated-equality funext univalence truncations +open import foundation.pairs-of-distinct-elements funext univalence truncations open import foundation.universe-levels -open import foundation-core.commuting-squares-of-maps +open import foundation-core.commuting-squares-of-maps funext open import foundation-core.function-types open import foundation-core.functoriality-dependent-pair-types open import foundation-core.homotopies diff --git a/src/foundation/repetitions-sequences.lagda.md b/src/foundation/repetitions-sequences.lagda.md index c52b33a71d..a4b35d1847 100644 --- a/src/foundation/repetitions-sequences.lagda.md +++ b/src/foundation/repetitions-sequences.lagda.md @@ -1,20 +1,28 @@ # Repetitions in sequences ```agda -module foundation.repetitions-sequences where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.repetitions-sequences + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import elementary-number-theory.natural-numbers -open import elementary-number-theory.strictly-ordered-pairs-of-natural-numbers +open import elementary-number-theory.strictly-ordered-pairs-of-natural-numbers funext univalence truncations open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.negated-equality -open import foundation.pairs-of-distinct-elements -open import foundation.repetitions-of-values +open import foundation.negated-equality funext univalence truncations +open import foundation.pairs-of-distinct-elements funext univalence truncations +open import foundation.repetitions-of-values funext univalence truncations open import foundation.sequences open import foundation.unit-type open import foundation.universe-levels diff --git a/src/foundation/replacement.lagda.md b/src/foundation/replacement.lagda.md index f399430bcb..6f39607ae0 100644 --- a/src/foundation/replacement.lagda.md +++ b/src/foundation/replacement.lagda.md @@ -1,17 +1,25 @@ # The type theoretic replacement axiom ```agda -module foundation.replacement where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.replacement + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.images -open import foundation.locally-small-types +open import foundation.images funext univalence truncations +open import foundation.locally-small-types funext univalence truncations open import foundation.universe-levels -open import foundation-core.small-types +open import foundation-core.small-types funext univalence truncations ```
diff --git a/src/foundation/retractions.lagda.md b/src/foundation/retractions.lagda.md index cf513e7240..8b358d3820 100644 --- a/src/foundation/retractions.lagda.md +++ b/src/foundation/retractions.lagda.md @@ -1,7 +1,11 @@ # Retractions ```agda -module foundation.retractions where +open import foundation.function-extensionality-axiom + +module foundation.retractions + (funext : function-extensionality) + where open import foundation-core.retractions public ``` @@ -10,8 +14,9 @@ open import foundation-core.retractions public ```agda open import foundation.action-on-identifications-functions -open import foundation.coslice +open import foundation.coslice funext open import foundation.dependent-pair-types +open import foundation.dependent-products-truncated-types funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition diff --git a/src/foundation/retracts-of-maps.lagda.md b/src/foundation/retracts-of-maps.lagda.md index bf904c18bc..77d5097e2c 100644 --- a/src/foundation/retracts-of-maps.lagda.md +++ b/src/foundation/retracts-of-maps.lagda.md @@ -1,28 +1,35 @@ # Retracts of maps ```agda -module foundation.retracts-of-maps where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.retracts-of-maps + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-prisms-of-maps -open import foundation.commuting-triangles-of-morphisms-arrows +open import foundation.commuting-prisms-of-maps funext univalence +open import foundation.commuting-triangles-of-morphisms-arrows funext open import foundation.dependent-pair-types -open import foundation.diagonal-maps-of-types -open import foundation.function-extensionality -open import foundation.functoriality-fibers-of-maps -open import foundation.homotopies-morphisms-arrows +open import foundation.diagonal-maps-of-types funext +open import foundation.function-extensionality funext +open import foundation.functoriality-fibers-of-maps funext +open import foundation.homotopies-morphisms-arrows funext open import foundation.homotopy-algebra -open import foundation.morphisms-arrows -open import foundation.postcomposition-functions -open import foundation.precomposition-functions +open import foundation.morphisms-arrows funext +open import foundation.postcomposition-functions funext +open import foundation.precomposition-functions funext +open import foundation.retracts-of-types funext univalence open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import foundation-core.commuting-squares-of-maps +open import foundation-core.commuting-squares-of-maps funext open import foundation-core.constant-maps open import foundation-core.equivalences open import foundation-core.fibers-of-maps @@ -30,7 +37,6 @@ open import foundation-core.function-types open import foundation-core.homotopies open import foundation-core.identity-types open import foundation-core.retractions -open import foundation-core.retracts-of-types open import foundation-core.sections ``` diff --git a/src/foundation/retracts-of-types.lagda.md b/src/foundation/retracts-of-types.lagda.md index 56c7476a61..609ca11df6 100644 --- a/src/foundation/retracts-of-types.lagda.md +++ b/src/foundation/retracts-of-types.lagda.md @@ -1,7 +1,13 @@ # Retracts of types ```agda -module foundation.retracts-of-types where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.retracts-of-types + (funext : function-extensionality) + (univalence : univalence-axiom) + where open import foundation-core.retracts-of-types public ``` @@ -10,14 +16,15 @@ open import foundation-core.retracts-of-types public ```agda open import foundation.dependent-pair-types -open import foundation.equivalences +open import foundation.equivalences funext +open import foundation.function-extensionality funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies +open import foundation.homotopies funext open import foundation.homotopy-algebra -open import foundation.homotopy-induction -open import foundation.logical-equivalences +open import foundation.homotopy-induction funext +open import foundation.logical-equivalences funext open import foundation.structure-identity-principle -open import foundation.univalence +open import foundation.univalence funext univalence open import foundation.universe-levels open import foundation.whiskering-homotopies-composition @@ -25,6 +32,8 @@ open import foundation-core.contractible-types open import foundation-core.function-types open import foundation-core.functoriality-dependent-pair-types open import foundation-core.identity-types +open import foundation-core.postcomposition-functions +open import foundation-core.precomposition-functions open import foundation-core.torsorial-type-families ``` @@ -180,6 +189,40 @@ iff-retract' : iff-retract' = inv-iff ∘ iff-retract ``` +### If `A` is a retract of `B` then `A → S` is a retract of `B → S` via precomposition + +```agda +module _ + {l1 l2 l3 : Level} {A : UU l1} {B : UU l2} (R : A retract-of B) (S : UU l3) + where + + retract-precomp : + (A → S) retract-of (B → S) + pr1 retract-precomp = + precomp (map-retraction-retract R) S + pr1 (pr2 retract-precomp) = + precomp (inclusion-retract R) S + pr2 (pr2 retract-precomp) h = + eq-htpy (h ·l is-retraction-map-retraction-retract R) +``` + +### If `A` is a retract of `B` then `S → A` is a retract of `S → B` via postcomposition + +```agda +module _ + {l1 l2 l3 : Level} {A : UU l1} {B : UU l2} (S : UU l3) (R : A retract-of B) + where + + retract-postcomp : + (S → A) retract-of (S → B) + pr1 retract-postcomp = + postcomp S (inclusion-retract R) + pr1 (pr2 retract-postcomp) = + postcomp S (map-retraction-retract R) + pr2 (pr2 retract-postcomp) h = + eq-htpy (is-retraction-map-retraction-retract R ·r h) +``` + ## See also - [Retracts of maps](foundation.retracts-of-maps.md) diff --git a/src/foundation/sections.lagda.md b/src/foundation/sections.lagda.md index 0c9cd52162..fdacae4a8e 100644 --- a/src/foundation/sections.lagda.md +++ b/src/foundation/sections.lagda.md @@ -1,7 +1,11 @@ # Sections ```agda -module foundation.sections where +open import foundation.function-extensionality-axiom + +module foundation.sections + (funext : function-extensionality) + where open import foundation-core.sections public ``` @@ -10,9 +14,10 @@ open import foundation-core.sections public ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-triangles-of-homotopies +open import foundation.commuting-triangles-of-homotopies funext open import foundation.dependent-pair-types -open import foundation.function-extensionality +open import foundation.dependent-products-contractible-types funext +open import foundation.function-extensionality funext open import foundation.structure-identity-principle open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels diff --git a/src/foundation/separated-types-subuniverses.lagda.md b/src/foundation/separated-types-subuniverses.lagda.md index cc812fa34d..e248872bf9 100644 --- a/src/foundation/separated-types-subuniverses.lagda.md +++ b/src/foundation/separated-types-subuniverses.lagda.md @@ -1,13 +1,20 @@ # Types separated at subuniverses ```agda -module foundation.separated-types-subuniverses where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.separated-types-subuniverses + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda -open import foundation.subuniverses +open import foundation.dependent-products-propositions funext +open import foundation.subuniverses funext univalence open import foundation.universe-levels open import foundation-core.identity-types diff --git a/src/foundation/sequential-limits.lagda.md b/src/foundation/sequential-limits.lagda.md index f2891ee0db..f12b04c93c 100644 --- a/src/foundation/sequential-limits.lagda.md +++ b/src/foundation/sequential-limits.lagda.md @@ -1,7 +1,15 @@ # Sequential limits ```agda -module foundation.sequential-limits where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.sequential-limits + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,15 +18,15 @@ module foundation.sequential-limits where open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.cones-over-inverse-sequential-diagrams +open import foundation.cones-over-inverse-sequential-diagrams funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types -open import foundation.equivalences +open import foundation.equality-dependent-function-types funext +open import foundation.equivalences funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopy-induction -open import foundation.inverse-sequential-diagrams +open import foundation.homotopy-induction funext +open import foundation.inverse-sequential-diagrams funext univalence truncations open import foundation.structure-identity-principle -open import foundation.universal-property-sequential-limits +open import foundation.universal-property-sequential-limits funext univalence truncations open import foundation.universe-levels open import foundation-core.commuting-squares-of-homotopies diff --git a/src/foundation/set-presented-types.lagda.md b/src/foundation/set-presented-types.lagda.md index 658f0388f7..195e8b8f65 100644 --- a/src/foundation/set-presented-types.lagda.md +++ b/src/foundation/set-presented-types.lagda.md @@ -1,30 +1,39 @@ # Set presented types ```agda -module foundation.set-presented-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.set-presented-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.coproduct-types +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.empty-types -open import foundation.equality-coproduct-types -open import foundation.equivalences -open import foundation.existential-quantification -open import foundation.fibers-of-maps -open import foundation.functoriality-coproduct-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.images -open import foundation.injective-maps -open import foundation.propositional-truncations -open import foundation.set-truncations -open import foundation.subtypes -open import foundation.surjective-maps +open import foundation.dependent-products-propositions funext +open import foundation.embeddings funext +open import foundation.empty-types funext univalence truncations +open import foundation.equality-coproduct-types funext univalence truncations +open import foundation.equivalences funext +open import foundation.existential-quantification funext univalence truncations +open import foundation.fibers-of-maps funext +open import foundation.functoriality-coproduct-types funext univalence truncations +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.images funext univalence truncations +open import foundation.injective-maps funext +open import foundation.propositional-truncations funext univalence +open import foundation.set-truncations funext univalence +open import foundation.subtypes funext univalence truncations +open import foundation.surjective-maps funext univalence truncations open import foundation.universe-levels open import foundation-core.function-types diff --git a/src/foundation/set-quotients.lagda.md b/src/foundation/set-quotients.lagda.md index 492fac2246..2545fa7619 100644 --- a/src/foundation/set-quotients.lagda.md +++ b/src/foundation/set-quotients.lagda.md @@ -1,7 +1,15 @@ # Set quotients ```agda -module foundation.set-quotients where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.set-quotients + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,30 +17,30 @@ module foundation.set-quotients where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.effective-maps-equivalence-relations -open import foundation.embeddings -open import foundation.equivalence-classes -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.identity-types -open import foundation.inhabited-subtypes -open import foundation.reflecting-maps-equivalence-relations -open import foundation.sets -open import foundation.slice -open import foundation.surjective-maps -open import foundation.uniqueness-set-quotients -open import foundation.universal-property-image -open import foundation.universal-property-set-quotients +open import foundation.dependent-products-propositions funext +open import foundation.effective-maps-equivalence-relations funext univalence truncations +open import foundation.embeddings funext +open import foundation.equivalence-classes funext univalence truncations +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.inhabited-subtypes funext univalence truncations +open import foundation.reflecting-maps-equivalence-relations funext univalence truncations +open import foundation.sets funext univalence +open import foundation.slice funext univalence +open import foundation.surjective-maps funext univalence truncations +open import foundation.uniqueness-set-quotients funext univalence truncations +open import foundation.universal-property-image funext univalence truncations +open import foundation.universal-property-set-quotients funext univalence truncations open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import foundation-core.equivalence-relations +open import foundation-core.equivalence-relations funext univalence truncations open import foundation-core.function-types -open import foundation-core.functoriality-dependent-function-types +open import foundation-core.functoriality-dependent-function-types funext open import foundation-core.homotopies open import foundation-core.propositions -open import foundation-core.small-types -open import foundation-core.subtypes +open import foundation-core.small-types funext univalence truncations +open import foundation-core.subtypes funext ```
diff --git a/src/foundation/set-truncations.lagda.md b/src/foundation/set-truncations.lagda.md index 154cc2d2b5..488a7e7bed 100644 --- a/src/foundation/set-truncations.lagda.md +++ b/src/foundation/set-truncations.lagda.md @@ -2,32 +2,38 @@ ```agda {-# OPTIONS --lossy-unification #-} +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom -module foundation.set-truncations where +module foundation.set-truncations + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.effective-maps-equivalence-relations -open import foundation.equality-coproduct-types -open import foundation.functoriality-cartesian-product-types -open import foundation.functoriality-coproduct-types -open import foundation.mere-equality -open import foundation.postcomposition-functions -open import foundation.reflecting-maps-equivalence-relations -open import foundation.sets -open import foundation.slice -open import foundation.surjective-maps -open import foundation.truncations -open import foundation.uniqueness-set-truncations +open import foundation.effective-maps-equivalence-relations funext univalence truncations +open import foundation.equality-coproduct-types funext univalence truncations +open import foundation.functoriality-cartesian-product-types funext +open import foundation.functoriality-coproduct-types funext univalence truncations +open import foundation.mere-equality funext univalence truncations +open import foundation.postcomposition-functions funext +open import foundation.reflecting-maps-equivalence-relations funext univalence truncations +open import foundation.sets funext univalence +open import foundation.slice funext univalence +open import foundation.surjective-maps funext univalence truncations +open import foundation.truncations funext univalence truncations +open import foundation.uniqueness-set-truncations funext univalence open import foundation.unit-type -open import foundation.universal-property-coproduct-types -open import foundation.universal-property-dependent-pair-types -open import foundation.universal-property-image -open import foundation.universal-property-set-quotients -open import foundation.universal-property-set-truncation +open import foundation.universal-property-coproduct-types funext +open import foundation.universal-property-dependent-pair-types funext +open import foundation.universal-property-image funext univalence truncations +open import foundation.universal-property-set-quotients funext univalence truncations +open import foundation.universal-property-set-truncation funext univalence truncations open import foundation.universe-levels open import foundation-core.cartesian-product-types @@ -37,7 +43,7 @@ open import foundation-core.embeddings open import foundation-core.empty-types open import foundation-core.equivalences open import foundation-core.function-types -open import foundation-core.functoriality-dependent-function-types +open import foundation-core.functoriality-dependent-function-types funext open import foundation-core.functoriality-dependent-pair-types open import foundation-core.homotopies open import foundation-core.identity-types diff --git a/src/foundation/sets.lagda.md b/src/foundation/sets.lagda.md index 32edfb667b..ce745d2751 100644 --- a/src/foundation/sets.lagda.md +++ b/src/foundation/sets.lagda.md @@ -1,7 +1,13 @@ # Sets ```agda -module foundation.sets where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.sets + (funext : function-extensionality) + (univalence : univalence-axiom) + where open import foundation-core.sets public ``` @@ -9,15 +15,17 @@ open import foundation-core.sets public
Imports ```agda -open import foundation.contractible-types +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.logical-equivalences -open import foundation.subuniverses -open import foundation.truncated-types -open import foundation.univalent-type-families +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-truncated-types funext +open import foundation.logical-equivalences funext +open import foundation.subuniverses funext univalence +open import foundation.truncated-types funext univalence +open import foundation.univalent-type-families funext univalence open import foundation.universe-levels -open import foundation-core.1-types +open import foundation-core.1-types funext univalence open import foundation-core.cartesian-product-types open import foundation-core.embeddings open import foundation-core.equivalences @@ -26,7 +34,7 @@ open import foundation-core.injective-maps open import foundation-core.precomposition-functions open import foundation-core.propositional-maps open import foundation-core.propositions -open import foundation-core.subtypes +open import foundation-core.subtypes funext open import foundation-core.torsorial-type-families open import foundation-core.truncation-levels ``` @@ -177,6 +185,28 @@ precomp-Set : precomp-Set f C = precomp f (type-Set C) ``` +### The type of equivalences between sets is a set + +```agda +abstract + is-set-equiv-is-set : + {l1 l2 : Level} {A : UU l1} {B : UU l2} → + is-set A → is-set B → is-set (A ≃ B) + is-set-equiv-is-set = is-trunc-equiv-is-trunc zero-𝕋 + +module _ + {l1 l2 : Level} (A : Set l1) (B : Set l2) + where + + equiv-Set : UU (l1 ⊔ l2) + equiv-Set = type-Set A ≃ type-Set B + + equiv-set-Set : Set (l1 ⊔ l2) + pr1 equiv-set-Set = equiv-Set + pr2 equiv-set-Set = + is-set-equiv-is-set (is-set-type-Set A) (is-set-type-Set B) +``` + ### Extensionality of sets ```agda diff --git a/src/foundation/sigma-closed-subuniverses.lagda.md b/src/foundation/sigma-closed-subuniverses.lagda.md index 29e8d7b87a..c006a98282 100644 --- a/src/foundation/sigma-closed-subuniverses.lagda.md +++ b/src/foundation/sigma-closed-subuniverses.lagda.md @@ -1,14 +1,20 @@ # Σ-closed subuniverses ```agda -module foundation.sigma-closed-subuniverses where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.sigma-closed-subuniverses + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.subuniverses +open import foundation.subuniverses funext univalence open import foundation.universe-levels open import foundation-core.function-types diff --git a/src/foundation/sigma-decomposition-subuniverse.lagda.md b/src/foundation/sigma-decomposition-subuniverse.lagda.md index ef0e6e73f6..065eed73b8 100644 --- a/src/foundation/sigma-decomposition-subuniverse.lagda.md +++ b/src/foundation/sigma-decomposition-subuniverse.lagda.md @@ -1,15 +1,21 @@ # Σ-decompositions of types into types in a subuniverse ```agda -module foundation.sigma-decomposition-subuniverse where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.sigma-decomposition-subuniverse + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.relaxed-sigma-decompositions -open import foundation.subuniverses +open import foundation.relaxed-sigma-decompositions funext univalence +open import foundation.subuniverses funext univalence open import foundation.universe-levels open import foundation-core.cartesian-product-types diff --git a/src/foundation/sigma-decompositions.lagda.md b/src/foundation/sigma-decompositions.lagda.md index 720de58abb..342e86d6c1 100644 --- a/src/foundation/sigma-decompositions.lagda.md +++ b/src/foundation/sigma-decompositions.lagda.md @@ -2,8 +2,15 @@ ```agda {-# OPTIONS --lossy-unification #-} - -module foundation.sigma-decompositions where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.sigma-decompositions + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -11,16 +18,17 @@ module foundation.sigma-decompositions where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalence-extensionality -open import foundation.equivalences +open import foundation.dependent-products-contractible-types funext +open import foundation.equivalence-extensionality funext +open import foundation.equivalences funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.inhabited-types -open import foundation.propositional-truncations -open import foundation.sets +open import foundation.inhabited-types funext univalence truncations +open import foundation.propositional-truncations funext univalence +open import foundation.sets funext univalence open import foundation.structure-identity-principle -open import foundation.transposition-identifications-along-equivalences +open import foundation.transposition-identifications-along-equivalences funext open import foundation.type-arithmetic-dependent-pair-types -open import foundation.univalence +open import foundation.univalence funext univalence open import foundation.universe-levels open import foundation-core.contractible-types diff --git a/src/foundation/singleton-subtypes.lagda.md b/src/foundation/singleton-subtypes.lagda.md index b624eca1cc..33008e2ecf 100644 --- a/src/foundation/singleton-subtypes.lagda.md +++ b/src/foundation/singleton-subtypes.lagda.md @@ -1,24 +1,33 @@ # Singleton subtypes ```agda -module foundation.singleton-subtypes where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.singleton-subtypes + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.connected-components -open import foundation.contractible-types +open import foundation.connected-components funext univalence truncations +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.functoriality-propositional-truncation -open import foundation.images-subtypes -open import foundation.inhabited-subtypes -open import foundation.logical-equivalences -open import foundation.propositional-truncations -open import foundation.sets +open import foundation.dependent-products-contractible-types funext +open import foundation.functoriality-propositional-truncation funext univalence truncations +open import foundation.images-subtypes funext univalence truncations +open import foundation.inhabited-subtypes funext univalence truncations +open import foundation.logical-equivalences funext +open import foundation.propositional-truncations funext univalence +open import foundation.sets funext univalence open import foundation.singleton-induction -open import foundation.subtypes -open import foundation.torsorial-type-families +open import foundation.subtypes funext univalence truncations +open import foundation.torsorial-type-families funext univalence truncations open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels diff --git a/src/foundation/slice.lagda.md b/src/foundation/slice.lagda.md index 0a41b6dd82..60d4d4cae9 100644 --- a/src/foundation/slice.lagda.md +++ b/src/foundation/slice.lagda.md @@ -1,23 +1,30 @@ # Morphisms in the slice category of types ```agda -module foundation.slice where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.slice + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda -open import foundation.commuting-triangles-of-homotopies +open import foundation.commuting-triangles-of-homotopies funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.function-extensionality funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.logical-equivalences +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.logical-equivalences funext open import foundation.structure-identity-principle open import foundation.type-arithmetic-dependent-pair-types -open import foundation.univalence +open import foundation.univalence funext univalence open import foundation.universe-levels open import foundation.whiskering-homotopies-composition @@ -34,7 +41,7 @@ open import foundation-core.propositions open import foundation-core.torsorial-type-families open import foundation-core.type-theoretic-principle-of-choice -open import trees.polynomial-endofunctors +open import trees.polynomial-endofunctors funext univalence ```
diff --git a/src/foundation/small-maps.lagda.md b/src/foundation/small-maps.lagda.md index 59c0c702b7..fadac73ca9 100644 --- a/src/foundation/small-maps.lagda.md +++ b/src/foundation/small-maps.lagda.md @@ -1,21 +1,30 @@ # Small maps ```agda -module foundation.small-maps where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.small-maps + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.locally-small-types -open import foundation.retracts-of-maps -open import foundation.split-idempotent-maps +open import foundation.dependent-products-propositions funext +open import foundation.locally-small-types funext univalence truncations +open import foundation.retracts-of-maps funext univalence +open import foundation.split-idempotent-maps funext univalence truncations open import foundation.universe-levels open import foundation-core.fibers-of-maps open import foundation-core.propositions -open import foundation-core.small-types +open import foundation-core.small-types funext univalence truncations ```
diff --git a/src/foundation/small-types.lagda.md b/src/foundation/small-types.lagda.md index 2d60593a75..3cee378014 100644 --- a/src/foundation/small-types.lagda.md +++ b/src/foundation/small-types.lagda.md @@ -1,21 +1,29 @@ # Small types ```agda -module foundation.small-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom -open import foundation-core.small-types public +module foundation.small-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where + +open import foundation-core.small-types funext univalence truncations public ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.images -open import foundation.locally-small-types -open import foundation.replacement -open import foundation.surjective-maps -open import foundation.uniqueness-image -open import foundation.universal-property-image +open import foundation.images funext univalence truncations +open import foundation.locally-small-types funext univalence truncations +open import foundation.replacement funext univalence truncations +open import foundation.surjective-maps funext univalence truncations +open import foundation.uniqueness-image funext univalence truncations +open import foundation.universal-property-image funext univalence truncations open import foundation.universe-levels open import foundation-core.embeddings diff --git a/src/foundation/small-universes.lagda.md b/src/foundation/small-universes.lagda.md index fda8cb43a0..c1bd395831 100644 --- a/src/foundation/small-universes.lagda.md +++ b/src/foundation/small-universes.lagda.md @@ -1,7 +1,15 @@ # Small universes ```agda -module foundation.small-universes where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.small-universes + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,7 +18,7 @@ module foundation.small-universes where open import foundation.universe-levels open import foundation-core.cartesian-product-types -open import foundation-core.small-types +open import foundation-core.small-types funext univalence truncations ```
diff --git a/src/foundation/span-diagrams.lagda.md b/src/foundation/span-diagrams.lagda.md index 3356a17241..f0beb3a3fa 100644 --- a/src/foundation/span-diagrams.lagda.md +++ b/src/foundation/span-diagrams.lagda.md @@ -1,14 +1,18 @@ # Span diagrams ```agda -module foundation.span-diagrams where +open import foundation.function-extensionality-axiom + +module foundation.span-diagrams + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.morphisms-arrows +open import foundation.morphisms-arrows funext open import foundation.spans open import foundation.universe-levels ``` diff --git a/src/foundation/spans-families-of-types.lagda.md b/src/foundation/spans-families-of-types.lagda.md index 9a6b00a030..5ee8aecb7e 100644 --- a/src/foundation/spans-families-of-types.lagda.md +++ b/src/foundation/spans-families-of-types.lagda.md @@ -9,9 +9,6 @@ module foundation.spans-families-of-types where ```agda open import foundation.dependent-pair-types open import foundation.universe-levels - -open import foundation-core.equivalences -open import foundation-core.function-types ```
diff --git a/src/foundation/spans-of-spans.lagda.md b/src/foundation/spans-of-spans.lagda.md index 792737abe6..8269b44723 100644 --- a/src/foundation/spans-of-spans.lagda.md +++ b/src/foundation/spans-of-spans.lagda.md @@ -1,15 +1,21 @@ # Spans of spans ```agda -module foundation.spans-of-spans where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.spans-of-spans + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda -open import foundation.commuting-squares-of-maps +open import foundation.commuting-squares-of-maps funext univalence open import foundation.dependent-pair-types -open import foundation.homotopies +open import foundation.homotopies funext open import foundation.spans open import foundation.universe-levels diff --git a/src/foundation/split-idempotent-maps.lagda.md b/src/foundation/split-idempotent-maps.lagda.md index e3a320b622..7776bf9a47 100644 --- a/src/foundation/split-idempotent-maps.lagda.md +++ b/src/foundation/split-idempotent-maps.lagda.md @@ -1,7 +1,15 @@ # Split idempotent maps ```agda -module foundation.split-idempotent-maps where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.split-idempotent-maps + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,29 +17,29 @@ module foundation.split-idempotent-maps where ```agda open import elementary-number-theory.natural-numbers -open import foundation.action-on-higher-identifications-functions +open import foundation.action-on-higher-identifications-functions funext open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalences +open import foundation.equivalences funext open import foundation.fixed-points-endofunctions open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies +open import foundation.homotopies funext open import foundation.homotopy-algebra -open import foundation.homotopy-induction -open import foundation.idempotent-maps -open import foundation.inverse-sequential-diagrams -open import foundation.locally-small-types -open import foundation.path-cosplit-maps -open import foundation.quasicoherently-idempotent-maps -open import foundation.retracts-of-types -open import foundation.sequential-limits +open import foundation.homotopy-induction funext +open import foundation.idempotent-maps funext +open import foundation.inverse-sequential-diagrams funext univalence truncations +open import foundation.locally-small-types funext univalence truncations +open import foundation.path-cosplit-maps funext univalence truncations +open import foundation.quasicoherently-idempotent-maps funext univalence truncations +open import foundation.retracts-of-types funext univalence +open import foundation.sequential-limits funext univalence truncations open import foundation.structure-identity-principle open import foundation.truncation-levels open import foundation.type-arithmetic-dependent-pair-types -open import foundation.univalence +open import foundation.univalence funext univalence open import foundation.universe-levels -open import foundation.weakly-constant-maps +open import foundation.weakly-constant-maps funext open import foundation.whiskering-homotopies-composition open import foundation-core.commuting-squares-of-homotopies @@ -44,7 +52,7 @@ open import foundation-core.propositions open import foundation-core.retractions open import foundation-core.sections open import foundation-core.sets -open import foundation-core.small-types +open import foundation-core.small-types funext univalence truncations open import foundation-core.torsorial-type-families ``` diff --git a/src/foundation/standard-apartness-relations.lagda.md b/src/foundation/standard-apartness-relations.lagda.md index 3a3df40ac0..c77991afe3 100644 --- a/src/foundation/standard-apartness-relations.lagda.md +++ b/src/foundation/standard-apartness-relations.lagda.md @@ -1,19 +1,27 @@ # Standard apartness relations ```agda -module foundation.standard-apartness-relations where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.standard-apartness-relations + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.apartness-relations -open import foundation.decidable-types +open import foundation.apartness-relations funext univalence truncations +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.law-of-excluded-middle -open import foundation.logical-equivalences -open import foundation.negated-equality -open import foundation.tight-apartness-relations +open import foundation.law-of-excluded-middle funext univalence truncations +open import foundation.logical-equivalences funext +open import foundation.negated-equality funext univalence truncations +open import foundation.tight-apartness-relations funext univalence truncations open import foundation.universe-levels open import foundation-core.identity-types diff --git a/src/foundation/standard-pullbacks.lagda.md b/src/foundation/standard-pullbacks.lagda.md index 8f0db009ca..5a416af381 100644 --- a/src/foundation/standard-pullbacks.lagda.md +++ b/src/foundation/standard-pullbacks.lagda.md @@ -1,23 +1,27 @@ # Standard pullbacks ```agda -module foundation.standard-pullbacks where +open import foundation.function-extensionality-axiom + +module foundation.standard-pullbacks + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cones-over-cospan-diagrams +open import foundation.cones-over-cospan-diagrams funext open import foundation.dependent-pair-types open import foundation.equality-cartesian-product-types -open import foundation.functoriality-cartesian-product-types -open import foundation.identity-types +open import foundation.functoriality-cartesian-product-types funext +open import foundation.identity-types funext open import foundation.structure-identity-principle open import foundation.universe-levels open import foundation-core.cartesian-product-types -open import foundation-core.commuting-squares-of-maps +open import foundation-core.commuting-squares-of-maps funext open import foundation-core.diagonal-maps-cartesian-products-of-types open import foundation-core.equality-dependent-pair-types open import foundation-core.equivalences @@ -27,7 +31,7 @@ open import foundation-core.homotopies open import foundation-core.retractions open import foundation-core.sections open import foundation-core.type-theoretic-principle-of-choice -open import foundation-core.universal-property-pullbacks +open import foundation-core.universal-property-pullbacks funext open import foundation-core.whiskering-identifications-concatenation ``` diff --git a/src/foundation/standard-ternary-pullbacks.lagda.md b/src/foundation/standard-ternary-pullbacks.lagda.md index 6ca4fd1596..4ae8ca7771 100644 --- a/src/foundation/standard-ternary-pullbacks.lagda.md +++ b/src/foundation/standard-ternary-pullbacks.lagda.md @@ -1,23 +1,27 @@ # Standard ternary pullbacks ```agda -module foundation.standard-ternary-pullbacks where +open import foundation.function-extensionality-axiom + +module foundation.standard-ternary-pullbacks + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cones-over-cospan-diagrams +open import foundation.cones-over-cospan-diagrams funext open import foundation.dependent-pair-types open import foundation.equality-cartesian-product-types -open import foundation.functoriality-cartesian-product-types -open import foundation.identity-types +open import foundation.functoriality-cartesian-product-types funext +open import foundation.identity-types funext open import foundation.structure-identity-principle open import foundation.universe-levels open import foundation-core.cartesian-product-types -open import foundation-core.commuting-squares-of-maps +open import foundation-core.commuting-squares-of-maps funext open import foundation-core.diagonal-maps-cartesian-products-of-types open import foundation-core.equality-dependent-pair-types open import foundation-core.equivalences @@ -27,7 +31,7 @@ open import foundation-core.homotopies open import foundation-core.retractions open import foundation-core.sections open import foundation-core.type-theoretic-principle-of-choice -open import foundation-core.universal-property-pullbacks +open import foundation-core.universal-property-pullbacks funext open import foundation-core.whiskering-identifications-concatenation ``` diff --git a/src/foundation/strict-symmetrization-binary-relations.lagda.md b/src/foundation/strict-symmetrization-binary-relations.lagda.md index 1c316d7ad4..7805e43f47 100644 --- a/src/foundation/strict-symmetrization-binary-relations.lagda.md +++ b/src/foundation/strict-symmetrization-binary-relations.lagda.md @@ -1,15 +1,23 @@ # Strict symmetrization of binary relations ```agda -module foundation.strict-symmetrization-binary-relations where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.strict-symmetrization-binary-relations + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.binary-relations -open import foundation.binary-relations-with-extensions -open import foundation.binary-relations-with-lifts +open import foundation.binary-relations funext univalence truncations +open import foundation.binary-relations-with-extensions funext univalence truncations +open import foundation.binary-relations-with-lifts funext univalence truncations open import foundation.dependent-pair-types open import foundation.universe-levels diff --git a/src/foundation/strictly-involutive-identity-types.lagda.md b/src/foundation/strictly-involutive-identity-types.lagda.md index 41d8a10e2d..501d9fc543 100644 --- a/src/foundation/strictly-involutive-identity-types.lagda.md +++ b/src/foundation/strictly-involutive-identity-types.lagda.md @@ -1,7 +1,13 @@ # Strictly involutive identity types ```agda -module foundation.strictly-involutive-identity-types where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.strictly-involutive-identity-types + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports @@ -11,11 +17,12 @@ open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types open import foundation.equality-cartesian-product-types -open import foundation.function-extensionality -open import foundation.multivariable-homotopies +open import foundation.function-extensionality funext +open import foundation.multivariable-homotopies funext open import foundation.strictly-right-unital-concatenation-identifications -open import foundation.univalence -open import foundation.universal-property-identity-systems +open import foundation.telescopes +open import foundation.univalence funext univalence +open import foundation.universal-property-identity-systems funext open import foundation.universe-levels open import foundation-core.cartesian-product-types diff --git a/src/foundation/strong-preunivalence.lagda.md b/src/foundation/strong-preunivalence.lagda.md index 051e55fa52..4b7edf1676 100644 --- a/src/foundation/strong-preunivalence.lagda.md +++ b/src/foundation/strong-preunivalence.lagda.md @@ -1,23 +1,33 @@ # The strong preunivalence axiom ```agda -module foundation.strong-preunivalence where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.strong-preunivalence + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.contractible-types +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.functoriality-dependent-pair-types -open import foundation.preunivalence -open import foundation.propositional-maps -open import foundation.propositions -open import foundation.sets -open import foundation.small-types -open import foundation.structured-equality-duality -open import foundation.univalence +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.preunivalence funext univalence +open import foundation.propositional-maps funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.small-types funext univalence truncations +open import foundation.structured-equality-duality funext univalence +open import foundation.univalence funext univalence open import foundation.universe-levels open import foundation-core.function-types diff --git a/src/foundation/strongly-extensional-maps.lagda.md b/src/foundation/strongly-extensional-maps.lagda.md index 9b5bfa198f..71a997d336 100644 --- a/src/foundation/strongly-extensional-maps.lagda.md +++ b/src/foundation/strongly-extensional-maps.lagda.md @@ -1,13 +1,21 @@ # Strongly extensional maps ```agda -module foundation.strongly-extensional-maps where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.strongly-extensional-maps + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.apartness-relations +open import foundation.apartness-relations funext univalence truncations open import foundation.universe-levels ``` diff --git a/src/foundation/structure.lagda.md b/src/foundation/structure.lagda.md index 6a5b9217b7..7a11b64df0 100644 --- a/src/foundation/structure.lagda.md +++ b/src/foundation/structure.lagda.md @@ -1,14 +1,20 @@ # Structure ```agda -module foundation.structure where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.structure + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.univalence +open import foundation.univalence funext univalence open import foundation.universe-levels open import foundation-core.equivalences diff --git a/src/foundation/structured-equality-duality.lagda.md b/src/foundation/structured-equality-duality.lagda.md index 534bf63cd7..1e62308cd6 100644 --- a/src/foundation/structured-equality-duality.lagda.md +++ b/src/foundation/structured-equality-duality.lagda.md @@ -1,19 +1,25 @@ # Structured equality duality ```agda -module foundation.structured-equality-duality where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.structured-equality-duality + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.maps-in-subuniverses -open import foundation.separated-types-subuniverses -open import foundation.structure -open import foundation.subuniverses +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.maps-in-subuniverses funext univalence +open import foundation.separated-types-subuniverses funext univalence +open import foundation.structure funext univalence +open import foundation.subuniverses funext univalence open import foundation.universe-levels open import foundation-core.equivalences diff --git a/src/foundation/structured-type-duality.lagda.md b/src/foundation/structured-type-duality.lagda.md index e7d04bcb07..5d775e966b 100644 --- a/src/foundation/structured-type-duality.lagda.md +++ b/src/foundation/structured-type-duality.lagda.md @@ -1,23 +1,31 @@ # Structured type duality ```agda -module foundation.structured-type-duality where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.structured-type-duality + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.structure +open import foundation.equivalences funext +open import foundation.structure funext univalence open import foundation.type-arithmetic-dependent-pair-types -open import foundation.type-duality -open import foundation.univalence +open import foundation.type-duality funext univalence truncations +open import foundation.univalence funext univalence open import foundation.universe-levels open import foundation-core.fibers-of-maps open import foundation-core.function-types -open import foundation-core.functoriality-dependent-function-types +open import foundation-core.functoriality-dependent-function-types funext open import foundation-core.functoriality-dependent-pair-types open import foundation-core.type-theoretic-principle-of-choice ``` diff --git a/src/foundation/subtype-duality.lagda.md b/src/foundation/subtype-duality.lagda.md index abd64501e7..cedf62dbb9 100644 --- a/src/foundation/subtype-duality.lagda.md +++ b/src/foundation/subtype-duality.lagda.md @@ -1,17 +1,25 @@ # Subtype duality ```agda -module foundation.subtype-duality where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.subtype-duality + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.inhabited-types -open import foundation.propositional-maps -open import foundation.structured-type-duality -open import foundation.surjective-maps +open import foundation.inhabited-types funext univalence truncations +open import foundation.propositional-maps funext +open import foundation.structured-type-duality funext univalence truncations +open import foundation.surjective-maps funext univalence truncations open import foundation.universe-levels open import foundation-core.embeddings diff --git a/src/foundation/subtypes.lagda.md b/src/foundation/subtypes.lagda.md index 291b0c918d..8864fce2b7 100644 --- a/src/foundation/subtypes.lagda.md +++ b/src/foundation/subtypes.lagda.md @@ -1,20 +1,29 @@ # Subtypes ```agda -module foundation.subtypes where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.subtypes + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where -open import foundation-core.subtypes public +open import foundation-core.subtypes funext public ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equality-dependent-function-types +open import foundation.dependent-products-propositions funext +open import foundation.embeddings funext +open import foundation.equality-dependent-function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.logical-equivalences -open import foundation.propositional-extensionality +open import foundation.logical-equivalences funext +open import foundation.propositional-extensionality funext univalence truncations open import foundation.universe-levels open import foundation-core.cartesian-product-types diff --git a/src/foundation/subuniverses.lagda.md b/src/foundation/subuniverses.lagda.md index ddeb1e28d6..d11764c506 100644 --- a/src/foundation/subuniverses.lagda.md +++ b/src/foundation/subuniverses.lagda.md @@ -1,18 +1,24 @@ # Subuniverses ```agda -module foundation.subuniverses where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.subuniverses + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types -open import foundation.equivalences +open import foundation.equality-dependent-function-types funext +open import foundation.equivalences funext open import foundation.fundamental-theorem-of-identity-types open import foundation.subtype-identity-principle -open import foundation.univalence +open import foundation.univalence funext univalence open import foundation.universe-levels open import foundation-core.contractible-types @@ -21,7 +27,7 @@ open import foundation-core.fibers-of-maps open import foundation-core.functoriality-dependent-pair-types open import foundation-core.identity-types open import foundation-core.propositions -open import foundation-core.subtypes +open import foundation-core.subtypes funext open import foundation-core.torsorial-type-families open import foundation-core.transport-along-identifications ``` diff --git a/src/foundation/surjective-maps.lagda.md b/src/foundation/surjective-maps.lagda.md index f6fc1ffb05..53ed5dc3c2 100644 --- a/src/foundation/surjective-maps.lagda.md +++ b/src/foundation/surjective-maps.lagda.md @@ -1,54 +1,65 @@ # Surjective maps ```agda -module foundation.surjective-maps where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.surjective-maps + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.connected-maps -open import foundation.contractible-types +open import foundation.connected-maps funext univalence truncations +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.diagonal-maps-of-types -open import foundation.embeddings +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.dependent-products-truncated-types funext +open import foundation.embeddings funext open import foundation.equality-cartesian-product-types -open import foundation.functoriality-cartesian-product-types +open import foundation.functoriality-cartesian-product-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopy-induction -open import foundation.identity-types -open import foundation.inhabited-types -open import foundation.postcomposition-dependent-functions -open import foundation.propositional-truncations +open import foundation.homotopy-induction funext +open import foundation.identity-types funext +open import foundation.inhabited-types funext univalence truncations +open import foundation.postcomposition-dependent-functions funext +open import foundation.propositional-truncations funext univalence open import foundation.split-surjective-maps open import foundation.structure-identity-principle open import foundation.subtype-identity-principle -open import foundation.truncated-types -open import foundation.univalence -open import foundation.universal-property-family-of-fibers-of-maps -open import foundation.universal-property-propositional-truncation +open import foundation.truncated-types funext univalence +open import foundation.univalence funext univalence +open import foundation.universal-property-family-of-fibers-of-maps funext +open import foundation.universal-property-propositional-truncation funext open import foundation.universe-levels open import foundation-core.cartesian-product-types open import foundation-core.constant-maps open import foundation-core.contractible-maps +open import foundation-core.diagonal-maps-of-types open import foundation-core.equivalences open import foundation-core.fibers-of-maps open import foundation-core.function-types -open import foundation-core.functoriality-dependent-function-types +open import foundation-core.functoriality-dependent-function-types funext open import foundation-core.homotopies open import foundation-core.precomposition-dependent-functions open import foundation-core.propositional-maps open import foundation-core.propositions open import foundation-core.sections open import foundation-core.sets -open import foundation-core.subtypes +open import foundation-core.subtypes funext open import foundation-core.torsorial-type-families -open import foundation-core.truncated-maps +open import foundation-core.truncated-maps funext open import foundation-core.truncation-levels -open import orthogonal-factorization-systems.extensions-maps +open import orthogonal-factorization-systems.extensions-maps funext univalence ```
diff --git a/src/foundation/symmetric-binary-relations.lagda.md b/src/foundation/symmetric-binary-relations.lagda.md index 7f5a829ff1..f648ae31ce 100644 --- a/src/foundation/symmetric-binary-relations.lagda.md +++ b/src/foundation/symmetric-binary-relations.lagda.md @@ -1,21 +1,28 @@ # Symmetric binary relations ```agda -module foundation.symmetric-binary-relations where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.symmetric-binary-relations + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.binary-relations +open import foundation.binary-relations funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalence-extensionality -open import foundation.function-extensionality -open import foundation.morphisms-binary-relations -open import foundation.symmetric-operations +open import foundation.equivalence-extensionality funext +open import foundation.morphisms-binary-relations funext univalence truncations +open import foundation.symmetric-operations funext univalence truncations open import foundation.universe-levels -open import foundation.unordered-pairs +open import foundation.unordered-pairs funext univalence truncations open import foundation-core.equivalences open import foundation-core.function-types @@ -23,7 +30,7 @@ open import foundation-core.homotopies open import foundation-core.identity-types open import foundation-core.transport-along-identifications -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/foundation/symmetric-cores-binary-relations.lagda.md b/src/foundation/symmetric-cores-binary-relations.lagda.md index 95c56d21dd..7fcb099405 100644 --- a/src/foundation/symmetric-cores-binary-relations.lagda.md +++ b/src/foundation/symmetric-cores-binary-relations.lagda.md @@ -1,25 +1,33 @@ # Symmetric cores of binary relations ```agda -module foundation.symmetric-cores-binary-relations where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.symmetric-cores-binary-relations + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.binary-relations -open import foundation.morphisms-binary-relations -open import foundation.postcomposition-functions -open import foundation.symmetric-binary-relations +open import foundation.binary-relations funext univalence truncations +open import foundation.morphisms-binary-relations funext univalence truncations +open import foundation.postcomposition-functions funext +open import foundation.symmetric-binary-relations funext univalence truncations open import foundation.transport-along-identifications -open import foundation.type-arithmetic-dependent-function-types +open import foundation.type-arithmetic-dependent-function-types funext univalence open import foundation.universe-levels -open import foundation.unordered-pairs +open import foundation.unordered-pairs funext univalence truncations open import foundation-core.equivalences -open import foundation-core.functoriality-dependent-function-types +open import foundation-core.functoriality-dependent-function-types funext -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/foundation/symmetric-difference.lagda.md b/src/foundation/symmetric-difference.lagda.md index 13308cf30a..85d808ed4f 100644 --- a/src/foundation/symmetric-difference.lagda.md +++ b/src/foundation/symmetric-difference.lagda.md @@ -1,26 +1,34 @@ # Symmetric difference of subtypes ```agda -module foundation.symmetric-difference where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.symmetric-difference + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.decidable-subtypes -open import foundation.decidable-types +open import foundation.decidable-subtypes funext univalence truncations +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.exclusive-sum -open import foundation.intersections-subtypes +open import foundation.exclusive-sum funext univalence truncations +open import foundation.intersections-subtypes funext univalence truncations open import foundation.universe-levels open import foundation-core.coproduct-types -open import foundation-core.decidable-propositions +open import foundation-core.decidable-propositions funext univalence truncations open import foundation-core.equivalences open import foundation-core.function-types open import foundation-core.identity-types open import foundation-core.propositions -open import foundation-core.subtypes +open import foundation-core.subtypes funext open import foundation-core.transport-along-identifications ``` diff --git a/src/foundation/symmetric-identity-types.lagda.md b/src/foundation/symmetric-identity-types.lagda.md index 7b34c892e3..1efbf436cd 100644 --- a/src/foundation/symmetric-identity-types.lagda.md +++ b/src/foundation/symmetric-identity-types.lagda.md @@ -1,7 +1,15 @@ # The symmetric identity types ```agda -module foundation.symmetric-identity-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.symmetric-identity-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,14 +17,14 @@ module foundation.symmetric-identity-types where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-extensionality -open import foundation.functoriality-dependent-function-types +open import foundation.function-extensionality funext +open import foundation.functoriality-dependent-function-types funext univalence open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopy-induction -open import foundation.identity-types +open import foundation.homotopy-induction funext +open import foundation.identity-types funext open import foundation.structure-identity-principle open import foundation.universe-levels -open import foundation.unordered-pairs +open import foundation.unordered-pairs funext univalence truncations open import foundation-core.contractible-types open import foundation-core.coproduct-types @@ -27,7 +35,7 @@ open import foundation-core.functoriality-dependent-pair-types open import foundation-core.homotopies open import foundation-core.torsorial-type-families -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/foundation/symmetric-operations.lagda.md b/src/foundation/symmetric-operations.lagda.md index f5ab5c00de..37f9577769 100644 --- a/src/foundation/symmetric-operations.lagda.md +++ b/src/foundation/symmetric-operations.lagda.md @@ -1,7 +1,15 @@ # Symmetric operations ```agda -module foundation.symmetric-operations where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.symmetric-operations + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,14 +18,15 @@ module foundation.symmetric-operations where open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalence-extensionality -open import foundation.function-extensionality -open import foundation.functoriality-coproduct-types +open import foundation.dependent-products-propositions funext +open import foundation.equivalence-extensionality funext +open import foundation.function-extensionality funext +open import foundation.functoriality-coproduct-types funext univalence truncations open import foundation.fundamental-theorem-of-identity-types -open import foundation.propositional-truncations -open import foundation.universal-property-propositional-truncation-into-sets +open import foundation.propositional-truncations funext univalence +open import foundation.universal-property-propositional-truncation-into-sets funext univalence truncations open import foundation.universe-levels -open import foundation.unordered-pairs +open import foundation.unordered-pairs funext univalence truncations open import foundation-core.coproduct-types open import foundation-core.equivalences @@ -26,12 +35,12 @@ open import foundation-core.homotopies open import foundation-core.identity-types open import foundation-core.propositions open import foundation-core.sets -open import foundation-core.subtypes +open import foundation-core.subtypes funext open import foundation-core.torsorial-type-families -open import univalent-combinatorics.2-element-types -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.2-element-types funext univalence truncations +open import univalent-combinatorics.finite-types funext univalence truncations +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/foundation/terminal-spans-families-of-types.lagda.md b/src/foundation/terminal-spans-families-of-types.lagda.md index 6b08b3e90f..baf55d18b1 100644 --- a/src/foundation/terminal-spans-families-of-types.lagda.md +++ b/src/foundation/terminal-spans-families-of-types.lagda.md @@ -1,16 +1,21 @@ # Terminal spans on families of types ```agda -module foundation.terminal-spans-families-of-types where +open import foundation.function-extensionality-axiom + +module foundation.terminal-spans-families-of-types + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.contractible-types -open import foundation.morphisms-spans-families-of-types +open import foundation.morphisms-spans-families-of-types funext open import foundation.spans-families-of-types open import foundation.universe-levels + +open import foundation-core.contractible-types ```
diff --git a/src/foundation/tight-apartness-relations.lagda.md b/src/foundation/tight-apartness-relations.lagda.md index f848664137..0fa14903d8 100644 --- a/src/foundation/tight-apartness-relations.lagda.md +++ b/src/foundation/tight-apartness-relations.lagda.md @@ -1,17 +1,25 @@ # Tight apartness relations ```agda -module foundation.tight-apartness-relations where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.tight-apartness-relations + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.apartness-relations -open import foundation.binary-relations +open import foundation.apartness-relations funext univalence truncations +open import foundation.binary-relations funext univalence truncations open import foundation.dependent-pair-types -open import foundation.function-extensionality -open import foundation.propositional-truncations +open import foundation.function-extensionality funext +open import foundation.propositional-truncations funext univalence open import foundation.universe-levels open import foundation-core.cartesian-product-types diff --git a/src/foundation/torsorial-type-families.lagda.md b/src/foundation/torsorial-type-families.lagda.md index 0929568e83..5c22f40477 100644 --- a/src/foundation/torsorial-type-families.lagda.md +++ b/src/foundation/torsorial-type-families.lagda.md @@ -1,7 +1,15 @@ # Torsorial type families ```agda -module foundation.torsorial-type-families where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.torsorial-type-families + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where open import foundation-core.torsorial-type-families public ``` @@ -9,11 +17,12 @@ open import foundation-core.torsorial-type-families public
Imports ```agda -open import foundation.contractible-types +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.logical-equivalences -open import foundation.universal-property-identity-types +open import foundation.logical-equivalences funext +open import foundation.universal-property-identity-types funext univalence truncations open import foundation.universe-levels open import foundation-core.equivalences diff --git a/src/foundation/total-partial-functions.lagda.md b/src/foundation/total-partial-functions.lagda.md index c8510fac75..9d82c1d0d4 100644 --- a/src/foundation/total-partial-functions.lagda.md +++ b/src/foundation/total-partial-functions.lagda.md @@ -1,13 +1,18 @@ # Total partial functions ```agda -module foundation.total-partial-functions where +open import foundation.function-extensionality-axiom + +module foundation.total-partial-functions + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions funext open import foundation.partial-functions open import foundation.universe-levels diff --git a/src/foundation/transfinite-cocomposition-of-maps.lagda.md b/src/foundation/transfinite-cocomposition-of-maps.lagda.md index 9d3f7d02ca..8d19594ff2 100644 --- a/src/foundation/transfinite-cocomposition-of-maps.lagda.md +++ b/src/foundation/transfinite-cocomposition-of-maps.lagda.md @@ -1,14 +1,22 @@ # Transfinite cocomposition of maps ```agda -module foundation.transfinite-cocomposition-of-maps where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.transfinite-cocomposition-of-maps + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.inverse-sequential-diagrams -open import foundation.sequential-limits +open import foundation.inverse-sequential-diagrams funext univalence truncations +open import foundation.sequential-limits funext univalence truncations open import foundation.universe-levels ``` diff --git a/src/foundation/transport-along-equivalences.lagda.md b/src/foundation/transport-along-equivalences.lagda.md index f46c28bfa9..dfafda32ab 100644 --- a/src/foundation/transport-along-equivalences.lagda.md +++ b/src/foundation/transport-along-equivalences.lagda.md @@ -1,22 +1,28 @@ # Transport along equivalences ```agda -module foundation.transport-along-equivalences where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.transport-along-equivalences + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda -open import foundation.action-on-equivalences-functions -open import foundation.action-on-equivalences-type-families +open import foundation.action-on-equivalences-functions funext univalence +open import foundation.action-on-equivalences-type-families funext univalence open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalence-extensionality -open import foundation.equivalence-induction -open import foundation.equivalences -open import foundation.function-extensionality +open import foundation.equivalence-extensionality funext +open import foundation.equivalence-induction funext univalence +open import foundation.equivalences funext +open import foundation.function-extensionality funext open import foundation.transport-along-identifications -open import foundation.univalence +open import foundation.univalence funext univalence open import foundation.universe-levels open import foundation-core.commuting-triangles-of-maps diff --git a/src/foundation/transport-along-higher-identifications.lagda.md b/src/foundation/transport-along-higher-identifications.lagda.md index f031e7713c..cbb5a2e1a2 100644 --- a/src/foundation/transport-along-higher-identifications.lagda.md +++ b/src/foundation/transport-along-higher-identifications.lagda.md @@ -1,22 +1,26 @@ # Transport along higher identifications ```agda -module foundation.transport-along-higher-identifications where +open import foundation.function-extensionality-axiom + +module foundation.transport-along-higher-identifications + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-homotopies -open import foundation.commuting-squares-of-identifications -open import foundation.function-types -open import foundation.homotopies +open import foundation.commuting-squares-of-homotopies funext +open import foundation.commuting-squares-of-identifications funext +open import foundation.function-types funext +open import foundation.homotopies funext open import foundation.homotopy-algebra -open import foundation.path-algebra +open import foundation.path-algebra funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import foundation.whiskering-identifications-concatenation +open import foundation.whiskering-identifications-concatenation funext open import foundation-core.identity-types open import foundation-core.transport-along-identifications diff --git a/src/foundation/transport-along-homotopies.lagda.md b/src/foundation/transport-along-homotopies.lagda.md index 577c47c512..02d5ea845b 100644 --- a/src/foundation/transport-along-homotopies.lagda.md +++ b/src/foundation/transport-along-homotopies.lagda.md @@ -1,16 +1,20 @@ # Transport along homotopies ```agda -module foundation.transport-along-homotopies where +open import foundation.function-extensionality-axiom + +module foundation.transport-along-homotopies + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.function-extensionality -open import foundation.homotopy-induction -open import foundation.transport-along-higher-identifications +open import foundation.function-extensionality funext +open import foundation.homotopy-induction funext +open import foundation.transport-along-higher-identifications funext open import foundation.universe-levels open import foundation-core.homotopies diff --git a/src/foundation/transport-split-type-families.lagda.md b/src/foundation/transport-split-type-families.lagda.md index f4fc0dad2f..8dc37b381d 100644 --- a/src/foundation/transport-split-type-families.lagda.md +++ b/src/foundation/transport-split-type-families.lagda.md @@ -1,28 +1,26 @@ # Transport-split type families ```agda -module foundation.transport-split-type-families where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.transport-split-type-families + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda -open import elementary-number-theory.natural-numbers - -open import foundation.action-on-equivalences-functions -open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types -open import foundation.dependent-pair-types -open import foundation.equivalence-extensionality -open import foundation.equivalence-injective-type-families -open import foundation.equivalences -open import foundation.function-extensionality +open import foundation.equivalence-injective-type-families funext univalence +open import foundation.equivalences funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.iterated-dependent-product-types +open import foundation.iterated-dependent-product-types funext +open import foundation.telescopes open import foundation.transport-along-identifications -open import foundation.unit-type -open import foundation.univalent-type-families -open import foundation.universal-property-identity-systems +open import foundation.univalent-type-families funext univalence +open import foundation.universal-property-identity-systems funext open import foundation.universe-levels open import foundation-core.embeddings diff --git a/src/foundation/transposition-identifications-along-equivalences.lagda.md b/src/foundation/transposition-identifications-along-equivalences.lagda.md index ef7e0b1cc7..876d697580 100644 --- a/src/foundation/transposition-identifications-along-equivalences.lagda.md +++ b/src/foundation/transposition-identifications-along-equivalences.lagda.md @@ -1,22 +1,24 @@ # Transposing identifications along equivalences ```agda -module foundation.transposition-identifications-along-equivalences where +open import foundation.function-extensionality-axiom + +module foundation.transposition-identifications-along-equivalences + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-triangles-of-identifications -open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.commuting-triangles-of-identifications funext +open import foundation.identity-types funext open import foundation.universe-levels -open import foundation.whiskering-homotopies-composition -open import foundation.whiskering-identifications-concatenation open import foundation-core.equivalences open import foundation-core.homotopies +open import foundation-core.whiskering-identifications-concatenation ```
diff --git a/src/foundation/transposition-identifications-along-retractions.lagda.md b/src/foundation/transposition-identifications-along-retractions.lagda.md index 2dfe11e3cb..250d3ca130 100644 --- a/src/foundation/transposition-identifications-along-retractions.lagda.md +++ b/src/foundation/transposition-identifications-along-retractions.lagda.md @@ -1,7 +1,11 @@ # Transposing identifications along retractions ```agda -module foundation.transposition-identifications-along-retractions where +open import foundation.function-extensionality-axiom + +module foundation.transposition-identifications-along-retractions + (funext : function-extensionality) + where ```
@@ -9,7 +13,7 @@ module foundation.transposition-identifications-along-retractions where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-extensionality +open import foundation.function-extensionality funext open import foundation.universe-levels open import foundation-core.equivalences diff --git a/src/foundation/transposition-identifications-along-sections.lagda.md b/src/foundation/transposition-identifications-along-sections.lagda.md index 9cffc6452a..0156644e4f 100644 --- a/src/foundation/transposition-identifications-along-sections.lagda.md +++ b/src/foundation/transposition-identifications-along-sections.lagda.md @@ -1,7 +1,11 @@ # Transposing identifications along sections ```agda -module foundation.transposition-identifications-along-sections where +open import foundation.function-extensionality-axiom + +module foundation.transposition-identifications-along-sections + (funext : function-extensionality) + where ```
@@ -9,7 +13,7 @@ module foundation.transposition-identifications-along-sections where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-extensionality +open import foundation.function-extensionality funext open import foundation.universe-levels open import foundation-core.equivalences diff --git a/src/foundation/transposition-span-diagrams.lagda.md b/src/foundation/transposition-span-diagrams.lagda.md index 1d9df617ee..b487e8e6b7 100644 --- a/src/foundation/transposition-span-diagrams.lagda.md +++ b/src/foundation/transposition-span-diagrams.lagda.md @@ -1,7 +1,11 @@ # Transposition of span diagrams ```agda -module foundation.transposition-span-diagrams where +open import foundation.function-extensionality-axiom + +module foundation.transposition-span-diagrams + (funext : function-extensionality) + where ```
Imports @@ -9,7 +13,7 @@ module foundation.transposition-span-diagrams where ```agda open import foundation.dependent-pair-types open import foundation.opposite-spans -open import foundation.span-diagrams +open import foundation.span-diagrams funext open import foundation.spans open import foundation.universe-levels ``` diff --git a/src/foundation/trivial-relaxed-sigma-decompositions.lagda.md b/src/foundation/trivial-relaxed-sigma-decompositions.lagda.md index 8ab55c81ac..9081ed36c4 100644 --- a/src/foundation/trivial-relaxed-sigma-decompositions.lagda.md +++ b/src/foundation/trivial-relaxed-sigma-decompositions.lagda.md @@ -1,16 +1,24 @@ # Trivial relaxed Σ-decompositions ```agda -module foundation.trivial-relaxed-sigma-decompositions where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.trivial-relaxed-sigma-decompositions + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda -open import foundation.contractible-types +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.relaxed-sigma-decompositions -open import foundation.transposition-identifications-along-equivalences +open import foundation.dependent-products-contractible-types funext +open import foundation.raising-universe-levels-unit-type +open import foundation.relaxed-sigma-decompositions funext univalence +open import foundation.transposition-identifications-along-equivalences funext open import foundation.type-arithmetic-dependent-pair-types open import foundation.unit-type open import foundation.universe-levels @@ -20,7 +28,7 @@ open import foundation-core.equivalences open import foundation-core.function-types open import foundation-core.identity-types open import foundation-core.propositions -open import foundation-core.subtypes +open import foundation-core.subtypes funext ```
diff --git a/src/foundation/trivial-sigma-decompositions.lagda.md b/src/foundation/trivial-sigma-decompositions.lagda.md index e50fa85044..7bddf789c1 100644 --- a/src/foundation/trivial-sigma-decompositions.lagda.md +++ b/src/foundation/trivial-sigma-decompositions.lagda.md @@ -1,20 +1,30 @@ # Trivial Σ-decompositions ```agda -module foundation.trivial-sigma-decompositions where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.trivial-sigma-decompositions + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.contractible-types +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.functoriality-propositional-truncation -open import foundation.inhabited-types -open import foundation.sigma-decompositions -open import foundation.transposition-identifications-along-equivalences +open import foundation.dependent-products-contractible-types funext +open import foundation.functoriality-propositional-truncation funext univalence truncations +open import foundation.inhabited-types funext univalence truncations +open import foundation.raising-universe-levels-unit-type +open import foundation.sigma-decompositions funext univalence truncations +open import foundation.transposition-identifications-along-equivalences funext open import foundation.type-arithmetic-dependent-pair-types -open import foundation.type-arithmetic-empty-type +open import foundation.type-arithmetic-empty-type funext univalence truncations open import foundation.unit-type open import foundation.universe-levels @@ -24,7 +34,7 @@ open import foundation-core.equivalences open import foundation-core.function-types open import foundation-core.identity-types open import foundation-core.propositions -open import foundation-core.subtypes +open import foundation-core.subtypes funext ```
diff --git a/src/foundation/truncated-equality.lagda.md b/src/foundation/truncated-equality.lagda.md index c88cab61f7..0a85eb29d0 100644 --- a/src/foundation/truncated-equality.lagda.md +++ b/src/foundation/truncated-equality.lagda.md @@ -1,13 +1,21 @@ # Truncated equality ```agda -module foundation.truncated-equality where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.truncated-equality + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.truncations +open import foundation.truncations funext univalence truncations open import foundation.universe-levels open import foundation-core.identity-types diff --git a/src/foundation/truncated-maps.lagda.md b/src/foundation/truncated-maps.lagda.md index 5107b35a68..c517e5fe0b 100644 --- a/src/foundation/truncated-maps.lagda.md +++ b/src/foundation/truncated-maps.lagda.md @@ -1,22 +1,28 @@ # Truncated maps ```agda -module foundation.truncated-maps where +open import foundation.function-extensionality-axiom -open import foundation-core.truncated-maps public +module foundation.truncated-maps + (funext : function-extensionality) + where + +open import foundation.dependent-products-truncated-types funext public +open import foundation-core.truncated-maps funext public ```
Imports ```agda -open import foundation.cones-over-cospan-diagrams +open import foundation.cones-over-cospan-diagrams funext open import foundation.dependent-pair-types -open import foundation.functoriality-fibers-of-maps +open import foundation.dependent-products-propositions funext +open import foundation.functoriality-fibers-of-maps funext open import foundation.universe-levels open import foundation-core.fibers-of-maps open import foundation-core.propositions -open import foundation-core.pullbacks +open import foundation-core.pullbacks funext open import foundation-core.truncated-types open import foundation-core.truncation-levels ``` diff --git a/src/foundation/truncated-types.lagda.md b/src/foundation/truncated-types.lagda.md index d2248f9dab..412b68fc88 100644 --- a/src/foundation/truncated-types.lagda.md +++ b/src/foundation/truncated-types.lagda.md @@ -1,7 +1,13 @@ # Truncated types ```agda -module foundation.truncated-types where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.truncated-types + (funext : function-extensionality) + (univalence : univalence-axiom) + where open import foundation-core.truncated-types public ``` @@ -12,17 +18,18 @@ open import foundation-core.truncated-types public open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.logical-equivalences +open import foundation.dependent-products-truncated-types funext +open import foundation.equivalences funext +open import foundation.logical-equivalences funext open import foundation.subtype-identity-principle open import foundation.truncation-levels -open import foundation.univalence +open import foundation.univalence funext univalence open import foundation.universe-levels open import foundation-core.embeddings open import foundation-core.identity-types open import foundation-core.propositions -open import foundation-core.subtypes +open import foundation-core.subtypes funext open import foundation-core.torsorial-type-families ``` diff --git a/src/foundation/truncation-equivalences.lagda.md b/src/foundation/truncation-equivalences.lagda.md index 5462a0bf32..de282a6acd 100644 --- a/src/foundation/truncation-equivalences.lagda.md +++ b/src/foundation/truncation-equivalences.lagda.md @@ -1,26 +1,36 @@ # `k`-Equivalences ```agda -module foundation.truncation-equivalences where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.truncation-equivalences + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.commuting-squares-of-maps -open import foundation.connected-maps -open import foundation.connected-types -open import foundation.contractible-types +open import foundation.commuting-squares-of-maps funext univalence +open import foundation.connected-maps funext univalence truncations +open import foundation.connected-types funext univalence truncations +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.functoriality-truncation -open import foundation.identity-types -open import foundation.precomposition-functions-into-subuniverses -open import foundation.propositional-truncations -open import foundation.truncations +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-truncated-types funext +open import foundation.functoriality-truncation funext univalence truncations +open import foundation.identity-types funext +open import foundation.precomposition-functions-into-subuniverses funext +open import foundation.propositional-truncations funext univalence +open import foundation.truncations funext univalence truncations open import foundation.type-arithmetic-dependent-pair-types -open import foundation.universal-property-dependent-pair-types -open import foundation.universal-property-equivalences -open import foundation.universal-property-truncation +open import foundation.universal-property-dependent-pair-types funext +open import foundation.universal-property-equivalences funext +open import foundation.universal-property-truncation funext univalence truncations open import foundation.universe-levels open import foundation-core.contractible-maps diff --git a/src/foundation/truncation-images-of-maps.lagda.md b/src/foundation/truncation-images-of-maps.lagda.md index 2aa88a1be2..823c34236f 100644 --- a/src/foundation/truncation-images-of-maps.lagda.md +++ b/src/foundation/truncation-images-of-maps.lagda.md @@ -1,26 +1,34 @@ # Truncation images of maps ```agda -module foundation.truncation-images-of-maps where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.truncation-images-of-maps + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.connected-maps +open import foundation.connected-maps funext univalence truncations open import foundation.dependent-pair-types -open import foundation.fibers-of-maps -open import foundation.functoriality-truncation -open import foundation.identity-types -open import foundation.truncations +open import foundation.fibers-of-maps funext +open import foundation.functoriality-truncation funext univalence truncations +open import foundation.identity-types funext +open import foundation.truncations funext univalence truncations open import foundation.universe-levels open import foundation-core.equality-dependent-pair-types open import foundation-core.equivalences open import foundation-core.functoriality-dependent-pair-types open import foundation-core.transport-along-identifications -open import foundation-core.truncated-maps +open import foundation-core.truncated-maps funext open import foundation-core.truncation-levels ``` diff --git a/src/foundation/truncation-modalities.lagda.md b/src/foundation/truncation-modalities.lagda.md index 4c38c783fb..ff1673cf4d 100644 --- a/src/foundation/truncation-modalities.lagda.md +++ b/src/foundation/truncation-modalities.lagda.md @@ -1,20 +1,28 @@ # The truncation modalities ```agda -module foundation.truncation-modalities where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.truncation-modalities + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.truncations +open import foundation.truncations funext univalence truncations open import foundation.universe-levels open import foundation-core.function-types open import foundation-core.truncation-levels -open import orthogonal-factorization-systems.modal-operators -open import orthogonal-factorization-systems.uniquely-eliminating-modalities +open import orthogonal-factorization-systems.modal-operators funext univalence truncations +open import orthogonal-factorization-systems.uniquely-eliminating-modalities funext univalence truncations ```
diff --git a/src/foundation/truncations.lagda.md b/src/foundation/truncations.lagda.md index 9523e78045..48d57ab8cf 100644 --- a/src/foundation/truncations.lagda.md +++ b/src/foundation/truncations.lagda.md @@ -1,21 +1,29 @@ # Truncations ```agda -module foundation.truncations where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.truncations + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.contractible-types +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.function-extensionality -open import foundation.functoriality-dependent-function-types +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-truncated-types funext +open import foundation.function-extensionality funext +open import foundation.functoriality-dependent-function-types funext univalence open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types -open import foundation.truncated-types -open import foundation.universal-property-dependent-pair-types +open import foundation.identity-types funext +open import foundation.truncated-types funext univalence +open import foundation.universal-property-dependent-pair-types funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition @@ -29,7 +37,7 @@ open import foundation-core.homotopies open import foundation-core.propositions open import foundation-core.torsorial-type-families open import foundation-core.truncation-levels -open import foundation-core.universal-property-truncation +open import foundation-core.universal-property-truncation funext ```
diff --git a/src/foundation/tuples-of-types.lagda.md b/src/foundation/tuples-of-types.lagda.md index 49b8e03fc5..63a9a115b8 100644 --- a/src/foundation/tuples-of-types.lagda.md +++ b/src/foundation/tuples-of-types.lagda.md @@ -1,7 +1,15 @@ # Tuples of types ```agda -module foundation.tuples-of-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.tuples-of-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -11,7 +19,7 @@ open import elementary-number-theory.natural-numbers open import foundation.universe-levels -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/foundation/type-arithmetic-booleans.lagda.md b/src/foundation/type-arithmetic-booleans.lagda.md index 5d7dfaad12..0b455a3719 100644 --- a/src/foundation/type-arithmetic-booleans.lagda.md +++ b/src/foundation/type-arithmetic-booleans.lagda.md @@ -7,10 +7,10 @@ module foundation.type-arithmetic-booleans where
Imports ```agda -open import foundation.booleans open import foundation.dependent-pair-types open import foundation.universe-levels +open import foundation-core.booleans open import foundation-core.coproduct-types open import foundation-core.equivalences open import foundation-core.function-types diff --git a/src/foundation/type-arithmetic-coproduct-types.lagda.md b/src/foundation/type-arithmetic-coproduct-types.lagda.md index 4bfa836a20..223cdaeae6 100644 --- a/src/foundation/type-arithmetic-coproduct-types.lagda.md +++ b/src/foundation/type-arithmetic-coproduct-types.lagda.md @@ -1,15 +1,23 @@ # Type arithmetic for coproduct types ```agda -module foundation.type-arithmetic-coproduct-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.type-arithmetic-coproduct-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.coproduct-types +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equality-coproduct-types +open import foundation.equality-coproduct-types funext univalence truncations open import foundation.universe-levels open import foundation-core.cartesian-product-types diff --git a/src/foundation/type-arithmetic-dependent-function-types.lagda.md b/src/foundation/type-arithmetic-dependent-function-types.lagda.md index 27533716f7..3e3b8d70b9 100644 --- a/src/foundation/type-arithmetic-dependent-function-types.lagda.md +++ b/src/foundation/type-arithmetic-dependent-function-types.lagda.md @@ -1,7 +1,13 @@ # Type arithmetic with dependent function types ```agda -module foundation.type-arithmetic-dependent-function-types where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.type-arithmetic-dependent-function-types + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports @@ -9,15 +15,15 @@ module foundation.type-arithmetic-dependent-function-types where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.functoriality-dependent-function-types -open import foundation.type-arithmetic-unit-type +open import foundation.dependent-products-contractible-types funext +open import foundation.functoriality-dependent-function-types funext univalence +open import foundation.type-arithmetic-unit-type funext open import foundation.unit-type open import foundation.universe-levels open import foundation-core.contractible-types open import foundation-core.equivalences open import foundation-core.homotopies -open import foundation-core.univalence ```
diff --git a/src/foundation/type-arithmetic-empty-type.lagda.md b/src/foundation/type-arithmetic-empty-type.lagda.md index 3e65340797..8721e8f3ba 100644 --- a/src/foundation/type-arithmetic-empty-type.lagda.md +++ b/src/foundation/type-arithmetic-empty-type.lagda.md @@ -1,13 +1,21 @@ # Type arithmetic with the empty type ```agda -module foundation.type-arithmetic-empty-type where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.type-arithmetic-empty-type + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.coproduct-types +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types open import foundation.universe-levels diff --git a/src/foundation/type-arithmetic-standard-pullbacks.lagda.md b/src/foundation/type-arithmetic-standard-pullbacks.lagda.md index 09335074fa..8e11e03bf1 100644 --- a/src/foundation/type-arithmetic-standard-pullbacks.lagda.md +++ b/src/foundation/type-arithmetic-standard-pullbacks.lagda.md @@ -1,17 +1,21 @@ # Type arithmetic with standard pullbacks ```agda -module foundation.type-arithmetic-standard-pullbacks where +open import foundation.function-extensionality-axiom + +module foundation.type-arithmetic-standard-pullbacks + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cones-over-cospan-diagrams +open import foundation.cones-over-cospan-diagrams funext open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types -open import foundation.standard-pullbacks -open import foundation.standard-ternary-pullbacks +open import foundation.equality-dependent-pair-types funext +open import foundation.standard-pullbacks funext +open import foundation.standard-ternary-pullbacks funext open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels diff --git a/src/foundation/type-arithmetic-unit-type.lagda.md b/src/foundation/type-arithmetic-unit-type.lagda.md index 7f3e6fc73e..d17a84dfad 100644 --- a/src/foundation/type-arithmetic-unit-type.lagda.md +++ b/src/foundation/type-arithmetic-unit-type.lagda.md @@ -1,14 +1,18 @@ # Type arithmetic with the unit type ```agda -module foundation.type-arithmetic-unit-type where +open import foundation.function-extensionality-axiom + +module foundation.type-arithmetic-unit-type + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-extensionality +open import foundation.dependent-products-contractible-types funext open import foundation.unit-type open import foundation.universe-levels @@ -16,7 +20,6 @@ open import foundation-core.cartesian-product-types open import foundation-core.equivalences open import foundation-core.function-types open import foundation-core.homotopies -open import foundation-core.identity-types open import foundation-core.retractions open import foundation-core.sections ``` diff --git a/src/foundation/type-duality.lagda.md b/src/foundation/type-duality.lagda.md index c2beea330e..bc99a6053d 100644 --- a/src/foundation/type-duality.lagda.md +++ b/src/foundation/type-duality.lagda.md @@ -1,7 +1,15 @@ # Type duality ```agda -module foundation.type-duality where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.type-duality + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,15 +17,16 @@ module foundation.type-duality where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality +open import foundation.equivalences funext +open import foundation.function-extensionality funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.locally-small-types -open import foundation.slice +open import foundation.locally-small-types funext univalence truncations +open import foundation.raising-universe-levels-unit-type +open import foundation.slice funext univalence open import foundation.type-arithmetic-dependent-pair-types open import foundation.unit-type -open import foundation.univalence -open import foundation.universal-property-equivalences +open import foundation.univalence funext univalence +open import foundation.universal-property-equivalences funext open import foundation.universe-levels open import foundation-core.contractible-maps @@ -25,15 +34,15 @@ open import foundation-core.contractible-types open import foundation-core.embeddings open import foundation-core.fibers-of-maps open import foundation-core.function-types -open import foundation-core.functoriality-dependent-function-types +open import foundation-core.functoriality-dependent-function-types funext open import foundation-core.functoriality-dependent-pair-types open import foundation-core.homotopies open import foundation-core.identity-types open import foundation-core.injective-maps -open import foundation-core.small-types +open import foundation-core.small-types funext univalence truncations open import foundation-core.torsorial-type-families -open import trees.polynomial-endofunctors +open import trees.polynomial-endofunctors funext univalence ```
diff --git a/src/foundation/type-theoretic-principle-of-choice.lagda.md b/src/foundation/type-theoretic-principle-of-choice.lagda.md index 984e3fd557..e27be4d1ed 100644 --- a/src/foundation/type-theoretic-principle-of-choice.lagda.md +++ b/src/foundation/type-theoretic-principle-of-choice.lagda.md @@ -1,7 +1,11 @@ # The type theoretic principle of choice ```agda -module foundation.type-theoretic-principle-of-choice where +open import foundation.function-extensionality-axiom + +module foundation.type-theoretic-principle-of-choice + (funext : function-extensionality) + where open import foundation-core.type-theoretic-principle-of-choice public ``` @@ -10,7 +14,7 @@ open import foundation-core.type-theoretic-principle-of-choice public ```agda open import foundation.dependent-pair-types -open import foundation.function-extensionality +open import foundation.function-extensionality funext open import foundation.implicit-function-types open import foundation.structure-identity-principle open import foundation.universe-levels diff --git a/src/foundation/uniformly-decidable-type-families.lagda.md b/src/foundation/uniformly-decidable-type-families.lagda.md index 01904ea182..831176b0ac 100644 --- a/src/foundation/uniformly-decidable-type-families.lagda.md +++ b/src/foundation/uniformly-decidable-type-families.lagda.md @@ -1,24 +1,35 @@ # Uniformly decidable type families ```agda -module foundation.uniformly-decidable-type-families where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.uniformly-decidable-type-families + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.contractible-types -open import foundation.coproduct-types -open import foundation.decidable-types +open import foundation.contractible-types funext univalence +open import foundation.coproduct-types funext univalence truncations +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equality-coproduct-types -open import foundation.inhabited-types -open import foundation.negation -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.truncated-types +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.dependent-products-truncated-types funext +open import foundation.equality-coproduct-types funext univalence truncations +open import foundation.inhabited-types funext univalence truncations +open import foundation.negation funext +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence +open import foundation.truncated-types funext univalence open import foundation.truncation-levels -open import foundation.type-arithmetic-empty-type +open import foundation.type-arithmetic-empty-type funext univalence truncations open import foundation.universe-levels open import foundation-core.cartesian-product-types diff --git a/src/foundation/unions-subtypes.lagda.md b/src/foundation/unions-subtypes.lagda.md index a3ae84790a..f27c74586f 100644 --- a/src/foundation/unions-subtypes.lagda.md +++ b/src/foundation/unions-subtypes.lagda.md @@ -1,27 +1,35 @@ # Unions of subtypes ```agda -module foundation.unions-subtypes where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.unions-subtypes + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.decidable-subtypes +open import foundation.decidable-subtypes funext univalence truncations open import foundation.dependent-pair-types -open import foundation.disjunction -open import foundation.large-locale-of-subtypes -open import foundation.powersets -open import foundation.propositional-truncations +open import foundation.disjunction funext univalence truncations +open import foundation.large-locale-of-subtypes funext univalence truncations +open import foundation.powersets funext univalence truncations +open import foundation.propositional-truncations funext univalence open import foundation.universe-levels -open import foundation-core.subtypes +open import foundation-core.subtypes funext -open import logic.de-morgan-propositions -open import logic.de-morgan-subtypes -open import logic.double-negation-stable-subtypes +open import logic.de-morgan-propositions funext univalence truncations +open import logic.de-morgan-subtypes funext univalence truncations +open import logic.double-negation-stable-subtypes funext univalence truncations -open import order-theory.least-upper-bounds-large-posets +open import order-theory.least-upper-bounds-large-posets funext univalence truncations ```
diff --git a/src/foundation/uniqueness-image.lagda.md b/src/foundation/uniqueness-image.lagda.md index 4711b5a4d1..a114abda4d 100644 --- a/src/foundation/uniqueness-image.lagda.md +++ b/src/foundation/uniqueness-image.lagda.md @@ -1,18 +1,26 @@ # Uniqueness of the image of a map ```agda -module foundation.uniqueness-image where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.uniqueness-image + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.images -open import foundation.slice +open import foundation.equivalences funext +open import foundation.images funext univalence truncations +open import foundation.slice funext univalence open import foundation.type-arithmetic-dependent-pair-types -open import foundation.universal-property-image +open import foundation.universal-property-image funext univalence truncations open import foundation.universe-levels open import foundation.whiskering-homotopies-composition diff --git a/src/foundation/uniqueness-quantification.lagda.md b/src/foundation/uniqueness-quantification.lagda.md index dbbce2a023..a915368edd 100644 --- a/src/foundation/uniqueness-quantification.lagda.md +++ b/src/foundation/uniqueness-quantification.lagda.md @@ -1,14 +1,22 @@ # Uniqueness quantification ```agda -module foundation.uniqueness-quantification where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.uniqueness-quantification + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext univalence truncations open import foundation.universe-levels open import foundation-core.contractible-types diff --git a/src/foundation/uniqueness-set-quotients.lagda.md b/src/foundation/uniqueness-set-quotients.lagda.md index 5fd4913def..5e73b75243 100644 --- a/src/foundation/uniqueness-set-quotients.lagda.md +++ b/src/foundation/uniqueness-set-quotients.lagda.md @@ -1,7 +1,15 @@ # The uniqueness of set quotients ```agda -module foundation.uniqueness-set-quotients where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.uniqueness-set-quotients + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,18 +17,17 @@ module foundation.uniqueness-set-quotients where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.reflecting-maps-equivalence-relations -open import foundation.sets +open import foundation.equivalences funext +open import foundation.reflecting-maps-equivalence-relations funext univalence truncations +open import foundation.sets funext univalence open import foundation.subtype-identity-principle -open import foundation.universal-property-equivalences -open import foundation.universal-property-set-quotients +open import foundation.universal-property-equivalences funext +open import foundation.universal-property-set-quotients funext univalence truncations open import foundation.universe-levels open import foundation.whiskering-homotopies-composition open import foundation-core.contractible-types -open import foundation-core.equivalence-relations +open import foundation-core.equivalence-relations funext univalence truncations open import foundation-core.function-types open import foundation-core.homotopies open import foundation-core.identity-types diff --git a/src/foundation/uniqueness-set-truncations.lagda.md b/src/foundation/uniqueness-set-truncations.lagda.md index 604c442e9f..b292c73586 100644 --- a/src/foundation/uniqueness-set-truncations.lagda.md +++ b/src/foundation/uniqueness-set-truncations.lagda.md @@ -1,17 +1,24 @@ # Uniqueness of set truncations ```agda -module foundation.uniqueness-set-truncations where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.uniqueness-set-truncations + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.mere-equality -open import foundation.sets -open import foundation.uniqueness-set-quotients -open import foundation.universal-property-set-truncation +open import foundation.mere-equality funext univalence truncations +open import foundation.sets funext univalence +open import foundation.uniqueness-set-quotients funext univalence truncations +open import foundation.universal-property-set-truncation funext univalence truncations open import foundation.universe-levels open import foundation-core.contractible-types diff --git a/src/foundation/uniqueness-truncation.lagda.md b/src/foundation/uniqueness-truncation.lagda.md index 25971b85f3..2a99c689bf 100644 --- a/src/foundation/uniqueness-truncation.lagda.md +++ b/src/foundation/uniqueness-truncation.lagda.md @@ -1,12 +1,17 @@ # Uniqueness of the truncations ```agda -module foundation.uniqueness-truncation where +open import foundation.function-extensionality-axiom + +module foundation.uniqueness-truncation + (funext : function-extensionality) + where ```
Imports ```agda +open import foundation.dependent-products-truncated-types funext open import foundation.universe-levels open import foundation-core.function-types diff --git a/src/foundation/unit-type.lagda.md b/src/foundation/unit-type.lagda.md index d1246282e0..87b935b6db 100644 --- a/src/foundation/unit-type.lagda.md +++ b/src/foundation/unit-type.lagda.md @@ -7,14 +7,12 @@ module foundation.unit-type where
Imports ```agda -open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.diagonal-maps-of-types -open import foundation.raising-universe-levels open import foundation.universe-levels open import foundation-core.constant-maps open import foundation-core.contractible-types +open import foundation-core.diagonal-maps-of-types open import foundation-core.equivalences open import foundation-core.homotopies open import foundation-core.identity-types @@ -72,25 +70,6 @@ module _ point = diagonal-exponential A unit ``` -### Raising the universe level of the unit type - -```agda -raise-unit : (l : Level) → UU l -raise-unit l = raise l unit - -raise-star : {l : Level} → raise l unit -raise-star = map-raise star - -raise-terminal-map : {l1 l2 : Level} (A : UU l1) → A → raise-unit l2 -raise-terminal-map {l2 = l2} A = const A raise-star - -compute-raise-unit : (l : Level) → unit ≃ raise-unit l -compute-raise-unit l = compute-raise l unit - -inv-compute-raise-unit : (l : Level) → raise-unit l ≃ unit -inv-compute-raise-unit l = inv-compute-raise l unit -``` - ## Properties ### The unit type is contractible @@ -100,11 +79,6 @@ abstract is-contr-unit : is-contr unit pr1 is-contr-unit = star pr2 is-contr-unit _ = refl - -abstract - is-contr-raise-unit : {l1 : Level} → is-contr (raise-unit l1) - is-contr-raise-unit {l1} = - is-contr-equiv' unit (compute-raise l1 unit) is-contr-unit ``` ### Any contractible type is equivalent to the unit type @@ -135,42 +109,6 @@ module _ is-contr-equiv-unit' e = (map-equiv e star , is-section-map-inv-equiv e) ``` -### Any contractible type is equivalent to the raised unit type - -```agda -module _ - {l1 l2 : Level} {A : UU l1} - where - - is-equiv-raise-terminal-map-is-contr : - is-contr A → is-equiv (raise-terminal-map {l2 = l2} A) - is-equiv-raise-terminal-map-is-contr H = - is-equiv-is-invertible - ( λ _ → center H) - ( λ where (map-raise x) → refl) - ( contraction H) - - equiv-raise-unit-is-contr : is-contr A → A ≃ raise-unit l2 - equiv-raise-unit-is-contr H = - raise-terminal-map A , is-equiv-raise-terminal-map-is-contr H - - is-contr-retraction-raise-terminal-map : - retraction (raise-terminal-map {l2 = l2} A) → is-contr A - is-contr-retraction-raise-terminal-map (h , H) = h raise-star , H - - is-contr-is-equiv-raise-terminal-map : - is-equiv (raise-terminal-map {l2 = l2} A) → is-contr A - is-contr-is-equiv-raise-terminal-map H = - is-contr-retraction-raise-terminal-map (retraction-is-equiv H) - - is-contr-equiv-raise-unit : A ≃ raise-unit l2 → is-contr A - is-contr-equiv-raise-unit e = - ( map-inv-equiv e raise-star) , - ( λ x → - ap (map-inv-equiv e) (eq-is-contr is-contr-raise-unit) ∙ - is-retraction-map-inv-equiv e x) -``` - ### The unit type is a proposition ```agda @@ -180,13 +118,6 @@ abstract unit-Prop : Prop lzero unit-Prop = unit , is-prop-unit - -abstract - is-prop-raise-unit : {l1 : Level} → is-prop (raise-unit l1) - is-prop-raise-unit {l1} = is-prop-equiv' (compute-raise l1 unit) is-prop-unit - -raise-unit-Prop : (l1 : Level) → Prop l1 -raise-unit-Prop l1 = raise-unit l1 , is-prop-raise-unit ``` ### The unit type is a set @@ -198,13 +129,6 @@ abstract unit-Set : Set lzero unit-Set = unit , is-set-unit - -abstract - is-set-raise-unit : {l1 : Level} → is-set (raise-unit l1) - is-set-raise-unit = is-trunc-succ-is-trunc neg-one-𝕋 is-prop-raise-unit - -raise-unit-Set : (l1 : Level) → Set l1 -raise-unit-Set l1 = raise-unit l1 , is-set-raise-unit ``` ### All parallel maps into `unit` are equal diff --git a/src/foundation/unital-binary-operations.lagda.md b/src/foundation/unital-binary-operations.lagda.md index 5c343797cf..ae3ffd6106 100644 --- a/src/foundation/unital-binary-operations.lagda.md +++ b/src/foundation/unital-binary-operations.lagda.md @@ -11,11 +11,11 @@ open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import foundation.whiskering-identifications-concatenation open import foundation-core.cartesian-product-types open import foundation-core.homotopies open import foundation-core.identity-types +open import foundation-core.whiskering-identifications-concatenation ```
diff --git a/src/foundation/univalence-implies-function-extensionality.lagda.md b/src/foundation/univalence-implies-function-extensionality.lagda.md index 8845653a49..0a2bb88b5e 100644 --- a/src/foundation/univalence-implies-function-extensionality.lagda.md +++ b/src/foundation/univalence-implies-function-extensionality.lagda.md @@ -1,19 +1,26 @@ # The univalence axiom implies function extensionality ```agda -module foundation.univalence-implies-function-extensionality where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.univalence-implies-function-extensionality + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalence-induction -open import foundation.function-extensionality -open import foundation.postcomposition-functions +open import foundation.equivalence-induction funext univalence +open import foundation.postcomposition-functions funext open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels -open import foundation.weak-function-extensionality +open import foundation.weak-function-extensionality funext univalence truncations open import foundation-core.contractible-maps open import foundation-core.contractible-types diff --git a/src/foundation/univalence.lagda.md b/src/foundation/univalence.lagda.md index 7b5a2bf621..0c3349139a 100644 --- a/src/foundation/univalence.lagda.md +++ b/src/foundation/univalence.lagda.md @@ -1,7 +1,11 @@ # The univalence axiom ```agda -module foundation.univalence where +open import foundation.function-extensionality-axiom + +module foundation.univalence + (funext : function-extensionality) + where open import foundation-core.univalence public ``` @@ -11,8 +15,8 @@ open import foundation-core.univalence public ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types -open import foundation.equivalences +open import foundation.equality-dependent-function-types funext +open import foundation.equivalences funext open import foundation.fundamental-theorem-of-identity-types open import foundation.universe-levels diff --git a/src/foundation/univalent-type-families.lagda.md b/src/foundation/univalent-type-families.lagda.md index 9a7c109a9a..e030cdbc54 100644 --- a/src/foundation/univalent-type-families.lagda.md +++ b/src/foundation/univalent-type-families.lagda.md @@ -1,7 +1,13 @@ # Univalent type families ```agda -module foundation.univalent-type-families where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.univalent-type-families + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports @@ -9,16 +15,18 @@ module foundation.univalent-type-families where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types -open import foundation.equivalences +open import foundation.dependent-products-propositions funext +open import foundation.equality-dependent-pair-types funext +open import foundation.equivalences funext open import foundation.fundamental-theorem-of-identity-types open import foundation.identity-systems -open import foundation.iterated-dependent-product-types -open import foundation.propositions -open import foundation.subuniverses +open import foundation.iterated-dependent-product-types funext +open import foundation.propositions funext univalence +open import foundation.subuniverses funext univalence +open import foundation.telescopes open import foundation.transport-along-identifications -open import foundation.univalence -open import foundation.universal-property-identity-systems +open import foundation.univalence funext univalence +open import foundation.universal-property-identity-systems funext open import foundation.universe-levels open import foundation-core.embeddings diff --git a/src/foundation/universal-property-booleans.lagda.md b/src/foundation/universal-property-booleans.lagda.md index b976f49d78..ca8acad8e1 100644 --- a/src/foundation/universal-property-booleans.lagda.md +++ b/src/foundation/universal-property-booleans.lagda.md @@ -1,18 +1,22 @@ # The universal property of booleans ```agda -module foundation.universal-property-booleans where +open import foundation.function-extensionality-axiom + +module foundation.universal-property-booleans + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.booleans open import foundation.dependent-pair-types open import foundation.equality-cartesian-product-types -open import foundation.function-extensionality +open import foundation.function-extensionality funext open import foundation.universe-levels +open import foundation-core.booleans open import foundation-core.cartesian-product-types open import foundation-core.equivalences open import foundation-core.function-types diff --git a/src/foundation/universal-property-cartesian-product-types.lagda.md b/src/foundation/universal-property-cartesian-product-types.lagda.md index c2053eae40..7c129890da 100644 --- a/src/foundation/universal-property-cartesian-product-types.lagda.md +++ b/src/foundation/universal-property-cartesian-product-types.lagda.md @@ -1,18 +1,22 @@ # The universal properties of cartesian product types ```agda -module foundation.universal-property-cartesian-product-types where +open import foundation.function-extensionality-axiom + +module foundation.universal-property-cartesian-product-types + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cones-over-cospan-diagrams +open import foundation.cones-over-cospan-diagrams funext open import foundation.dependent-pair-types -open import foundation.logical-equivalences -open import foundation.standard-pullbacks +open import foundation.logical-equivalences funext +open import foundation.standard-pullbacks funext open import foundation.unit-type -open import foundation.universal-property-dependent-pair-types +open import foundation.universal-property-dependent-pair-types funext open import foundation.universe-levels open import foundation-core.cartesian-product-types @@ -21,10 +25,10 @@ open import foundation-core.equivalences open import foundation-core.function-types open import foundation-core.homotopies open import foundation-core.identity-types -open import foundation-core.pullbacks +open import foundation-core.pullbacks funext open import foundation-core.retractions open import foundation-core.sections -open import foundation-core.universal-property-pullbacks +open import foundation-core.universal-property-pullbacks funext ```
diff --git a/src/foundation/universal-property-contractible-types.lagda.md b/src/foundation/universal-property-contractible-types.lagda.md index e581cf7ee1..b34656cced 100644 --- a/src/foundation/universal-property-contractible-types.lagda.md +++ b/src/foundation/universal-property-contractible-types.lagda.md @@ -1,7 +1,11 @@ # Universal property of contractible types ```agda -module foundation.universal-property-contractible-types where +open import foundation.function-extensionality-axiom + +module foundation.universal-property-contractible-types + (funext : function-extensionality) + where ```
Imports @@ -9,7 +13,7 @@ module foundation.universal-property-contractible-types where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-extensionality +open import foundation.function-extensionality funext open import foundation.singleton-induction open import foundation.universe-levels diff --git a/src/foundation/universal-property-coproduct-types.lagda.md b/src/foundation/universal-property-coproduct-types.lagda.md index 893e864163..7dab3fbff8 100644 --- a/src/foundation/universal-property-coproduct-types.lagda.md +++ b/src/foundation/universal-property-coproduct-types.lagda.md @@ -1,7 +1,11 @@ # The universal property of coproduct types ```agda -module foundation.universal-property-coproduct-types where +open import foundation.function-extensionality-axiom + +module foundation.universal-property-coproduct-types + (funext : function-extensionality) + where ```
Imports @@ -9,8 +13,8 @@ module foundation.universal-property-coproduct-types where ```agda open import foundation.dependent-pair-types open import foundation.equality-cartesian-product-types -open import foundation.function-extensionality -open import foundation.universal-property-equivalences +open import foundation.function-extensionality funext +open import foundation.universal-property-equivalences funext open import foundation.universe-levels open import foundation-core.cartesian-product-types diff --git a/src/foundation/universal-property-dependent-function-types.lagda.md b/src/foundation/universal-property-dependent-function-types.lagda.md index 9f7b72e52a..3872b9df61 100644 --- a/src/foundation/universal-property-dependent-function-types.lagda.md +++ b/src/foundation/universal-property-dependent-function-types.lagda.md @@ -1,23 +1,27 @@ # The universal property of dependent function types ```agda -module foundation.universal-property-dependent-function-types where +open import foundation.function-extensionality-axiom + +module foundation.universal-property-dependent-function-types + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-extensionality -open import foundation.identity-types +open import foundation.function-extensionality funext +open import foundation.identity-types funext open import foundation.spans-families-of-types -open import foundation.terminal-spans-families-of-types +open import foundation.terminal-spans-families-of-types funext open import foundation.universe-levels open import foundation-core.contractible-maps open import foundation-core.contractible-types open import foundation-core.equivalences -open import foundation-core.functoriality-dependent-function-types +open import foundation-core.functoriality-dependent-function-types funext open import foundation-core.functoriality-dependent-pair-types ``` diff --git a/src/foundation/universal-property-dependent-pair-types.lagda.md b/src/foundation/universal-property-dependent-pair-types.lagda.md index 54b12615b2..6f992d2697 100644 --- a/src/foundation/universal-property-dependent-pair-types.lagda.md +++ b/src/foundation/universal-property-dependent-pair-types.lagda.md @@ -1,22 +1,24 @@ # The universal property of dependent pair types ```agda -module foundation.universal-property-dependent-pair-types where +open import foundation.function-extensionality-axiom + +module foundation.universal-property-dependent-pair-types + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-extensionality +open import foundation.function-extensionality funext open import foundation.universe-levels open import foundation-core.equivalences open import foundation-core.functoriality-dependent-pair-types open import foundation-core.homotopies open import foundation-core.identity-types -open import foundation-core.retractions -open import foundation-core.sections ```
diff --git a/src/foundation/universal-property-empty-type.lagda.md b/src/foundation/universal-property-empty-type.lagda.md index c3fe4f7374..d02dd2cea3 100644 --- a/src/foundation/universal-property-empty-type.lagda.md +++ b/src/foundation/universal-property-empty-type.lagda.md @@ -1,15 +1,19 @@ # The universal property of the empty type ```agda -module foundation.universal-property-empty-type where +open import foundation.function-extensionality-axiom + +module foundation.universal-property-empty-type + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-extensionality -open import foundation.universal-property-equivalences +open import foundation.function-extensionality funext +open import foundation.universal-property-equivalences funext open import foundation.universe-levels open import foundation-core.contractible-types diff --git a/src/foundation/universal-property-equivalences.lagda.md b/src/foundation/universal-property-equivalences.lagda.md index 4f4300ef98..b4329e4480 100644 --- a/src/foundation/universal-property-equivalences.lagda.md +++ b/src/foundation/universal-property-equivalences.lagda.md @@ -1,15 +1,19 @@ # The universal property of equivalences ```agda -module foundation.universal-property-equivalences where +open import foundation.function-extensionality-axiom + +module foundation.universal-property-equivalences + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.dependent-universal-property-equivalences -open import foundation.precomposition-functions-into-subuniverses +open import foundation.dependent-universal-property-equivalences funext +open import foundation.precomposition-functions-into-subuniverses funext open import foundation.universe-levels open import foundation-core.equivalences diff --git a/src/foundation/universal-property-family-of-fibers-of-maps.lagda.md b/src/foundation/universal-property-family-of-fibers-of-maps.lagda.md index a9d2691df4..b1db3ccaf4 100644 --- a/src/foundation/universal-property-family-of-fibers-of-maps.lagda.md +++ b/src/foundation/universal-property-family-of-fibers-of-maps.lagda.md @@ -1,7 +1,11 @@ # The universal property of the family of fibers of maps ```agda -module foundation.universal-property-family-of-fibers-of-maps where +open import foundation.function-extensionality-axiom + +module foundation.universal-property-family-of-fibers-of-maps + (funext : function-extensionality) + where ```
Imports @@ -9,19 +13,18 @@ module foundation.universal-property-family-of-fibers-of-maps where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.diagonal-maps-of-types -open import foundation.families-of-equivalences -open import foundation.function-extensionality +open import foundation.families-of-equivalences funext +open import foundation.function-extensionality funext open import foundation.subtype-identity-principle open import foundation.universe-levels -open import foundation-core.constant-maps open import foundation-core.contractible-maps open import foundation-core.contractible-types +open import foundation-core.diagonal-maps-of-types open import foundation-core.equivalences open import foundation-core.fibers-of-maps open import foundation-core.function-types -open import foundation-core.functoriality-dependent-function-types +open import foundation-core.functoriality-dependent-function-types funext open import foundation-core.functoriality-dependent-pair-types open import foundation-core.homotopies open import foundation-core.identity-types @@ -29,8 +32,8 @@ open import foundation-core.precomposition-dependent-functions open import foundation-core.retractions open import foundation-core.sections -open import orthogonal-factorization-systems.extensions-double-lifts-families-of-elements -open import orthogonal-factorization-systems.lifts-families-of-elements +open import orthogonal-factorization-systems.extensions-double-lifts-families-of-elements funext +open import orthogonal-factorization-systems.lifts-families-of-elements funext ```
diff --git a/src/foundation/universal-property-fiber-products.lagda.md b/src/foundation/universal-property-fiber-products.lagda.md index 9c0b864ad8..0bce4552ef 100644 --- a/src/foundation/universal-property-fiber-products.lagda.md +++ b/src/foundation/universal-property-fiber-products.lagda.md @@ -1,16 +1,20 @@ # The universal property of fiber products ```agda -module foundation.universal-property-fiber-products where +open import foundation.function-extensionality-axiom + +module foundation.universal-property-fiber-products + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cones-over-cospan-diagrams +open import foundation.cones-over-cospan-diagrams funext open import foundation.dependent-pair-types open import foundation.equality-cartesian-product-types -open import foundation.standard-pullbacks +open import foundation.standard-pullbacks funext open import foundation.universe-levels open import foundation-core.cartesian-product-types @@ -21,8 +25,8 @@ open import foundation-core.function-types open import foundation-core.functoriality-dependent-pair-types open import foundation-core.homotopies open import foundation-core.identity-types -open import foundation-core.pullbacks -open import foundation-core.universal-property-pullbacks +open import foundation-core.pullbacks funext +open import foundation-core.universal-property-pullbacks funext ```
diff --git a/src/foundation/universal-property-identity-systems.lagda.md b/src/foundation/universal-property-identity-systems.lagda.md index a29595fa9d..094de014b1 100644 --- a/src/foundation/universal-property-identity-systems.lagda.md +++ b/src/foundation/universal-property-identity-systems.lagda.md @@ -1,7 +1,11 @@ # The universal property of identity systems ```agda -module foundation.universal-property-identity-systems where +open import foundation.function-extensionality-axiom + +module foundation.universal-property-identity-systems + (funext : function-extensionality) + where ```
Imports @@ -9,11 +13,10 @@ module foundation.universal-property-identity-systems where ```agda open import foundation.dependent-pair-types open import foundation.identity-systems -open import foundation.universal-property-contractible-types -open import foundation.universal-property-dependent-pair-types +open import foundation.universal-property-contractible-types funext +open import foundation.universal-property-dependent-pair-types funext open import foundation.universe-levels -open import foundation-core.contractible-types open import foundation-core.equivalences open import foundation-core.identity-types open import foundation-core.torsorial-type-families diff --git a/src/foundation/universal-property-identity-types.lagda.md b/src/foundation/universal-property-identity-types.lagda.md index 1412af1bae..e2073089c1 100644 --- a/src/foundation/universal-property-identity-types.lagda.md +++ b/src/foundation/universal-property-identity-types.lagda.md @@ -1,7 +1,15 @@ # The universal property of identity types ```agda -module foundation.universal-property-identity-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.universal-property-identity-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,17 +17,18 @@ module foundation.universal-property-identity-types where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.dependent-universal-property-equivalences -open import foundation.embeddings -open import foundation.equivalences -open import foundation.full-subtypes -open import foundation.function-extensionality -open import foundation.functoriality-dependent-function-types +open import foundation.dependent-products-propositions funext +open import foundation.dependent-universal-property-equivalences funext +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.full-subtypes funext univalence truncations +open import foundation.function-extensionality funext +open import foundation.functoriality-dependent-function-types funext univalence open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.preunivalence -open import foundation.univalence +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.preunivalence funext univalence +open import foundation.univalence funext univalence open import foundation.universe-levels open import foundation-core.contractible-maps diff --git a/src/foundation/universal-property-image.lagda.md b/src/foundation/universal-property-image.lagda.md index d3ce89ffd0..ba9095b4ea 100644 --- a/src/foundation/universal-property-image.lagda.md +++ b/src/foundation/universal-property-image.lagda.md @@ -1,21 +1,29 @@ # The universal property of the image of a map ```agda -module foundation.universal-property-image where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.universal-property-image + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.images -open import foundation.logical-equivalences -open import foundation.propositional-truncations -open import foundation.slice -open import foundation.surjective-maps +open import foundation.embeddings funext +open import foundation.images funext univalence truncations +open import foundation.logical-equivalences funext +open import foundation.propositional-truncations funext univalence +open import foundation.slice funext univalence +open import foundation.surjective-maps funext univalence truncations open import foundation.transport-along-identifications -open import foundation.universal-property-family-of-fibers-of-maps +open import foundation.universal-property-family-of-fibers-of-maps funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition @@ -24,7 +32,7 @@ open import foundation-core.contractible-types open import foundation-core.equivalences open import foundation-core.fibers-of-maps open import foundation-core.function-types -open import foundation-core.functoriality-dependent-function-types +open import foundation-core.functoriality-dependent-function-types funext open import foundation-core.functoriality-dependent-pair-types open import foundation-core.homotopies open import foundation-core.identity-types @@ -32,7 +40,7 @@ open import foundation-core.injective-maps open import foundation-core.propositional-maps open import foundation-core.propositions open import foundation-core.sections -open import foundation-core.subtypes +open import foundation-core.subtypes funext ```
diff --git a/src/foundation/universal-property-maybe.lagda.md b/src/foundation/universal-property-maybe.lagda.md index 0c8afea5e1..0f2d7a7988 100644 --- a/src/foundation/universal-property-maybe.lagda.md +++ b/src/foundation/universal-property-maybe.lagda.md @@ -1,15 +1,18 @@ # The universal property of the maybe monad ```agda -module foundation.universal-property-maybe where +open import foundation.function-extensionality-axiom + +module foundation.universal-property-maybe + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-extensionality -open import foundation.maybe +open import foundation.function-extensionality funext open import foundation.universe-levels open import foundation-core.cartesian-product-types @@ -18,6 +21,7 @@ open import foundation-core.equivalences open import foundation-core.function-types open import foundation-core.homotopies open import foundation-core.identity-types +open import foundation-core.maybe ```
diff --git a/src/foundation/universal-property-propositional-truncation-into-sets.lagda.md b/src/foundation/universal-property-propositional-truncation-into-sets.lagda.md index 124181f37d..35afcfebc1 100644 --- a/src/foundation/universal-property-propositional-truncation-into-sets.lagda.md +++ b/src/foundation/universal-property-propositional-truncation-into-sets.lagda.md @@ -1,7 +1,15 @@ # The universal property of propositional truncations with respect to sets ```agda -module foundation.universal-property-propositional-truncation-into-sets where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.universal-property-propositional-truncation-into-sets + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,10 +17,10 @@ module foundation.universal-property-propositional-truncation-into-sets where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-extensionality -open import foundation.propositional-truncations +open import foundation.function-extensionality funext +open import foundation.propositional-truncations funext univalence open import foundation.universe-levels -open import foundation.weakly-constant-maps +open import foundation.weakly-constant-maps funext open import foundation-core.equivalences open import foundation-core.fibers-of-maps @@ -21,7 +29,7 @@ open import foundation-core.homotopies open import foundation-core.identity-types open import foundation-core.propositions open import foundation-core.sets -open import foundation-core.subtypes +open import foundation-core.subtypes funext ```
diff --git a/src/foundation/universal-property-propositional-truncation.lagda.md b/src/foundation/universal-property-propositional-truncation.lagda.md index 61fbe14f5b..cc7b259807 100644 --- a/src/foundation/universal-property-propositional-truncation.lagda.md +++ b/src/foundation/universal-property-propositional-truncation.lagda.md @@ -1,28 +1,33 @@ # The universal property of propositional truncations ```agda -module foundation.universal-property-propositional-truncation where +open import foundation.function-extensionality-axiom + +module foundation.universal-property-propositional-truncation + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.functoriality-cartesian-product-types -open import foundation.logical-equivalences -open import foundation.precomposition-functions-into-subuniverses +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.function-extensionality funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.logical-equivalences funext +open import foundation.precomposition-functions-into-subuniverses funext open import foundation.subtype-identity-principle open import foundation.unit-type -open import foundation.universal-property-dependent-pair-types -open import foundation.universal-property-equivalences +open import foundation.universal-property-dependent-pair-types funext +open import foundation.universal-property-equivalences funext open import foundation.universe-levels open import foundation-core.contractible-maps open import foundation-core.contractible-types open import foundation-core.function-types -open import foundation-core.functoriality-dependent-function-types +open import foundation-core.functoriality-dependent-function-types funext open import foundation-core.functoriality-dependent-pair-types open import foundation-core.homotopies open import foundation-core.identity-types diff --git a/src/foundation/universal-property-pullbacks.lagda.md b/src/foundation/universal-property-pullbacks.lagda.md index 0b97e575fa..0960287c9c 100644 --- a/src/foundation/universal-property-pullbacks.lagda.md +++ b/src/foundation/universal-property-pullbacks.lagda.md @@ -1,23 +1,27 @@ # The universal property of pullbacks ```agda -module foundation.universal-property-pullbacks where +open import foundation.function-extensionality-axiom -open import foundation-core.universal-property-pullbacks public +module foundation.universal-property-pullbacks + (funext : function-extensionality) + where + +open import foundation-core.universal-property-pullbacks funext public ```
Imports ```agda -open import foundation.cones-over-cospan-diagrams +open import foundation.cones-over-cospan-diagrams funext open import foundation.dependent-pair-types -open import foundation.equivalences +open import foundation.equivalences funext open import foundation.subtype-identity-principle open import foundation.universe-levels open import foundation-core.contractible-types open import foundation-core.function-types -open import foundation-core.pullbacks +open import foundation-core.pullbacks funext ```
diff --git a/src/foundation/universal-property-sequential-limits.lagda.md b/src/foundation/universal-property-sequential-limits.lagda.md index d7377fae19..5d440b8185 100644 --- a/src/foundation/universal-property-sequential-limits.lagda.md +++ b/src/foundation/universal-property-sequential-limits.lagda.md @@ -1,18 +1,26 @@ # The universal property of sequential limits ```agda -module foundation.universal-property-sequential-limits where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.universal-property-sequential-limits + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cones-over-inverse-sequential-diagrams +open import foundation.cones-over-inverse-sequential-diagrams funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.inverse-sequential-diagrams -open import foundation.postcomposition-functions +open import foundation.equivalences funext +open import foundation.inverse-sequential-diagrams funext univalence truncations +open import foundation.postcomposition-functions funext open import foundation.subtype-identity-principle open import foundation.universe-levels diff --git a/src/foundation/universal-property-set-quotients.lagda.md b/src/foundation/universal-property-set-quotients.lagda.md index 10bfbb0310..28414dd9b7 100644 --- a/src/foundation/universal-property-set-quotients.lagda.md +++ b/src/foundation/universal-property-set-quotients.lagda.md @@ -2,8 +2,15 @@ ```agda {-# OPTIONS --lossy-unification #-} +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom -module foundation.universal-property-set-quotients where +module foundation.universal-property-set-quotients + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -11,26 +18,27 @@ module foundation.universal-property-set-quotients where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.dependent-universal-property-equivalences -open import foundation.effective-maps-equivalence-relations -open import foundation.epimorphisms-with-respect-to-sets -open import foundation.equivalence-classes -open import foundation.existential-quantification -open import foundation.function-extensionality +open import foundation.dependent-products-propositions funext +open import foundation.dependent-universal-property-equivalences funext +open import foundation.effective-maps-equivalence-relations funext univalence truncations +open import foundation.epimorphisms-with-respect-to-sets funext univalence truncations +open import foundation.equivalence-classes funext univalence truncations +open import foundation.existential-quantification funext univalence truncations +open import foundation.function-extensionality funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types -open import foundation.images -open import foundation.injective-maps -open import foundation.locally-small-types -open import foundation.logical-equivalences -open import foundation.propositional-extensionality -open import foundation.propositional-truncations -open import foundation.reflecting-maps-equivalence-relations -open import foundation.sets -open import foundation.surjective-maps +open import foundation.identity-types funext +open import foundation.images funext univalence truncations +open import foundation.injective-maps funext +open import foundation.locally-small-types funext univalence truncations +open import foundation.logical-equivalences funext +open import foundation.propositional-extensionality funext univalence truncations +open import foundation.propositional-truncations funext univalence +open import foundation.reflecting-maps-equivalence-relations funext univalence truncations +open import foundation.sets funext univalence +open import foundation.surjective-maps funext univalence truncations open import foundation.transport-along-identifications -open import foundation.universal-property-dependent-pair-types -open import foundation.universal-property-image +open import foundation.universal-property-dependent-pair-types funext +open import foundation.universal-property-image funext univalence truncations open import foundation.universe-levels open import foundation.whiskering-homotopies-composition @@ -39,7 +47,7 @@ open import foundation-core.commuting-triangles-of-maps open import foundation-core.contractible-maps open import foundation-core.contractible-types open import foundation-core.embeddings -open import foundation-core.equivalence-relations +open import foundation-core.equivalence-relations funext univalence truncations open import foundation-core.equivalences open import foundation-core.fibers-of-maps open import foundation-core.function-types @@ -47,11 +55,10 @@ open import foundation-core.functoriality-dependent-pair-types open import foundation-core.homotopies open import foundation-core.propositional-maps open import foundation-core.propositions -open import foundation-core.small-types -open import foundation-core.subtypes +open import foundation-core.small-types funext univalence truncations +open import foundation-core.subtypes funext open import foundation-core.torsorial-type-families open import foundation-core.type-theoretic-principle-of-choice -open import foundation-core.univalence ```
diff --git a/src/foundation/universal-property-set-truncation.lagda.md b/src/foundation/universal-property-set-truncation.lagda.md index c6a4069b7b..e941abc262 100644 --- a/src/foundation/universal-property-set-truncation.lagda.md +++ b/src/foundation/universal-property-set-truncation.lagda.md @@ -1,20 +1,28 @@ # The universal property of set truncations ```agda -module foundation.universal-property-set-truncation where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.universal-property-set-truncation + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-extensionality -open import foundation.mere-equality -open import foundation.reflecting-maps-equivalence-relations -open import foundation.sets +open import foundation.function-extensionality funext +open import foundation.mere-equality funext univalence truncations +open import foundation.reflecting-maps-equivalence-relations funext univalence truncations +open import foundation.sets funext univalence open import foundation.type-arithmetic-dependent-pair-types -open import foundation.universal-property-equivalences -open import foundation.universal-property-set-quotients +open import foundation.universal-property-equivalences funext +open import foundation.universal-property-set-quotients funext univalence truncations open import foundation.universe-levels open import foundation-core.contractible-maps diff --git a/src/foundation/universal-property-truncation.lagda.md b/src/foundation/universal-property-truncation.lagda.md index 3d261465a4..74c9e7dac8 100644 --- a/src/foundation/universal-property-truncation.lagda.md +++ b/src/foundation/universal-property-truncation.lagda.md @@ -1,30 +1,39 @@ # The universal property of truncations ```agda -module foundation.universal-property-truncation where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom -open import foundation-core.universal-property-truncation public +module foundation.universal-property-truncation + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where + +open import foundation-core.universal-property-truncation funext public ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.contractible-types +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.function-extensionality -open import foundation.identity-types -open import foundation.propositional-truncations -open import foundation.surjective-maps -open import foundation.type-arithmetic-dependent-function-types -open import foundation.universal-property-dependent-pair-types -open import foundation.universal-property-identity-types +open import foundation.dependent-products-contractible-types funext +open import foundation.function-extensionality funext +open import foundation.identity-types funext +open import foundation.propositional-truncations funext univalence +open import foundation.surjective-maps funext univalence truncations +open import foundation.type-arithmetic-dependent-function-types funext univalence +open import foundation.universal-property-dependent-pair-types funext +open import foundation.universal-property-identity-types funext univalence truncations open import foundation.universe-levels open import foundation-core.contractible-maps open import foundation-core.equivalences open import foundation-core.fibers-of-maps -open import foundation-core.functoriality-dependent-function-types +open import foundation-core.functoriality-dependent-function-types funext open import foundation-core.functoriality-dependent-pair-types open import foundation-core.torsorial-type-families open import foundation-core.truncated-types diff --git a/src/foundation/universal-property-unit-type.lagda.md b/src/foundation/universal-property-unit-type.lagda.md index 6d066ead4f..8e5d831866 100644 --- a/src/foundation/universal-property-unit-type.lagda.md +++ b/src/foundation/universal-property-unit-type.lagda.md @@ -1,21 +1,25 @@ # The universal property of the unit type ```agda -module foundation.universal-property-unit-type where +open import foundation.function-extensionality-axiom + +module foundation.universal-property-unit-type + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.diagonal-maps-of-types open import foundation.unit-type -open import foundation.universal-property-contractible-types -open import foundation.universal-property-equivalences +open import foundation.universal-property-contractible-types funext +open import foundation.universal-property-equivalences funext open import foundation.universe-levels open import foundation-core.constant-maps open import foundation-core.contractible-types +open import foundation-core.diagonal-maps-of-types open import foundation-core.equivalences open import foundation-core.homotopies open import foundation-core.precomposition-functions diff --git a/src/foundation/universal-quantification.lagda.md b/src/foundation/universal-quantification.lagda.md index e4b0bd024f..3026814539 100644 --- a/src/foundation/universal-quantification.lagda.md +++ b/src/foundation/universal-quantification.lagda.md @@ -1,16 +1,25 @@ # Universal quantification ```agda -module foundation.universal-quantification where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.universal-quantification + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions funext open import foundation.evaluation-functions -open import foundation.logical-equivalences -open import foundation.propositional-truncations +open import foundation.logical-equivalences funext +open import foundation.propositional-truncations funext univalence open import foundation.universe-levels open import foundation-core.equivalences diff --git a/src/foundation/unordered-pairs-of-types.lagda.md b/src/foundation/unordered-pairs-of-types.lagda.md index ccefe96921..39e3a3b0a4 100644 --- a/src/foundation/unordered-pairs-of-types.lagda.md +++ b/src/foundation/unordered-pairs-of-types.lagda.md @@ -1,7 +1,15 @@ # Unordered pairs of types ```agda -module foundation.unordered-pairs-of-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.unordered-pairs-of-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,15 +18,15 @@ module foundation.unordered-pairs-of-types where open import foundation.dependent-pair-types open import foundation.fundamental-theorem-of-identity-types open import foundation.structure-identity-principle -open import foundation.univalence +open import foundation.univalence funext univalence open import foundation.universe-levels -open import foundation.unordered-pairs +open import foundation.unordered-pairs funext univalence truncations open import foundation-core.equivalences open import foundation-core.identity-types open import foundation-core.torsorial-type-families -open import univalent-combinatorics.2-element-types +open import univalent-combinatorics.2-element-types funext univalence truncations ```
diff --git a/src/foundation/unordered-pairs.lagda.md b/src/foundation/unordered-pairs.lagda.md index 764054eed8..56e9241c16 100644 --- a/src/foundation/unordered-pairs.lagda.md +++ b/src/foundation/unordered-pairs.lagda.md @@ -1,29 +1,38 @@ # Unordered pairs of elements in a type ```agda -module foundation.unordered-pairs where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.unordered-pairs + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-triangles-of-maps -open import foundation.contractible-types -open import foundation.decidable-equality +open import foundation.commuting-triangles-of-maps funext univalence +open import foundation.contractible-types funext univalence +open import foundation.decidable-equality funext univalence truncations open import foundation.dependent-pair-types -open import foundation.dependent-universal-property-equivalences -open import foundation.existential-quantification -open import foundation.function-extensionality +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-universal-property-equivalences funext +open import foundation.existential-quantification funext univalence truncations +open import foundation.function-extensionality funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopy-induction -open import foundation.mere-equivalences -open import foundation.postcomposition-functions -open import foundation.propositional-truncations +open import foundation.homotopy-induction funext +open import foundation.mere-equivalences funext univalence truncations +open import foundation.postcomposition-functions funext +open import foundation.propositional-truncations funext univalence open import foundation.structure-identity-principle -open import foundation.type-arithmetic-dependent-function-types -open import foundation.universal-property-contractible-types -open import foundation.universal-property-dependent-pair-types +open import foundation.type-arithmetic-dependent-function-types funext univalence +open import foundation.universal-property-contractible-types funext +open import foundation.universal-property-dependent-pair-types funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition @@ -32,7 +41,7 @@ open import foundation-core.coproduct-types open import foundation-core.embeddings open import foundation-core.equivalences open import foundation-core.function-types -open import foundation-core.functoriality-dependent-function-types +open import foundation-core.functoriality-dependent-function-types funext open import foundation-core.functoriality-dependent-pair-types open import foundation-core.homotopies open import foundation-core.identity-types @@ -41,11 +50,11 @@ open import foundation-core.propositions open import foundation-core.sets open import foundation-core.torsorial-type-families -open import univalent-combinatorics.2-element-types -open import univalent-combinatorics.equality-standard-finite-types -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.standard-finite-types -open import univalent-combinatorics.universal-property-standard-finite-types +open import univalent-combinatorics.2-element-types funext univalence truncations +open import univalent-combinatorics.equality-standard-finite-types funext univalence truncations +open import univalent-combinatorics.finite-types funext univalence truncations +open import univalent-combinatorics.standard-finite-types funext univalence truncations +open import univalent-combinatorics.universal-property-standard-finite-types funext univalence truncations ```
diff --git a/src/foundation/unordered-tuples-of-types.lagda.md b/src/foundation/unordered-tuples-of-types.lagda.md index b208cabd92..81b5901a34 100644 --- a/src/foundation/unordered-tuples-of-types.lagda.md +++ b/src/foundation/unordered-tuples-of-types.lagda.md @@ -1,7 +1,15 @@ # Unordered tuples of types ```agda -module foundation.unordered-tuples-of-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.unordered-tuples-of-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -12,15 +20,15 @@ open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types open import foundation.fundamental-theorem-of-identity-types open import foundation.structure-identity-principle -open import foundation.univalence +open import foundation.univalence funext univalence open import foundation.universe-levels -open import foundation.unordered-tuples +open import foundation.unordered-tuples funext univalence truncations open import foundation-core.equivalences open import foundation-core.identity-types open import foundation-core.torsorial-type-families -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.finite-types funext univalence truncations ```
diff --git a/src/foundation/unordered-tuples.lagda.md b/src/foundation/unordered-tuples.lagda.md index 69977f8b8e..f9aaac554f 100644 --- a/src/foundation/unordered-tuples.lagda.md +++ b/src/foundation/unordered-tuples.lagda.md @@ -1,7 +1,15 @@ # Unordered `n`-tuples of elements in a type ```agda -module foundation.unordered-tuples where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.unordered-tuples + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,14 +17,15 @@ module foundation.unordered-tuples where ```agda open import elementary-number-theory.natural-numbers -open import foundation.1-types -open import foundation.decidable-equality +open import foundation.1-types funext univalence +open import foundation.decidable-equality funext univalence truncations open import foundation.dependent-pair-types +open import foundation.dependent-products-truncated-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopy-induction -open import foundation.postcomposition-functions +open import foundation.homotopy-induction funext +open import foundation.postcomposition-functions funext open import foundation.structure-identity-principle -open import foundation.truncated-types +open import foundation.truncated-types funext univalence open import foundation.truncation-levels open import foundation.universe-levels open import foundation.whiskering-homotopies-composition @@ -29,10 +38,10 @@ open import foundation-core.identity-types open import foundation-core.sets open import foundation-core.torsorial-type-families -open import univalent-combinatorics.complements-isolated-elements -open import univalent-combinatorics.equality-finite-types -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.complements-isolated-elements funext univalence truncations +open import univalent-combinatorics.equality-finite-types funext univalence truncations +open import univalent-combinatorics.finite-types funext univalence truncations +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/foundation/vectors-set-quotients.lagda.md b/src/foundation/vectors-set-quotients.lagda.md index 80e0ac123d..3c094ce5b3 100644 --- a/src/foundation/vectors-set-quotients.lagda.md +++ b/src/foundation/vectors-set-quotients.lagda.md @@ -2,8 +2,15 @@ ```agda {-# OPTIONS --lossy-unification #-} - -module foundation.vectors-set-quotients where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.vectors-set-quotients + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -12,35 +19,36 @@ module foundation.vectors-set-quotients where open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.cartesian-products-set-quotients +open import foundation.cartesian-products-set-quotients funext univalence truncations open import foundation.dependent-pair-types open import foundation.equality-cartesian-product-types -open import foundation.function-extensionality -open import foundation.multivariable-operations -open import foundation.products-equivalence-relations -open import foundation.raising-universe-levels -open import foundation.reflecting-maps-equivalence-relations -open import foundation.set-quotients -open import foundation.sets +open import foundation.function-extensionality funext +open import foundation.multivariable-operations funext univalence truncations +open import foundation.products-equivalence-relations funext univalence truncations +open import foundation.raising-universe-levels-unit-type +open import foundation.reflecting-maps-equivalence-relations funext univalence truncations +open import foundation.set-quotients funext univalence truncations +open import foundation.sets funext univalence open import foundation.unit-type -open import foundation.universal-property-set-quotients +open import foundation.universal-property-set-quotients funext univalence truncations open import foundation.universe-levels open import foundation-core.cartesian-product-types open import foundation-core.coproduct-types open import foundation-core.equality-dependent-pair-types -open import foundation-core.equivalence-relations +open import foundation-core.equivalence-relations funext univalence truncations open import foundation-core.equivalences open import foundation-core.function-types open import foundation-core.homotopies open import foundation-core.identity-types open import foundation-core.propositions +open import foundation-core.raising-universe-levels open import foundation-core.retractions open import foundation-core.sections -open import linear-algebra.vectors +open import linear-algebra.vectors funext univalence truncations -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/foundation/vertical-composition-spans-of-spans.lagda.md b/src/foundation/vertical-composition-spans-of-spans.lagda.md index 785b482745..3780ecab58 100644 --- a/src/foundation/vertical-composition-spans-of-spans.lagda.md +++ b/src/foundation/vertical-composition-spans-of-spans.lagda.md @@ -1,27 +1,35 @@ # Vertical composition of spans of spans ```agda -module foundation.vertical-composition-spans-of-spans where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.vertical-composition-spans-of-spans + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.commuting-triangles-of-maps -open import foundation.composition-spans +open import foundation.commuting-triangles-of-maps funext univalence +open import foundation.composition-spans funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.equivalences-arrows -open import foundation.equivalences-spans -open import foundation.homotopies -open import foundation.identity-types -open import foundation.morphisms-arrows +open import foundation.equivalences funext +open import foundation.equivalences-arrows funext univalence truncations +open import foundation.equivalences-spans funext univalence +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.morphisms-arrows funext open import foundation.morphisms-spans -open import foundation.pullbacks +open import foundation.pullbacks funext univalence truncations open import foundation.spans -open import foundation.spans-of-spans -open import foundation.standard-pullbacks -open import foundation.type-arithmetic-standard-pullbacks +open import foundation.spans-of-spans funext univalence +open import foundation.standard-pullbacks funext +open import foundation.type-arithmetic-standard-pullbacks funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition diff --git a/src/foundation/weak-function-extensionality.lagda.md b/src/foundation/weak-function-extensionality.lagda.md index 0abd8761d5..85569fbf7f 100644 --- a/src/foundation/weak-function-extensionality.lagda.md +++ b/src/foundation/weak-function-extensionality.lagda.md @@ -1,17 +1,24 @@ # Weak function extensionality ```agda -module foundation.weak-function-extensionality where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.weak-function-extensionality + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.decidable-equality -open import foundation.decidable-types +open import foundation.decidable-equality funext univalence truncations +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.function-extensionality open import foundation.fundamental-theorem-of-identity-types open import foundation.universe-levels diff --git a/src/foundation/weak-limited-principle-of-omniscience.lagda.md b/src/foundation/weak-limited-principle-of-omniscience.lagda.md index bc9b213e06..9de78fec34 100644 --- a/src/foundation/weak-limited-principle-of-omniscience.lagda.md +++ b/src/foundation/weak-limited-principle-of-omniscience.lagda.md @@ -1,7 +1,15 @@ # The weak limited principle of omniscience ```agda -module foundation.weak-limited-principle-of-omniscience where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.weak-limited-principle-of-omniscience + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,13 +17,13 @@ module foundation.weak-limited-principle-of-omniscience where ```agda open import elementary-number-theory.natural-numbers -open import foundation.booleans -open import foundation.disjunction -open import foundation.negation -open import foundation.universal-quantification +open import foundation.disjunction funext univalence truncations +open import foundation.negation funext +open import foundation.universal-quantification funext univalence truncations open import foundation.universe-levels -open import foundation-core.decidable-propositions +open import foundation-core.booleans +open import foundation-core.decidable-propositions funext univalence truncations open import foundation-core.propositions open import foundation-core.sets ``` diff --git a/src/foundation/weakly-constant-maps.lagda.md b/src/foundation/weakly-constant-maps.lagda.md index 741e4c32c8..3f08dfe7a1 100644 --- a/src/foundation/weakly-constant-maps.lagda.md +++ b/src/foundation/weakly-constant-maps.lagda.md @@ -1,7 +1,11 @@ # Weakly constant maps ```agda -module foundation.weakly-constant-maps where +open import foundation.function-extensionality-axiom + +module foundation.weakly-constant-maps + (funext : function-extensionality) + where ```
Imports @@ -10,8 +14,9 @@ module foundation.weakly-constant-maps where open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types open import foundation.fixed-points-endofunctions -open import foundation.identity-types -open import foundation.iterated-dependent-product-types +open import foundation.identity-types funext +open import foundation.iterated-dependent-product-types funext +open import foundation.telescopes open import foundation.universe-levels open import foundation-core.contractible-types diff --git a/src/foundation/whiskering-homotopies-concatenation.lagda.md b/src/foundation/whiskering-homotopies-concatenation.lagda.md index ef61dcad5c..4d47c5f8a2 100644 --- a/src/foundation/whiskering-homotopies-concatenation.lagda.md +++ b/src/foundation/whiskering-homotopies-concatenation.lagda.md @@ -1,7 +1,11 @@ # Whiskering homotopies with respect to concatenation ```agda -module foundation.whiskering-homotopies-concatenation where +open import foundation.function-extensionality-axiom + +module foundation.whiskering-homotopies-concatenation + (funext : function-extensionality) + where open import foundation-core.whiskering-homotopies-concatenation public ``` @@ -10,10 +14,10 @@ open import foundation-core.whiskering-homotopies-concatenation public ```agda open import foundation.universe-levels -open import foundation.whiskering-identifications-concatenation +open import foundation.whiskering-identifications-concatenation funext open import foundation-core.equivalences -open import foundation-core.functoriality-dependent-function-types +open import foundation-core.functoriality-dependent-function-types funext open import foundation-core.homotopies ``` diff --git a/src/foundation/whiskering-identifications-concatenation.lagda.md b/src/foundation/whiskering-identifications-concatenation.lagda.md index c2e632249a..b69b679f8e 100644 --- a/src/foundation/whiskering-identifications-concatenation.lagda.md +++ b/src/foundation/whiskering-identifications-concatenation.lagda.md @@ -1,7 +1,11 @@ # Whiskering identifications with respect to concatenation ```agda -module foundation.whiskering-identifications-concatenation where +open import foundation.function-extensionality-axiom + +module foundation.whiskering-identifications-concatenation + (funext : function-extensionality) + where open import foundation-core.whiskering-identifications-concatenation public ``` @@ -9,15 +13,11 @@ open import foundation-core.whiskering-identifications-concatenation public
Imports ```agda -open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import foundation.whiskering-operations open import foundation-core.equivalences -open import foundation-core.function-types -open import foundation-core.homotopies ```
diff --git a/src/foundation/wild-category-of-types.lagda.md b/src/foundation/wild-category-of-types.lagda.md index 60277a29a4..b61e297998 100644 --- a/src/foundation/wild-category-of-types.lagda.md +++ b/src/foundation/wild-category-of-types.lagda.md @@ -2,8 +2,15 @@ ```agda {-# OPTIONS --guardedness #-} - -module foundation.wild-category-of-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.wild-category-of-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -11,11 +18,11 @@ module foundation.wild-category-of-types where ```agda open import foundation.dependent-pair-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.globular-type-of-functions -open import foundation.homotopies -open import foundation.isomorphisms-of-sets -open import foundation.sets -open import foundation.strictly-involutive-identity-types +open import foundation.globular-type-of-functions funext univalence truncations +open import foundation.homotopies funext +open import foundation.isomorphisms-of-sets funext univalence +open import foundation.sets funext univalence +open import foundation.strictly-involutive-identity-types funext univalence open import foundation.universe-levels open import foundation-core.contractible-types @@ -26,13 +33,13 @@ open import foundation-core.identity-types open import globular-types.globular-types open import globular-types.large-globular-types -open import globular-types.large-reflexive-globular-types -open import globular-types.large-transitive-globular-types -open import globular-types.reflexive-globular-types -open import globular-types.transitive-globular-types +open import globular-types.large-reflexive-globular-types funext univalence truncations +open import globular-types.large-transitive-globular-types funext univalence truncations +open import globular-types.reflexive-globular-types funext univalence truncations +open import globular-types.transitive-globular-types funext univalence truncations -open import wild-category-theory.noncoherent-large-omega-precategories -open import wild-category-theory.noncoherent-omega-precategories +open import wild-category-theory.noncoherent-large-omega-precategories funext univalence truncations +open import wild-category-theory.noncoherent-omega-precategories funext univalence truncations ```
diff --git a/src/foundation/yoneda-identity-types.lagda.md b/src/foundation/yoneda-identity-types.lagda.md index 9f112941a7..cfc7f33e6e 100644 --- a/src/foundation/yoneda-identity-types.lagda.md +++ b/src/foundation/yoneda-identity-types.lagda.md @@ -1,7 +1,13 @@ # Yoneda identity types ```agda -module foundation.yoneda-identity-types where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module foundation.yoneda-identity-types + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports @@ -9,12 +15,13 @@ module foundation.yoneda-identity-types where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-extensionality -open import foundation.multivariable-homotopies +open import foundation.function-extensionality funext +open import foundation.multivariable-homotopies funext open import foundation.strictly-right-unital-concatenation-identifications +open import foundation.telescopes open import foundation.transport-along-identifications -open import foundation.univalence -open import foundation.universal-property-identity-systems +open import foundation.univalence funext univalence +open import foundation.universal-property-identity-systems funext open import foundation.universe-levels open import foundation-core.contractible-types diff --git a/src/globular-types.lagda.md b/src/globular-types.lagda.md index 260995b614..1bd01adac3 100644 --- a/src/globular-types.lagda.md +++ b/src/globular-types.lagda.md @@ -7,61 +7,69 @@ ## Modules in the globular types namespace ```agda -module globular-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom -open import globular-types.base-change-dependent-globular-types public -open import globular-types.base-change-dependent-reflexive-globular-types public -open import globular-types.binary-dependent-globular-types public -open import globular-types.binary-dependent-reflexive-globular-types public +module globular-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where + +open import globular-types.base-change-dependent-globular-types funext public +open import globular-types.base-change-dependent-reflexive-globular-types funext univalence truncations public +open import globular-types.binary-dependent-globular-types funext public +open import globular-types.binary-dependent-reflexive-globular-types funext univalence truncations public open import globular-types.binary-globular-maps public -open import globular-types.colax-reflexive-globular-maps public -open import globular-types.colax-transitive-globular-maps public +open import globular-types.colax-reflexive-globular-maps funext univalence truncations public +open import globular-types.colax-transitive-globular-maps funext univalence truncations public open import globular-types.composition-structure-globular-types public open import globular-types.constant-globular-types public -open import globular-types.dependent-globular-types public -open import globular-types.dependent-reflexive-globular-types public -open import globular-types.dependent-sums-globular-types public -open import globular-types.discrete-dependent-reflexive-globular-types public -open import globular-types.discrete-globular-types public -open import globular-types.discrete-reflexive-globular-types public -open import globular-types.empty-globular-types public -open import globular-types.equality-globular-types public -open import globular-types.exponentials-globular-types public -open import globular-types.fibers-globular-maps public -open import globular-types.globular-equivalences public -open import globular-types.globular-maps public +open import globular-types.dependent-globular-types funext public +open import globular-types.dependent-reflexive-globular-types funext univalence truncations public +open import globular-types.dependent-sums-globular-types funext public +open import globular-types.discrete-dependent-reflexive-globular-types funext univalence truncations public +open import globular-types.discrete-globular-types funext univalence truncations public +open import globular-types.discrete-reflexive-globular-types funext univalence truncations public +open import globular-types.empty-globular-types funext univalence truncations public +open import globular-types.equality-globular-types funext univalence truncations public +open import globular-types.exponentials-globular-types funext public +open import globular-types.fibers-globular-maps funext public +open import globular-types.globular-equivalences funext public +open import globular-types.globular-maps funext public open import globular-types.globular-types public -open import globular-types.large-colax-reflexive-globular-maps public -open import globular-types.large-colax-transitive-globular-maps public -open import globular-types.large-globular-maps public +open import globular-types.large-colax-reflexive-globular-maps funext univalence truncations public +open import globular-types.large-colax-transitive-globular-maps funext univalence truncations public +open import globular-types.large-globular-maps funext public open import globular-types.large-globular-types public -open import globular-types.large-lax-reflexive-globular-maps public -open import globular-types.large-lax-transitive-globular-maps public -open import globular-types.large-reflexive-globular-maps public -open import globular-types.large-reflexive-globular-types public -open import globular-types.large-symmetric-globular-types public -open import globular-types.large-transitive-globular-maps public -open import globular-types.large-transitive-globular-types public -open import globular-types.lax-reflexive-globular-maps public -open import globular-types.lax-transitive-globular-maps public -open import globular-types.points-globular-types public -open import globular-types.points-reflexive-globular-types public -open import globular-types.pointwise-extensions-binary-families-globular-types public -open import globular-types.pointwise-extensions-binary-families-reflexive-globular-types public -open import globular-types.pointwise-extensions-families-globular-types public -open import globular-types.pointwise-extensions-families-reflexive-globular-types public -open import globular-types.products-families-of-globular-types public -open import globular-types.reflexive-globular-equivalences public -open import globular-types.reflexive-globular-maps public -open import globular-types.reflexive-globular-types public -open import globular-types.sections-dependent-globular-types public -open import globular-types.superglobular-types public -open import globular-types.symmetric-globular-types public -open import globular-types.terminal-globular-types public -open import globular-types.transitive-globular-maps public -open import globular-types.transitive-globular-types public +open import globular-types.large-lax-reflexive-globular-maps funext univalence truncations public +open import globular-types.large-lax-transitive-globular-maps funext univalence truncations public +open import globular-types.large-reflexive-globular-maps funext univalence truncations public +open import globular-types.large-reflexive-globular-types funext univalence truncations public +open import globular-types.large-symmetric-globular-types funext univalence truncations public +open import globular-types.large-transitive-globular-maps funext univalence truncations public +open import globular-types.large-transitive-globular-types funext univalence truncations public +open import globular-types.lax-reflexive-globular-maps funext univalence truncations public +open import globular-types.lax-transitive-globular-maps funext univalence truncations public +open import globular-types.points-globular-types funext public +open import globular-types.points-reflexive-globular-types funext univalence truncations public +open import globular-types.pointwise-extensions-binary-families-globular-types funext public +open import globular-types.pointwise-extensions-binary-families-reflexive-globular-types funext univalence truncations public +open import globular-types.pointwise-extensions-families-globular-types funext public +open import globular-types.pointwise-extensions-families-reflexive-globular-types funext univalence truncations public +open import globular-types.products-families-of-globular-types funext public +open import globular-types.reflexive-globular-equivalences funext univalence truncations public +open import globular-types.reflexive-globular-maps funext univalence truncations public +open import globular-types.reflexive-globular-types funext univalence truncations public +open import globular-types.sections-dependent-globular-types funext public +open import globular-types.superglobular-types funext univalence truncations public +open import globular-types.symmetric-globular-types funext univalence truncations public +open import globular-types.terminal-globular-types funext univalence public +open import globular-types.transitive-globular-maps funext univalence truncations public +open import globular-types.transitive-globular-types funext univalence truncations public open import globular-types.unit-globular-type public -open import globular-types.unit-reflexive-globular-type public -open import globular-types.universal-globular-type public -open import globular-types.universal-reflexive-globular-type public +open import globular-types.unit-reflexive-globular-type funext univalence truncations public +open import globular-types.universal-globular-type funext public +open import globular-types.universal-reflexive-globular-type funext univalence truncations public ``` diff --git a/src/globular-types/base-change-dependent-globular-types.lagda.md b/src/globular-types/base-change-dependent-globular-types.lagda.md index c0408459c0..c52e0b2731 100644 --- a/src/globular-types/base-change-dependent-globular-types.lagda.md +++ b/src/globular-types/base-change-dependent-globular-types.lagda.md @@ -2,8 +2,11 @@ ```agda {-# OPTIONS --guardedness #-} +open import foundation.function-extensionality-axiom -module globular-types.base-change-dependent-globular-types where +module globular-types.base-change-dependent-globular-types + (funext : function-extensionality) + where ```
Imports @@ -11,8 +14,8 @@ module globular-types.base-change-dependent-globular-types where ```agda open import foundation.universe-levels -open import globular-types.dependent-globular-types -open import globular-types.globular-maps +open import globular-types.dependent-globular-types funext +open import globular-types.globular-maps funext open import globular-types.globular-types ``` diff --git a/src/globular-types/base-change-dependent-reflexive-globular-types.lagda.md b/src/globular-types/base-change-dependent-reflexive-globular-types.lagda.md index f1507037dd..465cce1912 100644 --- a/src/globular-types/base-change-dependent-reflexive-globular-types.lagda.md +++ b/src/globular-types/base-change-dependent-reflexive-globular-types.lagda.md @@ -2,23 +2,30 @@ ```agda {-# OPTIONS --guardedness #-} - -module globular-types.base-change-dependent-reflexive-globular-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module globular-types.base-change-dependent-reflexive-globular-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import globular-types.base-change-dependent-globular-types -open import globular-types.dependent-globular-types -open import globular-types.dependent-reflexive-globular-types +open import globular-types.base-change-dependent-globular-types funext +open import globular-types.dependent-globular-types funext +open import globular-types.dependent-reflexive-globular-types funext univalence truncations open import globular-types.globular-types -open import globular-types.reflexive-globular-maps -open import globular-types.reflexive-globular-types +open import globular-types.reflexive-globular-maps funext univalence truncations +open import globular-types.reflexive-globular-types funext univalence truncations ```
diff --git a/src/globular-types/binary-dependent-globular-types.lagda.md b/src/globular-types/binary-dependent-globular-types.lagda.md index de718af1c3..360a18dd8b 100644 --- a/src/globular-types/binary-dependent-globular-types.lagda.md +++ b/src/globular-types/binary-dependent-globular-types.lagda.md @@ -2,8 +2,11 @@ ```agda {-# OPTIONS --guardedness #-} +open import foundation.function-extensionality-axiom -module globular-types.binary-dependent-globular-types where +module globular-types.binary-dependent-globular-types + (funext : function-extensionality) + where ```
Imports @@ -12,7 +15,7 @@ module globular-types.binary-dependent-globular-types where open import foundation.universe-levels open import globular-types.globular-types -open import globular-types.points-globular-types +open import globular-types.points-globular-types funext ```
diff --git a/src/globular-types/binary-dependent-reflexive-globular-types.lagda.md b/src/globular-types/binary-dependent-reflexive-globular-types.lagda.md index 234b035227..05d59d60b5 100644 --- a/src/globular-types/binary-dependent-reflexive-globular-types.lagda.md +++ b/src/globular-types/binary-dependent-reflexive-globular-types.lagda.md @@ -2,8 +2,15 @@ ```agda {-# OPTIONS --guardedness #-} - -module globular-types.binary-dependent-reflexive-globular-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module globular-types.binary-dependent-reflexive-globular-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -11,10 +18,10 @@ module globular-types.binary-dependent-reflexive-globular-types where ```agda open import foundation.universe-levels -open import globular-types.binary-dependent-globular-types +open import globular-types.binary-dependent-globular-types funext open import globular-types.globular-types -open import globular-types.points-reflexive-globular-types -open import globular-types.reflexive-globular-types +open import globular-types.points-reflexive-globular-types funext univalence truncations +open import globular-types.reflexive-globular-types funext univalence truncations ```
diff --git a/src/globular-types/binary-globular-maps.lagda.md b/src/globular-types/binary-globular-maps.lagda.md index aa89346264..cc3ec422c4 100644 --- a/src/globular-types/binary-globular-maps.lagda.md +++ b/src/globular-types/binary-globular-maps.lagda.md @@ -11,7 +11,6 @@ module globular-types.binary-globular-maps where ```agda open import foundation.universe-levels -open import globular-types.globular-maps open import globular-types.globular-types ``` diff --git a/src/globular-types/colax-reflexive-globular-maps.lagda.md b/src/globular-types/colax-reflexive-globular-maps.lagda.md index 1e834a12a5..3c494eeb06 100644 --- a/src/globular-types/colax-reflexive-globular-maps.lagda.md +++ b/src/globular-types/colax-reflexive-globular-maps.lagda.md @@ -2,8 +2,15 @@ ```agda {-# OPTIONS --guardedness #-} - -module globular-types.colax-reflexive-globular-maps where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module globular-types.colax-reflexive-globular-maps + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -11,8 +18,8 @@ module globular-types.colax-reflexive-globular-maps where ```agda open import foundation.universe-levels -open import globular-types.globular-maps -open import globular-types.reflexive-globular-types +open import globular-types.globular-maps funext +open import globular-types.reflexive-globular-types funext univalence truncations ```
diff --git a/src/globular-types/colax-transitive-globular-maps.lagda.md b/src/globular-types/colax-transitive-globular-maps.lagda.md index cb012086d5..be2e338607 100644 --- a/src/globular-types/colax-transitive-globular-maps.lagda.md +++ b/src/globular-types/colax-transitive-globular-maps.lagda.md @@ -2,8 +2,15 @@ ```agda {-# OPTIONS --guardedness #-} - -module globular-types.colax-transitive-globular-maps where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module globular-types.colax-transitive-globular-maps + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -11,8 +18,8 @@ module globular-types.colax-transitive-globular-maps where ```agda open import foundation.universe-levels -open import globular-types.globular-maps -open import globular-types.transitive-globular-types +open import globular-types.globular-maps funext +open import globular-types.transitive-globular-types funext univalence truncations ```
diff --git a/src/globular-types/dependent-globular-types.lagda.md b/src/globular-types/dependent-globular-types.lagda.md index 41d4806001..928c6e3a11 100644 --- a/src/globular-types/dependent-globular-types.lagda.md +++ b/src/globular-types/dependent-globular-types.lagda.md @@ -2,8 +2,11 @@ ```agda {-# OPTIONS --guardedness #-} +open import foundation.function-extensionality-axiom -module globular-types.dependent-globular-types where +module globular-types.dependent-globular-types + (funext : function-extensionality) + where ```
Imports @@ -13,7 +16,7 @@ open import foundation.dependent-pair-types open import foundation.universe-levels open import globular-types.globular-types -open import globular-types.points-globular-types +open import globular-types.points-globular-types funext ```
diff --git a/src/globular-types/dependent-reflexive-globular-types.lagda.md b/src/globular-types/dependent-reflexive-globular-types.lagda.md index b82c493c5e..f6b23e75b6 100644 --- a/src/globular-types/dependent-reflexive-globular-types.lagda.md +++ b/src/globular-types/dependent-reflexive-globular-types.lagda.md @@ -2,8 +2,15 @@ ```agda {-# OPTIONS --guardedness #-} - -module globular-types.dependent-reflexive-globular-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module globular-types.dependent-reflexive-globular-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -12,10 +19,10 @@ module globular-types.dependent-reflexive-globular-types where open import foundation.dependent-pair-types open import foundation.universe-levels -open import globular-types.dependent-globular-types +open import globular-types.dependent-globular-types funext open import globular-types.globular-types -open import globular-types.points-reflexive-globular-types -open import globular-types.reflexive-globular-types +open import globular-types.points-reflexive-globular-types funext univalence truncations +open import globular-types.reflexive-globular-types funext univalence truncations ```
diff --git a/src/globular-types/dependent-sums-globular-types.lagda.md b/src/globular-types/dependent-sums-globular-types.lagda.md index ead7b91cb5..7e31c0ba22 100644 --- a/src/globular-types/dependent-sums-globular-types.lagda.md +++ b/src/globular-types/dependent-sums-globular-types.lagda.md @@ -2,8 +2,11 @@ ```agda {-# OPTIONS --guardedness #-} +open import foundation.function-extensionality-axiom -module globular-types.dependent-sums-globular-types where +module globular-types.dependent-sums-globular-types + (funext : function-extensionality) + where ```
Imports @@ -12,11 +15,11 @@ module globular-types.dependent-sums-globular-types where open import foundation.dependent-pair-types open import foundation.universe-levels -open import globular-types.base-change-dependent-globular-types -open import globular-types.dependent-globular-types -open import globular-types.globular-maps +open import globular-types.base-change-dependent-globular-types funext +open import globular-types.dependent-globular-types funext +open import globular-types.globular-maps funext open import globular-types.globular-types -open import globular-types.sections-dependent-globular-types +open import globular-types.sections-dependent-globular-types funext ```
diff --git a/src/globular-types/discrete-dependent-reflexive-globular-types.lagda.md b/src/globular-types/discrete-dependent-reflexive-globular-types.lagda.md index 782d45590d..4fd92ae1c5 100644 --- a/src/globular-types/discrete-dependent-reflexive-globular-types.lagda.md +++ b/src/globular-types/discrete-dependent-reflexive-globular-types.lagda.md @@ -2,8 +2,15 @@ ```agda {-# OPTIONS --guardedness #-} - -module globular-types.discrete-dependent-reflexive-globular-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module globular-types.discrete-dependent-reflexive-globular-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -11,10 +18,10 @@ module globular-types.discrete-dependent-reflexive-globular-types where ```agda open import foundation.universe-levels -open import globular-types.dependent-reflexive-globular-types -open import globular-types.discrete-reflexive-globular-types -open import globular-types.points-reflexive-globular-types -open import globular-types.reflexive-globular-types +open import globular-types.dependent-reflexive-globular-types funext univalence truncations +open import globular-types.discrete-reflexive-globular-types funext univalence truncations +open import globular-types.points-reflexive-globular-types funext univalence truncations +open import globular-types.reflexive-globular-types funext univalence truncations ```
diff --git a/src/globular-types/discrete-globular-types.lagda.md b/src/globular-types/discrete-globular-types.lagda.md index 77b4dd1141..6095219d97 100644 --- a/src/globular-types/discrete-globular-types.lagda.md +++ b/src/globular-types/discrete-globular-types.lagda.md @@ -2,19 +2,27 @@ ```agda {-# OPTIONS --guardedness #-} - -module globular-types.discrete-globular-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module globular-types.discrete-globular-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.discrete-binary-relations -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.discrete-binary-relations funext univalence truncations +open import foundation.propositions funext univalence open import foundation.universe-levels -open import globular-types.empty-globular-types +open import globular-types.empty-globular-types funext univalence truncations open import globular-types.globular-types ``` diff --git a/src/globular-types/discrete-reflexive-globular-types.lagda.md b/src/globular-types/discrete-reflexive-globular-types.lagda.md index 9e45c68d20..2455160d3f 100644 --- a/src/globular-types/discrete-reflexive-globular-types.lagda.md +++ b/src/globular-types/discrete-reflexive-globular-types.lagda.md @@ -2,21 +2,28 @@ ```agda {-# OPTIONS --guardedness #-} - -module globular-types.discrete-reflexive-globular-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module globular-types.discrete-reflexive-globular-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.identity-types -open import foundation.torsorial-type-families +open import foundation.identity-types funext +open import foundation.torsorial-type-families funext univalence truncations open import foundation.universe-levels open import globular-types.globular-types -open import globular-types.reflexive-globular-types -open import globular-types.symmetric-globular-types -open import globular-types.transitive-globular-types +open import globular-types.reflexive-globular-types funext univalence truncations +open import globular-types.symmetric-globular-types funext univalence truncations +open import globular-types.transitive-globular-types funext univalence truncations ```
diff --git a/src/globular-types/empty-globular-types.lagda.md b/src/globular-types/empty-globular-types.lagda.md index 9e19f67f78..4959e56cbe 100644 --- a/src/globular-types/empty-globular-types.lagda.md +++ b/src/globular-types/empty-globular-types.lagda.md @@ -2,14 +2,21 @@ ```agda {-# OPTIONS --guardedness #-} - -module globular-types.empty-globular-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module globular-types.empty-globular-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.empty-types +open import foundation.empty-types funext univalence truncations open import foundation.universe-levels open import globular-types.constant-globular-types diff --git a/src/globular-types/equality-globular-types.lagda.md b/src/globular-types/equality-globular-types.lagda.md index a93f6bde6f..d770f939a8 100644 --- a/src/globular-types/equality-globular-types.lagda.md +++ b/src/globular-types/equality-globular-types.lagda.md @@ -2,8 +2,15 @@ ```agda {-# OPTIONS --guardedness #-} - -module globular-types.equality-globular-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module globular-types.equality-globular-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -11,13 +18,13 @@ module globular-types.equality-globular-types where ```agda open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.binary-homotopies -open import foundation.cartesian-product-types +open import foundation.binary-homotopies funext +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types -open import foundation.torsorial-type-families -open import foundation.univalence +open import foundation.identity-types funext +open import foundation.torsorial-type-families funext univalence truncations +open import foundation.univalence funext univalence open import foundation.universe-levels open import foundation-core.coherently-invertible-maps diff --git a/src/globular-types/exponentials-globular-types.lagda.md b/src/globular-types/exponentials-globular-types.lagda.md index 85458109da..f7cad3f30b 100644 --- a/src/globular-types/exponentials-globular-types.lagda.md +++ b/src/globular-types/exponentials-globular-types.lagda.md @@ -2,8 +2,11 @@ ```agda {-# OPTIONS --guardedness #-} +open import foundation.function-extensionality-axiom -module globular-types.exponentials-globular-types where +module globular-types.exponentials-globular-types + (funext : function-extensionality) + where ```
Imports @@ -12,9 +15,9 @@ module globular-types.exponentials-globular-types where open import foundation.dependent-pair-types open import foundation.universe-levels -open import globular-types.globular-maps +open import globular-types.globular-maps funext open import globular-types.globular-types -open import globular-types.products-families-of-globular-types +open import globular-types.products-families-of-globular-types funext ```
diff --git a/src/globular-types/fibers-globular-maps.lagda.md b/src/globular-types/fibers-globular-maps.lagda.md index 62022c561b..0111a019db 100644 --- a/src/globular-types/fibers-globular-maps.lagda.md +++ b/src/globular-types/fibers-globular-maps.lagda.md @@ -2,20 +2,23 @@ ```agda {-# OPTIONS --guardedness #-} +open import foundation.function-extensionality-axiom -module globular-types.fibers-globular-maps where +module globular-types.fibers-globular-maps + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.fibers-of-maps -open import foundation.identity-types +open import foundation.fibers-of-maps funext +open import foundation.identity-types funext open import foundation.universe-levels -open import globular-types.dependent-globular-types -open import globular-types.globular-maps +open import globular-types.dependent-globular-types funext +open import globular-types.globular-maps funext open import globular-types.globular-types ``` diff --git a/src/globular-types/globular-equivalences.lagda.md b/src/globular-types/globular-equivalences.lagda.md index 5afece9603..4000718932 100644 --- a/src/globular-types/globular-equivalences.lagda.md +++ b/src/globular-types/globular-equivalences.lagda.md @@ -2,20 +2,23 @@ ```agda {-# OPTIONS --guardedness #-} +open import foundation.function-extensionality-axiom -module globular-types.globular-equivalences where +module globular-types.globular-equivalences + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.identity-types +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.identity-types funext open import foundation.universe-levels -open import globular-types.globular-maps +open import globular-types.globular-maps funext open import globular-types.globular-types ``` diff --git a/src/globular-types/globular-maps.lagda.md b/src/globular-types/globular-maps.lagda.md index 4cdc042698..903044ef8f 100644 --- a/src/globular-types/globular-maps.lagda.md +++ b/src/globular-types/globular-maps.lagda.md @@ -2,16 +2,19 @@ ```agda {-# OPTIONS --guardedness #-} +open import foundation.function-extensionality-axiom -module globular-types.globular-maps where +module globular-types.globular-maps + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.identity-types +open import foundation.function-types funext +open import foundation.identity-types funext open import foundation.universe-levels open import globular-types.globular-types diff --git a/src/globular-types/globular-types.lagda.md b/src/globular-types/globular-types.lagda.md index 11ecfe44fa..84c0ef6e25 100644 --- a/src/globular-types/globular-types.lagda.md +++ b/src/globular-types/globular-types.lagda.md @@ -10,7 +10,6 @@ module globular-types.globular-types where ```agda open import foundation.dependent-pair-types -open import foundation.identity-types open import foundation.universe-levels ``` diff --git a/src/globular-types/large-colax-reflexive-globular-maps.lagda.md b/src/globular-types/large-colax-reflexive-globular-maps.lagda.md index a293af9b2d..574837f3de 100644 --- a/src/globular-types/large-colax-reflexive-globular-maps.lagda.md +++ b/src/globular-types/large-colax-reflexive-globular-maps.lagda.md @@ -2,20 +2,27 @@ ```agda {-# OPTIONS --guardedness #-} - -module globular-types.large-colax-reflexive-globular-maps where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module globular-types.large-colax-reflexive-globular-maps + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.function-types +open import foundation.function-types funext open import foundation.universe-levels -open import globular-types.colax-reflexive-globular-maps -open import globular-types.large-globular-maps -open import globular-types.large-reflexive-globular-types -open import globular-types.reflexive-globular-types +open import globular-types.colax-reflexive-globular-maps funext univalence truncations +open import globular-types.large-globular-maps funext +open import globular-types.large-reflexive-globular-types funext univalence truncations +open import globular-types.reflexive-globular-types funext univalence truncations ```
diff --git a/src/globular-types/large-colax-transitive-globular-maps.lagda.md b/src/globular-types/large-colax-transitive-globular-maps.lagda.md index 89aa77b7db..3227f1af61 100644 --- a/src/globular-types/large-colax-transitive-globular-maps.lagda.md +++ b/src/globular-types/large-colax-transitive-globular-maps.lagda.md @@ -2,20 +2,27 @@ ```agda {-# OPTIONS --guardedness #-} - -module globular-types.large-colax-transitive-globular-maps where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module globular-types.large-colax-transitive-globular-maps + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.function-types +open import foundation.function-types funext open import foundation.universe-levels -open import globular-types.colax-transitive-globular-maps -open import globular-types.large-globular-maps -open import globular-types.large-transitive-globular-types -open import globular-types.transitive-globular-types +open import globular-types.colax-transitive-globular-maps funext univalence truncations +open import globular-types.large-globular-maps funext +open import globular-types.large-transitive-globular-types funext univalence truncations +open import globular-types.transitive-globular-types funext univalence truncations ```
diff --git a/src/globular-types/large-globular-maps.lagda.md b/src/globular-types/large-globular-maps.lagda.md index de2899cac3..ad80e85a7b 100644 --- a/src/globular-types/large-globular-maps.lagda.md +++ b/src/globular-types/large-globular-maps.lagda.md @@ -2,19 +2,22 @@ ```agda {-# OPTIONS --guardedness #-} +open import foundation.function-extensionality-axiom -module globular-types.large-globular-maps where +module globular-types.large-globular-maps + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.identity-types +open import foundation.function-types funext +open import foundation.identity-types funext open import foundation.universe-levels -open import globular-types.globular-maps +open import globular-types.globular-maps funext open import globular-types.globular-types open import globular-types.large-globular-types ``` diff --git a/src/globular-types/large-lax-reflexive-globular-maps.lagda.md b/src/globular-types/large-lax-reflexive-globular-maps.lagda.md index 4bde0a6526..ead0d03d87 100644 --- a/src/globular-types/large-lax-reflexive-globular-maps.lagda.md +++ b/src/globular-types/large-lax-reflexive-globular-maps.lagda.md @@ -2,20 +2,27 @@ ```agda {-# OPTIONS --guardedness #-} - -module globular-types.large-lax-reflexive-globular-maps where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module globular-types.large-lax-reflexive-globular-maps + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.function-types +open import foundation.function-types funext open import foundation.universe-levels -open import globular-types.large-globular-maps -open import globular-types.large-reflexive-globular-types -open import globular-types.lax-reflexive-globular-maps -open import globular-types.reflexive-globular-types +open import globular-types.large-globular-maps funext +open import globular-types.large-reflexive-globular-types funext univalence truncations +open import globular-types.lax-reflexive-globular-maps funext univalence truncations +open import globular-types.reflexive-globular-types funext univalence truncations ```
diff --git a/src/globular-types/large-lax-transitive-globular-maps.lagda.md b/src/globular-types/large-lax-transitive-globular-maps.lagda.md index d2534bf35f..63095d8775 100644 --- a/src/globular-types/large-lax-transitive-globular-maps.lagda.md +++ b/src/globular-types/large-lax-transitive-globular-maps.lagda.md @@ -2,20 +2,27 @@ ```agda {-# OPTIONS --guardedness #-} - -module globular-types.large-lax-transitive-globular-maps where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module globular-types.large-lax-transitive-globular-maps + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.function-types +open import foundation.function-types funext open import foundation.universe-levels -open import globular-types.large-globular-maps -open import globular-types.large-transitive-globular-types -open import globular-types.lax-transitive-globular-maps -open import globular-types.transitive-globular-types +open import globular-types.large-globular-maps funext +open import globular-types.large-transitive-globular-types funext univalence truncations +open import globular-types.lax-transitive-globular-maps funext univalence truncations +open import globular-types.transitive-globular-types funext univalence truncations ```
diff --git a/src/globular-types/large-reflexive-globular-maps.lagda.md b/src/globular-types/large-reflexive-globular-maps.lagda.md index 38cada0b7b..73b8127b70 100644 --- a/src/globular-types/large-reflexive-globular-maps.lagda.md +++ b/src/globular-types/large-reflexive-globular-maps.lagda.md @@ -2,20 +2,27 @@ ```agda {-# OPTIONS --guardedness #-} - -module globular-types.large-reflexive-globular-maps where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module globular-types.large-reflexive-globular-maps + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import globular-types.large-globular-maps -open import globular-types.large-reflexive-globular-types -open import globular-types.reflexive-globular-maps -open import globular-types.reflexive-globular-types +open import globular-types.large-globular-maps funext +open import globular-types.large-reflexive-globular-types funext univalence truncations +open import globular-types.reflexive-globular-maps funext univalence truncations +open import globular-types.reflexive-globular-types funext univalence truncations ```
diff --git a/src/globular-types/large-reflexive-globular-types.lagda.md b/src/globular-types/large-reflexive-globular-types.lagda.md index 5c87033440..c3ef4f1b85 100644 --- a/src/globular-types/large-reflexive-globular-types.lagda.md +++ b/src/globular-types/large-reflexive-globular-types.lagda.md @@ -2,21 +2,28 @@ ```agda {-# OPTIONS --guardedness #-} - -module globular-types.large-reflexive-globular-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module globular-types.large-reflexive-globular-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.binary-relations -open import foundation.large-binary-relations +open import foundation.binary-relations funext univalence truncations +open import foundation.large-binary-relations funext univalence truncations open import foundation.universe-levels open import globular-types.globular-types -open import globular-types.large-globular-maps +open import globular-types.large-globular-maps funext open import globular-types.large-globular-types -open import globular-types.reflexive-globular-types +open import globular-types.reflexive-globular-types funext univalence truncations ```
diff --git a/src/globular-types/large-symmetric-globular-types.lagda.md b/src/globular-types/large-symmetric-globular-types.lagda.md index 02e84ade5f..c06103d26a 100644 --- a/src/globular-types/large-symmetric-globular-types.lagda.md +++ b/src/globular-types/large-symmetric-globular-types.lagda.md @@ -2,19 +2,26 @@ ```agda {-# OPTIONS --guardedness #-} - -module globular-types.large-symmetric-globular-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module globular-types.large-symmetric-globular-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.large-binary-relations +open import foundation.large-binary-relations funext univalence truncations open import foundation.universe-levels open import globular-types.globular-types open import globular-types.large-globular-types -open import globular-types.symmetric-globular-types +open import globular-types.symmetric-globular-types funext univalence truncations ```
diff --git a/src/globular-types/large-transitive-globular-maps.lagda.md b/src/globular-types/large-transitive-globular-maps.lagda.md index c4800f5c99..3166d5bbde 100644 --- a/src/globular-types/large-transitive-globular-maps.lagda.md +++ b/src/globular-types/large-transitive-globular-maps.lagda.md @@ -2,22 +2,29 @@ ```agda {-# OPTIONS --guardedness #-} - -module globular-types.large-transitive-globular-maps where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module globular-types.large-transitive-globular-maps + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.function-types -open import foundation.identity-types +open import foundation.function-types funext +open import foundation.identity-types funext open import foundation.universe-levels -open import globular-types.large-globular-maps -open import globular-types.large-transitive-globular-types -open import globular-types.transitive-globular-maps -open import globular-types.transitive-globular-types +open import globular-types.large-globular-maps funext +open import globular-types.large-transitive-globular-types funext univalence truncations +open import globular-types.transitive-globular-maps funext univalence truncations +open import globular-types.transitive-globular-types funext univalence truncations ```
diff --git a/src/globular-types/large-transitive-globular-types.lagda.md b/src/globular-types/large-transitive-globular-types.lagda.md index 7981f454ba..1e3e037902 100644 --- a/src/globular-types/large-transitive-globular-types.lagda.md +++ b/src/globular-types/large-transitive-globular-types.lagda.md @@ -2,8 +2,15 @@ ```agda {-# OPTIONS --guardedness #-} - -module globular-types.large-transitive-globular-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module globular-types.large-transitive-globular-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -12,9 +19,9 @@ module globular-types.large-transitive-globular-types where open import foundation.universe-levels open import globular-types.globular-types -open import globular-types.large-globular-maps +open import globular-types.large-globular-maps funext open import globular-types.large-globular-types -open import globular-types.transitive-globular-types +open import globular-types.transitive-globular-types funext univalence truncations ```
diff --git a/src/globular-types/lax-reflexive-globular-maps.lagda.md b/src/globular-types/lax-reflexive-globular-maps.lagda.md index 910fa5260d..09c45221fb 100644 --- a/src/globular-types/lax-reflexive-globular-maps.lagda.md +++ b/src/globular-types/lax-reflexive-globular-maps.lagda.md @@ -2,8 +2,15 @@ ```agda {-# OPTIONS --guardedness #-} - -module globular-types.lax-reflexive-globular-maps where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module globular-types.lax-reflexive-globular-maps + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -11,8 +18,8 @@ module globular-types.lax-reflexive-globular-maps where ```agda open import foundation.universe-levels -open import globular-types.globular-maps -open import globular-types.reflexive-globular-types +open import globular-types.globular-maps funext +open import globular-types.reflexive-globular-types funext univalence truncations ```
diff --git a/src/globular-types/lax-transitive-globular-maps.lagda.md b/src/globular-types/lax-transitive-globular-maps.lagda.md index d06760ce39..289efcae2d 100644 --- a/src/globular-types/lax-transitive-globular-maps.lagda.md +++ b/src/globular-types/lax-transitive-globular-maps.lagda.md @@ -2,8 +2,15 @@ ```agda {-# OPTIONS --guardedness #-} - -module globular-types.lax-transitive-globular-maps where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module globular-types.lax-transitive-globular-maps + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -11,8 +18,8 @@ module globular-types.lax-transitive-globular-maps where ```agda open import foundation.universe-levels -open import globular-types.globular-maps -open import globular-types.transitive-globular-types +open import globular-types.globular-maps funext +open import globular-types.transitive-globular-types funext univalence truncations ```
diff --git a/src/globular-types/points-globular-types.lagda.md b/src/globular-types/points-globular-types.lagda.md index 94e81c6f56..bc5c486cdc 100644 --- a/src/globular-types/points-globular-types.lagda.md +++ b/src/globular-types/points-globular-types.lagda.md @@ -2,8 +2,11 @@ ```agda {-# OPTIONS --guardedness #-} +open import foundation.function-extensionality-axiom -module globular-types.points-globular-types where +module globular-types.points-globular-types + (funext : function-extensionality) + where ```
Imports @@ -12,7 +15,7 @@ module globular-types.points-globular-types where open import foundation.unit-type open import foundation.universe-levels -open import globular-types.globular-maps +open import globular-types.globular-maps funext open import globular-types.globular-types open import globular-types.unit-globular-type ``` diff --git a/src/globular-types/points-reflexive-globular-types.lagda.md b/src/globular-types/points-reflexive-globular-types.lagda.md index c18a467757..92353048ff 100644 --- a/src/globular-types/points-reflexive-globular-types.lagda.md +++ b/src/globular-types/points-reflexive-globular-types.lagda.md @@ -2,8 +2,15 @@ ```agda {-# OPTIONS --guardedness #-} +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom -module globular-types.points-reflexive-globular-types where +module globular-types.points-reflexive-globular-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -11,8 +18,8 @@ module globular-types.points-reflexive-globular-types where ```agda open import foundation.universe-levels -open import globular-types.points-globular-types -open import globular-types.reflexive-globular-types +open import globular-types.points-globular-types funext +open import globular-types.reflexive-globular-types funext univalence truncations ```
diff --git a/src/globular-types/pointwise-extensions-binary-families-globular-types.lagda.md b/src/globular-types/pointwise-extensions-binary-families-globular-types.lagda.md index 904d9b312f..f7ab7b8313 100644 --- a/src/globular-types/pointwise-extensions-binary-families-globular-types.lagda.md +++ b/src/globular-types/pointwise-extensions-binary-families-globular-types.lagda.md @@ -14,10 +14,10 @@ module open import foundation.dependent-pair-types open import foundation.universe-levels -open import globular-types.binary-dependent-globular-types -open import globular-types.globular-equivalences +open import globular-types.binary-dependent-globular-types funext +open import globular-types.globular-equivalences funext open import globular-types.globular-types -open import globular-types.points-globular-types +open import globular-types.points-globular-types funext ```
@@ -48,7 +48,10 @@ of `K` if it comes equipped with a family of ### The predicate of being a pointwise extension of a binary family of globular types ```agda +open import foundation.function-extensionality-axiom + module _ + (funext : function-extensionality) {l1 l2 l3 l4 l5 l6 l7 l8 : Level} {G : Globular-Type l1 l2} {H : Globular-Type l3 l4} (K : 0-cell-Globular-Type G → 0-cell-Globular-Type H → Globular-Type l5 l6) diff --git a/src/globular-types/pointwise-extensions-binary-families-reflexive-globular-types.lagda.md b/src/globular-types/pointwise-extensions-binary-families-reflexive-globular-types.lagda.md index c593d0e0a3..979fccbe68 100644 --- a/src/globular-types/pointwise-extensions-binary-families-reflexive-globular-types.lagda.md +++ b/src/globular-types/pointwise-extensions-binary-families-reflexive-globular-types.lagda.md @@ -14,10 +14,10 @@ module open import foundation.dependent-pair-types open import foundation.universe-levels -open import globular-types.binary-dependent-reflexive-globular-types -open import globular-types.points-reflexive-globular-types -open import globular-types.reflexive-globular-equivalences -open import globular-types.reflexive-globular-types +open import globular-types.binary-dependent-reflexive-globular-types funext univalence truncations +open import globular-types.points-reflexive-globular-types funext univalence truncations +open import globular-types.reflexive-globular-equivalences funext univalence truncations +open import globular-types.reflexive-globular-types funext univalence truncations ```
@@ -49,7 +49,14 @@ of `K` if it comes equipped with a family of ### The predicate of being a pointwise extension of a binary family of reflexive globular types ```agda +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + module _ + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) {l1 l2 l3 l4 l5 l6 l7 l8 : Level} {G : Reflexive-Globular-Type l1 l2} {H : Reflexive-Globular-Type l3 l4} (K : diff --git a/src/globular-types/pointwise-extensions-families-globular-types.lagda.md b/src/globular-types/pointwise-extensions-families-globular-types.lagda.md index 05d14be3df..6811a3c054 100644 --- a/src/globular-types/pointwise-extensions-families-globular-types.lagda.md +++ b/src/globular-types/pointwise-extensions-families-globular-types.lagda.md @@ -2,8 +2,11 @@ ```agda {-# OPTIONS --guardedness #-} +open import foundation.function-extensionality-axiom -module globular-types.pointwise-extensions-families-globular-types where +module globular-types.pointwise-extensions-families-globular-types + (funext : function-extensionality) + where ```
Imports @@ -12,10 +15,10 @@ module globular-types.pointwise-extensions-families-globular-types where open import foundation.dependent-pair-types open import foundation.universe-levels -open import globular-types.dependent-globular-types -open import globular-types.globular-equivalences +open import globular-types.dependent-globular-types funext +open import globular-types.globular-equivalences funext open import globular-types.globular-types -open import globular-types.points-globular-types +open import globular-types.points-globular-types funext ```
diff --git a/src/globular-types/pointwise-extensions-families-reflexive-globular-types.lagda.md b/src/globular-types/pointwise-extensions-families-reflexive-globular-types.lagda.md index 195002b2fe..5120bcabc0 100644 --- a/src/globular-types/pointwise-extensions-families-reflexive-globular-types.lagda.md +++ b/src/globular-types/pointwise-extensions-families-reflexive-globular-types.lagda.md @@ -14,13 +14,13 @@ module open import foundation.dependent-pair-types open import foundation.universe-levels -open import globular-types.dependent-globular-types -open import globular-types.dependent-reflexive-globular-types +open import globular-types.dependent-globular-types funext +open import globular-types.dependent-reflexive-globular-types funext univalence truncations open import globular-types.globular-types -open import globular-types.points-globular-types -open import globular-types.points-reflexive-globular-types -open import globular-types.reflexive-globular-equivalences -open import globular-types.reflexive-globular-types +open import globular-types.points-globular-types funext +open import globular-types.points-reflexive-globular-types funext univalence truncations +open import globular-types.reflexive-globular-equivalences funext univalence truncations +open import globular-types.reflexive-globular-types funext univalence truncations ```
@@ -49,7 +49,14 @@ indexed by the [points](globular-types.points-reflexive-globular-types.md) of ### The predicate of being a pointwise extension of a family of reflexive globular types ```agda +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + module _ + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) {l1 l2 l3 l4 l5 l6 : Level} {G : Reflexive-Globular-Type l1 l2} (H : 0-cell-Reflexive-Globular-Type G → Reflexive-Globular-Type l3 l4) (K : Dependent-Reflexive-Globular-Type l5 l6 G) diff --git a/src/globular-types/products-families-of-globular-types.lagda.md b/src/globular-types/products-families-of-globular-types.lagda.md index a3c5ae1d63..b754a3a5a5 100644 --- a/src/globular-types/products-families-of-globular-types.lagda.md +++ b/src/globular-types/products-families-of-globular-types.lagda.md @@ -2,8 +2,11 @@ ```agda {-# OPTIONS --guardedness #-} +open import foundation.function-extensionality-axiom -module globular-types.products-families-of-globular-types where +module globular-types.products-families-of-globular-types + (funext : function-extensionality) + where ```
Imports @@ -12,7 +15,7 @@ module globular-types.products-families-of-globular-types where open import foundation.dependent-pair-types open import foundation.universe-levels -open import globular-types.globular-maps +open import globular-types.globular-maps funext open import globular-types.globular-types ``` diff --git a/src/globular-types/reflexive-globular-equivalences.lagda.md b/src/globular-types/reflexive-globular-equivalences.lagda.md index 8d154f39af..7697d68d34 100644 --- a/src/globular-types/reflexive-globular-equivalences.lagda.md +++ b/src/globular-types/reflexive-globular-equivalences.lagda.md @@ -2,8 +2,15 @@ ```agda {-# OPTIONS --guardedness #-} - -module globular-types.reflexive-globular-equivalences where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module globular-types.reflexive-globular-equivalences + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -11,15 +18,15 @@ module globular-types.reflexive-globular-equivalences where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.identity-types +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.identity-types funext open import foundation.universe-levels -open import globular-types.globular-equivalences -open import globular-types.globular-maps -open import globular-types.reflexive-globular-maps -open import globular-types.reflexive-globular-types +open import globular-types.globular-equivalences funext +open import globular-types.globular-maps funext +open import globular-types.reflexive-globular-maps funext univalence truncations +open import globular-types.reflexive-globular-types funext univalence truncations ```
diff --git a/src/globular-types/reflexive-globular-maps.lagda.md b/src/globular-types/reflexive-globular-maps.lagda.md index 92bd88780a..7fd27decdb 100644 --- a/src/globular-types/reflexive-globular-maps.lagda.md +++ b/src/globular-types/reflexive-globular-maps.lagda.md @@ -2,18 +2,25 @@ ```agda {-# OPTIONS --guardedness #-} - -module globular-types.reflexive-globular-maps where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module globular-types.reflexive-globular-maps + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import globular-types.globular-maps -open import globular-types.reflexive-globular-types +open import globular-types.globular-maps funext +open import globular-types.reflexive-globular-types funext univalence truncations ```
diff --git a/src/globular-types/reflexive-globular-types.lagda.md b/src/globular-types/reflexive-globular-types.lagda.md index 8eec1e2951..3cc95e3eab 100644 --- a/src/globular-types/reflexive-globular-types.lagda.md +++ b/src/globular-types/reflexive-globular-types.lagda.md @@ -2,19 +2,26 @@ ```agda {-# OPTIONS --guardedness #-} - -module globular-types.reflexive-globular-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module globular-types.reflexive-globular-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.binary-relations +open import foundation.binary-relations funext univalence truncations open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import globular-types.globular-maps +open import globular-types.globular-maps funext open import globular-types.globular-types ``` diff --git a/src/globular-types/sections-dependent-globular-types.lagda.md b/src/globular-types/sections-dependent-globular-types.lagda.md index 382d8719a1..ed06c7762e 100644 --- a/src/globular-types/sections-dependent-globular-types.lagda.md +++ b/src/globular-types/sections-dependent-globular-types.lagda.md @@ -2,8 +2,11 @@ ```agda {-# OPTIONS --guardedness #-} +open import foundation.function-extensionality-axiom -module globular-types.sections-dependent-globular-types where +module globular-types.sections-dependent-globular-types + (funext : function-extensionality) + where ```
Imports @@ -11,7 +14,7 @@ module globular-types.sections-dependent-globular-types where ```agda open import foundation.universe-levels -open import globular-types.dependent-globular-types +open import globular-types.dependent-globular-types funext open import globular-types.globular-types ``` diff --git a/src/globular-types/superglobular-types.lagda.md b/src/globular-types/superglobular-types.lagda.md index eb34024fd4..2932b15718 100644 --- a/src/globular-types/superglobular-types.lagda.md +++ b/src/globular-types/superglobular-types.lagda.md @@ -2,8 +2,15 @@ ```agda {-# OPTIONS --guardedness #-} - -module globular-types.superglobular-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module globular-types.superglobular-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -12,12 +19,12 @@ module globular-types.superglobular-types where open import foundation.dependent-pair-types open import foundation.universe-levels -open import globular-types.binary-dependent-reflexive-globular-types +open import globular-types.binary-dependent-reflexive-globular-types funext univalence truncations open import globular-types.globular-types -open import globular-types.points-reflexive-globular-types -open import globular-types.pointwise-extensions-binary-families-reflexive-globular-types -open import globular-types.reflexive-globular-equivalences -open import globular-types.reflexive-globular-types +open import globular-types.points-reflexive-globular-types funext univalence truncations +open import globular-types.pointwise-extensions-binary-families-reflexive-globular-types funext univalence truncations +open import globular-types.reflexive-globular-equivalences funext univalence truncations +open import globular-types.reflexive-globular-types funext univalence truncations ```
diff --git a/src/globular-types/symmetric-globular-types.lagda.md b/src/globular-types/symmetric-globular-types.lagda.md index f8b627002c..411c35f157 100644 --- a/src/globular-types/symmetric-globular-types.lagda.md +++ b/src/globular-types/symmetric-globular-types.lagda.md @@ -2,16 +2,23 @@ ```agda {-# OPTIONS --guardedness #-} - -module globular-types.symmetric-globular-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module globular-types.symmetric-globular-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.binary-relations +open import foundation.binary-relations funext univalence truncations open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels open import globular-types.globular-types diff --git a/src/globular-types/terminal-globular-types.lagda.md b/src/globular-types/terminal-globular-types.lagda.md index b9007c4347..9e9f645850 100644 --- a/src/globular-types/terminal-globular-types.lagda.md +++ b/src/globular-types/terminal-globular-types.lagda.md @@ -2,17 +2,23 @@ ```agda {-# OPTIONS --guardedness #-} +open import foundation-core.univalence +open import foundation.function-extensionality-axiom -module globular-types.terminal-globular-types where +module globular-types.terminal-globular-types + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda -open import foundation.contractible-types +open import foundation.contractible-types funext univalence +open import foundation.dependent-products-contractible-types funext open import foundation.universe-levels -open import globular-types.globular-maps +open import globular-types.globular-maps funext open import globular-types.globular-types ``` diff --git a/src/globular-types/transitive-globular-maps.lagda.md b/src/globular-types/transitive-globular-maps.lagda.md index 3d7d093665..4fd1efe38d 100644 --- a/src/globular-types/transitive-globular-maps.lagda.md +++ b/src/globular-types/transitive-globular-maps.lagda.md @@ -2,19 +2,26 @@ ```agda {-# OPTIONS --guardedness #-} - -module globular-types.transitive-globular-maps where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module globular-types.transitive-globular-maps + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import globular-types.globular-maps -open import globular-types.transitive-globular-types +open import globular-types.globular-maps funext +open import globular-types.transitive-globular-types funext univalence truncations ```
diff --git a/src/globular-types/transitive-globular-types.lagda.md b/src/globular-types/transitive-globular-types.lagda.md index 368bad45fc..e8ca2438ef 100644 --- a/src/globular-types/transitive-globular-types.lagda.md +++ b/src/globular-types/transitive-globular-types.lagda.md @@ -2,19 +2,26 @@ ```agda {-# OPTIONS --guardedness #-} - -module globular-types.transitive-globular-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module globular-types.transitive-globular-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.binary-relations +open import foundation.binary-relations funext univalence truncations open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import globular-types.globular-maps +open import globular-types.globular-maps funext open import globular-types.globular-types ``` diff --git a/src/globular-types/unit-reflexive-globular-type.lagda.md b/src/globular-types/unit-reflexive-globular-type.lagda.md index 1c3e8752c0..c44ba27376 100644 --- a/src/globular-types/unit-reflexive-globular-type.lagda.md +++ b/src/globular-types/unit-reflexive-globular-type.lagda.md @@ -2,8 +2,15 @@ ```agda {-# OPTIONS --guardedness #-} - -module globular-types.unit-reflexive-globular-type where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module globular-types.unit-reflexive-globular-type + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -12,7 +19,7 @@ module globular-types.unit-reflexive-globular-type where open import foundation.unit-type open import foundation.universe-levels -open import globular-types.reflexive-globular-types +open import globular-types.reflexive-globular-types funext univalence truncations open import globular-types.unit-globular-type ``` diff --git a/src/globular-types/universal-globular-type.lagda.md b/src/globular-types/universal-globular-type.lagda.md index 2d67afcbf1..af3b5706f3 100644 --- a/src/globular-types/universal-globular-type.lagda.md +++ b/src/globular-types/universal-globular-type.lagda.md @@ -2,8 +2,11 @@ ```agda {-# OPTIONS --guardedness #-} +open import foundation.function-extensionality-axiom -module globular-types.universal-globular-type where +module globular-types.universal-globular-type + (funext : function-extensionality) + where ```
Imports @@ -13,9 +16,9 @@ open import foundation.dependent-pair-types open import foundation.spans open import foundation.universe-levels -open import globular-types.dependent-globular-types -open import globular-types.exponentials-globular-types -open import globular-types.globular-maps +open import globular-types.dependent-globular-types funext +open import globular-types.exponentials-globular-types funext +open import globular-types.globular-maps funext open import globular-types.globular-types ``` diff --git a/src/globular-types/universal-reflexive-globular-type.lagda.md b/src/globular-types/universal-reflexive-globular-type.lagda.md index d704e71b34..918e715961 100644 --- a/src/globular-types/universal-reflexive-globular-type.lagda.md +++ b/src/globular-types/universal-reflexive-globular-type.lagda.md @@ -2,8 +2,15 @@ ```agda {-# OPTIONS --guardedness #-} - -module globular-types.universal-reflexive-globular-type where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module globular-types.universal-reflexive-globular-type + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -12,7 +19,7 @@ module globular-types.universal-reflexive-globular-type where open import foundation.dependent-pair-types open import foundation.universe-levels -open import globular-types.reflexive-globular-types +open import globular-types.reflexive-globular-types funext univalence truncations ```
diff --git a/src/graph-theory.lagda.md b/src/graph-theory.lagda.md index c873b5ded2..25fe2bbf5e 100644 --- a/src/graph-theory.lagda.md +++ b/src/graph-theory.lagda.md @@ -3,85 +3,93 @@ ## Modules in the graph theory namespace ```agda -module graph-theory where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom -open import graph-theory.acyclic-undirected-graphs public -open import graph-theory.base-change-dependent-directed-graphs public -open import graph-theory.base-change-dependent-reflexive-graphs public -open import graph-theory.cartesian-products-directed-graphs public -open import graph-theory.cartesian-products-reflexive-graphs public -open import graph-theory.circuits-undirected-graphs public -open import graph-theory.closed-walks-undirected-graphs public -open import graph-theory.complete-bipartite-graphs public -open import graph-theory.complete-multipartite-graphs public -open import graph-theory.complete-undirected-graphs public -open import graph-theory.connected-undirected-graphs public -open import graph-theory.cycles-undirected-graphs public -open import graph-theory.dependent-directed-graphs public -open import graph-theory.dependent-products-directed-graphs public -open import graph-theory.dependent-products-reflexive-graphs public -open import graph-theory.dependent-reflexive-graphs public -open import graph-theory.dependent-sums-directed-graphs public -open import graph-theory.dependent-sums-reflexive-graphs public -open import graph-theory.directed-graph-duality public -open import graph-theory.directed-graph-structures-on-standard-finite-sets public -open import graph-theory.directed-graphs public -open import graph-theory.discrete-dependent-reflexive-graphs public -open import graph-theory.discrete-directed-graphs public -open import graph-theory.discrete-reflexive-graphs public -open import graph-theory.displayed-large-reflexive-graphs public -open import graph-theory.edge-coloured-undirected-graphs public -open import graph-theory.embeddings-directed-graphs public -open import graph-theory.embeddings-undirected-graphs public -open import graph-theory.enriched-undirected-graphs public -open import graph-theory.equivalences-dependent-directed-graphs public -open import graph-theory.equivalences-dependent-reflexive-graphs public -open import graph-theory.equivalences-directed-graphs public -open import graph-theory.equivalences-enriched-undirected-graphs public -open import graph-theory.equivalences-reflexive-graphs public -open import graph-theory.equivalences-undirected-graphs public -open import graph-theory.eulerian-circuits-undirected-graphs public -open import graph-theory.faithful-morphisms-undirected-graphs public -open import graph-theory.fibers-directed-graphs public -open import graph-theory.fibers-morphisms-directed-graphs public -open import graph-theory.fibers-morphisms-reflexive-graphs public -open import graph-theory.finite-graphs public -open import graph-theory.geometric-realizations-undirected-graphs public -open import graph-theory.higher-directed-graphs public -open import graph-theory.hypergraphs public -open import graph-theory.internal-hom-directed-graphs public -open import graph-theory.large-higher-directed-graphs public +module graph-theory + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where + +open import graph-theory.acyclic-undirected-graphs funext univalence truncations public +open import graph-theory.base-change-dependent-directed-graphs funext univalence truncations public +open import graph-theory.base-change-dependent-reflexive-graphs funext univalence truncations public +open import graph-theory.cartesian-products-directed-graphs funext univalence truncations public +open import graph-theory.cartesian-products-reflexive-graphs funext univalence truncations public +open import graph-theory.circuits-undirected-graphs funext univalence truncations public +open import graph-theory.closed-walks-undirected-graphs funext univalence truncations public +open import graph-theory.complete-bipartite-graphs funext univalence truncations public +open import graph-theory.complete-multipartite-graphs funext univalence truncations public +open import graph-theory.complete-undirected-graphs funext univalence truncations public +open import graph-theory.connected-undirected-graphs funext univalence truncations public +open import graph-theory.cycles-undirected-graphs funext univalence truncations public +open import graph-theory.dependent-directed-graphs funext univalence public +open import graph-theory.dependent-products-directed-graphs funext univalence truncations public +open import graph-theory.dependent-products-reflexive-graphs funext univalence truncations public +open import graph-theory.dependent-reflexive-graphs funext univalence truncations public +open import graph-theory.dependent-sums-directed-graphs funext univalence truncations public +open import graph-theory.dependent-sums-reflexive-graphs funext univalence truncations public +open import graph-theory.directed-graph-duality funext univalence truncations public +open import graph-theory.directed-graph-structures-on-standard-finite-sets funext univalence truncations public +open import graph-theory.directed-graphs funext univalence public +open import graph-theory.discrete-dependent-reflexive-graphs funext univalence truncations public +open import graph-theory.discrete-directed-graphs funext univalence truncations public +open import graph-theory.discrete-reflexive-graphs funext univalence truncations public +open import graph-theory.displayed-large-reflexive-graphs funext univalence truncations public +open import graph-theory.edge-coloured-undirected-graphs funext univalence truncations public +open import graph-theory.embeddings-directed-graphs funext univalence truncations public +open import graph-theory.embeddings-undirected-graphs funext univalence truncations public +open import graph-theory.enriched-undirected-graphs funext univalence truncations public +open import graph-theory.equivalences-dependent-directed-graphs funext univalence truncations public +open import graph-theory.equivalences-dependent-reflexive-graphs funext univalence truncations public +open import graph-theory.equivalences-directed-graphs funext univalence truncations public +open import graph-theory.equivalences-enriched-undirected-graphs funext univalence truncations public +open import graph-theory.equivalences-reflexive-graphs funext univalence truncations public +open import graph-theory.equivalences-undirected-graphs funext univalence truncations public +open import graph-theory.eulerian-circuits-undirected-graphs funext univalence truncations public +open import graph-theory.faithful-morphisms-undirected-graphs funext univalence truncations public +open import graph-theory.fibers-directed-graphs funext univalence truncations public +open import graph-theory.fibers-morphisms-directed-graphs funext univalence truncations public +open import graph-theory.fibers-morphisms-reflexive-graphs funext univalence truncations public +open import graph-theory.finite-graphs funext univalence truncations public +open import graph-theory.geometric-realizations-undirected-graphs funext univalence truncations public +open import graph-theory.higher-directed-graphs funext univalence truncations public +open import graph-theory.hypergraphs funext univalence truncations public +open import graph-theory.internal-hom-directed-graphs funext univalence truncations public +open import graph-theory.large-higher-directed-graphs funext univalence truncations public open import graph-theory.large-reflexive-graphs public -open import graph-theory.matchings public -open import graph-theory.mere-equivalences-undirected-graphs public -open import graph-theory.morphisms-dependent-directed-graphs public -open import graph-theory.morphisms-directed-graphs public -open import graph-theory.morphisms-reflexive-graphs public -open import graph-theory.morphisms-undirected-graphs public -open import graph-theory.neighbors-undirected-graphs public -open import graph-theory.orientations-undirected-graphs public -open import graph-theory.paths-undirected-graphs public -open import graph-theory.polygons public -open import graph-theory.raising-universe-levels-directed-graphs public -open import graph-theory.reflecting-maps-undirected-graphs public -open import graph-theory.reflexive-graphs public -open import graph-theory.regular-undirected-graphs public -open import graph-theory.sections-dependent-directed-graphs public -open import graph-theory.sections-dependent-reflexive-graphs public -open import graph-theory.simple-undirected-graphs public -open import graph-theory.stereoisomerism-enriched-undirected-graphs public -open import graph-theory.terminal-directed-graphs public -open import graph-theory.terminal-reflexive-graphs public -open import graph-theory.totally-faithful-morphisms-undirected-graphs public -open import graph-theory.trails-directed-graphs public -open import graph-theory.trails-undirected-graphs public -open import graph-theory.undirected-graph-structures-on-standard-finite-sets public -open import graph-theory.undirected-graphs public -open import graph-theory.universal-directed-graph public -open import graph-theory.universal-reflexive-graph public -open import graph-theory.vertex-covers public -open import graph-theory.voltage-graphs public -open import graph-theory.walks-directed-graphs public -open import graph-theory.walks-undirected-graphs public -open import graph-theory.wide-displayed-large-reflexive-graphs public +open import graph-theory.matchings funext univalence truncations public +open import graph-theory.mere-equivalences-undirected-graphs funext univalence truncations public +open import graph-theory.morphisms-dependent-directed-graphs funext univalence public +open import graph-theory.morphisms-directed-graphs funext univalence truncations public +open import graph-theory.morphisms-reflexive-graphs funext univalence truncations public +open import graph-theory.morphisms-undirected-graphs funext univalence truncations public +open import graph-theory.neighbors-undirected-graphs funext univalence truncations public +open import graph-theory.orientations-undirected-graphs funext univalence truncations public +open import graph-theory.paths-undirected-graphs funext univalence truncations public +open import graph-theory.polygons funext univalence truncations public +open import graph-theory.raising-universe-levels-directed-graphs funext univalence truncations public +open import graph-theory.reflecting-maps-undirected-graphs funext univalence truncations public +open import graph-theory.reflexive-graphs funext univalence truncations public +open import graph-theory.regular-undirected-graphs funext univalence truncations public +open import graph-theory.sections-dependent-directed-graphs funext univalence truncations public +open import graph-theory.sections-dependent-reflexive-graphs funext univalence truncations public +open import graph-theory.simple-undirected-graphs funext univalence truncations public +open import graph-theory.stereoisomerism-enriched-undirected-graphs funext univalence truncations public +open import graph-theory.terminal-directed-graphs funext univalence truncations public +open import graph-theory.terminal-reflexive-graphs funext univalence truncations public +open import graph-theory.totally-faithful-morphisms-undirected-graphs funext univalence truncations public +open import graph-theory.trails-directed-graphs funext univalence truncations public +open import graph-theory.trails-undirected-graphs funext univalence truncations public +open import graph-theory.undirected-graph-structures-on-standard-finite-sets funext univalence truncations public +open import graph-theory.undirected-graphs funext univalence truncations public +open import graph-theory.universal-directed-graph funext univalence truncations public +open import graph-theory.universal-reflexive-graph funext univalence truncations public +open import graph-theory.vertex-covers funext univalence truncations public +open import graph-theory.voltage-graphs funext univalence truncations public +open import graph-theory.walks-directed-graphs funext univalence truncations public +open import graph-theory.walks-undirected-graphs funext univalence truncations public +open import graph-theory.wide-displayed-large-reflexive-graphs funext univalence truncations public ``` diff --git a/src/graph-theory/acyclic-undirected-graphs.lagda.md b/src/graph-theory/acyclic-undirected-graphs.lagda.md index 300bd4eda8..376e1aa0ef 100644 --- a/src/graph-theory/acyclic-undirected-graphs.lagda.md +++ b/src/graph-theory/acyclic-undirected-graphs.lagda.md @@ -1,7 +1,15 @@ # Acyclic undirected graphs ```agda -module graph-theory.acyclic-undirected-graphs where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module graph-theory.acyclic-undirected-graphs + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,9 +17,9 @@ module graph-theory.acyclic-undirected-graphs where ```agda open import foundation.universe-levels -open import graph-theory.geometric-realizations-undirected-graphs -open import graph-theory.reflecting-maps-undirected-graphs -open import graph-theory.undirected-graphs +open import graph-theory.geometric-realizations-undirected-graphs funext univalence truncations +open import graph-theory.reflecting-maps-undirected-graphs funext univalence truncations +open import graph-theory.undirected-graphs funext univalence truncations ```
diff --git a/src/graph-theory/base-change-dependent-directed-graphs.lagda.md b/src/graph-theory/base-change-dependent-directed-graphs.lagda.md index 839b1619cd..f7496adc9d 100644 --- a/src/graph-theory/base-change-dependent-directed-graphs.lagda.md +++ b/src/graph-theory/base-change-dependent-directed-graphs.lagda.md @@ -1,7 +1,15 @@ # Base change of dependent directed graphs ```agda -module graph-theory.base-change-dependent-directed-graphs where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module graph-theory.base-change-dependent-directed-graphs + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,9 +18,9 @@ module graph-theory.base-change-dependent-directed-graphs where open import foundation.dependent-pair-types open import foundation.universe-levels -open import graph-theory.dependent-directed-graphs -open import graph-theory.directed-graphs -open import graph-theory.morphisms-directed-graphs +open import graph-theory.dependent-directed-graphs funext univalence +open import graph-theory.directed-graphs funext univalence +open import graph-theory.morphisms-directed-graphs funext univalence truncations ```
diff --git a/src/graph-theory/base-change-dependent-reflexive-graphs.lagda.md b/src/graph-theory/base-change-dependent-reflexive-graphs.lagda.md index d1168be9c8..3bf9512057 100644 --- a/src/graph-theory/base-change-dependent-reflexive-graphs.lagda.md +++ b/src/graph-theory/base-change-dependent-reflexive-graphs.lagda.md @@ -1,22 +1,30 @@ # Base change of dependent reflexive graphs ```agda -module graph-theory.base-change-dependent-reflexive-graphs where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module graph-theory.base-change-dependent-reflexive-graphs + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import graph-theory.base-change-dependent-directed-graphs -open import graph-theory.dependent-directed-graphs -open import graph-theory.dependent-reflexive-graphs -open import graph-theory.morphisms-reflexive-graphs -open import graph-theory.reflexive-graphs +open import graph-theory.base-change-dependent-directed-graphs funext univalence truncations +open import graph-theory.dependent-directed-graphs funext univalence +open import graph-theory.dependent-reflexive-graphs funext univalence truncations +open import graph-theory.morphisms-reflexive-graphs funext univalence truncations +open import graph-theory.reflexive-graphs funext univalence truncations ```
diff --git a/src/graph-theory/cartesian-products-directed-graphs.lagda.md b/src/graph-theory/cartesian-products-directed-graphs.lagda.md index 50840f8b15..40f47d7c36 100644 --- a/src/graph-theory/cartesian-products-directed-graphs.lagda.md +++ b/src/graph-theory/cartesian-products-directed-graphs.lagda.md @@ -1,18 +1,26 @@ # Cartesian products of directed graphs ```agda -module graph-theory.cartesian-products-directed-graphs where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module graph-theory.cartesian-products-directed-graphs + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types open import foundation.universe-levels -open import graph-theory.directed-graphs -open import graph-theory.morphisms-directed-graphs +open import graph-theory.directed-graphs funext univalence +open import graph-theory.morphisms-directed-graphs funext univalence truncations ```
diff --git a/src/graph-theory/cartesian-products-reflexive-graphs.lagda.md b/src/graph-theory/cartesian-products-reflexive-graphs.lagda.md index f68342b1c5..275a90e378 100644 --- a/src/graph-theory/cartesian-products-reflexive-graphs.lagda.md +++ b/src/graph-theory/cartesian-products-reflexive-graphs.lagda.md @@ -1,22 +1,30 @@ # Cartesian products of reflexive graphs ```agda -module graph-theory.cartesian-products-reflexive-graphs where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module graph-theory.cartesian-products-reflexive-graphs + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import graph-theory.cartesian-products-directed-graphs -open import graph-theory.directed-graphs -open import graph-theory.morphisms-directed-graphs -open import graph-theory.morphisms-reflexive-graphs -open import graph-theory.reflexive-graphs +open import graph-theory.cartesian-products-directed-graphs funext univalence truncations +open import graph-theory.directed-graphs funext univalence +open import graph-theory.morphisms-directed-graphs funext univalence truncations +open import graph-theory.morphisms-reflexive-graphs funext univalence truncations +open import graph-theory.reflexive-graphs funext univalence truncations ```
diff --git a/src/graph-theory/circuits-undirected-graphs.lagda.md b/src/graph-theory/circuits-undirected-graphs.lagda.md index e3a8ea7dcc..02a87310ab 100644 --- a/src/graph-theory/circuits-undirected-graphs.lagda.md +++ b/src/graph-theory/circuits-undirected-graphs.lagda.md @@ -1,7 +1,15 @@ # Circuits in undirected graphs ```agda -module graph-theory.circuits-undirected-graphs where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module graph-theory.circuits-undirected-graphs + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -12,9 +20,9 @@ open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types open import foundation.universe-levels -open import graph-theory.polygons -open import graph-theory.totally-faithful-morphisms-undirected-graphs -open import graph-theory.undirected-graphs +open import graph-theory.polygons funext univalence truncations +open import graph-theory.totally-faithful-morphisms-undirected-graphs funext univalence truncations +open import graph-theory.undirected-graphs funext univalence truncations ```
diff --git a/src/graph-theory/closed-walks-undirected-graphs.lagda.md b/src/graph-theory/closed-walks-undirected-graphs.lagda.md index 54484b5def..2e060cd4f5 100644 --- a/src/graph-theory/closed-walks-undirected-graphs.lagda.md +++ b/src/graph-theory/closed-walks-undirected-graphs.lagda.md @@ -1,7 +1,15 @@ # Closed walks in undirected graphs ```agda -module graph-theory.closed-walks-undirected-graphs where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module graph-theory.closed-walks-undirected-graphs + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -12,9 +20,9 @@ open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types open import foundation.universe-levels -open import graph-theory.morphisms-undirected-graphs -open import graph-theory.polygons -open import graph-theory.undirected-graphs +open import graph-theory.morphisms-undirected-graphs funext univalence truncations +open import graph-theory.polygons funext univalence truncations +open import graph-theory.undirected-graphs funext univalence truncations ```
diff --git a/src/graph-theory/complete-bipartite-graphs.lagda.md b/src/graph-theory/complete-bipartite-graphs.lagda.md index d671a66be1..4b113cad60 100644 --- a/src/graph-theory/complete-bipartite-graphs.lagda.md +++ b/src/graph-theory/complete-bipartite-graphs.lagda.md @@ -1,24 +1,32 @@ # Complete bipartite graphs ```agda -module graph-theory.complete-bipartite-graphs where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module graph-theory.complete-bipartite-graphs + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.coproduct-types +open import foundation.coproduct-types funext univalence truncations open import foundation.universe-levels -open import foundation.unordered-pairs +open import foundation.unordered-pairs funext univalence truncations -open import graph-theory.finite-graphs +open import graph-theory.finite-graphs funext univalence truncations -open import univalent-combinatorics.2-element-types -open import univalent-combinatorics.cartesian-product-types -open import univalent-combinatorics.coproduct-types -open import univalent-combinatorics.dependent-pair-types -open import univalent-combinatorics.fibers-of-maps -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.2-element-types funext univalence truncations +open import univalent-combinatorics.cartesian-product-types funext univalence truncations +open import univalent-combinatorics.coproduct-types funext univalence truncations +open import univalent-combinatorics.dependent-pair-types funext univalence truncations +open import univalent-combinatorics.fibers-of-maps funext univalence truncations +open import univalent-combinatorics.finite-types funext univalence truncations ```
diff --git a/src/graph-theory/complete-multipartite-graphs.lagda.md b/src/graph-theory/complete-multipartite-graphs.lagda.md index eafcab5fa0..741dd0e8cf 100644 --- a/src/graph-theory/complete-multipartite-graphs.lagda.md +++ b/src/graph-theory/complete-multipartite-graphs.lagda.md @@ -1,23 +1,31 @@ # Complete multipartite graphs ```agda -module graph-theory.complete-multipartite-graphs where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module graph-theory.complete-multipartite-graphs + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.universe-levels -open import foundation.unordered-pairs +open import foundation.unordered-pairs funext univalence truncations -open import graph-theory.finite-graphs +open import graph-theory.finite-graphs funext univalence truncations -open import univalent-combinatorics.2-element-types -open import univalent-combinatorics.dependent-function-types -open import univalent-combinatorics.dependent-pair-types -open import univalent-combinatorics.equality-finite-types -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.function-types +open import univalent-combinatorics.2-element-types funext univalence truncations +open import univalent-combinatorics.dependent-function-types funext univalence truncations +open import univalent-combinatorics.dependent-pair-types funext univalence truncations +open import univalent-combinatorics.equality-finite-types funext univalence truncations +open import univalent-combinatorics.finite-types funext univalence truncations +open import univalent-combinatorics.function-types funext univalence truncations ```
diff --git a/src/graph-theory/complete-undirected-graphs.lagda.md b/src/graph-theory/complete-undirected-graphs.lagda.md index 6adb8963c1..531ea219cd 100644 --- a/src/graph-theory/complete-undirected-graphs.lagda.md +++ b/src/graph-theory/complete-undirected-graphs.lagda.md @@ -1,7 +1,15 @@ # Complete undirected graphs ```agda -module graph-theory.complete-undirected-graphs where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module graph-theory.complete-undirected-graphs + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,10 +17,10 @@ module graph-theory.complete-undirected-graphs where ```agda open import foundation.universe-levels -open import graph-theory.complete-multipartite-graphs -open import graph-theory.finite-graphs +open import graph-theory.complete-multipartite-graphs funext univalence truncations +open import graph-theory.finite-graphs funext univalence truncations -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.finite-types funext univalence truncations ```
diff --git a/src/graph-theory/connected-undirected-graphs.lagda.md b/src/graph-theory/connected-undirected-graphs.lagda.md index fafe80a55b..dacc303b85 100644 --- a/src/graph-theory/connected-undirected-graphs.lagda.md +++ b/src/graph-theory/connected-undirected-graphs.lagda.md @@ -1,18 +1,27 @@ # Connected graphs ```agda -module graph-theory.connected-undirected-graphs where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module graph-theory.connected-undirected-graphs + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.propositional-truncations -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence open import foundation.universe-levels -open import graph-theory.undirected-graphs -open import graph-theory.walks-undirected-graphs +open import graph-theory.undirected-graphs funext univalence truncations +open import graph-theory.walks-undirected-graphs funext univalence truncations ```
diff --git a/src/graph-theory/cycles-undirected-graphs.lagda.md b/src/graph-theory/cycles-undirected-graphs.lagda.md index 2dd455a2f4..f58fe13ff7 100644 --- a/src/graph-theory/cycles-undirected-graphs.lagda.md +++ b/src/graph-theory/cycles-undirected-graphs.lagda.md @@ -1,7 +1,15 @@ # Cycles in undirected graphs ```agda -module graph-theory.cycles-undirected-graphs where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module graph-theory.cycles-undirected-graphs + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -12,9 +20,9 @@ open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types open import foundation.universe-levels -open import graph-theory.embeddings-undirected-graphs -open import graph-theory.polygons -open import graph-theory.undirected-graphs +open import graph-theory.embeddings-undirected-graphs funext univalence truncations +open import graph-theory.polygons funext univalence truncations +open import graph-theory.undirected-graphs funext univalence truncations ```
diff --git a/src/graph-theory/dependent-directed-graphs.lagda.md b/src/graph-theory/dependent-directed-graphs.lagda.md index bd7a43b39d..c2d0143f6a 100644 --- a/src/graph-theory/dependent-directed-graphs.lagda.md +++ b/src/graph-theory/dependent-directed-graphs.lagda.md @@ -1,7 +1,13 @@ # Dependent directed graphs ```agda -module graph-theory.dependent-directed-graphs where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module graph-theory.dependent-directed-graphs + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports @@ -10,7 +16,7 @@ module graph-theory.dependent-directed-graphs where open import foundation.dependent-pair-types open import foundation.universe-levels -open import graph-theory.directed-graphs +open import graph-theory.directed-graphs funext univalence ```
diff --git a/src/graph-theory/dependent-products-directed-graphs.lagda.md b/src/graph-theory/dependent-products-directed-graphs.lagda.md index 5e0174ead8..337a7beaf8 100644 --- a/src/graph-theory/dependent-products-directed-graphs.lagda.md +++ b/src/graph-theory/dependent-products-directed-graphs.lagda.md @@ -1,25 +1,33 @@ # Dependent products of directed graphs ```agda -module graph-theory.dependent-products-directed-graphs where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module graph-theory.dependent-products-directed-graphs + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.homotopies -open import foundation.retractions -open import foundation.sections +open import foundation.equivalences funext +open import foundation.homotopies funext +open import foundation.retractions funext +open import foundation.sections funext open import foundation.universe-levels -open import graph-theory.base-change-dependent-directed-graphs -open import graph-theory.cartesian-products-directed-graphs -open import graph-theory.dependent-directed-graphs -open import graph-theory.directed-graphs -open import graph-theory.morphisms-directed-graphs -open import graph-theory.sections-dependent-directed-graphs +open import graph-theory.base-change-dependent-directed-graphs funext univalence truncations +open import graph-theory.cartesian-products-directed-graphs funext univalence truncations +open import graph-theory.dependent-directed-graphs funext univalence +open import graph-theory.directed-graphs funext univalence +open import graph-theory.morphisms-directed-graphs funext univalence truncations +open import graph-theory.sections-dependent-directed-graphs funext univalence truncations ```
diff --git a/src/graph-theory/dependent-products-reflexive-graphs.lagda.md b/src/graph-theory/dependent-products-reflexive-graphs.lagda.md index 8ff497e2b5..f0019e58e6 100644 --- a/src/graph-theory/dependent-products-reflexive-graphs.lagda.md +++ b/src/graph-theory/dependent-products-reflexive-graphs.lagda.md @@ -1,45 +1,49 @@ # Dependent products of reflexive graphs ```agda -module graph-theory.dependent-products-reflexive-graphs where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module graph-theory.dependent-products-reflexive-graphs + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.binary-dependent-identifications open import foundation.binary-transport -open import foundation.commuting-squares-of-identifications -open import foundation.contractible-types +open import foundation.commuting-squares-of-identifications funext +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.functoriality-dependent-function-types -open import foundation.functoriality-dependent-pair-types +open import foundation.dependent-products-contractible-types funext +open import foundation.equality-dependent-function-types funext +open import foundation.equivalences funext +open import foundation.function-extensionality funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-function-types funext univalence +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types -open import foundation.reflexive-relations -open import foundation.retractions -open import foundation.sections +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.retractions funext +open import foundation.sections funext open import foundation.structure-identity-principle -open import foundation.torsorial-type-families -open import foundation.transport-along-identifications +open import foundation.torsorial-type-families funext univalence truncations open import foundation.universe-levels -open import graph-theory.base-change-dependent-reflexive-graphs -open import graph-theory.cartesian-products-reflexive-graphs -open import graph-theory.dependent-products-directed-graphs -open import graph-theory.dependent-reflexive-graphs -open import graph-theory.directed-graphs -open import graph-theory.morphisms-directed-graphs -open import graph-theory.morphisms-reflexive-graphs -open import graph-theory.reflexive-graphs -open import graph-theory.sections-dependent-reflexive-graphs +open import graph-theory.base-change-dependent-reflexive-graphs funext univalence truncations +open import graph-theory.cartesian-products-reflexive-graphs funext univalence truncations +open import graph-theory.dependent-reflexive-graphs funext univalence truncations +open import graph-theory.directed-graphs funext univalence +open import graph-theory.morphisms-directed-graphs funext univalence truncations +open import graph-theory.morphisms-reflexive-graphs funext univalence truncations +open import graph-theory.reflexive-graphs funext univalence truncations +open import graph-theory.sections-dependent-reflexive-graphs funext univalence truncations ```
diff --git a/src/graph-theory/dependent-reflexive-graphs.lagda.md b/src/graph-theory/dependent-reflexive-graphs.lagda.md index 76136f1504..2639512dc4 100644 --- a/src/graph-theory/dependent-reflexive-graphs.lagda.md +++ b/src/graph-theory/dependent-reflexive-graphs.lagda.md @@ -1,18 +1,26 @@ # Dependent reflexive graphs ```agda -module graph-theory.dependent-reflexive-graphs where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module graph-theory.dependent-reflexive-graphs + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences +open import foundation.equivalences funext open import foundation.universe-levels -open import graph-theory.dependent-directed-graphs -open import graph-theory.reflexive-graphs +open import graph-theory.dependent-directed-graphs funext univalence +open import graph-theory.reflexive-graphs funext univalence truncations ```
diff --git a/src/graph-theory/dependent-sums-directed-graphs.lagda.md b/src/graph-theory/dependent-sums-directed-graphs.lagda.md index 3c0ab314b5..f32d241039 100644 --- a/src/graph-theory/dependent-sums-directed-graphs.lagda.md +++ b/src/graph-theory/dependent-sums-directed-graphs.lagda.md @@ -1,7 +1,15 @@ # Dependent sums directed graphs ```agda -module graph-theory.dependent-sums-directed-graphs where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module graph-theory.dependent-sums-directed-graphs + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,11 +18,11 @@ module graph-theory.dependent-sums-directed-graphs where open import foundation.dependent-pair-types open import foundation.universe-levels -open import graph-theory.base-change-dependent-directed-graphs -open import graph-theory.dependent-directed-graphs -open import graph-theory.directed-graphs -open import graph-theory.morphisms-directed-graphs -open import graph-theory.sections-dependent-directed-graphs +open import graph-theory.base-change-dependent-directed-graphs funext univalence truncations +open import graph-theory.dependent-directed-graphs funext univalence +open import graph-theory.directed-graphs funext univalence +open import graph-theory.morphisms-directed-graphs funext univalence truncations +open import graph-theory.sections-dependent-directed-graphs funext univalence truncations ```
diff --git a/src/graph-theory/dependent-sums-reflexive-graphs.lagda.md b/src/graph-theory/dependent-sums-reflexive-graphs.lagda.md index f8b5131441..07531d07e9 100644 --- a/src/graph-theory/dependent-sums-reflexive-graphs.lagda.md +++ b/src/graph-theory/dependent-sums-reflexive-graphs.lagda.md @@ -1,31 +1,40 @@ # Dependent sums reflexive graphs ```agda -module graph-theory.dependent-sums-reflexive-graphs where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module graph-theory.dependent-sums-reflexive-graphs + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.contractible-types +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.identity-types +open import foundation.dependent-products-contractible-types funext +open import foundation.equivalences funext +open import foundation.identity-types funext open import foundation.structure-identity-principle open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels -open import graph-theory.base-change-dependent-reflexive-graphs -open import graph-theory.dependent-reflexive-graphs -open import graph-theory.dependent-sums-directed-graphs -open import graph-theory.directed-graphs -open import graph-theory.discrete-dependent-reflexive-graphs -open import graph-theory.discrete-reflexive-graphs -open import graph-theory.morphisms-directed-graphs -open import graph-theory.morphisms-reflexive-graphs -open import graph-theory.reflexive-graphs -open import graph-theory.sections-dependent-directed-graphs -open import graph-theory.sections-dependent-reflexive-graphs +open import graph-theory.base-change-dependent-reflexive-graphs funext univalence truncations +open import graph-theory.dependent-reflexive-graphs funext univalence truncations +open import graph-theory.dependent-sums-directed-graphs funext univalence truncations +open import graph-theory.directed-graphs funext univalence +open import graph-theory.discrete-dependent-reflexive-graphs funext univalence truncations +open import graph-theory.discrete-reflexive-graphs funext univalence truncations +open import graph-theory.morphisms-directed-graphs funext univalence truncations +open import graph-theory.morphisms-reflexive-graphs funext univalence truncations +open import graph-theory.reflexive-graphs funext univalence truncations +open import graph-theory.sections-dependent-directed-graphs funext univalence truncations +open import graph-theory.sections-dependent-reflexive-graphs funext univalence truncations ```
diff --git a/src/graph-theory/directed-graph-duality.lagda.md b/src/graph-theory/directed-graph-duality.lagda.md index 26a89c50fc..9b840d152f 100644 --- a/src/graph-theory/directed-graph-duality.lagda.md +++ b/src/graph-theory/directed-graph-duality.lagda.md @@ -1,29 +1,37 @@ # Directed graph duality ```agda -module graph-theory.directed-graph-duality where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module graph-theory.directed-graph-duality + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences +open import foundation.equivalences funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types -open import foundation.retractions -open import foundation.sections +open import foundation.identity-types funext +open import foundation.retractions funext +open import foundation.sections funext open import foundation.structure-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext univalence truncations open import foundation.universe-levels -open import graph-theory.dependent-directed-graphs -open import graph-theory.dependent-sums-directed-graphs -open import graph-theory.directed-graphs -open import graph-theory.equivalences-dependent-directed-graphs -open import graph-theory.equivalences-directed-graphs -open import graph-theory.fibers-morphisms-directed-graphs -open import graph-theory.morphisms-directed-graphs +open import graph-theory.dependent-directed-graphs funext univalence +open import graph-theory.dependent-sums-directed-graphs funext univalence truncations +open import graph-theory.directed-graphs funext univalence +open import graph-theory.equivalences-dependent-directed-graphs funext univalence truncations +open import graph-theory.equivalences-directed-graphs funext univalence truncations +open import graph-theory.fibers-morphisms-directed-graphs funext univalence truncations +open import graph-theory.morphisms-directed-graphs funext univalence truncations ```
diff --git a/src/graph-theory/directed-graph-structures-on-standard-finite-sets.lagda.md b/src/graph-theory/directed-graph-structures-on-standard-finite-sets.lagda.md index 79f8ee66f1..a8d4ca7b40 100644 --- a/src/graph-theory/directed-graph-structures-on-standard-finite-sets.lagda.md +++ b/src/graph-theory/directed-graph-structures-on-standard-finite-sets.lagda.md @@ -1,7 +1,15 @@ # Directed graph structures on standard finite sets ```agda -module graph-theory.directed-graph-structures-on-standard-finite-sets where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module graph-theory.directed-graph-structures-on-standard-finite-sets + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -12,7 +20,7 @@ open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types open import foundation.universe-levels -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/graph-theory/directed-graphs.lagda.md b/src/graph-theory/directed-graphs.lagda.md index 798b5afeb6..9a9e648c74 100644 --- a/src/graph-theory/directed-graphs.lagda.md +++ b/src/graph-theory/directed-graphs.lagda.md @@ -1,16 +1,22 @@ # Directed graphs ```agda -module graph-theory.directed-graphs where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module graph-theory.directed-graphs + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.identity-types +open import foundation.function-types funext +open import foundation.identity-types funext open import foundation.universe-levels ``` diff --git a/src/graph-theory/discrete-dependent-reflexive-graphs.lagda.md b/src/graph-theory/discrete-dependent-reflexive-graphs.lagda.md index 9d43af0730..33fedae7d6 100644 --- a/src/graph-theory/discrete-dependent-reflexive-graphs.lagda.md +++ b/src/graph-theory/discrete-dependent-reflexive-graphs.lagda.md @@ -1,18 +1,27 @@ # Discrete dependent reflexive graphs ```agda -module graph-theory.discrete-dependent-reflexive-graphs where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module graph-theory.discrete-dependent-reflexive-graphs + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.propositions funext univalence open import foundation.universe-levels -open import graph-theory.dependent-reflexive-graphs -open import graph-theory.discrete-reflexive-graphs -open import graph-theory.reflexive-graphs +open import graph-theory.dependent-reflexive-graphs funext univalence truncations +open import graph-theory.discrete-reflexive-graphs funext univalence truncations +open import graph-theory.reflexive-graphs funext univalence truncations ```
diff --git a/src/graph-theory/discrete-directed-graphs.lagda.md b/src/graph-theory/discrete-directed-graphs.lagda.md index c3ff8a436b..edd439a04c 100644 --- a/src/graph-theory/discrete-directed-graphs.lagda.md +++ b/src/graph-theory/discrete-directed-graphs.lagda.md @@ -1,29 +1,38 @@ # Discrete directed graphs ```agda -module graph-theory.discrete-directed-graphs where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module graph-theory.discrete-directed-graphs + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.contractible-types +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.discrete-binary-relations -open import foundation.empty-types -open import foundation.equivalences -open import foundation.homotopies -open import foundation.retractions -open import foundation.sections +open import foundation.dependent-products-contractible-types funext +open import foundation.discrete-binary-relations funext univalence truncations +open import foundation.empty-types funext univalence truncations +open import foundation.equivalences funext +open import foundation.homotopies funext +open import foundation.retractions funext +open import foundation.sections funext open import foundation.universe-levels open import foundation-core.identity-types open import foundation-core.propositions open import foundation-core.torsorial-type-families -open import graph-theory.directed-graphs -open import graph-theory.morphisms-directed-graphs -open import graph-theory.reflexive-graphs +open import graph-theory.directed-graphs funext univalence +open import graph-theory.morphisms-directed-graphs funext univalence truncations +open import graph-theory.reflexive-graphs funext univalence truncations ```
diff --git a/src/graph-theory/discrete-reflexive-graphs.lagda.md b/src/graph-theory/discrete-reflexive-graphs.lagda.md index e750402ea7..96441692fe 100644 --- a/src/graph-theory/discrete-reflexive-graphs.lagda.md +++ b/src/graph-theory/discrete-reflexive-graphs.lagda.md @@ -1,23 +1,32 @@ # Discrete reflexive graphs ```agda -module graph-theory.discrete-reflexive-graphs where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module graph-theory.discrete-reflexive-graphs + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.contractible-types +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.discrete-reflexive-relations +open import foundation.dependent-products-contractible-types funext +open import foundation.discrete-reflexive-relations funext univalence truncations open import foundation.universe-levels open import foundation-core.identity-types open import foundation-core.propositions open import foundation-core.torsorial-type-families -open import graph-theory.directed-graphs -open import graph-theory.reflexive-graphs +open import graph-theory.directed-graphs funext univalence +open import graph-theory.reflexive-graphs funext univalence truncations ```
diff --git a/src/graph-theory/displayed-large-reflexive-graphs.lagda.md b/src/graph-theory/displayed-large-reflexive-graphs.lagda.md index 7040f628b1..bb8e7c2a78 100644 --- a/src/graph-theory/displayed-large-reflexive-graphs.lagda.md +++ b/src/graph-theory/displayed-large-reflexive-graphs.lagda.md @@ -1,7 +1,15 @@ # Displayed large reflexive graphs ```agda -module graph-theory.displayed-large-reflexive-graphs where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module graph-theory.displayed-large-reflexive-graphs + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -11,7 +19,7 @@ open import foundation.dependent-pair-types open import foundation.universe-levels open import graph-theory.large-reflexive-graphs -open import graph-theory.reflexive-graphs +open import graph-theory.reflexive-graphs funext univalence truncations ```
diff --git a/src/graph-theory/edge-coloured-undirected-graphs.lagda.md b/src/graph-theory/edge-coloured-undirected-graphs.lagda.md index fe22d6bcf3..d270191b60 100644 --- a/src/graph-theory/edge-coloured-undirected-graphs.lagda.md +++ b/src/graph-theory/edge-coloured-undirected-graphs.lagda.md @@ -1,19 +1,27 @@ # Edge-coloured undirected graphs ```agda -module graph-theory.edge-coloured-undirected-graphs where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module graph-theory.edge-coloured-undirected-graphs + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.embeddings +open import foundation.embeddings funext open import foundation.universe-levels -open import foundation.unordered-pairs +open import foundation.unordered-pairs funext univalence truncations -open import graph-theory.neighbors-undirected-graphs -open import graph-theory.undirected-graphs +open import graph-theory.neighbors-undirected-graphs funext univalence truncations +open import graph-theory.undirected-graphs funext univalence truncations ```
diff --git a/src/graph-theory/embeddings-directed-graphs.lagda.md b/src/graph-theory/embeddings-directed-graphs.lagda.md index e483f06dc2..41e2d13204 100644 --- a/src/graph-theory/embeddings-directed-graphs.lagda.md +++ b/src/graph-theory/embeddings-directed-graphs.lagda.md @@ -1,19 +1,28 @@ # Embeddings of directed graphs ```agda -module graph-theory.embeddings-directed-graphs where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module graph-theory.embeddings-directed-graphs + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.embeddings funext +open import foundation.propositions funext univalence open import foundation.universe-levels -open import graph-theory.directed-graphs -open import graph-theory.morphisms-directed-graphs +open import graph-theory.directed-graphs funext univalence +open import graph-theory.morphisms-directed-graphs funext univalence truncations ```
diff --git a/src/graph-theory/embeddings-undirected-graphs.lagda.md b/src/graph-theory/embeddings-undirected-graphs.lagda.md index db07969f1c..d1fda63f8e 100644 --- a/src/graph-theory/embeddings-undirected-graphs.lagda.md +++ b/src/graph-theory/embeddings-undirected-graphs.lagda.md @@ -1,19 +1,28 @@ # Embeddings of undirected graphs ```agda -module graph-theory.embeddings-undirected-graphs where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module graph-theory.embeddings-undirected-graphs + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.embeddings funext +open import foundation.propositions funext univalence open import foundation.universe-levels -open import graph-theory.morphisms-undirected-graphs -open import graph-theory.undirected-graphs +open import graph-theory.morphisms-undirected-graphs funext univalence truncations +open import graph-theory.undirected-graphs funext univalence truncations ```
diff --git a/src/graph-theory/enriched-undirected-graphs.lagda.md b/src/graph-theory/enriched-undirected-graphs.lagda.md index 1f74332982..7eb29ab0ff 100644 --- a/src/graph-theory/enriched-undirected-graphs.lagda.md +++ b/src/graph-theory/enriched-undirected-graphs.lagda.md @@ -1,26 +1,34 @@ # Enriched undirected graphs ```agda -module graph-theory.enriched-undirected-graphs where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module graph-theory.enriched-undirected-graphs + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.connected-components +open import foundation.connected-components funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.universe-levels -open import graph-theory.neighbors-undirected-graphs -open import graph-theory.undirected-graphs +open import graph-theory.neighbors-undirected-graphs funext univalence truncations +open import graph-theory.undirected-graphs funext univalence truncations -open import higher-group-theory.higher-group-actions -open import higher-group-theory.higher-groups +open import higher-group-theory.higher-group-actions funext univalence truncations +open import higher-group-theory.higher-groups funext univalence truncations ```
diff --git a/src/graph-theory/equivalences-dependent-directed-graphs.lagda.md b/src/graph-theory/equivalences-dependent-directed-graphs.lagda.md index 2876ea23fa..26740baac3 100644 --- a/src/graph-theory/equivalences-dependent-directed-graphs.lagda.md +++ b/src/graph-theory/equivalences-dependent-directed-graphs.lagda.md @@ -1,26 +1,34 @@ # Equivalences of dependent directed graphs ```agda -module graph-theory.equivalences-dependent-directed-graphs where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module graph-theory.equivalences-dependent-directed-graphs + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types -open import foundation.equivalences -open import foundation.families-of-equivalences -open import foundation.function-types +open import foundation.equality-dependent-function-types funext +open import foundation.equivalences funext +open import foundation.families-of-equivalences funext +open import foundation.function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.structure-identity-principle -open import foundation.torsorial-type-families -open import foundation.univalence +open import foundation.torsorial-type-families funext univalence truncations +open import foundation.univalence funext univalence open import foundation.universe-levels -open import graph-theory.dependent-directed-graphs -open import graph-theory.directed-graphs +open import graph-theory.dependent-directed-graphs funext univalence +open import graph-theory.directed-graphs funext univalence ```
diff --git a/src/graph-theory/equivalences-dependent-reflexive-graphs.lagda.md b/src/graph-theory/equivalences-dependent-reflexive-graphs.lagda.md index 4197698468..6317dbae33 100644 --- a/src/graph-theory/equivalences-dependent-reflexive-graphs.lagda.md +++ b/src/graph-theory/equivalences-dependent-reflexive-graphs.lagda.md @@ -1,27 +1,35 @@ # Equivalences of dependent reflexive graphs ```agda -module graph-theory.equivalences-dependent-reflexive-graphs where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module graph-theory.equivalences-dependent-reflexive-graphs + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.dependent-identifications +open import foundation.dependent-identifications funext open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types -open import foundation.equivalences -open import foundation.families-of-equivalences +open import foundation.equality-dependent-function-types funext +open import foundation.equivalences funext +open import foundation.families-of-equivalences funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopy-induction -open import foundation.identity-types +open import foundation.homotopy-induction funext +open import foundation.identity-types funext open import foundation.structure-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext univalence truncations open import foundation.universe-levels -open import graph-theory.dependent-reflexive-graphs -open import graph-theory.equivalences-dependent-directed-graphs -open import graph-theory.reflexive-graphs +open import graph-theory.dependent-reflexive-graphs funext univalence truncations +open import graph-theory.equivalences-dependent-directed-graphs funext univalence truncations +open import graph-theory.reflexive-graphs funext univalence truncations ```
diff --git a/src/graph-theory/equivalences-directed-graphs.lagda.md b/src/graph-theory/equivalences-directed-graphs.lagda.md index a95e1ea270..45077442b6 100644 --- a/src/graph-theory/equivalences-directed-graphs.lagda.md +++ b/src/graph-theory/equivalences-directed-graphs.lagda.md @@ -1,7 +1,15 @@ # Equivalences of directed graphs ```agda -module graph-theory.equivalences-directed-graphs where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module graph-theory.equivalences-directed-graphs + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,28 +18,29 @@ module graph-theory.equivalences-directed-graphs where open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions open import foundation.binary-transport -open import foundation.cartesian-product-types -open import foundation.contractible-types +open import foundation.cartesian-product-types funext univalence +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types -open import foundation.equivalence-extensionality -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-function-types -open import foundation.functoriality-dependent-pair-types +open import foundation.dependent-products-contractible-types funext +open import foundation.equality-dependent-function-types funext +open import foundation.equivalence-extensionality funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-function-types funext univalence +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.identity-types +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.structure-identity-principle -open import foundation.torsorial-type-families -open import foundation.transposition-identifications-along-equivalences +open import foundation.torsorial-type-families funext univalence truncations +open import foundation.transposition-identifications-along-equivalences funext open import foundation.type-arithmetic-dependent-pair-types -open import foundation.type-theoretic-principle-of-choice -open import foundation.univalence +open import foundation.type-theoretic-principle-of-choice funext +open import foundation.univalence funext univalence open import foundation.universe-levels -open import graph-theory.directed-graphs -open import graph-theory.morphisms-directed-graphs +open import graph-theory.directed-graphs funext univalence +open import graph-theory.morphisms-directed-graphs funext univalence truncations ```
diff --git a/src/graph-theory/equivalences-enriched-undirected-graphs.lagda.md b/src/graph-theory/equivalences-enriched-undirected-graphs.lagda.md index 5655fafc9d..505c7b448b 100644 --- a/src/graph-theory/equivalences-enriched-undirected-graphs.lagda.md +++ b/src/graph-theory/equivalences-enriched-undirected-graphs.lagda.md @@ -1,29 +1,37 @@ # Equivalences of enriched undirected graphs ```agda -module graph-theory.equivalences-enriched-undirected-graphs where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module graph-theory.equivalences-enriched-undirected-graphs + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types -open import foundation.equivalence-extensionality -open import foundation.equivalences -open import foundation.function-types +open import foundation.equality-dependent-function-types funext +open import foundation.equivalence-extensionality funext +open import foundation.equivalences funext +open import foundation.function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext open import foundation.structure-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext univalence truncations open import foundation.transport-along-identifications open import foundation.universe-levels -open import graph-theory.enriched-undirected-graphs -open import graph-theory.equivalences-undirected-graphs -open import graph-theory.neighbors-undirected-graphs +open import graph-theory.enriched-undirected-graphs funext univalence truncations +open import graph-theory.equivalences-undirected-graphs funext univalence truncations +open import graph-theory.neighbors-undirected-graphs funext univalence truncations ```
diff --git a/src/graph-theory/equivalences-reflexive-graphs.lagda.md b/src/graph-theory/equivalences-reflexive-graphs.lagda.md index ae2ff0ebab..06e8c8560d 100644 --- a/src/graph-theory/equivalences-reflexive-graphs.lagda.md +++ b/src/graph-theory/equivalences-reflexive-graphs.lagda.md @@ -1,20 +1,28 @@ # Equivalences of reflexive graphs ```agda -module graph-theory.equivalences-reflexive-graphs where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module graph-theory.equivalences-reflexive-graphs + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.identity-types +open import foundation.equivalences funext +open import foundation.identity-types funext open import foundation.universe-levels -open import graph-theory.equivalences-directed-graphs -open import graph-theory.morphisms-reflexive-graphs -open import graph-theory.reflexive-graphs +open import graph-theory.equivalences-directed-graphs funext univalence truncations +open import graph-theory.morphisms-reflexive-graphs funext univalence truncations +open import graph-theory.reflexive-graphs funext univalence truncations ```
diff --git a/src/graph-theory/equivalences-undirected-graphs.lagda.md b/src/graph-theory/equivalences-undirected-graphs.lagda.md index 4b98ef0d5e..69cdb843bc 100644 --- a/src/graph-theory/equivalences-undirected-graphs.lagda.md +++ b/src/graph-theory/equivalences-undirected-graphs.lagda.md @@ -1,33 +1,42 @@ # Equivalences of undirected graphs ```agda -module graph-theory.equivalences-undirected-graphs where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module graph-theory.equivalences-undirected-graphs + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.contractible-types +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types -open import foundation.equivalence-extensionality -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-function-types -open import foundation.functoriality-dependent-pair-types +open import foundation.dependent-products-contractible-types funext +open import foundation.equality-dependent-function-types funext +open import foundation.equivalence-extensionality funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-function-types funext univalence +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.identity-types +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.structure-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext univalence truncations open import foundation.transport-along-identifications -open import foundation.univalence +open import foundation.univalence funext univalence open import foundation.universe-levels -open import foundation.unordered-pairs +open import foundation.unordered-pairs funext univalence truncations -open import graph-theory.morphisms-undirected-graphs -open import graph-theory.undirected-graphs +open import graph-theory.morphisms-undirected-graphs funext univalence truncations +open import graph-theory.undirected-graphs funext univalence truncations ```
diff --git a/src/graph-theory/eulerian-circuits-undirected-graphs.lagda.md b/src/graph-theory/eulerian-circuits-undirected-graphs.lagda.md index 5503cf3128..faf1a2bd25 100644 --- a/src/graph-theory/eulerian-circuits-undirected-graphs.lagda.md +++ b/src/graph-theory/eulerian-circuits-undirected-graphs.lagda.md @@ -1,7 +1,15 @@ # Eulerian circuits in undirected graphs ```agda -module graph-theory.eulerian-circuits-undirected-graphs where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module graph-theory.eulerian-circuits-undirected-graphs + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,13 +18,13 @@ module graph-theory.eulerian-circuits-undirected-graphs where open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.functoriality-dependent-pair-types +open import foundation.equivalences funext +open import foundation.functoriality-dependent-pair-types funext open import foundation.universe-levels -open import graph-theory.morphisms-undirected-graphs -open import graph-theory.polygons -open import graph-theory.undirected-graphs +open import graph-theory.morphisms-undirected-graphs funext univalence truncations +open import graph-theory.polygons funext univalence truncations +open import graph-theory.undirected-graphs funext univalence truncations ```
diff --git a/src/graph-theory/faithful-morphisms-undirected-graphs.lagda.md b/src/graph-theory/faithful-morphisms-undirected-graphs.lagda.md index 685ec29151..01dab76efc 100644 --- a/src/graph-theory/faithful-morphisms-undirected-graphs.lagda.md +++ b/src/graph-theory/faithful-morphisms-undirected-graphs.lagda.md @@ -1,19 +1,28 @@ # Faithful morphisms of undirected graphs ```agda -module graph-theory.faithful-morphisms-undirected-graphs where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module graph-theory.faithful-morphisms-undirected-graphs + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.embeddings funext +open import foundation.propositions funext univalence open import foundation.universe-levels -open import graph-theory.morphisms-undirected-graphs -open import graph-theory.undirected-graphs +open import graph-theory.morphisms-undirected-graphs funext univalence truncations +open import graph-theory.undirected-graphs funext univalence truncations ```
diff --git a/src/graph-theory/fibers-directed-graphs.lagda.md b/src/graph-theory/fibers-directed-graphs.lagda.md index ed82be7273..0035cc7245 100644 --- a/src/graph-theory/fibers-directed-graphs.lagda.md +++ b/src/graph-theory/fibers-directed-graphs.lagda.md @@ -1,29 +1,38 @@ # Fibers of directed graphs ```agda -module graph-theory.fibers-directed-graphs where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module graph-theory.fibers-directed-graphs + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.contractible-types -open import foundation.coproduct-types +open import foundation.contractible-types funext univalence +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types -open import foundation.equivalences -open import foundation.homotopies -open import foundation.identity-types -open import foundation.torsorial-type-families +open import foundation.dependent-products-contractible-types funext +open import foundation.equality-dependent-pair-types funext +open import foundation.equivalences funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.torsorial-type-families funext univalence truncations open import foundation.transport-along-identifications open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels -open import graph-theory.directed-graphs -open import graph-theory.morphisms-directed-graphs -open import graph-theory.walks-directed-graphs +open import graph-theory.directed-graphs funext univalence +open import graph-theory.morphisms-directed-graphs funext univalence truncations +open import graph-theory.walks-directed-graphs funext univalence truncations -open import trees.directed-trees +open import trees.directed-trees funext univalence truncations ```
diff --git a/src/graph-theory/fibers-morphisms-directed-graphs.lagda.md b/src/graph-theory/fibers-morphisms-directed-graphs.lagda.md index c6e11c4da1..01689a8da9 100644 --- a/src/graph-theory/fibers-morphisms-directed-graphs.lagda.md +++ b/src/graph-theory/fibers-morphisms-directed-graphs.lagda.md @@ -1,25 +1,33 @@ # Fibers of morphisms into directed graphs ```agda -module graph-theory.fibers-morphisms-directed-graphs where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module graph-theory.fibers-morphisms-directed-graphs + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.families-of-equivalences -open import foundation.fibers-of-maps -open import foundation.identity-types +open import foundation.equivalences funext +open import foundation.families-of-equivalences funext +open import foundation.fibers-of-maps funext +open import foundation.identity-types funext open import foundation.universe-levels -open import graph-theory.dependent-directed-graphs -open import graph-theory.dependent-sums-directed-graphs -open import graph-theory.directed-graphs -open import graph-theory.equivalences-dependent-directed-graphs -open import graph-theory.equivalences-directed-graphs -open import graph-theory.morphisms-directed-graphs +open import graph-theory.dependent-directed-graphs funext univalence +open import graph-theory.dependent-sums-directed-graphs funext univalence truncations +open import graph-theory.directed-graphs funext univalence +open import graph-theory.equivalences-dependent-directed-graphs funext univalence truncations +open import graph-theory.equivalences-directed-graphs funext univalence truncations +open import graph-theory.morphisms-directed-graphs funext univalence truncations ```
diff --git a/src/graph-theory/fibers-morphisms-reflexive-graphs.lagda.md b/src/graph-theory/fibers-morphisms-reflexive-graphs.lagda.md index 8ffde96bc4..4d4e1da588 100644 --- a/src/graph-theory/fibers-morphisms-reflexive-graphs.lagda.md +++ b/src/graph-theory/fibers-morphisms-reflexive-graphs.lagda.md @@ -1,7 +1,15 @@ # Fibers of morphisms into reflexive graphs ```agda -module graph-theory.fibers-morphisms-reflexive-graphs where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module graph-theory.fibers-morphisms-reflexive-graphs + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,25 +17,25 @@ module graph-theory.fibers-morphisms-reflexive-graphs where ```agda open import foundation.action-on-identifications-functions open import foundation.binary-transport -open import foundation.commuting-squares-of-identifications -open import foundation.dependent-identifications +open import foundation.commuting-squares-of-identifications funext +open import foundation.dependent-identifications funext open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types -open import foundation.equivalences -open import foundation.families-of-equivalences -open import foundation.fibers-of-maps -open import foundation.identity-types +open import foundation.equality-dependent-pair-types funext +open import foundation.equivalences funext +open import foundation.families-of-equivalences funext +open import foundation.fibers-of-maps funext +open import foundation.identity-types funext open import foundation.universe-levels -open import graph-theory.dependent-directed-graphs -open import graph-theory.dependent-reflexive-graphs -open import graph-theory.dependent-sums-reflexive-graphs -open import graph-theory.equivalences-dependent-directed-graphs -open import graph-theory.equivalences-dependent-reflexive-graphs -open import graph-theory.equivalences-reflexive-graphs -open import graph-theory.fibers-morphisms-directed-graphs -open import graph-theory.morphisms-reflexive-graphs -open import graph-theory.reflexive-graphs +open import graph-theory.dependent-directed-graphs funext univalence +open import graph-theory.dependent-reflexive-graphs funext univalence truncations +open import graph-theory.dependent-sums-reflexive-graphs funext univalence truncations +open import graph-theory.equivalences-dependent-directed-graphs funext univalence truncations +open import graph-theory.equivalences-dependent-reflexive-graphs funext univalence truncations +open import graph-theory.equivalences-reflexive-graphs funext univalence truncations +open import graph-theory.fibers-morphisms-directed-graphs funext univalence truncations +open import graph-theory.morphisms-reflexive-graphs funext univalence truncations +open import graph-theory.reflexive-graphs funext univalence truncations ```
diff --git a/src/graph-theory/finite-graphs.lagda.md b/src/graph-theory/finite-graphs.lagda.md index 6aff626a25..0df2ee0d1f 100644 --- a/src/graph-theory/finite-graphs.lagda.md +++ b/src/graph-theory/finite-graphs.lagda.md @@ -1,23 +1,31 @@ # Finite graphs ```agda -module graph-theory.finite-graphs where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module graph-theory.finite-graphs + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.fibers-of-maps -open import foundation.function-types -open import foundation.homotopies +open import foundation.equivalences funext +open import foundation.fibers-of-maps funext +open import foundation.function-types funext +open import foundation.homotopies funext open import foundation.universe-levels -open import foundation.unordered-pairs +open import foundation.unordered-pairs funext univalence truncations -open import graph-theory.undirected-graphs +open import graph-theory.undirected-graphs funext univalence truncations -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.finite-types funext univalence truncations ```
diff --git a/src/graph-theory/geometric-realizations-undirected-graphs.lagda.md b/src/graph-theory/geometric-realizations-undirected-graphs.lagda.md index bb8fa6abfc..7c3aca44ae 100644 --- a/src/graph-theory/geometric-realizations-undirected-graphs.lagda.md +++ b/src/graph-theory/geometric-realizations-undirected-graphs.lagda.md @@ -1,20 +1,28 @@ # Geometric realizations of undirected graphs ```agda -module graph-theory.geometric-realizations-undirected-graphs where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module graph-theory.geometric-realizations-undirected-graphs + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.symmetric-identity-types +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.symmetric-identity-types funext univalence truncations open import foundation.universe-levels -open import graph-theory.reflecting-maps-undirected-graphs -open import graph-theory.undirected-graphs +open import graph-theory.reflecting-maps-undirected-graphs funext univalence truncations +open import graph-theory.undirected-graphs funext univalence truncations ```
diff --git a/src/graph-theory/higher-directed-graphs.lagda.md b/src/graph-theory/higher-directed-graphs.lagda.md index 3357611b21..1e78bbf9c2 100644 --- a/src/graph-theory/higher-directed-graphs.lagda.md +++ b/src/graph-theory/higher-directed-graphs.lagda.md @@ -1,7 +1,15 @@ # Higher directed graphs ```agda -module graph-theory.higher-directed-graphs where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module graph-theory.higher-directed-graphs + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,15 +17,15 @@ module graph-theory.higher-directed-graphs where ```agda open import elementary-number-theory.natural-numbers -open import foundation.binary-relations -open import foundation.cartesian-product-types +open import foundation.binary-relations funext univalence truncations +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.identity-types +open import foundation.function-types funext +open import foundation.identity-types funext open import foundation.unit-type open import foundation.universe-levels -open import graph-theory.directed-graphs +open import graph-theory.directed-graphs funext univalence ```
diff --git a/src/graph-theory/hypergraphs.lagda.md b/src/graph-theory/hypergraphs.lagda.md index 018e504f13..50bd0f5306 100644 --- a/src/graph-theory/hypergraphs.lagda.md +++ b/src/graph-theory/hypergraphs.lagda.md @@ -1,7 +1,15 @@ # Hypergraphs ```agda -module graph-theory.hypergraphs where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module graph-theory.hypergraphs + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -11,7 +19,7 @@ open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types open import foundation.universe-levels -open import foundation.unordered-tuples +open import foundation.unordered-tuples funext univalence truncations ```
diff --git a/src/graph-theory/internal-hom-directed-graphs.lagda.md b/src/graph-theory/internal-hom-directed-graphs.lagda.md index c4625f214c..b6a5e91480 100644 --- a/src/graph-theory/internal-hom-directed-graphs.lagda.md +++ b/src/graph-theory/internal-hom-directed-graphs.lagda.md @@ -1,22 +1,30 @@ # Internal homs of directed graphs ```agda -module graph-theory.internal-hom-directed-graphs where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module graph-theory.internal-hom-directed-graphs + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.homotopies -open import foundation.retractions -open import foundation.sections +open import foundation.equivalences funext +open import foundation.homotopies funext +open import foundation.retractions funext +open import foundation.sections funext open import foundation.universe-levels -open import graph-theory.cartesian-products-directed-graphs -open import graph-theory.directed-graphs -open import graph-theory.morphisms-directed-graphs +open import graph-theory.cartesian-products-directed-graphs funext univalence truncations +open import graph-theory.directed-graphs funext univalence +open import graph-theory.morphisms-directed-graphs funext univalence truncations ```
diff --git a/src/graph-theory/large-higher-directed-graphs.lagda.md b/src/graph-theory/large-higher-directed-graphs.lagda.md index 6d805cf1a8..34c7926159 100644 --- a/src/graph-theory/large-higher-directed-graphs.lagda.md +++ b/src/graph-theory/large-higher-directed-graphs.lagda.md @@ -1,7 +1,15 @@ # Large higher directed graphs ```agda -module graph-theory.large-higher-directed-graphs where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module graph-theory.large-higher-directed-graphs + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,17 +17,18 @@ module graph-theory.large-higher-directed-graphs where ```agda open import elementary-number-theory.natural-numbers -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.identity-types -open import foundation.large-binary-relations -open import foundation.raising-universe-levels +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.large-binary-relations funext univalence truncations open import foundation.unit-type open import foundation.universe-levels -open import graph-theory.directed-graphs -open import graph-theory.higher-directed-graphs +open import foundation-core.raising-universe-levels + +open import graph-theory.directed-graphs funext univalence +open import graph-theory.higher-directed-graphs funext univalence truncations ```
diff --git a/src/graph-theory/large-reflexive-graphs.lagda.md b/src/graph-theory/large-reflexive-graphs.lagda.md index 0885e859a1..e752ceaf5e 100644 --- a/src/graph-theory/large-reflexive-graphs.lagda.md +++ b/src/graph-theory/large-reflexive-graphs.lagda.md @@ -7,7 +7,6 @@ module graph-theory.large-reflexive-graphs where
Imports ```agda -open import foundation.dependent-pair-types open import foundation.universe-levels ``` diff --git a/src/graph-theory/matchings.lagda.md b/src/graph-theory/matchings.lagda.md index 66d2d1cc2c..d991c23b14 100644 --- a/src/graph-theory/matchings.lagda.md +++ b/src/graph-theory/matchings.lagda.md @@ -1,24 +1,34 @@ # Matchings ```agda -module graph-theory.matchings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module graph-theory.matchings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.contractible-types -open import foundation.coproduct-types +open import foundation.contractible-types funext univalence +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.propositions +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence open import foundation.unit-type open import foundation.universe-levels -open import foundation.unordered-pairs +open import foundation.unordered-pairs funext univalence truncations -open import graph-theory.undirected-graphs +open import graph-theory.undirected-graphs funext univalence truncations -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/graph-theory/mere-equivalences-undirected-graphs.lagda.md b/src/graph-theory/mere-equivalences-undirected-graphs.lagda.md index 9376ae4058..88e9bb286f 100644 --- a/src/graph-theory/mere-equivalences-undirected-graphs.lagda.md +++ b/src/graph-theory/mere-equivalences-undirected-graphs.lagda.md @@ -1,18 +1,27 @@ # Mere equivalences of undirected graphs ```agda -module graph-theory.mere-equivalences-undirected-graphs where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module graph-theory.mere-equivalences-undirected-graphs + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.propositional-truncations -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence open import foundation.universe-levels -open import graph-theory.equivalences-undirected-graphs -open import graph-theory.undirected-graphs +open import graph-theory.equivalences-undirected-graphs funext univalence truncations +open import graph-theory.undirected-graphs funext univalence truncations ```
diff --git a/src/graph-theory/morphisms-dependent-directed-graphs.lagda.md b/src/graph-theory/morphisms-dependent-directed-graphs.lagda.md index ef0c365ed0..88668b670d 100644 --- a/src/graph-theory/morphisms-dependent-directed-graphs.lagda.md +++ b/src/graph-theory/morphisms-dependent-directed-graphs.lagda.md @@ -1,18 +1,24 @@ # Morphisms of dependent directed graphs ```agda -module graph-theory.morphisms-dependent-directed-graphs where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module graph-theory.morphisms-dependent-directed-graphs + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-types +open import foundation.function-types funext open import foundation.universe-levels -open import graph-theory.dependent-directed-graphs -open import graph-theory.directed-graphs +open import graph-theory.dependent-directed-graphs funext univalence +open import graph-theory.directed-graphs funext univalence ```
diff --git a/src/graph-theory/morphisms-directed-graphs.lagda.md b/src/graph-theory/morphisms-directed-graphs.lagda.md index 9c85662c76..1498b4b924 100644 --- a/src/graph-theory/morphisms-directed-graphs.lagda.md +++ b/src/graph-theory/morphisms-directed-graphs.lagda.md @@ -1,7 +1,15 @@ # Morphisms of directed graphs ```agda -module graph-theory.morphisms-directed-graphs where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module graph-theory.morphisms-directed-graphs + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,19 +18,19 @@ module graph-theory.morphisms-directed-graphs where open import foundation.binary-dependent-identifications open import foundation.binary-transport open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types +open import foundation.equality-dependent-function-types funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext open import foundation.structure-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext univalence truncations open import foundation.universe-levels -open import graph-theory.directed-graphs +open import graph-theory.directed-graphs funext univalence ```
diff --git a/src/graph-theory/morphisms-reflexive-graphs.lagda.md b/src/graph-theory/morphisms-reflexive-graphs.lagda.md index 855700002e..423cfd2875 100644 --- a/src/graph-theory/morphisms-reflexive-graphs.lagda.md +++ b/src/graph-theory/morphisms-reflexive-graphs.lagda.md @@ -1,7 +1,15 @@ # Morphisms of reflexive graphs ```agda -module graph-theory.morphisms-reflexive-graphs where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module graph-theory.morphisms-reflexive-graphs + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,22 +18,22 @@ module graph-theory.morphisms-reflexive-graphs where open import foundation.action-on-identifications-binary-dependent-functions open import foundation.action-on-identifications-functions open import foundation.binary-transport -open import foundation.commuting-squares-of-identifications +open import foundation.commuting-squares-of-identifications funext open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types +open import foundation.equality-dependent-function-types funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext open import foundation.structure-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext univalence truncations open import foundation.universe-levels -open import graph-theory.morphisms-directed-graphs -open import graph-theory.reflexive-graphs +open import graph-theory.morphisms-directed-graphs funext univalence truncations +open import graph-theory.reflexive-graphs funext univalence truncations ```
diff --git a/src/graph-theory/morphisms-undirected-graphs.lagda.md b/src/graph-theory/morphisms-undirected-graphs.lagda.md index aa80fba80a..5a44e7badc 100644 --- a/src/graph-theory/morphisms-undirected-graphs.lagda.md +++ b/src/graph-theory/morphisms-undirected-graphs.lagda.md @@ -1,31 +1,40 @@ # Morphisms of undirected graphs ```agda -module graph-theory.morphisms-undirected-graphs where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module graph-theory.morphisms-undirected-graphs + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.contractible-types +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-function-types -open import foundation.functoriality-dependent-pair-types +open import foundation.dependent-products-contractible-types funext +open import foundation.equality-dependent-function-types funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-function-types funext univalence +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext open import foundation.structure-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext univalence truncations open import foundation.transport-along-identifications open import foundation.universe-levels -open import foundation.unordered-pairs +open import foundation.unordered-pairs funext univalence truncations -open import graph-theory.undirected-graphs +open import graph-theory.undirected-graphs funext univalence truncations ```
diff --git a/src/graph-theory/neighbors-undirected-graphs.lagda.md b/src/graph-theory/neighbors-undirected-graphs.lagda.md index 9b6fba97e3..d287e5a29a 100644 --- a/src/graph-theory/neighbors-undirected-graphs.lagda.md +++ b/src/graph-theory/neighbors-undirected-graphs.lagda.md @@ -1,24 +1,32 @@ # Incidence in undirected graphs ```agda -module graph-theory.neighbors-undirected-graphs where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module graph-theory.neighbors-undirected-graphs + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types +open import foundation.equality-dependent-pair-types funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.universe-levels -open import foundation.unordered-pairs +open import foundation.unordered-pairs funext univalence truncations -open import graph-theory.equivalences-undirected-graphs -open import graph-theory.undirected-graphs +open import graph-theory.equivalences-undirected-graphs funext univalence truncations +open import graph-theory.undirected-graphs funext univalence truncations ```
diff --git a/src/graph-theory/orientations-undirected-graphs.lagda.md b/src/graph-theory/orientations-undirected-graphs.lagda.md index cdabb031fa..5fa0d924b0 100644 --- a/src/graph-theory/orientations-undirected-graphs.lagda.md +++ b/src/graph-theory/orientations-undirected-graphs.lagda.md @@ -1,7 +1,15 @@ # Orientations of undirected graphs ```agda -module graph-theory.orientations-undirected-graphs where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module graph-theory.orientations-undirected-graphs + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,9 +18,9 @@ module graph-theory.orientations-undirected-graphs where open import foundation.dependent-pair-types open import foundation.universe-levels -open import graph-theory.undirected-graphs +open import graph-theory.undirected-graphs funext univalence truncations -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.finite-types funext univalence truncations ```
diff --git a/src/graph-theory/paths-undirected-graphs.lagda.md b/src/graph-theory/paths-undirected-graphs.lagda.md index b811c34281..faaabc282f 100644 --- a/src/graph-theory/paths-undirected-graphs.lagda.md +++ b/src/graph-theory/paths-undirected-graphs.lagda.md @@ -1,7 +1,15 @@ # Paths in undirected graphs ```agda -module graph-theory.paths-undirected-graphs where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module graph-theory.paths-undirected-graphs + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,11 +18,11 @@ module graph-theory.paths-undirected-graphs where open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.injective-maps +open import foundation.injective-maps funext open import foundation.universe-levels -open import graph-theory.undirected-graphs -open import graph-theory.walks-undirected-graphs +open import graph-theory.undirected-graphs funext univalence truncations +open import graph-theory.walks-undirected-graphs funext univalence truncations ```
diff --git a/src/graph-theory/polygons.lagda.md b/src/graph-theory/polygons.lagda.md index 68f0117f77..5b00a76bd4 100644 --- a/src/graph-theory/polygons.lagda.md +++ b/src/graph-theory/polygons.lagda.md @@ -1,29 +1,37 @@ # Polygons ```agda -module graph-theory.polygons where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module graph-theory.polygons + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.modular-arithmetic +open import elementary-number-theory.modular-arithmetic funext univalence truncations open import elementary-number-theory.natural-numbers -open import foundation.decidable-equality +open import foundation.decidable-equality funext univalence truncations open import foundation.dependent-pair-types -open import foundation.fibers-of-maps -open import foundation.functoriality-propositional-truncation -open import foundation.mere-equivalences -open import foundation.sets +open import foundation.fibers-of-maps funext +open import foundation.functoriality-propositional-truncation funext univalence truncations +open import foundation.mere-equivalences funext univalence truncations +open import foundation.sets funext univalence open import foundation.universe-levels -open import foundation.unordered-pairs +open import foundation.unordered-pairs funext univalence truncations -open import graph-theory.equivalences-undirected-graphs -open import graph-theory.mere-equivalences-undirected-graphs -open import graph-theory.undirected-graphs +open import graph-theory.equivalences-undirected-graphs funext univalence truncations +open import graph-theory.mere-equivalences-undirected-graphs funext univalence truncations +open import graph-theory.undirected-graphs funext univalence truncations -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.finite-types funext univalence truncations ```
diff --git a/src/graph-theory/raising-universe-levels-directed-graphs.lagda.md b/src/graph-theory/raising-universe-levels-directed-graphs.lagda.md index ff763cffc0..880af80f41 100644 --- a/src/graph-theory/raising-universe-levels-directed-graphs.lagda.md +++ b/src/graph-theory/raising-universe-levels-directed-graphs.lagda.md @@ -1,20 +1,29 @@ # Raising universe levels of directed graphs ```agda -module graph-theory.raising-universe-levels-directed-graphs where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module graph-theory.raising-universe-levels-directed-graphs + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.raising-universe-levels +open import foundation.equivalences funext open import foundation.universe-levels -open import graph-theory.directed-graphs -open import graph-theory.equivalences-directed-graphs -open import graph-theory.walks-directed-graphs +open import foundation-core.raising-universe-levels + +open import graph-theory.directed-graphs funext univalence +open import graph-theory.equivalences-directed-graphs funext univalence truncations +open import graph-theory.walks-directed-graphs funext univalence truncations ```
diff --git a/src/graph-theory/reflecting-maps-undirected-graphs.lagda.md b/src/graph-theory/reflecting-maps-undirected-graphs.lagda.md index 5be62477ee..c7797f77e8 100644 --- a/src/graph-theory/reflecting-maps-undirected-graphs.lagda.md +++ b/src/graph-theory/reflecting-maps-undirected-graphs.lagda.md @@ -1,20 +1,29 @@ # Reflecting maps of undirected graphs ```agda -module graph-theory.reflecting-maps-undirected-graphs where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module graph-theory.reflecting-maps-undirected-graphs + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.contractible-types +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.symmetric-identity-types +open import foundation.dependent-products-contractible-types funext +open import foundation.symmetric-identity-types funext univalence truncations open import foundation.unit-type open import foundation.universe-levels -open import foundation.unordered-pairs +open import foundation.unordered-pairs funext univalence truncations -open import graph-theory.undirected-graphs +open import graph-theory.undirected-graphs funext univalence truncations ```
diff --git a/src/graph-theory/reflexive-graphs.lagda.md b/src/graph-theory/reflexive-graphs.lagda.md index 1ab53e86e5..4448a5f26d 100644 --- a/src/graph-theory/reflexive-graphs.lagda.md +++ b/src/graph-theory/reflexive-graphs.lagda.md @@ -1,7 +1,15 @@ # Reflexive graphs ```agda -module graph-theory.reflexive-graphs where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module graph-theory.reflexive-graphs + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,11 +17,11 @@ module graph-theory.reflexive-graphs where ```agda open import foundation.binary-dependent-identifications open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.reflexive-relations +open import foundation.identity-types funext +open import foundation.reflexive-relations funext univalence truncations open import foundation.universe-levels -open import graph-theory.directed-graphs +open import graph-theory.directed-graphs funext univalence ```
diff --git a/src/graph-theory/regular-undirected-graphs.lagda.md b/src/graph-theory/regular-undirected-graphs.lagda.md index 295ec95081..faea91f362 100644 --- a/src/graph-theory/regular-undirected-graphs.lagda.md +++ b/src/graph-theory/regular-undirected-graphs.lagda.md @@ -1,18 +1,27 @@ # Regular undirected graph ```agda -module graph-theory.regular-undirected-graphs where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module graph-theory.regular-undirected-graphs + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.mere-equivalences -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.mere-equivalences funext univalence truncations +open import foundation.propositions funext univalence open import foundation.universe-levels -open import graph-theory.neighbors-undirected-graphs -open import graph-theory.undirected-graphs +open import graph-theory.neighbors-undirected-graphs funext univalence truncations +open import graph-theory.undirected-graphs funext univalence truncations ```
diff --git a/src/graph-theory/sections-dependent-directed-graphs.lagda.md b/src/graph-theory/sections-dependent-directed-graphs.lagda.md index c8ca8c42d4..3d7279abf3 100644 --- a/src/graph-theory/sections-dependent-directed-graphs.lagda.md +++ b/src/graph-theory/sections-dependent-directed-graphs.lagda.md @@ -1,26 +1,34 @@ # Sections of dependent directed graphs ```agda -module graph-theory.sections-dependent-directed-graphs where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module graph-theory.sections-dependent-directed-graphs + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types -open import foundation.equivalences +open import foundation.equality-dependent-function-types funext +open import foundation.equivalences funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext open import foundation.structure-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext univalence truncations open import foundation.transport-along-identifications open import foundation.universe-levels -open import graph-theory.dependent-directed-graphs -open import graph-theory.directed-graphs +open import graph-theory.dependent-directed-graphs funext univalence +open import graph-theory.directed-graphs funext univalence ```
diff --git a/src/graph-theory/sections-dependent-reflexive-graphs.lagda.md b/src/graph-theory/sections-dependent-reflexive-graphs.lagda.md index 792b3557f8..d604986c98 100644 --- a/src/graph-theory/sections-dependent-reflexive-graphs.lagda.md +++ b/src/graph-theory/sections-dependent-reflexive-graphs.lagda.md @@ -1,7 +1,15 @@ # Sections of dependent reflexive graphs ```agda -module graph-theory.sections-dependent-reflexive-graphs where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module graph-theory.sections-dependent-reflexive-graphs + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -11,24 +19,24 @@ open import foundation.action-on-identifications-binary-dependent-functions open import foundation.action-on-identifications-dependent-functions open import foundation.action-on-identifications-functions open import foundation.binary-transport -open import foundation.commuting-squares-of-identifications +open import foundation.commuting-squares-of-identifications funext open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types -open import foundation.equivalences -open import foundation.function-types +open import foundation.equality-dependent-function-types funext +open import foundation.equivalences funext +open import foundation.function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types -open import foundation.reflexive-relations +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext +open import foundation.reflexive-relations funext univalence truncations open import foundation.structure-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext univalence truncations open import foundation.transport-along-identifications open import foundation.universe-levels -open import graph-theory.dependent-reflexive-graphs -open import graph-theory.reflexive-graphs -open import graph-theory.sections-dependent-directed-graphs +open import graph-theory.dependent-reflexive-graphs funext univalence truncations +open import graph-theory.reflexive-graphs funext univalence truncations +open import graph-theory.sections-dependent-directed-graphs funext univalence truncations ```
diff --git a/src/graph-theory/simple-undirected-graphs.lagda.md b/src/graph-theory/simple-undirected-graphs.lagda.md index b81f7668e6..ed1eb85e51 100644 --- a/src/graph-theory/simple-undirected-graphs.lagda.md +++ b/src/graph-theory/simple-undirected-graphs.lagda.md @@ -1,22 +1,31 @@ # Simple undirected graphs ```agda -module graph-theory.simple-undirected-graphs where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module graph-theory.simple-undirected-graphs + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.negation -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.embeddings funext +open import foundation.negation funext +open import foundation.propositions funext univalence open import foundation.universe-levels -open import foundation.unordered-pairs +open import foundation.unordered-pairs funext univalence truncations -open import graph-theory.undirected-graphs +open import graph-theory.undirected-graphs funext univalence truncations -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.finite-types funext univalence truncations ```
diff --git a/src/graph-theory/stereoisomerism-enriched-undirected-graphs.lagda.md b/src/graph-theory/stereoisomerism-enriched-undirected-graphs.lagda.md index 1fd241fbed..1f97c9d112 100644 --- a/src/graph-theory/stereoisomerism-enriched-undirected-graphs.lagda.md +++ b/src/graph-theory/stereoisomerism-enriched-undirected-graphs.lagda.md @@ -1,19 +1,27 @@ # Stereoisomerism for enriched undirected graphs ```agda -module graph-theory.stereoisomerism-enriched-undirected-graphs where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module graph-theory.stereoisomerism-enriched-undirected-graphs + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.homotopies +open import foundation.function-types funext +open import foundation.homotopies funext open import foundation.universe-levels -open import graph-theory.enriched-undirected-graphs -open import graph-theory.equivalences-undirected-graphs +open import graph-theory.enriched-undirected-graphs funext univalence truncations +open import graph-theory.equivalences-undirected-graphs funext univalence truncations ```
diff --git a/src/graph-theory/terminal-directed-graphs.lagda.md b/src/graph-theory/terminal-directed-graphs.lagda.md index d49804435a..84c9c0e6ab 100644 --- a/src/graph-theory/terminal-directed-graphs.lagda.md +++ b/src/graph-theory/terminal-directed-graphs.lagda.md @@ -1,20 +1,30 @@ # Terminal directed graphs ```agda -module graph-theory.terminal-directed-graphs where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module graph-theory.terminal-directed-graphs + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Idea ```agda -open import foundation.contractible-types +open import foundation.contractible-types funext univalence +open import foundation.dependent-products-contractible-types funext open import foundation.dependent-pair-types -open import foundation.propositions +open import foundation.propositions funext univalence +open import foundation.dependent-products-propositions funext open import foundation.unit-type open import foundation.universe-levels -open import graph-theory.directed-graphs -open import graph-theory.morphisms-directed-graphs +open import graph-theory.directed-graphs funext univalence +open import graph-theory.morphisms-directed-graphs funext univalence truncations ```
diff --git a/src/graph-theory/terminal-reflexive-graphs.lagda.md b/src/graph-theory/terminal-reflexive-graphs.lagda.md index 31ff8ae60a..5b49ddefc6 100644 --- a/src/graph-theory/terminal-reflexive-graphs.lagda.md +++ b/src/graph-theory/terminal-reflexive-graphs.lagda.md @@ -1,22 +1,32 @@ # Terminal reflexive graphs ```agda -module graph-theory.terminal-reflexive-graphs where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module graph-theory.terminal-reflexive-graphs + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Idea ```agda -open import foundation.contractible-types +open import foundation.contractible-types funext univalence +open import foundation.dependent-products-contractible-types funext open import foundation.dependent-pair-types -open import foundation.propositions +open import foundation.propositions funext univalence +open import foundation.dependent-products-propositions funext open import foundation.unit-type open import foundation.universe-levels -open import graph-theory.directed-graphs -open import graph-theory.reflexive-graphs -open import graph-theory.morphisms-reflexive-graphs -open import graph-theory.terminal-directed-graphs +open import graph-theory.directed-graphs funext univalence +open import graph-theory.reflexive-graphs funext univalence truncations +open import graph-theory.morphisms-reflexive-graphs funext univalence truncations +open import graph-theory.terminal-directed-graphs funext univalence truncations ```
diff --git a/src/graph-theory/totally-faithful-morphisms-undirected-graphs.lagda.md b/src/graph-theory/totally-faithful-morphisms-undirected-graphs.lagda.md index 7127494138..0aca7c1e9b 100644 --- a/src/graph-theory/totally-faithful-morphisms-undirected-graphs.lagda.md +++ b/src/graph-theory/totally-faithful-morphisms-undirected-graphs.lagda.md @@ -1,19 +1,27 @@ # Totally faithful morphisms of undirected graphs ```agda -module graph-theory.totally-faithful-morphisms-undirected-graphs where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module graph-theory.totally-faithful-morphisms-undirected-graphs + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.functoriality-dependent-pair-types +open import foundation.embeddings funext +open import foundation.functoriality-dependent-pair-types funext open import foundation.universe-levels -open import graph-theory.morphisms-undirected-graphs -open import graph-theory.undirected-graphs +open import graph-theory.morphisms-undirected-graphs funext univalence truncations +open import graph-theory.undirected-graphs funext univalence truncations ```
diff --git a/src/graph-theory/trails-directed-graphs.lagda.md b/src/graph-theory/trails-directed-graphs.lagda.md index 19c803955e..c9ea196706 100644 --- a/src/graph-theory/trails-directed-graphs.lagda.md +++ b/src/graph-theory/trails-directed-graphs.lagda.md @@ -1,18 +1,26 @@ # Trails in directed graphs ```agda -module graph-theory.trails-directed-graphs where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module graph-theory.trails-directed-graphs + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.injective-maps +open import foundation.injective-maps funext open import foundation.universe-levels -open import graph-theory.directed-graphs -open import graph-theory.walks-directed-graphs +open import graph-theory.directed-graphs funext univalence +open import graph-theory.walks-directed-graphs funext univalence truncations ```
diff --git a/src/graph-theory/trails-undirected-graphs.lagda.md b/src/graph-theory/trails-undirected-graphs.lagda.md index 3aaaa397cc..101299c046 100644 --- a/src/graph-theory/trails-undirected-graphs.lagda.md +++ b/src/graph-theory/trails-undirected-graphs.lagda.md @@ -1,7 +1,15 @@ # Trails in undirected graphs ```agda -module graph-theory.trails-undirected-graphs where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module graph-theory.trails-undirected-graphs + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,14 +17,15 @@ module graph-theory.trails-undirected-graphs where ```agda open import elementary-number-theory.natural-numbers -open import foundation.decidable-types +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.injective-maps -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.injective-maps funext +open import foundation.propositions funext univalence open import foundation.universe-levels -open import graph-theory.undirected-graphs -open import graph-theory.walks-undirected-graphs +open import graph-theory.undirected-graphs funext univalence truncations +open import graph-theory.walks-undirected-graphs funext univalence truncations ```
diff --git a/src/graph-theory/undirected-graph-structures-on-standard-finite-sets.lagda.md b/src/graph-theory/undirected-graph-structures-on-standard-finite-sets.lagda.md index b16324d61e..8dfca53172 100644 --- a/src/graph-theory/undirected-graph-structures-on-standard-finite-sets.lagda.md +++ b/src/graph-theory/undirected-graph-structures-on-standard-finite-sets.lagda.md @@ -1,7 +1,15 @@ # Undirected graph structures on standard finite sets ```agda -module graph-theory.undirected-graph-structures-on-standard-finite-sets where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module graph-theory.undirected-graph-structures-on-standard-finite-sets + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -11,9 +19,9 @@ open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types open import foundation.universe-levels -open import foundation.unordered-pairs +open import foundation.unordered-pairs funext univalence truncations -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/graph-theory/undirected-graphs.lagda.md b/src/graph-theory/undirected-graphs.lagda.md index dda08c3492..d453b951e5 100644 --- a/src/graph-theory/undirected-graphs.lagda.md +++ b/src/graph-theory/undirected-graphs.lagda.md @@ -1,20 +1,28 @@ # Undirected graphs ```agda -module graph-theory.undirected-graphs where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module graph-theory.undirected-graphs + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences +open import foundation.equivalences funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import foundation.unordered-pairs +open import foundation.unordered-pairs funext univalence truncations -open import graph-theory.directed-graphs +open import graph-theory.directed-graphs funext univalence ```
diff --git a/src/graph-theory/universal-directed-graph.lagda.md b/src/graph-theory/universal-directed-graph.lagda.md index d7242623d2..fd5ecf98d4 100644 --- a/src/graph-theory/universal-directed-graph.lagda.md +++ b/src/graph-theory/universal-directed-graph.lagda.md @@ -1,7 +1,15 @@ # The universal directed graph ```agda -module graph-theory.universal-directed-graph where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module graph-theory.universal-directed-graph + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,11 +18,11 @@ module graph-theory.universal-directed-graph where open import foundation.dependent-pair-types open import foundation.universe-levels -open import graph-theory.base-change-dependent-directed-graphs -open import graph-theory.dependent-directed-graphs -open import graph-theory.directed-graphs -open import graph-theory.equivalences-dependent-directed-graphs -open import graph-theory.morphisms-directed-graphs +open import graph-theory.base-change-dependent-directed-graphs funext univalence truncations +open import graph-theory.dependent-directed-graphs funext univalence +open import graph-theory.directed-graphs funext univalence +open import graph-theory.equivalences-dependent-directed-graphs funext univalence truncations +open import graph-theory.morphisms-directed-graphs funext univalence truncations ```
diff --git a/src/graph-theory/universal-reflexive-graph.lagda.md b/src/graph-theory/universal-reflexive-graph.lagda.md index 3b3fd8042f..e0f1e55e85 100644 --- a/src/graph-theory/universal-reflexive-graph.lagda.md +++ b/src/graph-theory/universal-reflexive-graph.lagda.md @@ -1,7 +1,15 @@ # The universal reflexive graph ```agda -module graph-theory.universal-reflexive-graph where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module graph-theory.universal-reflexive-graph + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,10 +18,10 @@ module graph-theory.universal-reflexive-graph where open import foundation.dependent-pair-types open import foundation.universe-levels -open import graph-theory.dependent-directed-graphs -open import graph-theory.dependent-reflexive-graphs -open import graph-theory.directed-graphs -open import graph-theory.reflexive-graphs +open import graph-theory.dependent-directed-graphs funext univalence +open import graph-theory.dependent-reflexive-graphs funext univalence truncations +open import graph-theory.directed-graphs funext univalence +open import graph-theory.reflexive-graphs funext univalence truncations ```
diff --git a/src/graph-theory/vertex-covers.lagda.md b/src/graph-theory/vertex-covers.lagda.md index 462cda70c8..a563964317 100644 --- a/src/graph-theory/vertex-covers.lagda.md +++ b/src/graph-theory/vertex-covers.lagda.md @@ -1,24 +1,32 @@ # Vertex covers ```agda -module graph-theory.vertex-covers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module graph-theory.vertex-covers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.cartesian-product-types -open import foundation.coproduct-types +open import foundation.cartesian-product-types funext univalence +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.propositional-truncations +open import foundation.identity-types funext +open import foundation.propositional-truncations funext univalence open import foundation.unit-type open import foundation.universe-levels -open import foundation.unordered-pairs +open import foundation.unordered-pairs funext univalence truncations -open import graph-theory.undirected-graphs +open import graph-theory.undirected-graphs funext univalence truncations -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/graph-theory/voltage-graphs.lagda.md b/src/graph-theory/voltage-graphs.lagda.md index bc99323d60..00ccefd658 100644 --- a/src/graph-theory/voltage-graphs.lagda.md +++ b/src/graph-theory/voltage-graphs.lagda.md @@ -1,7 +1,15 @@ # Voltage graphs ```agda -module graph-theory.voltage-graphs where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module graph-theory.voltage-graphs + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,9 +18,9 @@ module graph-theory.voltage-graphs where open import foundation.dependent-pair-types open import foundation.universe-levels -open import graph-theory.directed-graphs +open import graph-theory.directed-graphs funext univalence -open import group-theory.groups +open import group-theory.groups funext univalence truncations ```
diff --git a/src/graph-theory/walks-directed-graphs.lagda.md b/src/graph-theory/walks-directed-graphs.lagda.md index b7e9537b73..abfd54bcdb 100644 --- a/src/graph-theory/walks-directed-graphs.lagda.md +++ b/src/graph-theory/walks-directed-graphs.lagda.md @@ -1,7 +1,15 @@ # Walks in directed graphs ```agda -module graph-theory.walks-directed-graphs where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module graph-theory.walks-directed-graphs + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,27 +18,29 @@ module graph-theory.walks-directed-graphs where open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types -open import foundation.commuting-squares-of-maps -open import foundation.contractible-types -open import foundation.coproduct-types +open import foundation.cartesian-product-types funext univalence +open import foundation.commuting-squares-of-maps funext univalence +open import foundation.contractible-types funext univalence +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-cartesian-product-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.negated-equality -open import foundation.raising-universe-levels -open import foundation.torsorial-type-families +open import foundation.dependent-products-contractible-types funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.negated-equality funext univalence truncations +open import foundation.torsorial-type-families funext univalence truncations open import foundation.transport-along-identifications open import foundation.universe-levels -open import graph-theory.directed-graphs -open import graph-theory.equivalences-directed-graphs -open import graph-theory.morphisms-directed-graphs +open import foundation-core.raising-universe-levels + +open import graph-theory.directed-graphs funext univalence +open import graph-theory.equivalences-directed-graphs funext univalence truncations +open import graph-theory.morphisms-directed-graphs funext univalence truncations ```
diff --git a/src/graph-theory/walks-undirected-graphs.lagda.md b/src/graph-theory/walks-undirected-graphs.lagda.md index b73510b8b4..6f3b6360c1 100644 --- a/src/graph-theory/walks-undirected-graphs.lagda.md +++ b/src/graph-theory/walks-undirected-graphs.lagda.md @@ -1,36 +1,46 @@ # Walks in undirected graphs ```agda -module graph-theory.walks-undirected-graphs where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module graph-theory.walks-undirected-graphs + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.equality-natural-numbers +open import elementary-number-theory.equality-natural-numbers funext univalence truncations open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.contractible-types -open import foundation.coproduct-types -open import foundation.decidable-types +open import foundation.contractible-types funext univalence +open import foundation.coproduct-types funext univalence truncations +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-coproduct-types +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.empty-types funext univalence truncations +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-coproduct-types funext univalence truncations open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.torsorial-type-families -open import foundation.type-arithmetic-coproduct-types +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.torsorial-type-families funext univalence truncations +open import foundation.type-arithmetic-coproduct-types funext univalence truncations open import foundation.unit-type open import foundation.universe-levels -open import foundation.unordered-pairs +open import foundation.unordered-pairs funext univalence truncations -open import graph-theory.undirected-graphs +open import graph-theory.undirected-graphs funext univalence truncations -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/graph-theory/wide-displayed-large-reflexive-graphs.lagda.md b/src/graph-theory/wide-displayed-large-reflexive-graphs.lagda.md index 4392870452..e1782ab314 100644 --- a/src/graph-theory/wide-displayed-large-reflexive-graphs.lagda.md +++ b/src/graph-theory/wide-displayed-large-reflexive-graphs.lagda.md @@ -1,20 +1,28 @@ # Wide displayed large reflexive graphs ```agda -module graph-theory.wide-displayed-large-reflexive-graphs where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module graph-theory.wide-displayed-large-reflexive-graphs + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.cartesian-product-types -open import foundation.coproduct-types +open import foundation.cartesian-product-types funext univalence +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types open import foundation.unit-type open import foundation.universe-levels open import graph-theory.large-reflexive-graphs -open import graph-theory.reflexive-graphs +open import graph-theory.reflexive-graphs funext univalence truncations ```
diff --git a/src/group-theory.lagda.md b/src/group-theory.lagda.md index 6d7a7e8e31..f4df61cc2c 100644 --- a/src/group-theory.lagda.md +++ b/src/group-theory.lagda.md @@ -3,203 +3,211 @@ ## Modules in the group theory namespace ```agda -module group-theory where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom -open import group-theory.abelian-groups public -open import group-theory.abelianization-groups public -open import group-theory.addition-homomorphisms-abelian-groups public -open import group-theory.automorphism-groups public -open import group-theory.cartesian-products-abelian-groups public -open import group-theory.cartesian-products-concrete-groups public -open import group-theory.cartesian-products-groups public -open import group-theory.cartesian-products-monoids public -open import group-theory.cartesian-products-semigroups public -open import group-theory.category-of-abelian-groups public +module group-theory + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where + +open import group-theory.abelian-groups funext univalence truncations public +open import group-theory.abelianization-groups funext univalence truncations public +open import group-theory.addition-homomorphisms-abelian-groups funext univalence truncations public +open import group-theory.automorphism-groups funext univalence truncations public +open import group-theory.cartesian-products-abelian-groups funext univalence truncations public +open import group-theory.cartesian-products-concrete-groups funext univalence truncations public +open import group-theory.cartesian-products-groups funext univalence truncations public +open import group-theory.cartesian-products-monoids funext univalence truncations public +open import group-theory.cartesian-products-semigroups funext univalence public +open import group-theory.category-of-abelian-groups funext univalence truncations public open import group-theory.category-of-concrete-groups public -open import group-theory.category-of-group-actions public -open import group-theory.category-of-groups public -open import group-theory.category-of-orbits-groups public -open import group-theory.category-of-semigroups public -open import group-theory.cayleys-theorem public -open import group-theory.centers-groups public -open import group-theory.centers-monoids public -open import group-theory.centers-semigroups public -open import group-theory.central-elements-groups public -open import group-theory.central-elements-monoids public -open import group-theory.central-elements-semigroups public -open import group-theory.centralizer-subgroups public -open import group-theory.characteristic-subgroups public -open import group-theory.commutative-monoids public -open import group-theory.commutator-subgroups public -open import group-theory.commutators-of-elements-groups public -open import group-theory.commuting-elements-groups public -open import group-theory.commuting-elements-monoids public -open import group-theory.commuting-elements-semigroups public -open import group-theory.commuting-squares-of-group-homomorphisms public -open import group-theory.concrete-group-actions public -open import group-theory.concrete-groups public -open import group-theory.concrete-monoids public -open import group-theory.congruence-relations-abelian-groups public -open import group-theory.congruence-relations-commutative-monoids public -open import group-theory.congruence-relations-groups public -open import group-theory.congruence-relations-monoids public -open import group-theory.congruence-relations-semigroups public -open import group-theory.conjugation public -open import group-theory.conjugation-concrete-groups public -open import group-theory.contravariant-pushforward-concrete-group-actions public -open import group-theory.cores-monoids public -open import group-theory.cyclic-groups public -open import group-theory.decidable-subgroups public -open import group-theory.dependent-products-abelian-groups public -open import group-theory.dependent-products-commutative-monoids public -open import group-theory.dependent-products-groups public -open import group-theory.dependent-products-monoids public -open import group-theory.dependent-products-semigroups public -open import group-theory.dihedral-group-construction public -open import group-theory.dihedral-groups public -open import group-theory.e8-lattice public -open import group-theory.elements-of-finite-order-groups public -open import group-theory.embeddings-abelian-groups public -open import group-theory.embeddings-groups public -open import group-theory.endomorphism-rings-abelian-groups public -open import group-theory.epimorphisms-groups public -open import group-theory.equivalences-concrete-group-actions public -open import group-theory.equivalences-concrete-groups public -open import group-theory.equivalences-group-actions public -open import group-theory.equivalences-semigroups public -open import group-theory.exponents-abelian-groups public -open import group-theory.exponents-groups public -open import group-theory.free-concrete-group-actions public -open import group-theory.free-groups-with-one-generator public -open import group-theory.full-subgroups public -open import group-theory.full-subsemigroups public -open import group-theory.function-abelian-groups public -open import group-theory.function-commutative-monoids public -open import group-theory.function-groups public -open import group-theory.function-monoids public -open import group-theory.function-semigroups public -open import group-theory.functoriality-quotient-groups public -open import group-theory.furstenberg-groups public -open import group-theory.generating-elements-groups public -open import group-theory.generating-sets-groups public -open import group-theory.group-actions public -open import group-theory.groups public -open import group-theory.homomorphisms-abelian-groups public -open import group-theory.homomorphisms-commutative-monoids public -open import group-theory.homomorphisms-concrete-group-actions public -open import group-theory.homomorphisms-concrete-groups public -open import group-theory.homomorphisms-generated-subgroups public -open import group-theory.homomorphisms-group-actions public -open import group-theory.homomorphisms-groups public -open import group-theory.homomorphisms-groups-equipped-with-normal-subgroups public -open import group-theory.homomorphisms-monoids public -open import group-theory.homomorphisms-semigroups public -open import group-theory.homotopy-automorphism-groups public -open import group-theory.images-of-group-homomorphisms public -open import group-theory.images-of-semigroup-homomorphisms public -open import group-theory.integer-multiples-of-elements-abelian-groups public -open import group-theory.integer-powers-of-elements-groups public -open import group-theory.intersections-subgroups-abelian-groups public -open import group-theory.intersections-subgroups-groups public -open import group-theory.inverse-semigroups public -open import group-theory.invertible-elements-monoids public -open import group-theory.isomorphisms-abelian-groups public -open import group-theory.isomorphisms-concrete-groups public -open import group-theory.isomorphisms-group-actions public -open import group-theory.isomorphisms-groups public -open import group-theory.isomorphisms-monoids public -open import group-theory.isomorphisms-semigroups public -open import group-theory.iterated-cartesian-products-concrete-groups public -open import group-theory.kernels-homomorphisms-abelian-groups public -open import group-theory.kernels-homomorphisms-concrete-groups public -open import group-theory.kernels-homomorphisms-groups public -open import group-theory.large-semigroups public -open import group-theory.loop-groups-sets public -open import group-theory.mere-equivalences-concrete-group-actions public -open import group-theory.mere-equivalences-group-actions public -open import group-theory.minkowski-multiplication-commutative-monoids public -open import group-theory.minkowski-multiplication-monoids public -open import group-theory.minkowski-multiplication-semigroups public -open import group-theory.monoid-actions public -open import group-theory.monoids public -open import group-theory.monomorphisms-concrete-groups public -open import group-theory.monomorphisms-groups public -open import group-theory.multiples-of-elements-abelian-groups public -open import group-theory.nontrivial-groups public -open import group-theory.normal-closures-subgroups public -open import group-theory.normal-cores-subgroups public -open import group-theory.normal-subgroups public -open import group-theory.normal-subgroups-concrete-groups public -open import group-theory.normal-submonoids public -open import group-theory.normal-submonoids-commutative-monoids public -open import group-theory.normalizer-subgroups public -open import group-theory.nullifying-group-homomorphisms public -open import group-theory.opposite-groups public -open import group-theory.opposite-semigroups public -open import group-theory.orbit-stabilizer-theorem-concrete-groups public -open import group-theory.orbits-concrete-group-actions public -open import group-theory.orbits-group-actions public -open import group-theory.orders-of-elements-groups public -open import group-theory.perfect-cores public -open import group-theory.perfect-groups public -open import group-theory.perfect-subgroups public -open import group-theory.powers-of-elements-commutative-monoids public -open import group-theory.powers-of-elements-groups public -open import group-theory.powers-of-elements-monoids public -open import group-theory.precategory-of-commutative-monoids public -open import group-theory.precategory-of-concrete-groups public -open import group-theory.precategory-of-group-actions public -open import group-theory.precategory-of-groups public -open import group-theory.precategory-of-monoids public -open import group-theory.precategory-of-orbits-monoid-actions public -open import group-theory.precategory-of-semigroups public -open import group-theory.principal-group-actions public -open import group-theory.principal-torsors-concrete-groups public -open import group-theory.products-of-elements-monoids public -open import group-theory.products-of-tuples-of-elements-commutative-monoids public -open import group-theory.pullbacks-subgroups public -open import group-theory.pullbacks-subsemigroups public -open import group-theory.quotient-groups public -open import group-theory.quotient-groups-concrete-groups public -open import group-theory.quotients-abelian-groups public -open import group-theory.rational-commutative-monoids public -open import group-theory.representations-monoids-precategories public -open import group-theory.saturated-congruence-relations-commutative-monoids public -open import group-theory.saturated-congruence-relations-monoids public -open import group-theory.semigroups public -open import group-theory.sheargroups public -open import group-theory.shriek-concrete-group-actions public -open import group-theory.stabilizer-groups public -open import group-theory.stabilizer-groups-concrete-group-actions public -open import group-theory.subgroups public -open import group-theory.subgroups-abelian-groups public -open import group-theory.subgroups-concrete-groups public -open import group-theory.subgroups-generated-by-elements-groups public -open import group-theory.subgroups-generated-by-families-of-elements-groups public -open import group-theory.subgroups-generated-by-subsets-groups public -open import group-theory.submonoids public -open import group-theory.submonoids-commutative-monoids public -open import group-theory.subsemigroups public -open import group-theory.subsets-abelian-groups public -open import group-theory.subsets-commutative-monoids public -open import group-theory.subsets-groups public -open import group-theory.subsets-monoids public -open import group-theory.subsets-semigroups public -open import group-theory.substitution-functor-concrete-group-actions public -open import group-theory.substitution-functor-group-actions public -open import group-theory.surjective-group-homomorphisms public -open import group-theory.surjective-semigroup-homomorphisms public -open import group-theory.symmetric-concrete-groups public -open import group-theory.symmetric-groups public -open import group-theory.torsion-elements-groups public -open import group-theory.torsion-free-groups public -open import group-theory.torsors public -open import group-theory.transitive-concrete-group-actions public -open import group-theory.transitive-group-actions public -open import group-theory.trivial-concrete-groups public -open import group-theory.trivial-group-homomorphisms public -open import group-theory.trivial-groups public -open import group-theory.trivial-subgroups public -open import group-theory.unordered-tuples-of-elements-commutative-monoids public -open import group-theory.wild-representations-monoids public +open import group-theory.category-of-group-actions funext univalence truncations public +open import group-theory.category-of-groups funext univalence truncations public +open import group-theory.category-of-orbits-groups funext univalence truncations public +open import group-theory.category-of-semigroups funext univalence truncations public +open import group-theory.cayleys-theorem funext univalence truncations public +open import group-theory.centers-groups funext univalence truncations public +open import group-theory.centers-monoids funext univalence truncations public +open import group-theory.centers-semigroups funext univalence truncations public +open import group-theory.central-elements-groups funext univalence truncations public +open import group-theory.central-elements-monoids funext univalence truncations public +open import group-theory.central-elements-semigroups funext univalence public +open import group-theory.centralizer-subgroups funext univalence truncations public +open import group-theory.characteristic-subgroups funext univalence truncations public +open import group-theory.commutative-monoids funext univalence truncations public +open import group-theory.commutator-subgroups funext univalence truncations public +open import group-theory.commutators-of-elements-groups funext univalence truncations public +open import group-theory.commuting-elements-groups funext univalence truncations public +open import group-theory.commuting-elements-monoids funext univalence truncations public +open import group-theory.commuting-elements-semigroups funext univalence public +open import group-theory.commuting-squares-of-group-homomorphisms funext univalence truncations public +open import group-theory.concrete-group-actions funext univalence truncations public +open import group-theory.concrete-groups funext univalence truncations public +open import group-theory.concrete-monoids funext univalence truncations public +open import group-theory.congruence-relations-abelian-groups funext univalence truncations public +open import group-theory.congruence-relations-commutative-monoids funext univalence truncations public +open import group-theory.congruence-relations-groups funext univalence truncations public +open import group-theory.congruence-relations-monoids funext univalence truncations public +open import group-theory.congruence-relations-semigroups funext univalence truncations public +open import group-theory.conjugation funext univalence truncations public +open import group-theory.conjugation-concrete-groups funext univalence truncations public +open import group-theory.contravariant-pushforward-concrete-group-actions funext univalence truncations public +open import group-theory.cores-monoids funext univalence truncations public +open import group-theory.cyclic-groups funext univalence truncations public +open import group-theory.decidable-subgroups funext univalence truncations public +open import group-theory.dependent-products-abelian-groups funext univalence truncations public +open import group-theory.dependent-products-commutative-monoids funext univalence truncations public +open import group-theory.dependent-products-groups funext univalence truncations public +open import group-theory.dependent-products-monoids funext univalence truncations public +open import group-theory.dependent-products-semigroups funext univalence public +open import group-theory.dihedral-group-construction funext univalence truncations public +open import group-theory.dihedral-groups funext univalence truncations public +open import group-theory.e8-lattice funext univalence truncations public +open import group-theory.elements-of-finite-order-groups funext univalence truncations public +open import group-theory.embeddings-abelian-groups funext univalence truncations public +open import group-theory.embeddings-groups funext univalence truncations public +open import group-theory.endomorphism-rings-abelian-groups funext univalence truncations public +open import group-theory.epimorphisms-groups funext univalence truncations public +open import group-theory.equivalences-concrete-group-actions funext univalence truncations public +open import group-theory.equivalences-concrete-groups funext univalence truncations public +open import group-theory.equivalences-group-actions funext univalence truncations public +open import group-theory.equivalences-semigroups funext univalence truncations public +open import group-theory.exponents-abelian-groups funext univalence truncations public +open import group-theory.exponents-groups funext univalence truncations public +open import group-theory.free-concrete-group-actions funext univalence truncations public +open import group-theory.free-groups-with-one-generator funext univalence truncations public +open import group-theory.full-subgroups funext univalence truncations public +open import group-theory.full-subsemigroups funext univalence truncations public +open import group-theory.function-abelian-groups funext univalence truncations public +open import group-theory.function-commutative-monoids funext univalence truncations public +open import group-theory.function-groups funext univalence truncations public +open import group-theory.function-monoids funext univalence truncations public +open import group-theory.function-semigroups funext univalence public +open import group-theory.functoriality-quotient-groups funext univalence truncations public +open import group-theory.furstenberg-groups funext univalence truncations public +open import group-theory.generating-elements-groups funext univalence truncations public +open import group-theory.generating-sets-groups funext univalence truncations public +open import group-theory.group-actions funext univalence truncations public +open import group-theory.groups funext univalence truncations public +open import group-theory.homomorphisms-abelian-groups funext univalence truncations public +open import group-theory.homomorphisms-commutative-monoids funext univalence truncations public +open import group-theory.homomorphisms-concrete-group-actions funext univalence truncations public +open import group-theory.homomorphisms-concrete-groups funext univalence truncations public +open import group-theory.homomorphisms-generated-subgroups funext univalence truncations public +open import group-theory.homomorphisms-group-actions funext univalence truncations public +open import group-theory.homomorphisms-groups funext univalence truncations public +open import group-theory.homomorphisms-groups-equipped-with-normal-subgroups funext univalence truncations public +open import group-theory.homomorphisms-monoids funext univalence truncations public +open import group-theory.homomorphisms-semigroups funext univalence truncations public +open import group-theory.homotopy-automorphism-groups funext univalence truncations public +open import group-theory.images-of-group-homomorphisms funext univalence truncations public +open import group-theory.images-of-semigroup-homomorphisms funext univalence truncations public +open import group-theory.integer-multiples-of-elements-abelian-groups funext univalence truncations public +open import group-theory.integer-powers-of-elements-groups funext univalence truncations public +open import group-theory.intersections-subgroups-abelian-groups funext univalence truncations public +open import group-theory.intersections-subgroups-groups funext univalence truncations public +open import group-theory.inverse-semigroups funext univalence public +open import group-theory.invertible-elements-monoids funext univalence truncations public +open import group-theory.isomorphisms-abelian-groups funext univalence truncations public +open import group-theory.isomorphisms-concrete-groups funext univalence truncations public +open import group-theory.isomorphisms-group-actions funext univalence truncations public +open import group-theory.isomorphisms-groups funext univalence truncations public +open import group-theory.isomorphisms-monoids funext univalence truncations public +open import group-theory.isomorphisms-semigroups funext univalence truncations public +open import group-theory.iterated-cartesian-products-concrete-groups funext univalence truncations public +open import group-theory.kernels-homomorphisms-abelian-groups funext univalence truncations public +open import group-theory.kernels-homomorphisms-concrete-groups funext univalence truncations public +open import group-theory.kernels-homomorphisms-groups funext univalence truncations public +open import group-theory.large-semigroups funext univalence public +open import group-theory.loop-groups-sets funext univalence truncations public +open import group-theory.mere-equivalences-concrete-group-actions funext univalence truncations public +open import group-theory.mere-equivalences-group-actions funext univalence truncations public +open import group-theory.minkowski-multiplication-commutative-monoids funext univalence truncations public +open import group-theory.minkowski-multiplication-monoids funext univalence truncations public +open import group-theory.minkowski-multiplication-semigroups funext univalence truncations public +open import group-theory.monoid-actions funext univalence truncations public +open import group-theory.monoids funext univalence truncations public +open import group-theory.monomorphisms-concrete-groups funext univalence truncations public +open import group-theory.monomorphisms-groups funext univalence truncations public +open import group-theory.multiples-of-elements-abelian-groups funext univalence truncations public +open import group-theory.nontrivial-groups funext univalence truncations public +open import group-theory.normal-closures-subgroups funext univalence truncations public +open import group-theory.normal-cores-subgroups funext univalence truncations public +open import group-theory.normal-subgroups funext univalence truncations public +open import group-theory.normal-subgroups-concrete-groups funext univalence truncations public +open import group-theory.normal-submonoids funext univalence truncations public +open import group-theory.normal-submonoids-commutative-monoids funext univalence truncations public +open import group-theory.normalizer-subgroups funext univalence truncations public +open import group-theory.nullifying-group-homomorphisms funext univalence truncations public +open import group-theory.opposite-groups funext univalence truncations public +open import group-theory.opposite-semigroups funext univalence public +open import group-theory.orbit-stabilizer-theorem-concrete-groups funext univalence truncations public +open import group-theory.orbits-concrete-group-actions funext univalence truncations public +open import group-theory.orbits-group-actions funext univalence truncations public +open import group-theory.orders-of-elements-groups funext univalence truncations public +open import group-theory.perfect-cores funext univalence truncations public +open import group-theory.perfect-groups funext univalence truncations public +open import group-theory.perfect-subgroups funext univalence truncations public +open import group-theory.powers-of-elements-commutative-monoids funext univalence truncations public +open import group-theory.powers-of-elements-groups funext univalence truncations public +open import group-theory.powers-of-elements-monoids funext univalence truncations public +open import group-theory.precategory-of-commutative-monoids funext univalence truncations public +open import group-theory.precategory-of-concrete-groups funext univalence truncations public +open import group-theory.precategory-of-group-actions funext univalence truncations public +open import group-theory.precategory-of-groups funext univalence truncations public +open import group-theory.precategory-of-monoids funext univalence truncations public +open import group-theory.precategory-of-orbits-monoid-actions funext univalence truncations public +open import group-theory.precategory-of-semigroups funext univalence truncations public +open import group-theory.principal-group-actions funext univalence truncations public +open import group-theory.principal-torsors-concrete-groups funext univalence truncations public +open import group-theory.products-of-elements-monoids funext univalence truncations public +open import group-theory.products-of-tuples-of-elements-commutative-monoids funext univalence truncations public +open import group-theory.pullbacks-subgroups funext univalence truncations public +open import group-theory.pullbacks-subsemigroups funext univalence truncations public +open import group-theory.quotient-groups funext univalence truncations public +open import group-theory.quotient-groups-concrete-groups funext univalence truncations public +open import group-theory.quotients-abelian-groups funext univalence truncations public +open import group-theory.rational-commutative-monoids funext univalence truncations public +open import group-theory.representations-monoids-precategories funext univalence truncations public +open import group-theory.saturated-congruence-relations-commutative-monoids funext univalence truncations public +open import group-theory.saturated-congruence-relations-monoids funext univalence truncations public +open import group-theory.semigroups funext univalence public +open import group-theory.sheargroups funext univalence public +open import group-theory.shriek-concrete-group-actions funext univalence truncations public +open import group-theory.stabilizer-groups funext univalence truncations public +open import group-theory.stabilizer-groups-concrete-group-actions funext univalence truncations public +open import group-theory.subgroups funext univalence truncations public +open import group-theory.subgroups-abelian-groups funext univalence truncations public +open import group-theory.subgroups-concrete-groups funext univalence truncations public +open import group-theory.subgroups-generated-by-elements-groups funext univalence truncations public +open import group-theory.subgroups-generated-by-families-of-elements-groups funext univalence truncations public +open import group-theory.subgroups-generated-by-subsets-groups funext univalence truncations public +open import group-theory.submonoids funext univalence truncations public +open import group-theory.submonoids-commutative-monoids funext univalence truncations public +open import group-theory.subsemigroups funext univalence truncations public +open import group-theory.subsets-abelian-groups funext univalence truncations public +open import group-theory.subsets-commutative-monoids funext univalence truncations public +open import group-theory.subsets-groups funext univalence truncations public +open import group-theory.subsets-monoids funext univalence truncations public +open import group-theory.subsets-semigroups funext univalence truncations public +open import group-theory.substitution-functor-concrete-group-actions funext univalence truncations public +open import group-theory.substitution-functor-group-actions funext univalence truncations public +open import group-theory.surjective-group-homomorphisms funext univalence truncations public +open import group-theory.surjective-semigroup-homomorphisms funext univalence truncations public +open import group-theory.symmetric-concrete-groups funext univalence truncations public +open import group-theory.symmetric-groups funext univalence truncations public +open import group-theory.torsion-elements-groups funext univalence truncations public +open import group-theory.torsion-free-groups funext univalence truncations public +open import group-theory.torsors funext univalence truncations public +open import group-theory.transitive-concrete-group-actions funext univalence truncations public +open import group-theory.transitive-group-actions funext univalence truncations public +open import group-theory.trivial-concrete-groups funext univalence truncations public +open import group-theory.trivial-group-homomorphisms funext univalence truncations public +open import group-theory.trivial-groups funext univalence truncations public +open import group-theory.trivial-subgroups funext univalence truncations public +open import group-theory.unordered-tuples-of-elements-commutative-monoids funext univalence truncations public +open import group-theory.wild-representations-monoids funext univalence truncations public ``` diff --git a/src/group-theory/abelian-groups.lagda.md b/src/group-theory/abelian-groups.lagda.md index 6023e6276d..d645011501 100644 --- a/src/group-theory/abelian-groups.lagda.md +++ b/src/group-theory/abelian-groups.lagda.md @@ -1,7 +1,15 @@ # Abelian groups ```agda -module group-theory.abelian-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.abelian-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,41 +17,42 @@ module group-theory.abelian-groups where ```agda open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.binary-embeddings +open import foundation.binary-embeddings funext open import foundation.binary-equivalences -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalences -open import foundation.full-subtypes -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.injective-maps +open import foundation.dependent-products-propositions funext +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.full-subtypes funext univalence truncations +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.injective-maps funext open import foundation.interchange-law -open import foundation.propositions -open import foundation.sets +open import foundation.propositions funext univalence +open import foundation.sets funext univalence open import foundation.universe-levels -open import group-theory.central-elements-groups -open import group-theory.commutative-monoids -open import group-theory.commutator-subgroups -open import group-theory.commutators-of-elements-groups -open import group-theory.conjugation -open import group-theory.groups -open import group-theory.homomorphisms-groups -open import group-theory.monoids -open import group-theory.nullifying-group-homomorphisms -open import group-theory.pullbacks-subgroups -open import group-theory.semigroups -open import group-theory.subgroups -open import group-theory.subgroups-generated-by-families-of-elements-groups -open import group-theory.trivial-subgroups - -open import lists.concatenation-lists +open import group-theory.central-elements-groups funext univalence truncations +open import group-theory.commutative-monoids funext univalence truncations +open import group-theory.commutator-subgroups funext univalence truncations +open import group-theory.commutators-of-elements-groups funext univalence truncations +open import group-theory.conjugation funext univalence truncations +open import group-theory.groups funext univalence truncations +open import group-theory.homomorphisms-groups funext univalence truncations +open import group-theory.monoids funext univalence truncations +open import group-theory.nullifying-group-homomorphisms funext univalence truncations +open import group-theory.pullbacks-subgroups funext univalence truncations +open import group-theory.semigroups funext univalence +open import group-theory.subgroups funext univalence truncations +open import group-theory.subgroups-generated-by-families-of-elements-groups funext univalence truncations +open import group-theory.trivial-subgroups funext univalence truncations + +open import lists.concatenation-lists funext univalence truncations open import lists.lists -open import structured-types.pointed-types-equipped-with-automorphisms +open import structured-types.pointed-types-equipped-with-automorphisms funext univalence truncations ```
diff --git a/src/group-theory/abelianization-groups.lagda.md b/src/group-theory/abelianization-groups.lagda.md index 5698ee542f..c7f181b877 100644 --- a/src/group-theory/abelianization-groups.lagda.md +++ b/src/group-theory/abelianization-groups.lagda.md @@ -2,42 +2,49 @@ ```agda {-# OPTIONS --lossy-unification #-} - -module group-theory.abelianization-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.abelianization-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.adjunctions-large-categories -open import category-theory.adjunctions-large-precategories -open import category-theory.functors-large-categories -open import category-theory.functors-large-precategories -open import category-theory.natural-transformations-functors-large-categories -open import category-theory.natural-transformations-functors-large-precategories - -open import foundation.commuting-squares-of-maps +open import category-theory.adjunctions-large-categories funext univalence truncations +open import category-theory.adjunctions-large-precategories funext univalence truncations +open import category-theory.functors-large-categories funext univalence truncations +open import category-theory.functors-large-precategories funext univalence truncations +open import category-theory.natural-transformations-functors-large-categories funext univalence truncations +open import category-theory.natural-transformations-functors-large-precategories funext univalence truncations + +open import foundation.commuting-squares-of-maps funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.identity-types -open import foundation.set-quotients -open import foundation.sets +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.set-quotients funext univalence truncations +open import foundation.sets funext univalence open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import group-theory.abelian-groups -open import group-theory.category-of-abelian-groups -open import group-theory.category-of-groups -open import group-theory.commutator-subgroups -open import group-theory.commuting-squares-of-group-homomorphisms -open import group-theory.functoriality-quotient-groups -open import group-theory.groups -open import group-theory.homomorphisms-abelian-groups -open import group-theory.homomorphisms-groups -open import group-theory.normal-subgroups -open import group-theory.nullifying-group-homomorphisms -open import group-theory.quotient-groups +open import group-theory.abelian-groups funext univalence truncations +open import group-theory.category-of-abelian-groups funext univalence truncations +open import group-theory.category-of-groups funext univalence truncations +open import group-theory.commutator-subgroups funext univalence truncations +open import group-theory.commuting-squares-of-group-homomorphisms funext univalence truncations +open import group-theory.functoriality-quotient-groups funext univalence truncations +open import group-theory.groups funext univalence truncations +open import group-theory.homomorphisms-abelian-groups funext univalence truncations +open import group-theory.homomorphisms-groups funext univalence truncations +open import group-theory.normal-subgroups funext univalence truncations +open import group-theory.nullifying-group-homomorphisms funext univalence truncations +open import group-theory.quotient-groups funext univalence truncations ```
diff --git a/src/group-theory/addition-homomorphisms-abelian-groups.lagda.md b/src/group-theory/addition-homomorphisms-abelian-groups.lagda.md index 8c5fd68978..e4b42d8044 100644 --- a/src/group-theory/addition-homomorphisms-abelian-groups.lagda.md +++ b/src/group-theory/addition-homomorphisms-abelian-groups.lagda.md @@ -1,7 +1,15 @@ # Pointwise addition of morphisms of abelian groups ```agda -module group-theory.addition-homomorphisms-abelian-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.addition-homomorphisms-abelian-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,13 +17,13 @@ module group-theory.addition-homomorphisms-abelian-groups where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.groups -open import group-theory.homomorphisms-abelian-groups -open import group-theory.semigroups +open import group-theory.abelian-groups funext univalence truncations +open import group-theory.groups funext univalence truncations +open import group-theory.homomorphisms-abelian-groups funext univalence truncations +open import group-theory.semigroups funext univalence ```
diff --git a/src/group-theory/automorphism-groups.lagda.md b/src/group-theory/automorphism-groups.lagda.md index 2214cbb69c..ba55f83f93 100644 --- a/src/group-theory/automorphism-groups.lagda.md +++ b/src/group-theory/automorphism-groups.lagda.md @@ -1,30 +1,35 @@ # Automorphism groups ```agda -module group-theory.automorphism-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.automorphism-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.1-types -open import foundation.connected-components -open import foundation.contractible-types +open import foundation.1-types funext univalence +open import foundation.connected-components funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalences +open import foundation.equivalences funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types -open import foundation.mere-equality -open import foundation.propositional-truncations -open import foundation.subtype-identity-principle -open import foundation.torsorial-type-families +open import foundation.identity-types funext +open import foundation.mere-equality funext univalence truncations +open import foundation.torsorial-type-families funext univalence truncations open import foundation.universe-levels -open import group-theory.concrete-groups -open import group-theory.equivalences-concrete-groups +open import group-theory.concrete-groups funext univalence truncations +open import group-theory.equivalences-concrete-groups funext univalence truncations -open import higher-group-theory.automorphism-groups -open import higher-group-theory.higher-groups +open import higher-group-theory.automorphism-groups funext univalence truncations +open import higher-group-theory.higher-groups funext univalence truncations ```
diff --git a/src/group-theory/cartesian-products-abelian-groups.lagda.md b/src/group-theory/cartesian-products-abelian-groups.lagda.md index 2bf663196b..1b383abe04 100644 --- a/src/group-theory/cartesian-products-abelian-groups.lagda.md +++ b/src/group-theory/cartesian-products-abelian-groups.lagda.md @@ -1,7 +1,15 @@ # Cartesian products of abelian groups ```agda -module group-theory.cartesian-products-abelian-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.cartesian-products-abelian-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,15 +17,15 @@ module group-theory.cartesian-products-abelian-groups where ```agda open import foundation.dependent-pair-types open import foundation.equality-cartesian-product-types -open import foundation.identity-types -open import foundation.sets +open import foundation.identity-types funext +open import foundation.sets funext univalence open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.cartesian-products-groups -open import group-theory.groups -open import group-theory.monoids -open import group-theory.semigroups +open import group-theory.abelian-groups funext univalence truncations +open import group-theory.cartesian-products-groups funext univalence truncations +open import group-theory.groups funext univalence truncations +open import group-theory.monoids funext univalence truncations +open import group-theory.semigroups funext univalence ```
diff --git a/src/group-theory/cartesian-products-concrete-groups.lagda.md b/src/group-theory/cartesian-products-concrete-groups.lagda.md index a60202281c..4ca0bcf423 100644 --- a/src/group-theory/cartesian-products-concrete-groups.lagda.md +++ b/src/group-theory/cartesian-products-concrete-groups.lagda.md @@ -1,31 +1,41 @@ # Cartesian products of concrete groups ```agda -module group-theory.cartesian-products-concrete-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.cartesian-products-concrete-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.0-connected-types -open import foundation.1-types -open import foundation.cartesian-product-types +open import foundation.0-connected-types funext univalence truncations +open import foundation.1-types funext univalence +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.identity-types -open import foundation.mere-equality -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.sets -open import foundation.truncated-types +open import foundation.dependent-products-propositions funext +open import foundation.dependent-products-truncated-types funext +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.mere-equality funext univalence truncations +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.truncated-types funext univalence open import foundation.truncation-levels open import foundation.universe-levels -open import group-theory.concrete-groups -open import group-theory.groups +open import group-theory.concrete-groups funext univalence truncations +open import group-theory.groups funext univalence truncations -open import higher-group-theory.cartesian-products-higher-groups -open import higher-group-theory.higher-groups +open import higher-group-theory.cartesian-products-higher-groups funext univalence truncations +open import higher-group-theory.higher-groups funext univalence truncations open import structured-types.pointed-types ``` diff --git a/src/group-theory/cartesian-products-groups.lagda.md b/src/group-theory/cartesian-products-groups.lagda.md index 84748d8b87..781795883c 100644 --- a/src/group-theory/cartesian-products-groups.lagda.md +++ b/src/group-theory/cartesian-products-groups.lagda.md @@ -1,7 +1,15 @@ # Cartesian products of groups ```agda -module group-theory.cartesian-products-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.cartesian-products-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,14 +17,14 @@ module group-theory.cartesian-products-groups where ```agda open import foundation.dependent-pair-types open import foundation.equality-cartesian-product-types -open import foundation.identity-types -open import foundation.sets +open import foundation.identity-types funext +open import foundation.sets funext univalence open import foundation.universe-levels -open import group-theory.cartesian-products-monoids -open import group-theory.groups -open import group-theory.monoids -open import group-theory.semigroups +open import group-theory.cartesian-products-monoids funext univalence truncations +open import group-theory.groups funext univalence truncations +open import group-theory.monoids funext univalence truncations +open import group-theory.semigroups funext univalence ```
diff --git a/src/group-theory/cartesian-products-monoids.lagda.md b/src/group-theory/cartesian-products-monoids.lagda.md index c83c132714..ab3c49da76 100644 --- a/src/group-theory/cartesian-products-monoids.lagda.md +++ b/src/group-theory/cartesian-products-monoids.lagda.md @@ -1,7 +1,15 @@ # Cartesian products of monoids ```agda -module group-theory.cartesian-products-monoids where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.cartesian-products-monoids + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,13 +17,13 @@ module group-theory.cartesian-products-monoids where ```agda open import foundation.dependent-pair-types open import foundation.equality-cartesian-product-types -open import foundation.identity-types -open import foundation.sets +open import foundation.identity-types funext +open import foundation.sets funext univalence open import foundation.universe-levels -open import group-theory.cartesian-products-semigroups -open import group-theory.monoids -open import group-theory.semigroups +open import group-theory.cartesian-products-semigroups funext univalence +open import group-theory.monoids funext univalence truncations +open import group-theory.semigroups funext univalence ```
diff --git a/src/group-theory/cartesian-products-semigroups.lagda.md b/src/group-theory/cartesian-products-semigroups.lagda.md index e14a38dbc2..dd336716d8 100644 --- a/src/group-theory/cartesian-products-semigroups.lagda.md +++ b/src/group-theory/cartesian-products-semigroups.lagda.md @@ -1,7 +1,13 @@ # Cartesian products of semigroups ```agda -module group-theory.cartesian-products-semigroups where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.cartesian-products-semigroups + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports @@ -9,11 +15,11 @@ module group-theory.cartesian-products-semigroups where ```agda open import foundation.dependent-pair-types open import foundation.equality-cartesian-product-types -open import foundation.identity-types -open import foundation.sets +open import foundation.identity-types funext +open import foundation.sets funext univalence open import foundation.universe-levels -open import group-theory.semigroups +open import group-theory.semigroups funext univalence ```
diff --git a/src/group-theory/category-of-abelian-groups.lagda.md b/src/group-theory/category-of-abelian-groups.lagda.md index abb1ac4341..16e71f2645 100644 --- a/src/group-theory/category-of-abelian-groups.lagda.md +++ b/src/group-theory/category-of-abelian-groups.lagda.md @@ -1,23 +1,31 @@ # The category of abelian groups ```agda -module group-theory.category-of-abelian-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.category-of-abelian-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.full-large-subcategories -open import category-theory.functors-large-categories -open import category-theory.large-categories -open import category-theory.large-precategories -open import category-theory.precategories +open import category-theory.categories funext univalence truncations +open import category-theory.full-large-subcategories funext univalence truncations +open import category-theory.functors-large-categories funext univalence truncations +open import category-theory.large-categories funext univalence truncations +open import category-theory.large-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.category-of-groups +open import group-theory.abelian-groups funext univalence truncations +open import group-theory.category-of-groups funext univalence truncations ```
diff --git a/src/group-theory/category-of-group-actions.lagda.md b/src/group-theory/category-of-group-actions.lagda.md index 1205990345..c31e1937cd 100644 --- a/src/group-theory/category-of-group-actions.lagda.md +++ b/src/group-theory/category-of-group-actions.lagda.md @@ -1,27 +1,35 @@ # The category of group actions ```agda -module group-theory.category-of-group-actions where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.category-of-group-actions + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.isomorphisms-in-large-precategories -open import category-theory.large-categories -open import category-theory.large-precategories -open import category-theory.precategories +open import category-theory.categories funext univalence truncations +open import category-theory.isomorphisms-in-large-precategories funext univalence truncations +open import category-theory.large-categories funext univalence truncations +open import category-theory.large-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations open import foundation.dependent-pair-types open import foundation.fundamental-theorem-of-identity-types open import foundation.universe-levels -open import group-theory.group-actions -open import group-theory.groups -open import group-theory.homomorphisms-group-actions -open import group-theory.isomorphisms-group-actions -open import group-theory.precategory-of-group-actions +open import group-theory.group-actions funext univalence truncations +open import group-theory.groups funext univalence truncations +open import group-theory.homomorphisms-group-actions funext univalence truncations +open import group-theory.isomorphisms-group-actions funext univalence truncations +open import group-theory.precategory-of-group-actions funext univalence truncations ```
diff --git a/src/group-theory/category-of-groups.lagda.md b/src/group-theory/category-of-groups.lagda.md index 5b7a7ec268..0d35679ae8 100644 --- a/src/group-theory/category-of-groups.lagda.md +++ b/src/group-theory/category-of-groups.lagda.md @@ -1,24 +1,32 @@ # The category of groups ```agda -module group-theory.category-of-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.category-of-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.large-categories +open import category-theory.categories funext univalence truncations +open import category-theory.large-categories funext univalence truncations -open import foundation.1-types -open import foundation.equivalences +open import foundation.1-types funext univalence +open import foundation.equivalences funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import group-theory.groups -open import group-theory.isomorphisms-groups -open import group-theory.precategory-of-groups +open import group-theory.groups funext univalence truncations +open import group-theory.isomorphisms-groups funext univalence truncations +open import group-theory.precategory-of-groups funext univalence truncations ```
diff --git a/src/group-theory/category-of-orbits-groups.lagda.md b/src/group-theory/category-of-orbits-groups.lagda.md index e8ddd2bdc0..2297c6e3d4 100644 --- a/src/group-theory/category-of-orbits-groups.lagda.md +++ b/src/group-theory/category-of-orbits-groups.lagda.md @@ -1,30 +1,38 @@ # The orbit category of a group ```agda -module group-theory.category-of-orbits-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.category-of-orbits-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.full-large-subcategories -open import category-theory.isomorphisms-in-large-precategories -open import category-theory.large-categories -open import category-theory.large-precategories -open import category-theory.precategories +open import category-theory.categories funext univalence truncations +open import category-theory.full-large-subcategories funext univalence truncations +open import category-theory.isomorphisms-in-large-precategories funext univalence truncations +open import category-theory.large-categories funext univalence truncations +open import category-theory.large-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations open import foundation.dependent-pair-types open import foundation.fundamental-theorem-of-identity-types open import foundation.universe-levels -open import group-theory.category-of-group-actions -open import group-theory.group-actions -open import group-theory.groups -open import group-theory.homomorphisms-group-actions -open import group-theory.isomorphisms-group-actions -open import group-theory.precategory-of-group-actions -open import group-theory.transitive-group-actions +open import group-theory.category-of-group-actions funext univalence truncations +open import group-theory.group-actions funext univalence truncations +open import group-theory.groups funext univalence truncations +open import group-theory.homomorphisms-group-actions funext univalence truncations +open import group-theory.isomorphisms-group-actions funext univalence truncations +open import group-theory.precategory-of-group-actions funext univalence truncations +open import group-theory.transitive-group-actions funext univalence truncations ```
diff --git a/src/group-theory/category-of-semigroups.lagda.md b/src/group-theory/category-of-semigroups.lagda.md index a610b13437..b5248e14a2 100644 --- a/src/group-theory/category-of-semigroups.lagda.md +++ b/src/group-theory/category-of-semigroups.lagda.md @@ -1,25 +1,33 @@ # The category of semigroups ```agda -module group-theory.category-of-semigroups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.category-of-semigroups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.large-categories +open import category-theory.categories funext univalence truncations +open import category-theory.large-categories funext univalence truncations -open import foundation.1-types +open import foundation.1-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences +open import foundation.equivalences funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import group-theory.isomorphisms-semigroups -open import group-theory.precategory-of-semigroups -open import group-theory.semigroups +open import group-theory.isomorphisms-semigroups funext univalence truncations +open import group-theory.precategory-of-semigroups funext univalence truncations +open import group-theory.semigroups funext univalence ```
diff --git a/src/group-theory/cayleys-theorem.lagda.md b/src/group-theory/cayleys-theorem.lagda.md index 7df1fa969a..b2616e482e 100644 --- a/src/group-theory/cayleys-theorem.lagda.md +++ b/src/group-theory/cayleys-theorem.lagda.md @@ -1,24 +1,31 @@ # Cayley's theorem ```agda -module group-theory.cayleys-theorem where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.cayleys-theorem + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalence-extensionality -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.sets +open import foundation.embeddings funext +open import foundation.equivalence-extensionality funext +open import foundation.identity-types funext +open import foundation.injective-maps funext open import foundation.universe-levels -open import group-theory.embeddings-groups -open import group-theory.groups -open import group-theory.homomorphisms-groups -open import group-theory.symmetric-groups +open import group-theory.embeddings-groups funext univalence truncations +open import group-theory.groups funext univalence truncations +open import group-theory.homomorphisms-groups funext univalence truncations +open import group-theory.symmetric-groups funext univalence truncations ```
diff --git a/src/group-theory/centers-groups.lagda.md b/src/group-theory/centers-groups.lagda.md index a92e3af960..22a49cb6fe 100644 --- a/src/group-theory/centers-groups.lagda.md +++ b/src/group-theory/centers-groups.lagda.md @@ -1,22 +1,31 @@ # The center of a group ```agda -module group-theory.centers-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.centers-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence open import foundation.universe-levels -open import group-theory.central-elements-groups -open import group-theory.groups -open import group-theory.homomorphisms-groups -open import group-theory.normal-subgroups -open import group-theory.subgroups +open import group-theory.central-elements-groups funext univalence truncations +open import group-theory.groups funext univalence truncations +open import group-theory.homomorphisms-groups funext univalence truncations +open import group-theory.normal-subgroups funext univalence truncations +open import group-theory.subgroups funext univalence truncations ```
diff --git a/src/group-theory/centers-monoids.lagda.md b/src/group-theory/centers-monoids.lagda.md index 39deb28916..1a18f672a3 100644 --- a/src/group-theory/centers-monoids.lagda.md +++ b/src/group-theory/centers-monoids.lagda.md @@ -1,21 +1,30 @@ # Center of a monoid ```agda -module group-theory.centers-monoids where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.centers-monoids + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence open import foundation.universe-levels -open import group-theory.central-elements-monoids -open import group-theory.homomorphisms-monoids -open import group-theory.monoids -open import group-theory.submonoids +open import group-theory.central-elements-monoids funext univalence truncations +open import group-theory.homomorphisms-monoids funext univalence truncations +open import group-theory.monoids funext univalence truncations +open import group-theory.submonoids funext univalence truncations ```
diff --git a/src/group-theory/centers-semigroups.lagda.md b/src/group-theory/centers-semigroups.lagda.md index 9997e96a0c..22f340c04c 100644 --- a/src/group-theory/centers-semigroups.lagda.md +++ b/src/group-theory/centers-semigroups.lagda.md @@ -1,21 +1,30 @@ # Center of a semigroup ```agda -module group-theory.centers-semigroups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.centers-semigroups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence open import foundation.universe-levels -open import group-theory.central-elements-semigroups -open import group-theory.homomorphisms-semigroups -open import group-theory.semigroups -open import group-theory.subsemigroups +open import group-theory.central-elements-semigroups funext univalence +open import group-theory.homomorphisms-semigroups funext univalence truncations +open import group-theory.semigroups funext univalence +open import group-theory.subsemigroups funext univalence truncations ```
diff --git a/src/group-theory/central-elements-groups.lagda.md b/src/group-theory/central-elements-groups.lagda.md index 21cd4b9353..83be65e4db 100644 --- a/src/group-theory/central-elements-groups.lagda.md +++ b/src/group-theory/central-elements-groups.lagda.md @@ -1,21 +1,30 @@ # Central elements of groups ```agda -module group-theory.central-elements-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.central-elements-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.identity-types -open import foundation.propositions -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels -open import group-theory.central-elements-monoids -open import group-theory.conjugation -open import group-theory.groups +open import group-theory.central-elements-monoids funext univalence truncations +open import group-theory.conjugation funext univalence truncations +open import group-theory.groups funext univalence truncations ```
diff --git a/src/group-theory/central-elements-monoids.lagda.md b/src/group-theory/central-elements-monoids.lagda.md index bece727ced..d31bf20796 100644 --- a/src/group-theory/central-elements-monoids.lagda.md +++ b/src/group-theory/central-elements-monoids.lagda.md @@ -1,18 +1,27 @@ # Central elements of monoids ```agda -module group-theory.central-elements-monoids where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.central-elements-monoids + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.identity-types -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence open import foundation.universe-levels -open import group-theory.central-elements-semigroups -open import group-theory.monoids +open import group-theory.central-elements-semigroups funext univalence +open import group-theory.monoids funext univalence truncations ```
diff --git a/src/group-theory/central-elements-semigroups.lagda.md b/src/group-theory/central-elements-semigroups.lagda.md index cedeca3a11..a85a0c1d13 100644 --- a/src/group-theory/central-elements-semigroups.lagda.md +++ b/src/group-theory/central-elements-semigroups.lagda.md @@ -1,19 +1,26 @@ # Central elements of semirings ```agda -module group-theory.central-elements-semigroups where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.central-elements-semigroups + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets +open import foundation.dependent-products-propositions funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence open import foundation.universe-levels -open import group-theory.semigroups +open import group-theory.semigroups funext univalence ```
diff --git a/src/group-theory/centralizer-subgroups.lagda.md b/src/group-theory/centralizer-subgroups.lagda.md index 9e44de697c..3f6baa75aa 100644 --- a/src/group-theory/centralizer-subgroups.lagda.md +++ b/src/group-theory/centralizer-subgroups.lagda.md @@ -1,7 +1,15 @@ # Centralizer subgroups ```agda -module group-theory.centralizer-subgroups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.centralizer-subgroups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,16 +17,17 @@ module group-theory.centralizer-subgroups where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels -open import group-theory.conjugation -open import group-theory.groups -open import group-theory.subgroups -open import group-theory.subsets-groups +open import group-theory.conjugation funext univalence truncations +open import group-theory.groups funext univalence truncations +open import group-theory.subgroups funext univalence truncations +open import group-theory.subsets-groups funext univalence truncations ```
diff --git a/src/group-theory/characteristic-subgroups.lagda.md b/src/group-theory/characteristic-subgroups.lagda.md index 023e2b5cee..3c5b73b822 100644 --- a/src/group-theory/characteristic-subgroups.lagda.md +++ b/src/group-theory/characteristic-subgroups.lagda.md @@ -1,19 +1,28 @@ # Characteristic subgroups ```agda -module group-theory.characteristic-subgroups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.characteristic-subgroups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.propositions funext univalence open import foundation.universe-levels -open import group-theory.groups -open import group-theory.images-of-group-homomorphisms -open import group-theory.isomorphisms-groups -open import group-theory.subgroups +open import group-theory.groups funext univalence truncations +open import group-theory.images-of-group-homomorphisms funext univalence truncations +open import group-theory.isomorphisms-groups funext univalence truncations +open import group-theory.subgroups funext univalence truncations ```
diff --git a/src/group-theory/commutative-monoids.lagda.md b/src/group-theory/commutative-monoids.lagda.md index 89b8b3f6aa..d732e1129f 100644 --- a/src/group-theory/commutative-monoids.lagda.md +++ b/src/group-theory/commutative-monoids.lagda.md @@ -1,7 +1,15 @@ # Commutative monoids ```agda -module group-theory.commutative-monoids where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.commutative-monoids + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,16 +17,18 @@ module group-theory.commutative-monoids where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.dependent-products-propositions funext +open import foundation.identity-types funext open import foundation.interchange-law -open import foundation.iterated-dependent-product-types -open import foundation.propositions -open import foundation.sets +open import foundation.iterated-dependent-product-types funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.telescopes open import foundation.unital-binary-operations open import foundation.universe-levels -open import group-theory.monoids -open import group-theory.semigroups +open import group-theory.monoids funext univalence truncations +open import group-theory.semigroups funext univalence ```
diff --git a/src/group-theory/commutator-subgroups.lagda.md b/src/group-theory/commutator-subgroups.lagda.md index 1300e1e9be..6aa23396d0 100644 --- a/src/group-theory/commutator-subgroups.lagda.md +++ b/src/group-theory/commutator-subgroups.lagda.md @@ -1,31 +1,39 @@ # Commutator subgroups ```agda -module group-theory.commutator-subgroups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.commutator-subgroups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.existential-quantification -open import foundation.function-types -open import foundation.identity-types -open import foundation.propositional-truncations +open import foundation.existential-quantification funext univalence truncations +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.propositional-truncations funext univalence open import foundation.universe-levels -open import group-theory.commutators-of-elements-groups -open import group-theory.conjugation -open import group-theory.groups -open import group-theory.homomorphisms-groups -open import group-theory.images-of-group-homomorphisms -open import group-theory.normal-subgroups -open import group-theory.pullbacks-subgroups -open import group-theory.subgroups -open import group-theory.subgroups-generated-by-families-of-elements-groups -open import group-theory.subgroups-generated-by-subsets-groups -open import group-theory.subsets-groups +open import group-theory.commutators-of-elements-groups funext univalence truncations +open import group-theory.conjugation funext univalence truncations +open import group-theory.groups funext univalence truncations +open import group-theory.homomorphisms-groups funext univalence truncations +open import group-theory.images-of-group-homomorphisms funext univalence truncations +open import group-theory.normal-subgroups funext univalence truncations +open import group-theory.pullbacks-subgroups funext univalence truncations +open import group-theory.subgroups funext univalence truncations +open import group-theory.subgroups-generated-by-families-of-elements-groups funext univalence truncations +open import group-theory.subgroups-generated-by-subsets-groups funext univalence truncations +open import group-theory.subsets-groups funext univalence truncations ```
diff --git a/src/group-theory/commutators-of-elements-groups.lagda.md b/src/group-theory/commutators-of-elements-groups.lagda.md index 086b8fcc4d..c25bc85253 100644 --- a/src/group-theory/commutators-of-elements-groups.lagda.md +++ b/src/group-theory/commutators-of-elements-groups.lagda.md @@ -1,20 +1,28 @@ # Commutators of elements in groups ```agda -module group-theory.commutators-of-elements-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.commutators-of-elements-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import group-theory.commuting-elements-groups -open import group-theory.conjugation -open import group-theory.groups -open import group-theory.homomorphisms-groups +open import group-theory.commuting-elements-groups funext univalence truncations +open import group-theory.conjugation funext univalence truncations +open import group-theory.groups funext univalence truncations +open import group-theory.homomorphisms-groups funext univalence truncations ```
diff --git a/src/group-theory/commuting-elements-groups.lagda.md b/src/group-theory/commuting-elements-groups.lagda.md index 9e76af7d68..3a02aefc43 100644 --- a/src/group-theory/commuting-elements-groups.lagda.md +++ b/src/group-theory/commuting-elements-groups.lagda.md @@ -1,18 +1,27 @@ # Commuting elements of groups ```agda -module group-theory.commuting-elements-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.commuting-elements-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.identity-types -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence open import foundation.universe-levels -open import group-theory.commuting-elements-monoids -open import group-theory.groups +open import group-theory.commuting-elements-monoids funext univalence truncations +open import group-theory.groups funext univalence truncations ```
diff --git a/src/group-theory/commuting-elements-monoids.lagda.md b/src/group-theory/commuting-elements-monoids.lagda.md index 3f74bcc1d1..9ae8fcff2c 100644 --- a/src/group-theory/commuting-elements-monoids.lagda.md +++ b/src/group-theory/commuting-elements-monoids.lagda.md @@ -1,18 +1,27 @@ # Commuting elements of monoids ```agda -module group-theory.commuting-elements-monoids where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.commuting-elements-monoids + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.identity-types -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence open import foundation.universe-levels -open import group-theory.commuting-elements-semigroups -open import group-theory.monoids +open import group-theory.commuting-elements-semigroups funext univalence +open import group-theory.monoids funext univalence truncations ```
diff --git a/src/group-theory/commuting-elements-semigroups.lagda.md b/src/group-theory/commuting-elements-semigroups.lagda.md index 4c5d7998e8..a1267a4ec4 100644 --- a/src/group-theory/commuting-elements-semigroups.lagda.md +++ b/src/group-theory/commuting-elements-semigroups.lagda.md @@ -1,19 +1,26 @@ # Commuting elements of semigroups ```agda -module group-theory.commuting-elements-semigroups where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.commuting-elements-semigroups + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets +open import foundation.dependent-products-propositions funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence open import foundation.universe-levels -open import group-theory.semigroups +open import group-theory.semigroups funext univalence ```
diff --git a/src/group-theory/commuting-squares-of-group-homomorphisms.lagda.md b/src/group-theory/commuting-squares-of-group-homomorphisms.lagda.md index e8e02a54ec..af76e4c6f2 100644 --- a/src/group-theory/commuting-squares-of-group-homomorphisms.lagda.md +++ b/src/group-theory/commuting-squares-of-group-homomorphisms.lagda.md @@ -1,17 +1,25 @@ # Commuting squares of group homomorphisms ```agda -module group-theory.commuting-squares-of-group-homomorphisms where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.commuting-squares-of-group-homomorphisms + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.commuting-squares-of-maps +open import foundation.commuting-squares-of-maps funext univalence open import foundation.universe-levels -open import group-theory.groups -open import group-theory.homomorphisms-groups +open import group-theory.groups funext univalence truncations +open import group-theory.homomorphisms-groups funext univalence truncations ```
diff --git a/src/group-theory/concrete-group-actions.lagda.md b/src/group-theory/concrete-group-actions.lagda.md index a379534da8..e9ba1e1090 100644 --- a/src/group-theory/concrete-group-actions.lagda.md +++ b/src/group-theory/concrete-group-actions.lagda.md @@ -1,18 +1,26 @@ # Concrete group actions ```agda -module group-theory.concrete-group-actions where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.concrete-group-actions + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.function-types -open import foundation.sets +open import foundation.function-types funext +open import foundation.sets funext univalence open import foundation.transport-along-identifications open import foundation.universe-levels -open import group-theory.concrete-groups +open import group-theory.concrete-groups funext univalence truncations ```
diff --git a/src/group-theory/concrete-groups.lagda.md b/src/group-theory/concrete-groups.lagda.md index 17b5b67ad6..dcfcea80e4 100644 --- a/src/group-theory/concrete-groups.lagda.md +++ b/src/group-theory/concrete-groups.lagda.md @@ -1,31 +1,41 @@ # Concrete groups ```agda -module group-theory.concrete-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.concrete-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.0-connected-types -open import foundation.1-types +open import foundation.0-connected-types funext univalence truncations +open import foundation.1-types funext univalence open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.mere-equality -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.sets -open import foundation.truncated-types +open import foundation.dependent-products-propositions funext +open import foundation.dependent-products-truncated-types funext +open import foundation.identity-types funext +open import foundation.mere-equality funext univalence truncations +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.truncated-types funext univalence open import foundation.truncation-levels open import foundation.universe-levels -open import group-theory.groups -open import group-theory.monoids -open import group-theory.opposite-groups -open import group-theory.opposite-semigroups -open import group-theory.semigroups +open import group-theory.groups funext univalence truncations +open import group-theory.monoids funext univalence truncations +open import group-theory.opposite-groups funext univalence truncations +open import group-theory.opposite-semigroups funext univalence +open import group-theory.semigroups funext univalence -open import higher-group-theory.higher-groups +open import higher-group-theory.higher-groups funext univalence truncations open import structured-types.pointed-types ``` diff --git a/src/group-theory/concrete-monoids.lagda.md b/src/group-theory/concrete-monoids.lagda.md index 702c2b25d3..9a9b70192c 100644 --- a/src/group-theory/concrete-monoids.lagda.md +++ b/src/group-theory/concrete-monoids.lagda.md @@ -1,22 +1,30 @@ # Concrete monoids ```agda -module group-theory.concrete-monoids where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.concrete-monoids + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.categories +open import category-theory.categories funext univalence truncations -open import foundation.0-connected-types -open import foundation.cartesian-product-types +open import foundation.0-connected-types funext univalence truncations +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types open import foundation.universe-levels -open import group-theory.cores-monoids -open import group-theory.monoids -open import group-theory.torsors +open import group-theory.cores-monoids funext univalence truncations +open import group-theory.monoids funext univalence truncations +open import group-theory.torsors funext univalence truncations ```
diff --git a/src/group-theory/congruence-relations-abelian-groups.lagda.md b/src/group-theory/congruence-relations-abelian-groups.lagda.md index f9f130587d..264eee8a75 100644 --- a/src/group-theory/congruence-relations-abelian-groups.lagda.md +++ b/src/group-theory/congruence-relations-abelian-groups.lagda.md @@ -1,22 +1,31 @@ # Congruence relations on abelian groups ```agda -module group-theory.congruence-relations-abelian-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.congruence-relations-abelian-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.binary-relations -open import foundation.equivalence-relations -open import foundation.equivalences -open import foundation.identity-types -open import foundation.propositions -open import foundation.torsorial-type-families +open import foundation.binary-relations funext univalence truncations +open import foundation.dependent-products-propositions funext +open import foundation.equivalence-relations funext univalence truncations +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.torsorial-type-families funext univalence truncations open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.congruence-relations-groups +open import group-theory.abelian-groups funext univalence truncations +open import group-theory.congruence-relations-groups funext univalence truncations ```
diff --git a/src/group-theory/congruence-relations-commutative-monoids.lagda.md b/src/group-theory/congruence-relations-commutative-monoids.lagda.md index 2b79291e89..9bb1f82e98 100644 --- a/src/group-theory/congruence-relations-commutative-monoids.lagda.md +++ b/src/group-theory/congruence-relations-commutative-monoids.lagda.md @@ -1,22 +1,31 @@ # Congruence relations on commutative monoids ```agda -module group-theory.congruence-relations-commutative-monoids where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.congruence-relations-commutative-monoids + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.binary-relations -open import foundation.equivalence-relations -open import foundation.equivalences -open import foundation.identity-types -open import foundation.propositions -open import foundation.torsorial-type-families +open import foundation.binary-relations funext univalence truncations +open import foundation.dependent-products-propositions funext +open import foundation.equivalence-relations funext univalence truncations +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.torsorial-type-families funext univalence truncations open import foundation.universe-levels -open import group-theory.commutative-monoids -open import group-theory.congruence-relations-monoids +open import group-theory.commutative-monoids funext univalence truncations +open import group-theory.congruence-relations-monoids funext univalence truncations ```
diff --git a/src/group-theory/congruence-relations-groups.lagda.md b/src/group-theory/congruence-relations-groups.lagda.md index ca3018bb5d..63f8c8b6df 100644 --- a/src/group-theory/congruence-relations-groups.lagda.md +++ b/src/group-theory/congruence-relations-groups.lagda.md @@ -1,26 +1,35 @@ # Congruence relations on groups ```agda -module group-theory.congruence-relations-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.congruence-relations-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.binary-relations +open import foundation.binary-relations funext univalence truncations open import foundation.binary-transport open import foundation.dependent-pair-types -open import foundation.equivalence-relations -open import foundation.equivalences -open import foundation.identity-types -open import foundation.propositions -open import foundation.torsorial-type-families +open import foundation.dependent-products-propositions funext +open import foundation.equivalence-relations funext univalence truncations +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.torsorial-type-families funext univalence truncations open import foundation.universe-levels -open import group-theory.congruence-relations-semigroups -open import group-theory.conjugation -open import group-theory.groups +open import group-theory.congruence-relations-semigroups funext univalence truncations +open import group-theory.conjugation funext univalence truncations +open import group-theory.groups funext univalence truncations ```
diff --git a/src/group-theory/congruence-relations-monoids.lagda.md b/src/group-theory/congruence-relations-monoids.lagda.md index ce5778b509..af883002f5 100644 --- a/src/group-theory/congruence-relations-monoids.lagda.md +++ b/src/group-theory/congruence-relations-monoids.lagda.md @@ -1,23 +1,32 @@ # Congruence relations on monoids ```agda -module group-theory.congruence-relations-monoids where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.congruence-relations-monoids + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.binary-relations +open import foundation.binary-relations funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalence-relations -open import foundation.equivalences -open import foundation.identity-types -open import foundation.propositions -open import foundation.torsorial-type-families +open import foundation.dependent-products-propositions funext +open import foundation.equivalence-relations funext univalence truncations +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.torsorial-type-families funext univalence truncations open import foundation.universe-levels -open import group-theory.congruence-relations-semigroups -open import group-theory.monoids +open import group-theory.congruence-relations-semigroups funext univalence truncations +open import group-theory.monoids funext univalence truncations ```
diff --git a/src/group-theory/congruence-relations-semigroups.lagda.md b/src/group-theory/congruence-relations-semigroups.lagda.md index 5ebc48e734..33e395d1f3 100644 --- a/src/group-theory/congruence-relations-semigroups.lagda.md +++ b/src/group-theory/congruence-relations-semigroups.lagda.md @@ -1,24 +1,33 @@ # Congruence relations on semigroups ```agda -module group-theory.congruence-relations-semigroups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.congruence-relations-semigroups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.binary-relations +open import foundation.binary-relations funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalence-relations -open import foundation.equivalences +open import foundation.dependent-products-propositions funext +open import foundation.equivalence-relations funext univalence truncations +open import foundation.equivalences funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types -open import foundation.propositions +open import foundation.identity-types funext +open import foundation.propositions funext univalence open import foundation.subtype-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext univalence truncations open import foundation.universe-levels -open import group-theory.semigroups +open import group-theory.semigroups funext univalence ```
diff --git a/src/group-theory/conjugation-concrete-groups.lagda.md b/src/group-theory/conjugation-concrete-groups.lagda.md index 4b3aa4c395..65ed6d51de 100644 --- a/src/group-theory/conjugation-concrete-groups.lagda.md +++ b/src/group-theory/conjugation-concrete-groups.lagda.md @@ -1,21 +1,29 @@ # Conjugation on concrete groups ```agda -module group-theory.conjugation-concrete-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.conjugation-concrete-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.homotopies -open import foundation.identity-types +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.universe-levels -open import group-theory.concrete-groups -open import group-theory.conjugation -open import group-theory.homomorphisms-concrete-groups +open import group-theory.concrete-groups funext univalence truncations +open import group-theory.conjugation funext univalence truncations +open import group-theory.homomorphisms-concrete-groups funext univalence truncations -open import higher-group-theory.conjugation +open import higher-group-theory.conjugation funext univalence truncations ```
diff --git a/src/group-theory/conjugation.lagda.md b/src/group-theory/conjugation.lagda.md index 55baaed82e..ded959092c 100644 --- a/src/group-theory/conjugation.lagda.md +++ b/src/group-theory/conjugation.lagda.md @@ -1,7 +1,15 @@ # Conjugation in groups ```agda -module group-theory.conjugation where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.conjugation + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -11,24 +19,24 @@ open import elementary-number-theory.integers open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalence-extensionality -open import foundation.equivalences -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.retractions -open import foundation.sections -open import foundation.subtypes -open import foundation.transposition-identifications-along-retractions -open import foundation.transposition-identifications-along-sections +open import foundation.equivalence-extensionality funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.retractions funext +open import foundation.sections funext +open import foundation.subtypes funext univalence truncations +open import foundation.transposition-identifications-along-retractions funext +open import foundation.transposition-identifications-along-sections funext open import foundation.universe-levels -open import group-theory.group-actions -open import group-theory.groups -open import group-theory.homomorphisms-groups -open import group-theory.integer-powers-of-elements-groups -open import group-theory.isomorphisms-groups -open import group-theory.subsets-groups +open import group-theory.group-actions funext univalence truncations +open import group-theory.groups funext univalence truncations +open import group-theory.homomorphisms-groups funext univalence truncations +open import group-theory.integer-powers-of-elements-groups funext univalence truncations +open import group-theory.isomorphisms-groups funext univalence truncations +open import group-theory.subsets-groups funext univalence truncations ```
diff --git a/src/group-theory/contravariant-pushforward-concrete-group-actions.lagda.md b/src/group-theory/contravariant-pushforward-concrete-group-actions.lagda.md index a9aa640c3c..6b84a9f49c 100644 --- a/src/group-theory/contravariant-pushforward-concrete-group-actions.lagda.md +++ b/src/group-theory/contravariant-pushforward-concrete-group-actions.lagda.md @@ -1,7 +1,15 @@ # Contravariant pushforwards of concrete group actions ```agda -module group-theory.contravariant-pushforward-concrete-group-actions where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.contravariant-pushforward-concrete-group-actions + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,8 +17,8 @@ module group-theory.contravariant-pushforward-concrete-group-actions where ```agda open import foundation.universe-levels -open import group-theory.concrete-groups -open import group-theory.homomorphisms-concrete-groups +open import group-theory.concrete-groups funext univalence truncations +open import group-theory.homomorphisms-concrete-groups funext univalence truncations ```
diff --git a/src/group-theory/cores-monoids.lagda.md b/src/group-theory/cores-monoids.lagda.md index 50328b33a1..e6bcf67151 100644 --- a/src/group-theory/cores-monoids.lagda.md +++ b/src/group-theory/cores-monoids.lagda.md @@ -1,29 +1,38 @@ # Cores of monoids ```agda -module group-theory.cores-monoids where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.cores-monoids + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.functors-large-precategories +open import category-theory.functors-large-precategories funext univalence truncations open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels -open import group-theory.groups -open import group-theory.homomorphisms-groups -open import group-theory.homomorphisms-monoids -open import group-theory.invertible-elements-monoids -open import group-theory.monoids -open import group-theory.precategory-of-groups -open import group-theory.precategory-of-monoids -open import group-theory.semigroups -open import group-theory.submonoids +open import group-theory.groups funext univalence truncations +open import group-theory.homomorphisms-groups funext univalence truncations +open import group-theory.homomorphisms-monoids funext univalence truncations +open import group-theory.invertible-elements-monoids funext univalence truncations +open import group-theory.monoids funext univalence truncations +open import group-theory.precategory-of-groups funext univalence truncations +open import group-theory.precategory-of-monoids funext univalence truncations +open import group-theory.semigroups funext univalence +open import group-theory.submonoids funext univalence truncations ```
diff --git a/src/group-theory/cyclic-groups.lagda.md b/src/group-theory/cyclic-groups.lagda.md index 08c862b1fc..2d8b45bab1 100644 --- a/src/group-theory/cyclic-groups.lagda.md +++ b/src/group-theory/cyclic-groups.lagda.md @@ -1,25 +1,34 @@ # Cyclic groups ```agda -module group-theory.cyclic-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.cyclic-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.existential-quantification -open import foundation.identity-types -open import foundation.inhabited-subtypes -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.sets -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.existential-quantification funext univalence truncations +open import foundation.identity-types funext +open import foundation.inhabited-subtypes funext univalence truncations +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.generating-elements-groups -open import group-theory.groups +open import group-theory.abelian-groups funext univalence truncations +open import group-theory.generating-elements-groups funext univalence truncations +open import group-theory.groups funext univalence truncations ```
diff --git a/src/group-theory/decidable-subgroups.lagda.md b/src/group-theory/decidable-subgroups.lagda.md index e523eb23cb..3b34101c2f 100644 --- a/src/group-theory/decidable-subgroups.lagda.md +++ b/src/group-theory/decidable-subgroups.lagda.md @@ -1,31 +1,40 @@ # Decidable subgroups of groups ```agda -module group-theory.decidable-subgroups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.decidable-subgroups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.binary-relations -open import foundation.decidable-subtypes +open import foundation.binary-relations funext univalence truncations +open import foundation.decidable-subtypes funext univalence truncations open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalence-relations -open import foundation.equivalences -open import foundation.function-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets +open import foundation.dependent-products-propositions funext +open import foundation.embeddings funext +open import foundation.equivalence-relations funext univalence truncations +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence open import foundation.subtype-identity-principle -open import foundation.subtypes +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels -open import group-theory.groups -open import group-theory.homomorphisms-groups -open import group-theory.semigroups -open import group-theory.subgroups -open import group-theory.subsets-groups +open import group-theory.groups funext univalence truncations +open import group-theory.homomorphisms-groups funext univalence truncations +open import group-theory.semigroups funext univalence +open import group-theory.subgroups funext univalence truncations +open import group-theory.subsets-groups funext univalence truncations ```
diff --git a/src/group-theory/dependent-products-abelian-groups.lagda.md b/src/group-theory/dependent-products-abelian-groups.lagda.md index 94aa816e80..0e5a432656 100644 --- a/src/group-theory/dependent-products-abelian-groups.lagda.md +++ b/src/group-theory/dependent-products-abelian-groups.lagda.md @@ -1,23 +1,31 @@ # Dependent products of abelian groups ```agda -module group-theory.dependent-products-abelian-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.dependent-products-abelian-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-extensionality -open import foundation.identity-types -open import foundation.sets +open import foundation.function-extensionality funext +open import foundation.identity-types funext +open import foundation.sets funext univalence open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.dependent-products-groups -open import group-theory.groups -open import group-theory.monoids -open import group-theory.semigroups +open import group-theory.abelian-groups funext univalence truncations +open import group-theory.dependent-products-groups funext univalence truncations +open import group-theory.groups funext univalence truncations +open import group-theory.monoids funext univalence truncations +open import group-theory.semigroups funext univalence ```
diff --git a/src/group-theory/dependent-products-commutative-monoids.lagda.md b/src/group-theory/dependent-products-commutative-monoids.lagda.md index 6d9fdd11e9..de14058718 100644 --- a/src/group-theory/dependent-products-commutative-monoids.lagda.md +++ b/src/group-theory/dependent-products-commutative-monoids.lagda.md @@ -1,21 +1,29 @@ # Dependent products of commutative monoids ```agda -module group-theory.dependent-products-commutative-monoids where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.dependent-products-commutative-monoids + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-extensionality -open import foundation.identity-types -open import foundation.sets +open import foundation.function-extensionality funext +open import foundation.identity-types funext +open import foundation.sets funext univalence open import foundation.universe-levels -open import group-theory.commutative-monoids -open import group-theory.dependent-products-monoids -open import group-theory.monoids +open import group-theory.commutative-monoids funext univalence truncations +open import group-theory.dependent-products-monoids funext univalence truncations +open import group-theory.monoids funext univalence truncations ```
diff --git a/src/group-theory/dependent-products-groups.lagda.md b/src/group-theory/dependent-products-groups.lagda.md index 6c0d59730a..d654de831d 100644 --- a/src/group-theory/dependent-products-groups.lagda.md +++ b/src/group-theory/dependent-products-groups.lagda.md @@ -1,22 +1,30 @@ # Dependent products of groups ```agda -module group-theory.dependent-products-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.dependent-products-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-extensionality -open import foundation.identity-types -open import foundation.sets +open import foundation.function-extensionality funext +open import foundation.identity-types funext +open import foundation.sets funext univalence open import foundation.universe-levels -open import group-theory.dependent-products-semigroups -open import group-theory.groups -open import group-theory.monoids -open import group-theory.semigroups +open import group-theory.dependent-products-semigroups funext univalence +open import group-theory.groups funext univalence truncations +open import group-theory.monoids funext univalence truncations +open import group-theory.semigroups funext univalence ```
diff --git a/src/group-theory/dependent-products-monoids.lagda.md b/src/group-theory/dependent-products-monoids.lagda.md index f2602a6622..cf54b776c3 100644 --- a/src/group-theory/dependent-products-monoids.lagda.md +++ b/src/group-theory/dependent-products-monoids.lagda.md @@ -1,21 +1,29 @@ # Dependent products of monoids ```agda -module group-theory.dependent-products-monoids where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.dependent-products-monoids + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-extensionality -open import foundation.identity-types -open import foundation.sets +open import foundation.function-extensionality funext +open import foundation.identity-types funext +open import foundation.sets funext univalence open import foundation.universe-levels -open import group-theory.dependent-products-semigroups -open import group-theory.monoids -open import group-theory.semigroups +open import group-theory.dependent-products-semigroups funext univalence +open import group-theory.monoids funext univalence truncations +open import group-theory.semigroups funext univalence ```
diff --git a/src/group-theory/dependent-products-semigroups.lagda.md b/src/group-theory/dependent-products-semigroups.lagda.md index 5194e020a4..9cf4b5bc38 100644 --- a/src/group-theory/dependent-products-semigroups.lagda.md +++ b/src/group-theory/dependent-products-semigroups.lagda.md @@ -1,19 +1,25 @@ # Dependent products of semigroups ```agda -module group-theory.dependent-products-semigroups where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.dependent-products-semigroups + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-extensionality -open import foundation.identity-types -open import foundation.sets +open import foundation.function-extensionality funext +open import foundation.identity-types funext +open import foundation.sets funext univalence open import foundation.universe-levels -open import group-theory.semigroups +open import group-theory.semigroups funext univalence ```
diff --git a/src/group-theory/dihedral-group-construction.lagda.md b/src/group-theory/dihedral-group-construction.lagda.md index 6aba36c7df..5f24468b10 100644 --- a/src/group-theory/dihedral-group-construction.lagda.md +++ b/src/group-theory/dihedral-group-construction.lagda.md @@ -1,24 +1,32 @@ # The dihedral group construction ```agda -module group-theory.dihedral-group-construction where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.dihedral-group-construction + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.coproduct-types +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equality-coproduct-types -open import foundation.identity-types -open import foundation.sets +open import foundation.equality-coproduct-types funext univalence truncations +open import foundation.identity-types funext +open import foundation.sets funext univalence open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.groups -open import group-theory.monoids -open import group-theory.semigroups +open import group-theory.abelian-groups funext univalence truncations +open import group-theory.groups funext univalence truncations +open import group-theory.monoids funext univalence truncations +open import group-theory.semigroups funext univalence ```
diff --git a/src/group-theory/dihedral-groups.lagda.md b/src/group-theory/dihedral-groups.lagda.md index 83fd4ee34a..b1857397f3 100644 --- a/src/group-theory/dihedral-groups.lagda.md +++ b/src/group-theory/dihedral-groups.lagda.md @@ -1,19 +1,27 @@ # The dihedral groups ```agda -module group-theory.dihedral-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.dihedral-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import elementary-number-theory.natural-numbers -open import elementary-number-theory.standard-cyclic-groups +open import elementary-number-theory.standard-cyclic-groups funext univalence truncations open import foundation.universe-levels -open import group-theory.dihedral-group-construction -open import group-theory.groups +open import group-theory.dihedral-group-construction funext univalence truncations +open import group-theory.groups funext univalence truncations ```
diff --git a/src/group-theory/e8-lattice.lagda.md b/src/group-theory/e8-lattice.lagda.md index 004bb360a5..52488adc65 100644 --- a/src/group-theory/e8-lattice.lagda.md +++ b/src/group-theory/e8-lattice.lagda.md @@ -1,19 +1,28 @@ # The `E₈`-lattice ```agda -module group-theory.e8-lattice where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.e8-lattice + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda +open import elementary-number-theory.equality-integers funext univalence truncations open import elementary-number-theory.integers -open import foundation.equality-coproduct-types -open import foundation.sets +open import foundation.equality-coproduct-types funext univalence truncations +open import foundation.sets funext univalence open import foundation.universe-levels -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/group-theory/elements-of-finite-order-groups.lagda.md b/src/group-theory/elements-of-finite-order-groups.lagda.md index de05cf476b..01e810536e 100644 --- a/src/group-theory/elements-of-finite-order-groups.lagda.md +++ b/src/group-theory/elements-of-finite-order-groups.lagda.md @@ -1,23 +1,32 @@ # Elements of finite order ```agda -module group-theory.elements-of-finite-order-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.elements-of-finite-order-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.group-of-integers -open import elementary-number-theory.nonzero-integers +open import elementary-number-theory.group-of-integers funext univalence truncations +open import elementary-number-theory.nonzero-integers funext univalence truncations -open import foundation.existential-quantification -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.existential-quantification funext univalence truncations +open import foundation.propositions funext univalence open import foundation.universe-levels -open import group-theory.groups -open import group-theory.orders-of-elements-groups -open import group-theory.subgroups -open import group-theory.subgroups-generated-by-elements-groups +open import group-theory.groups funext univalence truncations +open import group-theory.orders-of-elements-groups funext univalence truncations +open import group-theory.subgroups funext univalence truncations +open import group-theory.subgroups-generated-by-elements-groups funext univalence truncations ```
diff --git a/src/group-theory/embeddings-abelian-groups.lagda.md b/src/group-theory/embeddings-abelian-groups.lagda.md index 9061f2dbe1..5787e1ed66 100644 --- a/src/group-theory/embeddings-abelian-groups.lagda.md +++ b/src/group-theory/embeddings-abelian-groups.lagda.md @@ -1,19 +1,27 @@ # Embeddings of abelian groups ```agda -module group-theory.embeddings-abelian-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.embeddings-abelian-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.embeddings +open import foundation.embeddings funext open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.embeddings-groups -open import group-theory.homomorphisms-abelian-groups -open import group-theory.subgroups-abelian-groups +open import group-theory.abelian-groups funext univalence truncations +open import group-theory.embeddings-groups funext univalence truncations +open import group-theory.homomorphisms-abelian-groups funext univalence truncations +open import group-theory.subgroups-abelian-groups funext univalence truncations ```
diff --git a/src/group-theory/embeddings-groups.lagda.md b/src/group-theory/embeddings-groups.lagda.md index 9d7b7c5dab..86777856fa 100644 --- a/src/group-theory/embeddings-groups.lagda.md +++ b/src/group-theory/embeddings-groups.lagda.md @@ -1,19 +1,27 @@ # Embeddings of groups ```agda -module group-theory.embeddings-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.embeddings-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.embeddings +open import foundation.embeddings funext open import foundation.universe-levels -open import group-theory.groups -open import group-theory.homomorphisms-groups -open import group-theory.subgroups +open import group-theory.groups funext univalence truncations +open import group-theory.homomorphisms-groups funext univalence truncations +open import group-theory.subgroups funext univalence truncations ```
diff --git a/src/group-theory/endomorphism-rings-abelian-groups.lagda.md b/src/group-theory/endomorphism-rings-abelian-groups.lagda.md index d3dfb679a9..9f0d436163 100644 --- a/src/group-theory/endomorphism-rings-abelian-groups.lagda.md +++ b/src/group-theory/endomorphism-rings-abelian-groups.lagda.md @@ -1,7 +1,15 @@ # The endomorphism rings of abelian groups ```agda -module group-theory.endomorphism-rings-abelian-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.endomorphism-rings-abelian-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,11 +18,11 @@ module group-theory.endomorphism-rings-abelian-groups where open import foundation.dependent-pair-types open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.addition-homomorphisms-abelian-groups -open import group-theory.homomorphisms-abelian-groups +open import group-theory.abelian-groups funext univalence truncations +open import group-theory.addition-homomorphisms-abelian-groups funext univalence truncations +open import group-theory.homomorphisms-abelian-groups funext univalence truncations -open import ring-theory.rings +open import ring-theory.rings funext univalence truncations ```
diff --git a/src/group-theory/epimorphisms-groups.lagda.md b/src/group-theory/epimorphisms-groups.lagda.md index be41b90450..6e0ad91a95 100644 --- a/src/group-theory/epimorphisms-groups.lagda.md +++ b/src/group-theory/epimorphisms-groups.lagda.md @@ -1,21 +1,30 @@ # Epimorphisms in groups ```agda -module group-theory.epimorphisms-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.epimorphisms-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.epimorphisms-in-large-precategories +open import category-theory.epimorphisms-in-large-precategories funext univalence truncations -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.propositions funext univalence open import foundation.universe-levels -open import group-theory.groups -open import group-theory.homomorphisms-groups -open import group-theory.isomorphisms-groups -open import group-theory.precategory-of-groups +open import group-theory.groups funext univalence truncations +open import group-theory.homomorphisms-groups funext univalence truncations +open import group-theory.isomorphisms-groups funext univalence truncations +open import group-theory.precategory-of-groups funext univalence truncations ```
diff --git a/src/group-theory/equivalences-concrete-group-actions.lagda.md b/src/group-theory/equivalences-concrete-group-actions.lagda.md index 27c37431a5..77b541fdc7 100644 --- a/src/group-theory/equivalences-concrete-group-actions.lagda.md +++ b/src/group-theory/equivalences-concrete-group-actions.lagda.md @@ -1,27 +1,36 @@ # Equivalences of concrete group actions ```agda -module group-theory.equivalences-concrete-group-actions where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.equivalences-concrete-group-actions + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.1-types +open import foundation.1-types funext univalence open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equality-dependent-function-types -open import foundation.equivalences -open import foundation.functoriality-dependent-function-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets -open import foundation.torsorial-type-families +open import foundation.dependent-products-propositions funext +open import foundation.embeddings funext +open import foundation.equality-dependent-function-types funext +open import foundation.equivalences funext +open import foundation.functoriality-dependent-function-types funext univalence +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.torsorial-type-families funext univalence truncations open import foundation.universe-levels -open import group-theory.concrete-group-actions -open import group-theory.concrete-groups -open import group-theory.homomorphisms-concrete-group-actions +open import group-theory.concrete-group-actions funext univalence truncations +open import group-theory.concrete-groups funext univalence truncations +open import group-theory.homomorphisms-concrete-group-actions funext univalence truncations ```
diff --git a/src/group-theory/equivalences-concrete-groups.lagda.md b/src/group-theory/equivalences-concrete-groups.lagda.md index 52676af8d8..539d702247 100644 --- a/src/group-theory/equivalences-concrete-groups.lagda.md +++ b/src/group-theory/equivalences-concrete-groups.lagda.md @@ -1,25 +1,33 @@ # Equivalences of concrete groups ```agda -module group-theory.equivalences-concrete-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.equivalences-concrete-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences +open import foundation.equivalences funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types -open import foundation.sets +open import foundation.identity-types funext +open import foundation.sets funext univalence open import foundation.subtype-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext univalence truncations open import foundation.universe-levels -open import group-theory.concrete-groups +open import group-theory.concrete-groups funext univalence truncations -open import higher-group-theory.equivalences-higher-groups -open import higher-group-theory.higher-groups +open import higher-group-theory.equivalences-higher-groups funext univalence truncations +open import higher-group-theory.higher-groups funext univalence truncations ```
diff --git a/src/group-theory/equivalences-group-actions.lagda.md b/src/group-theory/equivalences-group-actions.lagda.md index cabae428b7..04543a1ee1 100644 --- a/src/group-theory/equivalences-group-actions.lagda.md +++ b/src/group-theory/equivalences-group-actions.lagda.md @@ -1,34 +1,43 @@ # Equivalences of group actions ```agda -module group-theory.equivalences-group-actions where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.equivalences-group-actions + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.commuting-squares-of-maps -open import foundation.contractible-types +open import foundation.commuting-squares-of-maps funext univalence +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalence-extensionality -open import foundation.equivalences -open import foundation.functoriality-dependent-function-types -open import foundation.functoriality-dependent-pair-types +open import foundation.dependent-products-contractible-types funext +open import foundation.equivalence-extensionality funext +open import foundation.equivalences funext +open import foundation.functoriality-dependent-function-types funext univalence +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.sets +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.sets funext univalence open import foundation.structure-identity-principle open import foundation.subtype-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext univalence truncations open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels -open import group-theory.group-actions -open import group-theory.groups -open import group-theory.homomorphisms-group-actions -open import group-theory.homomorphisms-groups -open import group-theory.symmetric-groups +open import group-theory.group-actions funext univalence truncations +open import group-theory.groups funext univalence truncations +open import group-theory.homomorphisms-group-actions funext univalence truncations +open import group-theory.homomorphisms-groups funext univalence truncations +open import group-theory.symmetric-groups funext univalence truncations ```
diff --git a/src/group-theory/equivalences-semigroups.lagda.md b/src/group-theory/equivalences-semigroups.lagda.md index b0ec4a907d..d2d059cb0c 100644 --- a/src/group-theory/equivalences-semigroups.lagda.md +++ b/src/group-theory/equivalences-semigroups.lagda.md @@ -1,28 +1,37 @@ # Equivalences between semigroups ```agda -module group-theory.equivalences-semigroups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.equivalences-semigroups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.function-extensionality funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence open import foundation.structure-identity-principle open import foundation.subtype-identity-principle -open import foundation.subtypes -open import foundation.torsorial-type-families -open import foundation.univalence +open import foundation.subtypes funext univalence truncations +open import foundation.torsorial-type-families funext univalence truncations +open import foundation.univalence funext univalence open import foundation.universe-levels -open import group-theory.homomorphisms-semigroups -open import group-theory.semigroups +open import group-theory.homomorphisms-semigroups funext univalence truncations +open import group-theory.semigroups funext univalence ```
diff --git a/src/group-theory/exponents-abelian-groups.lagda.md b/src/group-theory/exponents-abelian-groups.lagda.md index 1f2bfdd78f..7c32b70261 100644 --- a/src/group-theory/exponents-abelian-groups.lagda.md +++ b/src/group-theory/exponents-abelian-groups.lagda.md @@ -1,19 +1,27 @@ # Exponents of abelian groups ```agda -module group-theory.exponents-abelian-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.exponents-abelian-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.group-of-integers +open import elementary-number-theory.group-of-integers funext univalence truncations open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.exponents-groups -open import group-theory.subgroups-abelian-groups +open import group-theory.abelian-groups funext univalence truncations +open import group-theory.exponents-groups funext univalence truncations +open import group-theory.subgroups-abelian-groups funext univalence truncations ```
diff --git a/src/group-theory/exponents-groups.lagda.md b/src/group-theory/exponents-groups.lagda.md index 4df222fea0..7bfb4795c2 100644 --- a/src/group-theory/exponents-groups.lagda.md +++ b/src/group-theory/exponents-groups.lagda.md @@ -1,21 +1,29 @@ # Exponents of groups ```agda -module group-theory.exponents-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.exponents-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.group-of-integers +open import elementary-number-theory.group-of-integers funext univalence truncations open import foundation.universe-levels -open import group-theory.free-groups-with-one-generator -open import group-theory.groups -open import group-theory.intersections-subgroups-groups -open import group-theory.kernels-homomorphisms-groups -open import group-theory.subgroups +open import group-theory.free-groups-with-one-generator funext univalence truncations +open import group-theory.groups funext univalence truncations +open import group-theory.intersections-subgroups-groups funext univalence truncations +open import group-theory.kernels-homomorphisms-groups funext univalence truncations +open import group-theory.subgroups funext univalence truncations ```
diff --git a/src/group-theory/free-concrete-group-actions.lagda.md b/src/group-theory/free-concrete-group-actions.lagda.md index 7eb0462d9f..39e6829ab6 100644 --- a/src/group-theory/free-concrete-group-actions.lagda.md +++ b/src/group-theory/free-concrete-group-actions.lagda.md @@ -1,22 +1,31 @@ # Free concrete group actions ```agda -module group-theory.free-concrete-group-actions where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.free-concrete-group-actions + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.propositions -open import foundation.sets +open import foundation.dependent-products-propositions funext +open import foundation.function-types funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence open import foundation.universe-levels -open import group-theory.concrete-group-actions -open import group-theory.concrete-groups +open import group-theory.concrete-group-actions funext univalence truncations +open import group-theory.concrete-groups funext univalence truncations -open import higher-group-theory.free-higher-group-actions +open import higher-group-theory.free-higher-group-actions funext univalence truncations ```
diff --git a/src/group-theory/free-groups-with-one-generator.lagda.md b/src/group-theory/free-groups-with-one-generator.lagda.md index e66fdcf4d7..e56d7f5a24 100644 --- a/src/group-theory/free-groups-with-one-generator.lagda.md +++ b/src/group-theory/free-groups-with-one-generator.lagda.md @@ -1,31 +1,39 @@ # Free groups with one generator ```agda -module group-theory.free-groups-with-one-generator where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.free-groups-with-one-generator + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.addition-integers -open import elementary-number-theory.group-of-integers +open import elementary-number-theory.addition-integers funext univalence truncations +open import elementary-number-theory.group-of-integers funext univalence truncations open import elementary-number-theory.integers open import foundation.action-on-identifications-functions -open import foundation.contractible-maps +open import foundation.contractible-maps funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.identity-types -open import foundation.sets -open import foundation.subtypes -open import foundation.torsorial-type-families +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.sets funext univalence +open import foundation.subtypes funext univalence truncations +open import foundation.torsorial-type-families funext univalence truncations open import foundation.universe-levels -open import group-theory.groups -open import group-theory.homomorphisms-groups -open import group-theory.integer-powers-of-elements-groups +open import group-theory.groups funext univalence truncations +open import group-theory.homomorphisms-groups funext univalence truncations +open import group-theory.integer-powers-of-elements-groups funext univalence truncations -open import structured-types.initial-pointed-type-equipped-with-automorphism +open import structured-types.initial-pointed-type-equipped-with-automorphism funext univalence truncations ```
diff --git a/src/group-theory/full-subgroups.lagda.md b/src/group-theory/full-subgroups.lagda.md index 5200efc0f3..fc5f9b99f7 100644 --- a/src/group-theory/full-subgroups.lagda.md +++ b/src/group-theory/full-subgroups.lagda.md @@ -1,23 +1,32 @@ # The full subgroup of a group ```agda -module group-theory.full-subgroups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.full-subgroups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.full-subtypes -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.full-subtypes funext univalence truncations +open import foundation.propositions funext univalence open import foundation.universe-levels -open import group-theory.groups -open import group-theory.homomorphisms-groups -open import group-theory.isomorphisms-groups -open import group-theory.subgroups -open import group-theory.subsets-groups +open import group-theory.groups funext univalence truncations +open import group-theory.homomorphisms-groups funext univalence truncations +open import group-theory.isomorphisms-groups funext univalence truncations +open import group-theory.subgroups funext univalence truncations +open import group-theory.subsets-groups funext univalence truncations ```
diff --git a/src/group-theory/full-subsemigroups.lagda.md b/src/group-theory/full-subsemigroups.lagda.md index 507941cd28..e5a180e62e 100644 --- a/src/group-theory/full-subsemigroups.lagda.md +++ b/src/group-theory/full-subsemigroups.lagda.md @@ -1,24 +1,33 @@ # The full subsemigroup of a semigroup ```agda -module group-theory.full-subsemigroups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.full-subsemigroups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.full-subtypes -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.full-subtypes funext univalence truncations +open import foundation.propositions funext univalence open import foundation.universe-levels -open import group-theory.equivalences-semigroups -open import group-theory.homomorphisms-semigroups -open import group-theory.isomorphisms-semigroups -open import group-theory.semigroups -open import group-theory.subsemigroups -open import group-theory.subsets-semigroups +open import group-theory.equivalences-semigroups funext univalence truncations +open import group-theory.homomorphisms-semigroups funext univalence truncations +open import group-theory.isomorphisms-semigroups funext univalence truncations +open import group-theory.semigroups funext univalence +open import group-theory.subsemigroups funext univalence truncations +open import group-theory.subsets-semigroups funext univalence truncations ```
diff --git a/src/group-theory/function-abelian-groups.lagda.md b/src/group-theory/function-abelian-groups.lagda.md index 6836e3eed4..a1f08a31b4 100644 --- a/src/group-theory/function-abelian-groups.lagda.md +++ b/src/group-theory/function-abelian-groups.lagda.md @@ -1,21 +1,29 @@ # Function groups of abelian groups ```agda -module group-theory.function-abelian-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.function-abelian-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.identity-types -open import foundation.sets +open import foundation.identity-types funext +open import foundation.sets funext univalence open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.dependent-products-abelian-groups -open import group-theory.groups -open import group-theory.monoids -open import group-theory.semigroups +open import group-theory.abelian-groups funext univalence truncations +open import group-theory.dependent-products-abelian-groups funext univalence truncations +open import group-theory.groups funext univalence truncations +open import group-theory.monoids funext univalence truncations +open import group-theory.semigroups funext univalence ```
diff --git a/src/group-theory/function-commutative-monoids.lagda.md b/src/group-theory/function-commutative-monoids.lagda.md index 57b44087dc..a37db3a50f 100644 --- a/src/group-theory/function-commutative-monoids.lagda.md +++ b/src/group-theory/function-commutative-monoids.lagda.md @@ -1,19 +1,27 @@ # Function commutative monoids ```agda -module group-theory.function-commutative-monoids where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.function-commutative-monoids + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.identity-types -open import foundation.sets +open import foundation.identity-types funext +open import foundation.sets funext univalence open import foundation.universe-levels -open import group-theory.commutative-monoids -open import group-theory.dependent-products-commutative-monoids -open import group-theory.monoids +open import group-theory.commutative-monoids funext univalence truncations +open import group-theory.dependent-products-commutative-monoids funext univalence truncations +open import group-theory.monoids funext univalence truncations ```
diff --git a/src/group-theory/function-groups.lagda.md b/src/group-theory/function-groups.lagda.md index b9d8cff7aa..f0120fc659 100644 --- a/src/group-theory/function-groups.lagda.md +++ b/src/group-theory/function-groups.lagda.md @@ -1,21 +1,29 @@ # Function groups ```agda -module group-theory.function-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.function-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.sets +open import foundation.identity-types funext +open import foundation.sets funext univalence open import foundation.universe-levels -open import group-theory.dependent-products-groups -open import group-theory.groups -open import group-theory.monoids -open import group-theory.semigroups +open import group-theory.dependent-products-groups funext univalence truncations +open import group-theory.groups funext univalence truncations +open import group-theory.monoids funext univalence truncations +open import group-theory.semigroups funext univalence ```
diff --git a/src/group-theory/function-monoids.lagda.md b/src/group-theory/function-monoids.lagda.md index bef75c807a..bc8d559eb5 100644 --- a/src/group-theory/function-monoids.lagda.md +++ b/src/group-theory/function-monoids.lagda.md @@ -1,19 +1,27 @@ # Function monoids ```agda -module group-theory.function-monoids where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.function-monoids + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.identity-types -open import foundation.sets +open import foundation.identity-types funext +open import foundation.sets funext univalence open import foundation.universe-levels -open import group-theory.dependent-products-monoids -open import group-theory.monoids -open import group-theory.semigroups +open import group-theory.dependent-products-monoids funext univalence truncations +open import group-theory.monoids funext univalence truncations +open import group-theory.semigroups funext univalence ```
diff --git a/src/group-theory/function-semigroups.lagda.md b/src/group-theory/function-semigroups.lagda.md index 06605fc58c..ecb7aa05de 100644 --- a/src/group-theory/function-semigroups.lagda.md +++ b/src/group-theory/function-semigroups.lagda.md @@ -1,18 +1,24 @@ # Function semigroups ```agda -module group-theory.function-semigroups where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.function-semigroups + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda -open import foundation.identity-types -open import foundation.sets +open import foundation.identity-types funext +open import foundation.sets funext univalence open import foundation.universe-levels -open import group-theory.dependent-products-semigroups -open import group-theory.semigroups +open import group-theory.dependent-products-semigroups funext univalence +open import group-theory.semigroups funext univalence ```
diff --git a/src/group-theory/functoriality-quotient-groups.lagda.md b/src/group-theory/functoriality-quotient-groups.lagda.md index 6b48fc225f..08552d8d50 100644 --- a/src/group-theory/functoriality-quotient-groups.lagda.md +++ b/src/group-theory/functoriality-quotient-groups.lagda.md @@ -2,28 +2,36 @@ ```agda {-# OPTIONS --lossy-unification #-} - -module group-theory.functoriality-quotient-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.functoriality-quotient-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-maps -open import foundation.contractible-types +open import foundation.commuting-squares-of-maps funext univalence +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types +open import foundation.dependent-products-contractible-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.universe-levels -open import group-theory.commuting-squares-of-group-homomorphisms -open import group-theory.groups -open import group-theory.homomorphisms-groups -open import group-theory.homomorphisms-groups-equipped-with-normal-subgroups -open import group-theory.normal-subgroups -open import group-theory.nullifying-group-homomorphisms -open import group-theory.quotient-groups +open import group-theory.commuting-squares-of-group-homomorphisms funext univalence truncations +open import group-theory.groups funext univalence truncations +open import group-theory.homomorphisms-groups funext univalence truncations +open import group-theory.homomorphisms-groups-equipped-with-normal-subgroups funext univalence truncations +open import group-theory.normal-subgroups funext univalence truncations +open import group-theory.nullifying-group-homomorphisms funext univalence truncations +open import group-theory.quotient-groups funext univalence truncations ```
diff --git a/src/group-theory/furstenberg-groups.lagda.md b/src/group-theory/furstenberg-groups.lagda.md index a9e760780e..df1adb4240 100644 --- a/src/group-theory/furstenberg-groups.lagda.md +++ b/src/group-theory/furstenberg-groups.lagda.md @@ -1,17 +1,25 @@ # Furstenberg groups ```agda -module group-theory.furstenberg-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.furstenberg-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.propositional-truncations -open import foundation.sets +open import foundation.identity-types funext +open import foundation.propositional-truncations funext univalence +open import foundation.sets funext univalence open import foundation.universe-levels ``` diff --git a/src/group-theory/generating-elements-groups.lagda.md b/src/group-theory/generating-elements-groups.lagda.md index 41643d2ee7..6bf66ea1e3 100644 --- a/src/group-theory/generating-elements-groups.lagda.md +++ b/src/group-theory/generating-elements-groups.lagda.md @@ -1,53 +1,63 @@ # Generating elements of groups ```agda -module group-theory.generating-elements-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.generating-elements-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import commutative-algebra.commutative-rings +open import commutative-algebra.commutative-rings funext univalence truncations open import elementary-number-theory.integers open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalences -open import foundation.identity-types -open import foundation.images -open import foundation.injective-maps -open import foundation.propositional-maps -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.sets -open import foundation.subtypes -open import foundation.surjective-maps +open import foundation.dependent-products-propositions funext +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.images funext univalence truncations +open import foundation.injective-maps funext +open import foundation.propositional-maps funext +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence +open import foundation.raising-universe-levels-unit-type +open import foundation.sets funext univalence +open import foundation.subtypes funext univalence truncations +open import foundation.surjective-maps funext univalence truncations open import foundation.unit-type open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.addition-homomorphisms-abelian-groups -open import group-theory.commuting-elements-groups -open import group-theory.conjugation -open import group-theory.endomorphism-rings-abelian-groups -open import group-theory.free-groups-with-one-generator -open import group-theory.full-subgroups -open import group-theory.groups -open import group-theory.homomorphisms-groups -open import group-theory.integer-multiples-of-elements-abelian-groups -open import group-theory.integer-powers-of-elements-groups -open import group-theory.isomorphisms-abelian-groups -open import group-theory.normal-subgroups -open import group-theory.quotient-groups -open import group-theory.subgroups-generated-by-elements-groups -open import group-theory.subsets-groups -open import group-theory.trivial-group-homomorphisms - -open import ring-theory.integer-multiples-of-elements-rings -open import ring-theory.rings -open import ring-theory.transporting-ring-structure-along-isomorphisms-abelian-groups +open import group-theory.abelian-groups funext univalence truncations +open import group-theory.addition-homomorphisms-abelian-groups funext univalence truncations +open import group-theory.commuting-elements-groups funext univalence truncations +open import group-theory.conjugation funext univalence truncations +open import group-theory.endomorphism-rings-abelian-groups funext univalence truncations +open import group-theory.free-groups-with-one-generator funext univalence truncations +open import group-theory.full-subgroups funext univalence truncations +open import group-theory.groups funext univalence truncations +open import group-theory.homomorphisms-groups funext univalence truncations +open import group-theory.integer-multiples-of-elements-abelian-groups funext univalence truncations +open import group-theory.integer-powers-of-elements-groups funext univalence truncations +open import group-theory.isomorphisms-abelian-groups funext univalence truncations +open import group-theory.normal-subgroups funext univalence truncations +open import group-theory.quotient-groups funext univalence truncations +open import group-theory.subgroups-generated-by-elements-groups funext univalence truncations +open import group-theory.subsets-groups funext univalence truncations +open import group-theory.trivial-group-homomorphisms funext univalence truncations + +open import ring-theory.integer-multiples-of-elements-rings funext univalence truncations +open import ring-theory.rings funext univalence truncations +open import ring-theory.transporting-ring-structure-along-isomorphisms-abelian-groups funext univalence truncations ```
diff --git a/src/group-theory/generating-sets-groups.lagda.md b/src/group-theory/generating-sets-groups.lagda.md index 513c92471a..acedc183d1 100644 --- a/src/group-theory/generating-sets-groups.lagda.md +++ b/src/group-theory/generating-sets-groups.lagda.md @@ -1,7 +1,15 @@ # Generating sets of groups ```agda -module group-theory.generating-sets-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.generating-sets-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,10 +17,10 @@ module group-theory.generating-sets-groups where ```agda open import foundation.universe-levels -open import group-theory.full-subgroups -open import group-theory.groups -open import group-theory.subgroups-generated-by-subsets-groups -open import group-theory.subsets-groups +open import group-theory.full-subgroups funext univalence truncations +open import group-theory.groups funext univalence truncations +open import group-theory.subgroups-generated-by-subsets-groups funext univalence truncations +open import group-theory.subsets-groups funext univalence truncations ```
diff --git a/src/group-theory/group-actions.lagda.md b/src/group-theory/group-actions.lagda.md index b0648b9beb..3a0a72e625 100644 --- a/src/group-theory/group-actions.lagda.md +++ b/src/group-theory/group-actions.lagda.md @@ -1,7 +1,15 @@ # Group actions ```agda -module group-theory.group-actions where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.group-actions + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,19 +17,17 @@ module group-theory.group-actions where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.sets +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.sets funext univalence open import foundation.universe-levels -open import group-theory.groups -open import group-theory.homomorphisms-groups -open import group-theory.subgroups -open import group-theory.symmetric-groups -open import group-theory.trivial-group-homomorphisms +open import group-theory.groups funext univalence truncations +open import group-theory.homomorphisms-groups funext univalence truncations +open import group-theory.symmetric-groups funext univalence truncations +open import group-theory.trivial-group-homomorphisms funext univalence truncations ```
diff --git a/src/group-theory/groups.lagda.md b/src/group-theory/groups.lagda.md index ae04f5eb0d..74c271cb1f 100644 --- a/src/group-theory/groups.lagda.md +++ b/src/group-theory/groups.lagda.md @@ -1,7 +1,15 @@ # Abstract groups ```agda -module group-theory.groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,34 +17,35 @@ module group-theory.groups where ```agda open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.binary-embeddings +open import foundation.binary-embeddings funext open import foundation.binary-equivalences -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.involutions -open import foundation.propositions -open import foundation.sets -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.function-extensionality funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.involutions funext univalence +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels -open import group-theory.invertible-elements-monoids -open import group-theory.monoids -open import group-theory.products-of-elements-monoids -open import group-theory.semigroups +open import group-theory.invertible-elements-monoids funext univalence truncations +open import group-theory.monoids funext univalence truncations +open import group-theory.products-of-elements-monoids funext univalence truncations +open import group-theory.semigroups funext univalence -open import lists.concatenation-lists +open import lists.concatenation-lists funext univalence truncations open import lists.lists -open import structured-types.h-spaces +open import structured-types.h-spaces funext univalence truncations open import structured-types.pointed-types -open import structured-types.pointed-types-equipped-with-automorphisms +open import structured-types.pointed-types-equipped-with-automorphisms funext univalence truncations ```
diff --git a/src/group-theory/homomorphisms-abelian-groups.lagda.md b/src/group-theory/homomorphisms-abelian-groups.lagda.md index 172b824ed0..6bab728463 100644 --- a/src/group-theory/homomorphisms-abelian-groups.lagda.md +++ b/src/group-theory/homomorphisms-abelian-groups.lagda.md @@ -1,27 +1,35 @@ # Homomorphisms of abelian groups ```agda -module group-theory.homomorphisms-abelian-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.homomorphisms-abelian-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.large-categories +open import category-theory.large-categories funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.identity-types -open import foundation.sets -open import foundation.torsorial-type-families +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.sets funext univalence +open import foundation.torsorial-type-families funext univalence truncations open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.category-of-abelian-groups -open import group-theory.homomorphisms-commutative-monoids -open import group-theory.homomorphisms-groups -open import group-theory.homomorphisms-semigroups +open import group-theory.abelian-groups funext univalence truncations +open import group-theory.category-of-abelian-groups funext univalence truncations +open import group-theory.homomorphisms-commutative-monoids funext univalence truncations +open import group-theory.homomorphisms-groups funext univalence truncations +open import group-theory.homomorphisms-semigroups funext univalence truncations ```
diff --git a/src/group-theory/homomorphisms-commutative-monoids.lagda.md b/src/group-theory/homomorphisms-commutative-monoids.lagda.md index b5783ad749..054ff342ae 100644 --- a/src/group-theory/homomorphisms-commutative-monoids.lagda.md +++ b/src/group-theory/homomorphisms-commutative-monoids.lagda.md @@ -1,21 +1,29 @@ # Homomorphisms of commutative monoids ```agda -module group-theory.homomorphisms-commutative-monoids where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.homomorphisms-commutative-monoids + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.equivalences -open import foundation.identity-types -open import foundation.sets -open import foundation.torsorial-type-families +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.sets funext univalence +open import foundation.torsorial-type-families funext univalence truncations open import foundation.universe-levels -open import group-theory.commutative-monoids -open import group-theory.homomorphisms-monoids -open import group-theory.homomorphisms-semigroups +open import group-theory.commutative-monoids funext univalence truncations +open import group-theory.homomorphisms-monoids funext univalence truncations +open import group-theory.homomorphisms-semigroups funext univalence truncations ```
diff --git a/src/group-theory/homomorphisms-concrete-group-actions.lagda.md b/src/group-theory/homomorphisms-concrete-group-actions.lagda.md index 62057b8e87..7daadd675a 100644 --- a/src/group-theory/homomorphisms-concrete-group-actions.lagda.md +++ b/src/group-theory/homomorphisms-concrete-group-actions.lagda.md @@ -1,26 +1,35 @@ # Morphisms of concrete group actions ```agda -module group-theory.homomorphisms-concrete-group-actions where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.homomorphisms-concrete-group-actions + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.0-connected-types -open import foundation.equality-dependent-function-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets +open import foundation.0-connected-types funext univalence truncations +open import foundation.dependent-products-propositions funext +open import foundation.equality-dependent-function-types funext +open import foundation.equivalences funext +open import foundation.function-extensionality funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence open import foundation.transport-along-identifications open import foundation.universe-levels -open import group-theory.concrete-group-actions -open import group-theory.concrete-groups +open import group-theory.concrete-group-actions funext univalence truncations +open import group-theory.concrete-groups funext univalence truncations ```
diff --git a/src/group-theory/homomorphisms-concrete-groups.lagda.md b/src/group-theory/homomorphisms-concrete-groups.lagda.md index d61de489f6..95d0ad42fb 100644 --- a/src/group-theory/homomorphisms-concrete-groups.lagda.md +++ b/src/group-theory/homomorphisms-concrete-groups.lagda.md @@ -1,24 +1,32 @@ # Homomorphisms of concrete groups ```agda -module group-theory.homomorphisms-concrete-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.homomorphisms-concrete-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.0-connected-types +open import foundation.0-connected-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.identity-types -open import foundation.sets +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.sets funext univalence open import foundation.truncation-levels open import foundation.universe-levels -open import group-theory.concrete-groups -open import group-theory.homomorphisms-groups +open import group-theory.concrete-groups funext univalence truncations +open import group-theory.homomorphisms-groups funext univalence truncations -open import higher-group-theory.homomorphisms-higher-groups +open import higher-group-theory.homomorphisms-higher-groups funext univalence truncations ```
diff --git a/src/group-theory/homomorphisms-generated-subgroups.lagda.md b/src/group-theory/homomorphisms-generated-subgroups.lagda.md index 3f3d1b219b..e7f930e3d2 100644 --- a/src/group-theory/homomorphisms-generated-subgroups.lagda.md +++ b/src/group-theory/homomorphisms-generated-subgroups.lagda.md @@ -1,42 +1,52 @@ # Homomorphisms of generated subgroups ```agda -module group-theory.homomorphisms-generated-subgroups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.homomorphisms-generated-subgroups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types -open import foundation.coproduct-types +open import foundation.cartesian-product-types funext univalence +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equality-dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.identity-types -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.sets -open import foundation.subtypes -open import foundation.truncated-types +open import foundation.dependent-products-propositions funext +open import foundation.dependent-products-truncated-types funext +open import foundation.embeddings funext +open import foundation.equality-dependent-pair-types funext +open import foundation.equivalences funext +open import foundation.function-extensionality funext +open import foundation.identity-types funext +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.subtypes funext univalence truncations +open import foundation.truncated-types funext univalence open import foundation.truncation-levels open import foundation.unit-type open import foundation.universe-levels -open import group-theory.epimorphisms-groups -open import group-theory.full-subgroups -open import group-theory.generating-sets-groups -open import group-theory.groups -open import group-theory.homomorphisms-groups -open import group-theory.subgroups -open import group-theory.subgroups-generated-by-subsets-groups -open import group-theory.subsets-groups +open import group-theory.epimorphisms-groups funext univalence truncations +open import group-theory.full-subgroups funext univalence truncations +open import group-theory.generating-sets-groups funext univalence truncations +open import group-theory.groups funext univalence truncations +open import group-theory.homomorphisms-groups funext univalence truncations +open import group-theory.subgroups funext univalence truncations +open import group-theory.subgroups-generated-by-subsets-groups funext univalence truncations +open import group-theory.subsets-groups funext univalence truncations open import lists.lists -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/group-theory/homomorphisms-group-actions.lagda.md b/src/group-theory/homomorphisms-group-actions.lagda.md index b9f76c3392..68b3b08ab2 100644 --- a/src/group-theory/homomorphisms-group-actions.lagda.md +++ b/src/group-theory/homomorphisms-group-actions.lagda.md @@ -1,29 +1,39 @@ # Homomorphisms of group actions ```agda -module group-theory.homomorphisms-group-actions where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.homomorphisms-group-actions + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.commuting-squares-of-maps +open import foundation.commuting-squares-of-maps funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types -open import foundation.iterated-dependent-product-types -open import foundation.propositions -open import foundation.sets +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext +open import foundation.iterated-dependent-product-types funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence open import foundation.subtype-identity-principle -open import foundation.torsorial-type-families +open import foundation.telescopes +open import foundation.torsorial-type-families funext univalence truncations open import foundation.universe-levels -open import group-theory.group-actions -open import group-theory.groups +open import group-theory.group-actions funext univalence truncations +open import group-theory.groups funext univalence truncations ```
diff --git a/src/group-theory/homomorphisms-groups-equipped-with-normal-subgroups.lagda.md b/src/group-theory/homomorphisms-groups-equipped-with-normal-subgroups.lagda.md index 824132ed84..0ba4bb1510 100644 --- a/src/group-theory/homomorphisms-groups-equipped-with-normal-subgroups.lagda.md +++ b/src/group-theory/homomorphisms-groups-equipped-with-normal-subgroups.lagda.md @@ -1,23 +1,31 @@ # Homomorphisms of groups equipped with normal subgroups ```agda -module group-theory.homomorphisms-groups-equipped-with-normal-subgroups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.homomorphisms-groups-equipped-with-normal-subgroups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.identity-types -open import foundation.subtypes +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels -open import group-theory.groups -open import group-theory.homomorphisms-groups -open import group-theory.normal-subgroups -open import group-theory.pullbacks-subgroups -open import group-theory.subgroups +open import group-theory.groups funext univalence truncations +open import group-theory.homomorphisms-groups funext univalence truncations +open import group-theory.normal-subgroups funext univalence truncations +open import group-theory.pullbacks-subgroups funext univalence truncations +open import group-theory.subgroups funext univalence truncations ```
diff --git a/src/group-theory/homomorphisms-groups.lagda.md b/src/group-theory/homomorphisms-groups.lagda.md index a4e286a07f..6a654c6cc3 100644 --- a/src/group-theory/homomorphisms-groups.lagda.md +++ b/src/group-theory/homomorphisms-groups.lagda.md @@ -1,25 +1,34 @@ # Homomorphisms of groups ```agda -module group-theory.homomorphisms-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.homomorphisms-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets -open import foundation.torsorial-type-families +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.torsorial-type-families funext univalence truncations open import foundation.universe-levels -open import group-theory.groups -open import group-theory.homomorphisms-monoids -open import group-theory.homomorphisms-semigroups +open import group-theory.groups funext univalence truncations +open import group-theory.homomorphisms-monoids funext univalence truncations +open import group-theory.homomorphisms-semigroups funext univalence truncations ```
diff --git a/src/group-theory/homomorphisms-monoids.lagda.md b/src/group-theory/homomorphisms-monoids.lagda.md index f8c37265bd..2681a0523b 100644 --- a/src/group-theory/homomorphisms-monoids.lagda.md +++ b/src/group-theory/homomorphisms-monoids.lagda.md @@ -1,7 +1,15 @@ # Homomorphisms of monoids ```agda -module group-theory.homomorphisms-monoids where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.homomorphisms-monoids + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,20 +17,21 @@ module group-theory.homomorphisms-monoids where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalences +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence open import foundation.subtype-identity-principle -open import foundation.subtypes -open import foundation.torsorial-type-families +open import foundation.subtypes funext univalence truncations +open import foundation.torsorial-type-families funext univalence truncations open import foundation.universe-levels -open import group-theory.homomorphisms-semigroups -open import group-theory.invertible-elements-monoids -open import group-theory.monoids +open import group-theory.homomorphisms-semigroups funext univalence truncations +open import group-theory.invertible-elements-monoids funext univalence truncations +open import group-theory.monoids funext univalence truncations ```
diff --git a/src/group-theory/homomorphisms-semigroups.lagda.md b/src/group-theory/homomorphisms-semigroups.lagda.md index b00a30a3fa..29946cdb52 100644 --- a/src/group-theory/homomorphisms-semigroups.lagda.md +++ b/src/group-theory/homomorphisms-semigroups.lagda.md @@ -1,7 +1,15 @@ # Homomorphisms of semigroups ```agda -module group-theory.homomorphisms-semigroups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.homomorphisms-semigroups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,19 +17,20 @@ module group-theory.homomorphisms-semigroups where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence open import foundation.subtype-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext univalence truncations open import foundation.universe-levels -open import group-theory.semigroups +open import group-theory.semigroups funext univalence ```
diff --git a/src/group-theory/homotopy-automorphism-groups.lagda.md b/src/group-theory/homotopy-automorphism-groups.lagda.md index f9cd8b06dc..9db80d2a98 100644 --- a/src/group-theory/homotopy-automorphism-groups.lagda.md +++ b/src/group-theory/homotopy-automorphism-groups.lagda.md @@ -1,33 +1,28 @@ # Homotopy automorphism groups ```agda -module group-theory.homotopy-automorphism-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.homotopy-automorphism-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.1-types -open import foundation.connected-components -open import foundation.contractible-types -open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types -open import foundation.mere-equality -open import foundation.propositional-truncations -open import foundation.subtype-identity-principle -open import foundation.torsorial-type-families open import foundation.truncation-levels -open import foundation.truncations +open import foundation.truncations funext univalence truncations open import foundation.universe-levels -open import group-theory.automorphism-groups -open import group-theory.concrete-groups -open import group-theory.equivalences-concrete-groups +open import group-theory.automorphism-groups funext univalence truncations +open import group-theory.concrete-groups funext univalence truncations -open import higher-group-theory.automorphism-groups -open import higher-group-theory.higher-groups +open import higher-group-theory.higher-groups funext univalence truncations open import structured-types.pointed-types ``` diff --git a/src/group-theory/images-of-group-homomorphisms.lagda.md b/src/group-theory/images-of-group-homomorphisms.lagda.md index 90366ef507..3b427d468d 100644 --- a/src/group-theory/images-of-group-homomorphisms.lagda.md +++ b/src/group-theory/images-of-group-homomorphisms.lagda.md @@ -1,31 +1,39 @@ # Images of group homomorphisms ```agda -module group-theory.images-of-group-homomorphisms where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.images-of-group-homomorphisms + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.images -open import foundation.images-subtypes -open import foundation.logical-equivalences -open import foundation.propositional-truncations -open import foundation.subtypes -open import foundation.universal-property-image +open import foundation.identity-types funext +open import foundation.images funext univalence truncations +open import foundation.images-subtypes funext univalence truncations +open import foundation.logical-equivalences funext +open import foundation.propositional-truncations funext univalence +open import foundation.subtypes funext univalence truncations +open import foundation.universal-property-image funext univalence truncations open import foundation.universe-levels -open import group-theory.groups -open import group-theory.homomorphisms-groups -open import group-theory.pullbacks-subgroups -open import group-theory.subgroups -open import group-theory.subsets-groups +open import group-theory.groups funext univalence truncations +open import group-theory.homomorphisms-groups funext univalence truncations +open import group-theory.pullbacks-subgroups funext univalence truncations +open import group-theory.subgroups funext univalence truncations +open import group-theory.subsets-groups funext univalence truncations -open import order-theory.galois-connections-large-posets -open import order-theory.order-preserving-maps-large-posets -open import order-theory.order-preserving-maps-large-preorders +open import order-theory.galois-connections-large-posets funext univalence truncations +open import order-theory.order-preserving-maps-large-posets funext univalence truncations +open import order-theory.order-preserving-maps-large-preorders funext univalence truncations ```
diff --git a/src/group-theory/images-of-semigroup-homomorphisms.lagda.md b/src/group-theory/images-of-semigroup-homomorphisms.lagda.md index eced916451..530b375db1 100644 --- a/src/group-theory/images-of-semigroup-homomorphisms.lagda.md +++ b/src/group-theory/images-of-semigroup-homomorphisms.lagda.md @@ -1,30 +1,38 @@ # Images of semigroup homomorphisms ```agda -module group-theory.images-of-semigroup-homomorphisms where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.images-of-semigroup-homomorphisms + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.images -open import foundation.images-subtypes -open import foundation.logical-equivalences -open import foundation.propositional-truncations -open import foundation.universal-property-image +open import foundation.identity-types funext +open import foundation.images funext univalence truncations +open import foundation.images-subtypes funext univalence truncations +open import foundation.logical-equivalences funext +open import foundation.propositional-truncations funext univalence +open import foundation.universal-property-image funext univalence truncations open import foundation.universe-levels -open import group-theory.homomorphisms-semigroups -open import group-theory.pullbacks-subsemigroups -open import group-theory.semigroups -open import group-theory.subsemigroups -open import group-theory.subsets-semigroups +open import group-theory.homomorphisms-semigroups funext univalence truncations +open import group-theory.pullbacks-subsemigroups funext univalence truncations +open import group-theory.semigroups funext univalence +open import group-theory.subsemigroups funext univalence truncations +open import group-theory.subsets-semigroups funext univalence truncations -open import order-theory.galois-connections-large-posets -open import order-theory.order-preserving-maps-large-posets -open import order-theory.order-preserving-maps-large-preorders +open import order-theory.galois-connections-large-posets funext univalence truncations +open import order-theory.order-preserving-maps-large-posets funext univalence truncations +open import order-theory.order-preserving-maps-large-preorders funext univalence truncations ```
diff --git a/src/group-theory/integer-multiples-of-elements-abelian-groups.lagda.md b/src/group-theory/integer-multiples-of-elements-abelian-groups.lagda.md index e592961eb4..3730fc5bc9 100644 --- a/src/group-theory/integer-multiples-of-elements-abelian-groups.lagda.md +++ b/src/group-theory/integer-multiples-of-elements-abelian-groups.lagda.md @@ -1,27 +1,36 @@ # Integer multiples of elements in abelian groups ```agda -module group-theory.integer-multiples-of-elements-abelian-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.integer-multiples-of-elements-abelian-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.addition-integers +open import elementary-number-theory.addition-integers funext univalence truncations open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-integers +open import elementary-number-theory.multiplication-integers funext univalence truncations open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.homomorphisms-abelian-groups -open import group-theory.integer-powers-of-elements-groups -open import group-theory.multiples-of-elements-abelian-groups +open import group-theory.abelian-groups funext univalence truncations +open import group-theory.homomorphisms-abelian-groups funext univalence truncations +open import group-theory.integer-powers-of-elements-groups funext univalence truncations +open import group-theory.multiples-of-elements-abelian-groups funext univalence truncations ```
diff --git a/src/group-theory/integer-powers-of-elements-groups.lagda.md b/src/group-theory/integer-powers-of-elements-groups.lagda.md index 47de6edf13..0fa1d4e159 100644 --- a/src/group-theory/integer-powers-of-elements-groups.lagda.md +++ b/src/group-theory/integer-powers-of-elements-groups.lagda.md @@ -1,31 +1,40 @@ # Integer powers of elements of groups ```agda -module group-theory.integer-powers-of-elements-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.integer-powers-of-elements-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.addition-integers +open import elementary-number-theory.addition-integers funext univalence truncations open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-integers +open import elementary-number-theory.multiplication-integers funext univalence truncations open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.coproduct-types -open import foundation.existential-quantification -open import foundation.identity-types -open import foundation.iterating-automorphisms -open import foundation.propositions +open import foundation.coproduct-types funext univalence truncations +open import foundation.dependent-products-propositions funext +open import foundation.existential-quantification funext univalence truncations +open import foundation.identity-types funext +open import foundation.iterating-automorphisms funext univalence truncations +open import foundation.propositions funext univalence open import foundation.universe-levels -open import group-theory.commuting-elements-groups -open import group-theory.groups -open import group-theory.homomorphisms-groups -open import group-theory.powers-of-elements-groups +open import group-theory.commuting-elements-groups funext univalence truncations +open import group-theory.groups funext univalence truncations +open import group-theory.homomorphisms-groups funext univalence truncations +open import group-theory.powers-of-elements-groups funext univalence truncations -open import structured-types.initial-pointed-type-equipped-with-automorphism +open import structured-types.initial-pointed-type-equipped-with-automorphism funext univalence truncations ```
diff --git a/src/group-theory/intersections-subgroups-abelian-groups.lagda.md b/src/group-theory/intersections-subgroups-abelian-groups.lagda.md index fe6d807e06..9890abbd0d 100644 --- a/src/group-theory/intersections-subgroups-abelian-groups.lagda.md +++ b/src/group-theory/intersections-subgroups-abelian-groups.lagda.md @@ -1,18 +1,26 @@ # Intersections of subgroups of abelian groups ```agda -module group-theory.intersections-subgroups-abelian-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.intersections-subgroups-abelian-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.subtypes +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.intersections-subgroups-groups -open import group-theory.subgroups-abelian-groups +open import group-theory.abelian-groups funext univalence truncations +open import group-theory.intersections-subgroups-groups funext univalence truncations +open import group-theory.subgroups-abelian-groups funext univalence truncations ```
diff --git a/src/group-theory/intersections-subgroups-groups.lagda.md b/src/group-theory/intersections-subgroups-groups.lagda.md index 485c7fe03b..c772d50236 100644 --- a/src/group-theory/intersections-subgroups-groups.lagda.md +++ b/src/group-theory/intersections-subgroups-groups.lagda.md @@ -1,22 +1,30 @@ # Intersections of subgroups of groups ```agda -module group-theory.intersections-subgroups-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.intersections-subgroups-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.intersections-subtypes -open import foundation.subtypes +open import foundation.intersections-subtypes funext univalence truncations +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels -open import group-theory.groups -open import group-theory.subgroups -open import group-theory.subsets-groups +open import group-theory.groups funext univalence truncations +open import group-theory.subgroups funext univalence truncations +open import group-theory.subsets-groups funext univalence truncations -open import order-theory.greatest-lower-bounds-large-posets +open import order-theory.greatest-lower-bounds-large-posets funext univalence truncations ```
diff --git a/src/group-theory/inverse-semigroups.lagda.md b/src/group-theory/inverse-semigroups.lagda.md index 983cf5a04e..cdbc2eae32 100644 --- a/src/group-theory/inverse-semigroups.lagda.md +++ b/src/group-theory/inverse-semigroups.lagda.md @@ -1,20 +1,27 @@ # Inverse semigroups ```agda -module group-theory.inverse-semigroups where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.inverse-semigroups + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda -open import foundation.cartesian-product-types -open import foundation.contractible-types +open import foundation.cartesian-product-types funext univalence +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.sets +open import foundation.dependent-products-contractible-types funext +open import foundation.identity-types funext +open import foundation.sets funext univalence open import foundation.universe-levels -open import group-theory.semigroups +open import group-theory.semigroups funext univalence ```
diff --git a/src/group-theory/invertible-elements-monoids.lagda.md b/src/group-theory/invertible-elements-monoids.lagda.md index c50cf77558..2135d2f5c2 100644 --- a/src/group-theory/invertible-elements-monoids.lagda.md +++ b/src/group-theory/invertible-elements-monoids.lagda.md @@ -1,27 +1,37 @@ # Invertible elements in monoids ```agda -module group-theory.invertible-elements-monoids where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.invertible-elements-monoids + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types -open import foundation.contractible-types +open import foundation.cartesian-product-types funext univalence +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.propositions -open import foundation.sets -open import foundation.subtypes +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels -open import group-theory.monoids +open import group-theory.monoids funext univalence truncations ```
diff --git a/src/group-theory/isomorphisms-abelian-groups.lagda.md b/src/group-theory/isomorphisms-abelian-groups.lagda.md index 9d7b07d36e..92fb2b15e8 100644 --- a/src/group-theory/isomorphisms-abelian-groups.lagda.md +++ b/src/group-theory/isomorphisms-abelian-groups.lagda.md @@ -1,29 +1,39 @@ # Isomorphisms of abelian groups ```agda -module group-theory.isomorphisms-abelian-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.isomorphisms-abelian-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.contractible-types +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.propositions -open import foundation.subtypes -open import foundation.torsorial-type-families +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.subtypes funext univalence truncations +open import foundation.torsorial-type-families funext univalence truncations open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.homomorphisms-abelian-groups -open import group-theory.isomorphisms-groups +open import group-theory.abelian-groups funext univalence truncations +open import group-theory.homomorphisms-abelian-groups funext univalence truncations +open import group-theory.isomorphisms-groups funext univalence truncations ```
diff --git a/src/group-theory/isomorphisms-concrete-groups.lagda.md b/src/group-theory/isomorphisms-concrete-groups.lagda.md index 0815e62ecb..176b56e96c 100644 --- a/src/group-theory/isomorphisms-concrete-groups.lagda.md +++ b/src/group-theory/isomorphisms-concrete-groups.lagda.md @@ -1,18 +1,26 @@ # Isomorphisms of concrete groups ```agda -module group-theory.isomorphisms-concrete-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.isomorphisms-concrete-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.isomorphisms-in-large-precategories +open import category-theory.isomorphisms-in-large-precategories funext univalence truncations open import foundation.universe-levels -open import group-theory.concrete-groups -open import group-theory.precategory-of-concrete-groups +open import group-theory.concrete-groups funext univalence truncations +open import group-theory.precategory-of-concrete-groups funext univalence truncations ```
diff --git a/src/group-theory/isomorphisms-group-actions.lagda.md b/src/group-theory/isomorphisms-group-actions.lagda.md index 49635eee09..1945e54596 100644 --- a/src/group-theory/isomorphisms-group-actions.lagda.md +++ b/src/group-theory/isomorphisms-group-actions.lagda.md @@ -1,33 +1,43 @@ # Isomorphisms of group actions ```agda -module group-theory.isomorphisms-group-actions where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.isomorphisms-group-actions + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.isomorphisms-in-large-precategories +open import category-theory.isomorphisms-in-large-precategories funext univalence truncations -open import foundation.commuting-squares-of-maps -open import foundation.contractible-types +open import foundation.commuting-squares-of-maps funext univalence +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.functoriality-dependent-pair-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.propositions -open import foundation.subtypes -open import foundation.torsorial-type-families +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.function-extensionality funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.propositions funext univalence +open import foundation.subtypes funext univalence truncations +open import foundation.torsorial-type-families funext univalence truncations open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels -open import group-theory.equivalences-group-actions -open import group-theory.group-actions -open import group-theory.groups -open import group-theory.homomorphisms-group-actions -open import group-theory.precategory-of-group-actions +open import group-theory.equivalences-group-actions funext univalence truncations +open import group-theory.group-actions funext univalence truncations +open import group-theory.groups funext univalence truncations +open import group-theory.homomorphisms-group-actions funext univalence truncations +open import group-theory.precategory-of-group-actions funext univalence truncations ```
diff --git a/src/group-theory/isomorphisms-groups.lagda.md b/src/group-theory/isomorphisms-groups.lagda.md index 0ab46ae767..1e511dab15 100644 --- a/src/group-theory/isomorphisms-groups.lagda.md +++ b/src/group-theory/isomorphisms-groups.lagda.md @@ -1,32 +1,42 @@ # Isomorphisms of groups ```agda -module group-theory.isomorphisms-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.isomorphisms-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.isomorphisms-in-large-precategories +open import category-theory.isomorphisms-in-large-precategories funext univalence truncations -open import foundation.contractible-types +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.propositions -open import foundation.subtypes -open import foundation.torsorial-type-families +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.subtypes funext univalence truncations +open import foundation.torsorial-type-families funext univalence truncations open import foundation.universe-levels -open import group-theory.category-of-semigroups -open import group-theory.equivalences-semigroups -open import group-theory.groups -open import group-theory.homomorphisms-groups -open import group-theory.isomorphisms-semigroups -open import group-theory.precategory-of-groups +open import group-theory.category-of-semigroups funext univalence truncations +open import group-theory.equivalences-semigroups funext univalence truncations +open import group-theory.groups funext univalence truncations +open import group-theory.homomorphisms-groups funext univalence truncations +open import group-theory.isomorphisms-semigroups funext univalence truncations +open import group-theory.precategory-of-groups funext univalence truncations ```
diff --git a/src/group-theory/isomorphisms-monoids.lagda.md b/src/group-theory/isomorphisms-monoids.lagda.md index 5ed4766a19..f0fe5971c9 100644 --- a/src/group-theory/isomorphisms-monoids.lagda.md +++ b/src/group-theory/isomorphisms-monoids.lagda.md @@ -1,26 +1,35 @@ # Isomorphisms of monoids ```agda -module group-theory.isomorphisms-monoids where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.isomorphisms-monoids + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.isomorphisms-in-large-precategories - -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets +open import category-theory.isomorphisms-in-large-precategories funext univalence truncations + +open import foundation.dependent-products-propositions funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence open import foundation.transport-along-identifications open import foundation.universe-levels -open import group-theory.homomorphisms-monoids -open import group-theory.invertible-elements-monoids -open import group-theory.monoids -open import group-theory.precategory-of-monoids +open import group-theory.homomorphisms-monoids funext univalence truncations +open import group-theory.invertible-elements-monoids funext univalence truncations +open import group-theory.monoids funext univalence truncations +open import group-theory.precategory-of-monoids funext univalence truncations ```
diff --git a/src/group-theory/isomorphisms-semigroups.lagda.md b/src/group-theory/isomorphisms-semigroups.lagda.md index 2c2bb15a9a..79a4666fd9 100644 --- a/src/group-theory/isomorphisms-semigroups.lagda.md +++ b/src/group-theory/isomorphisms-semigroups.lagda.md @@ -1,33 +1,42 @@ # Isomorphisms of semigroups ```agda -module group-theory.isomorphisms-semigroups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.isomorphisms-semigroups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.isomorphisms-in-large-precategories +open import category-theory.isomorphisms-in-large-precategories funext univalence truncations open import foundation.action-on-identifications-functions -open import foundation.contractible-types +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.propositions -open import foundation.subtypes -open import foundation.torsorial-type-families +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.subtypes funext univalence truncations +open import foundation.torsorial-type-families funext univalence truncations open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels -open import group-theory.equivalences-semigroups -open import group-theory.homomorphisms-semigroups -open import group-theory.precategory-of-semigroups -open import group-theory.semigroups +open import group-theory.equivalences-semigroups funext univalence truncations +open import group-theory.homomorphisms-semigroups funext univalence truncations +open import group-theory.precategory-of-semigroups funext univalence truncations +open import group-theory.semigroups funext univalence ```
diff --git a/src/group-theory/iterated-cartesian-products-concrete-groups.lagda.md b/src/group-theory/iterated-cartesian-products-concrete-groups.lagda.md index db2815fc12..6084534853 100644 --- a/src/group-theory/iterated-cartesian-products-concrete-groups.lagda.md +++ b/src/group-theory/iterated-cartesian-products-concrete-groups.lagda.md @@ -1,7 +1,15 @@ # Iterated cartesian products of concrete groups ```agda -module group-theory.iterated-cartesian-products-concrete-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.iterated-cartesian-products-concrete-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,35 +17,39 @@ module group-theory.iterated-cartesian-products-concrete-groups where ```agda open import elementary-number-theory.natural-numbers -open import foundation.0-connected-types -open import foundation.1-types -open import foundation.contractible-types -open import foundation.coproduct-types +open import foundation.0-connected-types funext univalence truncations +open import foundation.1-types funext univalence +open import foundation.contractible-types funext univalence +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-cartesian-product-types -open import foundation.identity-types -open import foundation.iterated-cartesian-product-types -open import foundation.mere-equality -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.sets -open import foundation.truncated-types +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.dependent-products-truncated-types funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.identity-types funext +open import foundation.iterated-cartesian-product-types funext univalence truncations +open import foundation.mere-equality funext univalence truncations +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence +open import foundation.raising-universe-levels-unit-type +open import foundation.sets funext univalence +open import foundation.truncated-types funext univalence open import foundation.truncation-levels open import foundation.unit-type open import foundation.universe-levels -open import group-theory.cartesian-products-concrete-groups -open import group-theory.concrete-groups -open import group-theory.groups -open import group-theory.trivial-concrete-groups +open import group-theory.cartesian-products-concrete-groups funext univalence truncations +open import group-theory.concrete-groups funext univalence truncations +open import group-theory.groups funext univalence truncations +open import group-theory.trivial-concrete-groups funext univalence truncations -open import higher-group-theory.higher-groups +open import higher-group-theory.higher-groups funext univalence truncations open import structured-types.pointed-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/group-theory/kernels-homomorphisms-abelian-groups.lagda.md b/src/group-theory/kernels-homomorphisms-abelian-groups.lagda.md index 9772e78e5d..1e94d3e8ad 100644 --- a/src/group-theory/kernels-homomorphisms-abelian-groups.lagda.md +++ b/src/group-theory/kernels-homomorphisms-abelian-groups.lagda.md @@ -1,7 +1,15 @@ # Kernels of homomorphisms between abelian groups ```agda -module group-theory.kernels-homomorphisms-abelian-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.kernels-homomorphisms-abelian-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,12 +17,12 @@ module group-theory.kernels-homomorphisms-abelian-groups where ```agda open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.embeddings-abelian-groups -open import group-theory.homomorphisms-abelian-groups -open import group-theory.kernels-homomorphisms-groups -open import group-theory.subgroups-abelian-groups -open import group-theory.subsets-abelian-groups +open import group-theory.abelian-groups funext univalence truncations +open import group-theory.embeddings-abelian-groups funext univalence truncations +open import group-theory.homomorphisms-abelian-groups funext univalence truncations +open import group-theory.kernels-homomorphisms-groups funext univalence truncations +open import group-theory.subgroups-abelian-groups funext univalence truncations +open import group-theory.subsets-abelian-groups funext univalence truncations ```
diff --git a/src/group-theory/kernels-homomorphisms-concrete-groups.lagda.md b/src/group-theory/kernels-homomorphisms-concrete-groups.lagda.md index fa5ce10e8c..380c4bf465 100644 --- a/src/group-theory/kernels-homomorphisms-concrete-groups.lagda.md +++ b/src/group-theory/kernels-homomorphisms-concrete-groups.lagda.md @@ -1,26 +1,34 @@ # Kernels of homomorphisms of concrete groups ```agda -module group-theory.kernels-homomorphisms-concrete-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.kernels-homomorphisms-concrete-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.0-connected-types -open import foundation.1-types -open import foundation.connected-components +open import foundation.0-connected-types funext univalence truncations +open import foundation.1-types funext univalence +open import foundation.connected-components funext univalence truncations open import foundation.dependent-pair-types -open import foundation.fibers-of-maps -open import foundation.sets -open import foundation.truncated-maps +open import foundation.fibers-of-maps funext +open import foundation.sets funext univalence +open import foundation.truncated-maps funext open import foundation.truncation-levels open import foundation.universe-levels -open import group-theory.concrete-groups -open import group-theory.homomorphisms-concrete-groups +open import group-theory.concrete-groups funext univalence truncations +open import group-theory.homomorphisms-concrete-groups funext univalence truncations -open import higher-group-theory.higher-groups +open import higher-group-theory.higher-groups funext univalence truncations open import structured-types.pointed-types ``` diff --git a/src/group-theory/kernels-homomorphisms-groups.lagda.md b/src/group-theory/kernels-homomorphisms-groups.lagda.md index ba177596f8..c995cc5616 100644 --- a/src/group-theory/kernels-homomorphisms-groups.lagda.md +++ b/src/group-theory/kernels-homomorphisms-groups.lagda.md @@ -1,7 +1,15 @@ # Kernels of homomorphisms of groups ```agda -module group-theory.kernels-homomorphisms-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.kernels-homomorphisms-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,18 +17,19 @@ module group-theory.kernels-homomorphisms-groups where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions funext open import foundation.equality-cartesian-product-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence open import foundation.universe-levels -open import group-theory.embeddings-groups -open import group-theory.groups -open import group-theory.homomorphisms-groups -open import group-theory.normal-subgroups -open import group-theory.subgroups -open import group-theory.subsets-groups +open import group-theory.embeddings-groups funext univalence truncations +open import group-theory.groups funext univalence truncations +open import group-theory.homomorphisms-groups funext univalence truncations +open import group-theory.normal-subgroups funext univalence truncations +open import group-theory.subgroups funext univalence truncations +open import group-theory.subsets-groups funext univalence truncations ```
diff --git a/src/group-theory/large-semigroups.lagda.md b/src/group-theory/large-semigroups.lagda.md index b4d82ec9cb..843e732b58 100644 --- a/src/group-theory/large-semigroups.lagda.md +++ b/src/group-theory/large-semigroups.lagda.md @@ -1,18 +1,24 @@ # Large semigroups ```agda -module group-theory.large-semigroups where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.large-semigroups + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.sets +open import foundation.identity-types funext +open import foundation.sets funext univalence open import foundation.universe-levels -open import group-theory.semigroups +open import group-theory.semigroups funext univalence ```
diff --git a/src/group-theory/loop-groups-sets.lagda.md b/src/group-theory/loop-groups-sets.lagda.md index 15fdf92516..eec945bc40 100644 --- a/src/group-theory/loop-groups-sets.lagda.md +++ b/src/group-theory/loop-groups-sets.lagda.md @@ -1,7 +1,15 @@ # Concrete automorphism groups on sets ```agda -module group-theory.loop-groups-sets where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.loop-groups-sets + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,29 +17,31 @@ module group-theory.loop-groups-sets where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.identity-truncated-types -open import foundation.identity-types -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.sets -open import foundation.truncated-types +open import foundation.dependent-products-propositions funext +open import foundation.dependent-products-truncated-types funext +open import foundation.equality-dependent-pair-types funext +open import foundation.equivalences funext +open import foundation.function-extensionality funext +open import foundation.function-types funext +open import foundation.identity-truncated-types funext univalence +open import foundation.identity-types funext +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.truncated-types funext univalence open import foundation.truncation-levels -open import foundation.univalence +open import foundation.univalence funext univalence open import foundation.universe-levels -open import group-theory.automorphism-groups -open import group-theory.concrete-groups -open import group-theory.groups -open import group-theory.homomorphisms-groups -open import group-theory.homomorphisms-semigroups -open import group-theory.isomorphisms-groups -open import group-theory.monoids -open import group-theory.semigroups -open import group-theory.symmetric-groups +open import group-theory.automorphism-groups funext univalence truncations +open import group-theory.concrete-groups funext univalence truncations +open import group-theory.groups funext univalence truncations +open import group-theory.homomorphisms-groups funext univalence truncations +open import group-theory.homomorphisms-semigroups funext univalence truncations +open import group-theory.isomorphisms-groups funext univalence truncations +open import group-theory.monoids funext univalence truncations +open import group-theory.semigroups funext univalence +open import group-theory.symmetric-groups funext univalence truncations ```
diff --git a/src/group-theory/mere-equivalences-concrete-group-actions.lagda.md b/src/group-theory/mere-equivalences-concrete-group-actions.lagda.md index 5e895381eb..bb6606f9ed 100644 --- a/src/group-theory/mere-equivalences-concrete-group-actions.lagda.md +++ b/src/group-theory/mere-equivalences-concrete-group-actions.lagda.md @@ -1,21 +1,30 @@ # Mere equivalences of concrete group actions ```agda -module group-theory.mere-equivalences-concrete-group-actions where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.mere-equivalences-concrete-group-actions + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.functoriality-propositional-truncation -open import foundation.mere-equality -open import foundation.propositional-truncations -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.functoriality-propositional-truncation funext univalence truncations +open import foundation.mere-equality funext univalence truncations +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence open import foundation.universe-levels -open import group-theory.concrete-group-actions -open import group-theory.concrete-groups -open import group-theory.equivalences-concrete-group-actions +open import group-theory.concrete-group-actions funext univalence truncations +open import group-theory.concrete-groups funext univalence truncations +open import group-theory.equivalences-concrete-group-actions funext univalence truncations ```
diff --git a/src/group-theory/mere-equivalences-group-actions.lagda.md b/src/group-theory/mere-equivalences-group-actions.lagda.md index 72c1412d12..f05ac0199b 100644 --- a/src/group-theory/mere-equivalences-group-actions.lagda.md +++ b/src/group-theory/mere-equivalences-group-actions.lagda.md @@ -1,19 +1,28 @@ # Mere equivalences of group actions ```agda -module group-theory.mere-equivalences-group-actions where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.mere-equivalences-group-actions + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.propositional-truncations -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence open import foundation.universe-levels -open import group-theory.equivalences-group-actions -open import group-theory.group-actions -open import group-theory.groups +open import group-theory.equivalences-group-actions funext univalence truncations +open import group-theory.group-actions funext univalence truncations +open import group-theory.groups funext univalence truncations ```
diff --git a/src/group-theory/minkowski-multiplication-commutative-monoids.lagda.md b/src/group-theory/minkowski-multiplication-commutative-monoids.lagda.md index e86970fa14..3d095fa1f2 100644 --- a/src/group-theory/minkowski-multiplication-commutative-monoids.lagda.md +++ b/src/group-theory/minkowski-multiplication-commutative-monoids.lagda.md @@ -1,28 +1,32 @@ # Minkowski multiplication of subsets of a commutative monoid ```agda -module group-theory.minkowski-multiplication-commutative-monoids where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.minkowski-multiplication-commutative-monoids + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.existential-quantification -open import foundation.identity-types -open import foundation.inhabited-subtypes -open import foundation.powersets -open import foundation.subtypes +open import foundation.existential-quantification funext univalence truncations +open import foundation.identity-types funext +open import foundation.inhabited-subtypes funext univalence truncations +open import foundation.powersets funext univalence truncations +open import foundation.subtypes funext univalence truncations open import foundation.unital-binary-operations open import foundation.universe-levels -open import group-theory.commutative-monoids -open import group-theory.minkowski-multiplication-monoids -open import group-theory.monoids -open import group-theory.subsets-commutative-monoids - -open import logic.functoriality-existential-quantification +open import group-theory.commutative-monoids funext univalence truncations +open import group-theory.minkowski-multiplication-monoids funext univalence truncations +open import group-theory.subsets-commutative-monoids funext univalence truncations ```
diff --git a/src/group-theory/minkowski-multiplication-monoids.lagda.md b/src/group-theory/minkowski-multiplication-monoids.lagda.md index 1739e3919e..c7bc3f0bbd 100644 --- a/src/group-theory/minkowski-multiplication-monoids.lagda.md +++ b/src/group-theory/minkowski-multiplication-monoids.lagda.md @@ -1,7 +1,15 @@ # Minkowski multiplication on subsets of a monoid ```agda -module group-theory.minkowski-multiplication-monoids where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.minkowski-multiplication-monoids + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,19 +17,18 @@ module group-theory.minkowski-multiplication-monoids where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.existential-quantification -open import foundation.identity-types -open import foundation.inhabited-subtypes -open import foundation.powersets -open import foundation.subtypes +open import foundation.existential-quantification funext univalence truncations +open import foundation.identity-types funext +open import foundation.inhabited-subtypes funext univalence truncations +open import foundation.powersets funext univalence truncations +open import foundation.subtypes funext univalence truncations open import foundation.transport-along-identifications open import foundation.unital-binary-operations open import foundation.universe-levels -open import group-theory.minkowski-multiplication-semigroups -open import group-theory.monoids -open import group-theory.semigroups -open import group-theory.subsets-monoids +open import group-theory.minkowski-multiplication-semigroups funext univalence truncations +open import group-theory.monoids funext univalence truncations +open import group-theory.subsets-monoids funext univalence truncations ```
diff --git a/src/group-theory/minkowski-multiplication-semigroups.lagda.md b/src/group-theory/minkowski-multiplication-semigroups.lagda.md index a7215e29fe..4f49da752d 100644 --- a/src/group-theory/minkowski-multiplication-semigroups.lagda.md +++ b/src/group-theory/minkowski-multiplication-semigroups.lagda.md @@ -1,31 +1,38 @@ # Minkowski multiplication on subsets of a semigroup ```agda -module group-theory.minkowski-multiplication-semigroups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.minkowski-multiplication-semigroups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types -open import foundation.conjunction +open import foundation.cartesian-product-types funext univalence +open import foundation.conjunction funext univalence truncations open import foundation.dependent-pair-types -open import foundation.existential-quantification -open import foundation.function-types -open import foundation.functoriality-cartesian-product-types -open import foundation.identity-types -open import foundation.inhabited-subtypes -open import foundation.powersets -open import foundation.propositions -open import foundation.sets -open import foundation.subtypes +open import foundation.existential-quantification funext univalence truncations +open import foundation.function-types funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.identity-types funext +open import foundation.inhabited-subtypes funext univalence truncations +open import foundation.powersets funext univalence truncations +open import foundation.sets funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels -open import group-theory.semigroups -open import group-theory.subsets-semigroups +open import group-theory.semigroups funext univalence +open import group-theory.subsets-semigroups funext univalence truncations -open import logic.functoriality-existential-quantification +open import logic.functoriality-existential-quantification funext univalence truncations ```
diff --git a/src/group-theory/monoid-actions.lagda.md b/src/group-theory/monoid-actions.lagda.md index c1f806f207..f4fbcbe12e 100644 --- a/src/group-theory/monoid-actions.lagda.md +++ b/src/group-theory/monoid-actions.lagda.md @@ -1,7 +1,15 @@ # Monoid actions ```agda -module group-theory.monoid-actions where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.monoid-actions + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,14 +17,13 @@ module group-theory.monoid-actions where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.endomorphisms -open import foundation.function-extensionality -open import foundation.identity-types -open import foundation.sets +open import foundation.endomorphisms funext univalence truncations +open import foundation.identity-types funext +open import foundation.sets funext univalence open import foundation.universe-levels -open import group-theory.homomorphisms-monoids -open import group-theory.monoids +open import group-theory.homomorphisms-monoids funext univalence truncations +open import group-theory.monoids funext univalence truncations ```
diff --git a/src/group-theory/monoids.lagda.md b/src/group-theory/monoids.lagda.md index 6a0c542cfc..de3daf7686 100644 --- a/src/group-theory/monoids.lagda.md +++ b/src/group-theory/monoids.lagda.md @@ -1,25 +1,34 @@ # Monoids ```agda -module group-theory.monoids where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.monoids + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.unit-type open import foundation.unital-binary-operations open import foundation.universe-levels -open import group-theory.semigroups +open import group-theory.semigroups funext univalence -open import structured-types.h-spaces -open import structured-types.wild-monoids +open import structured-types.h-spaces funext univalence truncations +open import structured-types.wild-monoids funext univalence truncations ```
diff --git a/src/group-theory/monomorphisms-concrete-groups.lagda.md b/src/group-theory/monomorphisms-concrete-groups.lagda.md index 243579c974..f5236525e9 100644 --- a/src/group-theory/monomorphisms-concrete-groups.lagda.md +++ b/src/group-theory/monomorphisms-concrete-groups.lagda.md @@ -1,19 +1,28 @@ # Monomorphisms of concrete groups ```agda -module group-theory.monomorphisms-concrete-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.monomorphisms-concrete-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.embeddings funext +open import foundation.propositions funext univalence open import foundation.universe-levels -open import group-theory.concrete-groups -open import group-theory.homomorphisms-concrete-groups +open import group-theory.concrete-groups funext univalence truncations +open import group-theory.homomorphisms-concrete-groups funext univalence truncations ```
diff --git a/src/group-theory/monomorphisms-groups.lagda.md b/src/group-theory/monomorphisms-groups.lagda.md index eeebe4fb6c..75ef93f271 100644 --- a/src/group-theory/monomorphisms-groups.lagda.md +++ b/src/group-theory/monomorphisms-groups.lagda.md @@ -1,21 +1,30 @@ # Monomorphisms in the category of groups ```agda -module group-theory.monomorphisms-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.monomorphisms-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.monomorphisms-in-large-precategories +open import category-theory.monomorphisms-in-large-precategories funext univalence truncations -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.propositions funext univalence open import foundation.universe-levels -open import group-theory.groups -open import group-theory.homomorphisms-groups -open import group-theory.isomorphisms-groups -open import group-theory.precategory-of-groups +open import group-theory.groups funext univalence truncations +open import group-theory.homomorphisms-groups funext univalence truncations +open import group-theory.isomorphisms-groups funext univalence truncations +open import group-theory.precategory-of-groups funext univalence truncations ```
diff --git a/src/group-theory/multiples-of-elements-abelian-groups.lagda.md b/src/group-theory/multiples-of-elements-abelian-groups.lagda.md index 475f609270..bbcbb1993a 100644 --- a/src/group-theory/multiples-of-elements-abelian-groups.lagda.md +++ b/src/group-theory/multiples-of-elements-abelian-groups.lagda.md @@ -1,7 +1,15 @@ # Multiples of elements in abelian groups ```agda -module group-theory.multiples-of-elements-abelian-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.multiples-of-elements-abelian-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -11,12 +19,13 @@ open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import foundation.identity-types -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.powers-of-elements-groups +open import group-theory.abelian-groups funext univalence truncations +open import group-theory.powers-of-elements-groups funext univalence truncations ```
diff --git a/src/group-theory/nontrivial-groups.lagda.md b/src/group-theory/nontrivial-groups.lagda.md index 725296c895..2cac80ec82 100644 --- a/src/group-theory/nontrivial-groups.lagda.md +++ b/src/group-theory/nontrivial-groups.lagda.md @@ -1,34 +1,44 @@ # Nontrivial groups ```agda -module group-theory.nontrivial-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.nontrivial-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.contractible-types +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.disjunction -open import foundation.embeddings -open import foundation.empty-types -open import foundation.existential-quantification -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.logical-equivalences -open import foundation.negated-equality -open import foundation.negation -open import foundation.propositional-extensionality -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.sets +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.disjunction funext univalence truncations +open import foundation.embeddings funext +open import foundation.empty-types funext univalence truncations +open import foundation.existential-quantification funext univalence truncations +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.logical-equivalences funext +open import foundation.negated-equality funext univalence truncations +open import foundation.negation funext +open import foundation.propositional-extensionality funext univalence truncations +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence +open import foundation.sets funext univalence open import foundation.unit-type open import foundation.universe-levels -open import group-theory.groups -open import group-theory.subgroups -open import group-theory.trivial-groups +open import group-theory.groups funext univalence truncations +open import group-theory.subgroups funext univalence truncations +open import group-theory.trivial-groups funext univalence truncations ```
diff --git a/src/group-theory/normal-closures-subgroups.lagda.md b/src/group-theory/normal-closures-subgroups.lagda.md index 704d72a7b2..720ca5d44e 100644 --- a/src/group-theory/normal-closures-subgroups.lagda.md +++ b/src/group-theory/normal-closures-subgroups.lagda.md @@ -1,32 +1,40 @@ # Normal closures of subgroups ```agda -module group-theory.normal-closures-subgroups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.normal-closures-subgroups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.existential-quantification -open import foundation.fibers-of-maps -open import foundation.function-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.propositional-truncations -open import foundation.subtypes +open import foundation.existential-quantification funext univalence truncations +open import foundation.fibers-of-maps funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.propositional-truncations funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels -open import group-theory.conjugation -open import group-theory.groups -open import group-theory.normal-subgroups -open import group-theory.subgroups -open import group-theory.subgroups-generated-by-subsets-groups -open import group-theory.subsets-groups +open import group-theory.conjugation funext univalence truncations +open import group-theory.groups funext univalence truncations +open import group-theory.normal-subgroups funext univalence truncations +open import group-theory.subgroups funext univalence truncations +open import group-theory.subgroups-generated-by-subsets-groups funext univalence truncations +open import group-theory.subsets-groups funext univalence truncations -open import order-theory.galois-connections-large-posets -open import order-theory.order-preserving-maps-large-posets -open import order-theory.order-preserving-maps-large-preorders +open import order-theory.galois-connections-large-posets funext univalence truncations +open import order-theory.order-preserving-maps-large-posets funext univalence truncations +open import order-theory.order-preserving-maps-large-preorders funext univalence truncations ```
diff --git a/src/group-theory/normal-cores-subgroups.lagda.md b/src/group-theory/normal-cores-subgroups.lagda.md index 0e7447ffd7..0ef1e5db4f 100644 --- a/src/group-theory/normal-cores-subgroups.lagda.md +++ b/src/group-theory/normal-cores-subgroups.lagda.md @@ -1,7 +1,15 @@ # Normal cores of subgroups ```agda -module group-theory.normal-cores-subgroups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.normal-cores-subgroups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,24 +17,24 @@ module group-theory.normal-cores-subgroups where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalences -open import foundation.identity-types -open import foundation.intersections-subtypes -open import foundation.logical-equivalences -open import foundation.propositional-maps -open import foundation.subtypes +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.intersections-subtypes funext univalence truncations +open import foundation.logical-equivalences funext +open import foundation.propositional-maps funext +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels -open import group-theory.conjugation -open import group-theory.groups -open import group-theory.normal-subgroups -open import group-theory.subgroups -open import group-theory.subsets-groups +open import group-theory.conjugation funext univalence truncations +open import group-theory.groups funext univalence truncations +open import group-theory.normal-subgroups funext univalence truncations +open import group-theory.subgroups funext univalence truncations +open import group-theory.subsets-groups funext univalence truncations -open import order-theory.galois-connections-large-posets -open import order-theory.order-preserving-maps-large-posets -open import order-theory.order-preserving-maps-large-preorders +open import order-theory.galois-connections-large-posets funext univalence truncations +open import order-theory.order-preserving-maps-large-posets funext univalence truncations +open import order-theory.order-preserving-maps-large-preorders funext univalence truncations ```
diff --git a/src/group-theory/normal-subgroups-concrete-groups.lagda.md b/src/group-theory/normal-subgroups-concrete-groups.lagda.md index 5e095bd183..98405e6f06 100644 --- a/src/group-theory/normal-subgroups-concrete-groups.lagda.md +++ b/src/group-theory/normal-subgroups-concrete-groups.lagda.md @@ -1,7 +1,15 @@ # Normal subgroups of concrete groups ```agda -module group-theory.normal-subgroups-concrete-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.normal-subgroups-concrete-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,10 +17,10 @@ module group-theory.normal-subgroups-concrete-groups where ```agda open import foundation.universe-levels -open import group-theory.concrete-group-actions -open import group-theory.concrete-groups -open import group-theory.subgroups-concrete-groups -open import group-theory.transitive-concrete-group-actions +open import group-theory.concrete-group-actions funext univalence truncations +open import group-theory.concrete-groups funext univalence truncations +open import group-theory.subgroups-concrete-groups funext univalence truncations +open import group-theory.transitive-concrete-group-actions funext univalence truncations ```
diff --git a/src/group-theory/normal-subgroups.lagda.md b/src/group-theory/normal-subgroups.lagda.md index 1691141439..36c82b1649 100644 --- a/src/group-theory/normal-subgroups.lagda.md +++ b/src/group-theory/normal-subgroups.lagda.md @@ -1,40 +1,49 @@ # Normal subgroups ```agda -module group-theory.normal-subgroups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.normal-subgroups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.binary-relations +open import foundation.binary-relations funext univalence truncations open import foundation.binary-transport open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalence-relations -open import foundation.equivalences -open import foundation.function-types -open import foundation.identity-types -open import foundation.large-binary-relations -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.embeddings funext +open import foundation.equivalence-relations funext univalence truncations +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.large-binary-relations funext univalence truncations +open import foundation.propositions funext univalence open import foundation.subtype-identity-principle -open import foundation.subtypes +open import foundation.subtypes funext univalence truncations open import foundation.transport-along-identifications open import foundation.universe-levels -open import group-theory.congruence-relations-groups -open import group-theory.conjugation -open import group-theory.groups -open import group-theory.subgroups -open import group-theory.subsets-groups - -open import order-theory.large-posets -open import order-theory.large-preorders -open import order-theory.order-preserving-maps-large-posets -open import order-theory.order-preserving-maps-large-preorders -open import order-theory.posets -open import order-theory.preorders +open import group-theory.congruence-relations-groups funext univalence truncations +open import group-theory.conjugation funext univalence truncations +open import group-theory.groups funext univalence truncations +open import group-theory.subgroups funext univalence truncations +open import group-theory.subsets-groups funext univalence truncations + +open import order-theory.large-posets funext univalence truncations +open import order-theory.large-preorders funext univalence truncations +open import order-theory.order-preserving-maps-large-posets funext univalence truncations +open import order-theory.order-preserving-maps-large-preorders funext univalence truncations +open import order-theory.posets funext univalence truncations +open import order-theory.preorders funext univalence truncations ```
diff --git a/src/group-theory/normal-submonoids-commutative-monoids.lagda.md b/src/group-theory/normal-submonoids-commutative-monoids.lagda.md index 64d971f8b0..a4dced7364 100644 --- a/src/group-theory/normal-submonoids-commutative-monoids.lagda.md +++ b/src/group-theory/normal-submonoids-commutative-monoids.lagda.md @@ -1,33 +1,42 @@ # Normal submonoids of commutative monoids ```agda -module group-theory.normal-submonoids-commutative-monoids where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.normal-submonoids-commutative-monoids + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.binary-relations +open import foundation.binary-relations funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalence-relations -open import foundation.equivalences -open import foundation.function-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.propositions -open import foundation.retracts-of-types -open import foundation.sets +open import foundation.dependent-products-propositions funext +open import foundation.equivalence-relations funext univalence truncations +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.propositions funext univalence +open import foundation.retracts-of-types funext univalence +open import foundation.sets funext univalence open import foundation.subtype-identity-principle -open import foundation.subtypes +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels -open import group-theory.commutative-monoids -open import group-theory.congruence-relations-commutative-monoids -open import group-theory.monoids -open import group-theory.saturated-congruence-relations-commutative-monoids -open import group-theory.semigroups -open import group-theory.submonoids-commutative-monoids -open import group-theory.subsets-commutative-monoids +open import group-theory.commutative-monoids funext univalence truncations +open import group-theory.congruence-relations-commutative-monoids funext univalence truncations +open import group-theory.monoids funext univalence truncations +open import group-theory.saturated-congruence-relations-commutative-monoids funext univalence truncations +open import group-theory.semigroups funext univalence +open import group-theory.submonoids-commutative-monoids funext univalence truncations +open import group-theory.subsets-commutative-monoids funext univalence truncations ```
diff --git a/src/group-theory/normal-submonoids.lagda.md b/src/group-theory/normal-submonoids.lagda.md index 45aaa58a2c..5ef3bcd5d4 100644 --- a/src/group-theory/normal-submonoids.lagda.md +++ b/src/group-theory/normal-submonoids.lagda.md @@ -1,33 +1,42 @@ # Normal submonoids ```agda -module group-theory.normal-submonoids where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.normal-submonoids + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.binary-relations +open import foundation.binary-relations funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalence-relations -open import foundation.equivalences -open import foundation.function-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.propositions -open import foundation.retracts-of-types -open import foundation.sets +open import foundation.dependent-products-propositions funext +open import foundation.equivalence-relations funext univalence truncations +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.propositions funext univalence +open import foundation.retracts-of-types funext univalence +open import foundation.sets funext univalence open import foundation.subtype-identity-principle -open import foundation.subtypes +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels -open import group-theory.congruence-relations-monoids -open import group-theory.monoids -open import group-theory.saturated-congruence-relations-monoids -open import group-theory.semigroups -open import group-theory.submonoids -open import group-theory.subsets-monoids +open import group-theory.congruence-relations-monoids funext univalence truncations +open import group-theory.monoids funext univalence truncations +open import group-theory.saturated-congruence-relations-monoids funext univalence truncations +open import group-theory.semigroups funext univalence +open import group-theory.submonoids funext univalence truncations +open import group-theory.subsets-monoids funext univalence truncations ```
diff --git a/src/group-theory/normalizer-subgroups.lagda.md b/src/group-theory/normalizer-subgroups.lagda.md index dfdbbcae1a..f6a8081903 100644 --- a/src/group-theory/normalizer-subgroups.lagda.md +++ b/src/group-theory/normalizer-subgroups.lagda.md @@ -1,26 +1,35 @@ # Normalizer subgroups ```agda -module group-theory.normalizer-subgroups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.normalizer-subgroups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types -open import foundation.functoriality-dependent-pair-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.propositions -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.equality-dependent-pair-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.propositions funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels -open import group-theory.conjugation -open import group-theory.groups -open import group-theory.homomorphisms-groups -open import group-theory.subgroups -open import group-theory.subsets-groups +open import group-theory.conjugation funext univalence truncations +open import group-theory.groups funext univalence truncations +open import group-theory.homomorphisms-groups funext univalence truncations +open import group-theory.subgroups funext univalence truncations +open import group-theory.subsets-groups funext univalence truncations ```
diff --git a/src/group-theory/nullifying-group-homomorphisms.lagda.md b/src/group-theory/nullifying-group-homomorphisms.lagda.md index 92dfe9bbae..6111d6509d 100644 --- a/src/group-theory/nullifying-group-homomorphisms.lagda.md +++ b/src/group-theory/nullifying-group-homomorphisms.lagda.md @@ -1,26 +1,35 @@ # Nullifying group homomorphisms ```agda -module group-theory.nullifying-group-homomorphisms where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.nullifying-group-homomorphisms + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.identity-types -open import foundation.propositions -open import foundation.reflecting-maps-equivalence-relations -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.reflecting-maps-equivalence-relations funext univalence truncations +open import foundation.subtypes funext univalence truncations open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels -open import group-theory.groups -open import group-theory.homomorphisms-groups -open import group-theory.homomorphisms-groups-equipped-with-normal-subgroups -open import group-theory.kernels-homomorphisms-groups -open import group-theory.normal-subgroups +open import group-theory.groups funext univalence truncations +open import group-theory.homomorphisms-groups funext univalence truncations +open import group-theory.homomorphisms-groups-equipped-with-normal-subgroups funext univalence truncations +open import group-theory.kernels-homomorphisms-groups funext univalence truncations +open import group-theory.normal-subgroups funext univalence truncations ```
diff --git a/src/group-theory/opposite-groups.lagda.md b/src/group-theory/opposite-groups.lagda.md index 1b8b84aac2..404d954bf9 100644 --- a/src/group-theory/opposite-groups.lagda.md +++ b/src/group-theory/opposite-groups.lagda.md @@ -1,7 +1,15 @@ # The opposite of a group ```agda -module group-theory.opposite-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.opposite-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,10 +18,10 @@ module group-theory.opposite-groups where open import foundation.dependent-pair-types open import foundation.universe-levels -open import group-theory.groups -open import group-theory.isomorphisms-groups -open import group-theory.monoids -open import group-theory.opposite-semigroups +open import group-theory.groups funext univalence truncations +open import group-theory.isomorphisms-groups funext univalence truncations +open import group-theory.monoids funext univalence truncations +open import group-theory.opposite-semigroups funext univalence ```
diff --git a/src/group-theory/opposite-semigroups.lagda.md b/src/group-theory/opposite-semigroups.lagda.md index 860ad6a7de..475d73365b 100644 --- a/src/group-theory/opposite-semigroups.lagda.md +++ b/src/group-theory/opposite-semigroups.lagda.md @@ -1,18 +1,24 @@ # The opposite of a semigroup ```agda -module group-theory.opposite-semigroups where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.opposite-semigroups + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.sets +open import foundation.identity-types funext +open import foundation.sets funext univalence open import foundation.universe-levels -open import group-theory.semigroups +open import group-theory.semigroups funext univalence ```
diff --git a/src/group-theory/orbit-stabilizer-theorem-concrete-groups.lagda.md b/src/group-theory/orbit-stabilizer-theorem-concrete-groups.lagda.md index d9cc6ffa5b..2ee6217f21 100644 --- a/src/group-theory/orbit-stabilizer-theorem-concrete-groups.lagda.md +++ b/src/group-theory/orbit-stabilizer-theorem-concrete-groups.lagda.md @@ -1,7 +1,15 @@ # The orbit-stabilizer theorem for concrete groups ```agda -module group-theory.orbit-stabilizer-theorem-concrete-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.orbit-stabilizer-theorem-concrete-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,10 +18,10 @@ module group-theory.orbit-stabilizer-theorem-concrete-groups where open import foundation.dependent-pair-types open import foundation.universe-levels -open import group-theory.concrete-group-actions -open import group-theory.concrete-groups -open import group-theory.mere-equivalences-concrete-group-actions -open import group-theory.stabilizer-groups-concrete-group-actions +open import group-theory.concrete-group-actions funext univalence truncations +open import group-theory.concrete-groups funext univalence truncations +open import group-theory.mere-equivalences-concrete-group-actions funext univalence truncations +open import group-theory.stabilizer-groups-concrete-group-actions funext univalence truncations open import structured-types.pointed-types ``` diff --git a/src/group-theory/orbits-concrete-group-actions.lagda.md b/src/group-theory/orbits-concrete-group-actions.lagda.md index 1217af68ab..9308b2ce78 100644 --- a/src/group-theory/orbits-concrete-group-actions.lagda.md +++ b/src/group-theory/orbits-concrete-group-actions.lagda.md @@ -1,19 +1,27 @@ # Orbits of concrete group actions ```agda -module group-theory.orbits-concrete-group-actions where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.orbits-concrete-group-actions + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.sets +open import foundation.function-types funext +open import foundation.sets funext univalence open import foundation.universe-levels -open import group-theory.concrete-group-actions -open import group-theory.concrete-groups +open import group-theory.concrete-group-actions funext univalence truncations +open import group-theory.concrete-groups funext univalence truncations ```
diff --git a/src/group-theory/orbits-group-actions.lagda.md b/src/group-theory/orbits-group-actions.lagda.md index 6cacd944fa..f39284864c 100644 --- a/src/group-theory/orbits-group-actions.lagda.md +++ b/src/group-theory/orbits-group-actions.lagda.md @@ -1,18 +1,26 @@ # Orbits of group actions ```agda -module group-theory.orbits-group-actions where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.orbits-group-actions + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import group-theory.group-actions -open import group-theory.groups +open import group-theory.group-actions funext univalence truncations +open import group-theory.groups funext univalence truncations ```
diff --git a/src/group-theory/orders-of-elements-groups.lagda.md b/src/group-theory/orders-of-elements-groups.lagda.md index 78115f630b..ab75d5ec4b 100644 --- a/src/group-theory/orders-of-elements-groups.lagda.md +++ b/src/group-theory/orders-of-elements-groups.lagda.md @@ -1,23 +1,31 @@ # The order of an element in a group ```agda -module group-theory.orders-of-elements-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.orders-of-elements-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.group-of-integers +open import elementary-number-theory.group-of-integers funext univalence truncations open import elementary-number-theory.integers open import foundation.universe-levels -open import group-theory.free-groups-with-one-generator -open import group-theory.groups -open import group-theory.kernels-homomorphisms-groups -open import group-theory.normal-subgroups -open import group-theory.subgroups -open import group-theory.subsets-groups +open import group-theory.free-groups-with-one-generator funext univalence truncations +open import group-theory.groups funext univalence truncations +open import group-theory.kernels-homomorphisms-groups funext univalence truncations +open import group-theory.normal-subgroups funext univalence truncations +open import group-theory.subgroups funext univalence truncations +open import group-theory.subsets-groups funext univalence truncations ```
diff --git a/src/group-theory/perfect-cores.lagda.md b/src/group-theory/perfect-cores.lagda.md index cb10247ebe..bf1e27a79c 100644 --- a/src/group-theory/perfect-cores.lagda.md +++ b/src/group-theory/perfect-cores.lagda.md @@ -1,18 +1,26 @@ # Perfect cores ```agda -module group-theory.perfect-cores where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.perfect-cores + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.logical-equivalences +open import foundation.logical-equivalences funext open import foundation.universe-levels -open import group-theory.groups -open import group-theory.perfect-subgroups -open import group-theory.subgroups +open import group-theory.groups funext univalence truncations +open import group-theory.perfect-subgroups funext univalence truncations +open import group-theory.subgroups funext univalence truncations ```
diff --git a/src/group-theory/perfect-groups.lagda.md b/src/group-theory/perfect-groups.lagda.md index 830d29efab..257e059ad7 100644 --- a/src/group-theory/perfect-groups.lagda.md +++ b/src/group-theory/perfect-groups.lagda.md @@ -1,18 +1,27 @@ # Perfect groups ```agda -module group-theory.perfect-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.perfect-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.propositions funext univalence open import foundation.universe-levels -open import group-theory.commutator-subgroups -open import group-theory.full-subgroups -open import group-theory.groups +open import group-theory.commutator-subgroups funext univalence truncations +open import group-theory.full-subgroups funext univalence truncations +open import group-theory.groups funext univalence truncations ```
diff --git a/src/group-theory/perfect-subgroups.lagda.md b/src/group-theory/perfect-subgroups.lagda.md index 9e4dac3fc1..6859cbc88d 100644 --- a/src/group-theory/perfect-subgroups.lagda.md +++ b/src/group-theory/perfect-subgroups.lagda.md @@ -1,18 +1,27 @@ # Perfect subgroups ```agda -module group-theory.perfect-subgroups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.perfect-subgroups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.propositions funext univalence open import foundation.universe-levels -open import group-theory.groups -open import group-theory.perfect-groups -open import group-theory.subgroups +open import group-theory.groups funext univalence truncations +open import group-theory.perfect-groups funext univalence truncations +open import group-theory.subgroups funext univalence truncations ```
diff --git a/src/group-theory/powers-of-elements-commutative-monoids.lagda.md b/src/group-theory/powers-of-elements-commutative-monoids.lagda.md index 344471dcb0..cf24b4f5a6 100644 --- a/src/group-theory/powers-of-elements-commutative-monoids.lagda.md +++ b/src/group-theory/powers-of-elements-commutative-monoids.lagda.md @@ -1,7 +1,15 @@ # Powers of elements in commutative monoids ```agda -module group-theory.powers-of-elements-commutative-monoids where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.powers-of-elements-commutative-monoids + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -11,13 +19,14 @@ open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import foundation.identity-types -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence open import foundation.universe-levels -open import group-theory.commutative-monoids -open import group-theory.homomorphisms-commutative-monoids -open import group-theory.powers-of-elements-monoids +open import group-theory.commutative-monoids funext univalence truncations +open import group-theory.homomorphisms-commutative-monoids funext univalence truncations +open import group-theory.powers-of-elements-monoids funext univalence truncations ```
diff --git a/src/group-theory/powers-of-elements-groups.lagda.md b/src/group-theory/powers-of-elements-groups.lagda.md index 745ee9159a..06a0fbd98b 100644 --- a/src/group-theory/powers-of-elements-groups.lagda.md +++ b/src/group-theory/powers-of-elements-groups.lagda.md @@ -1,7 +1,15 @@ # Powers of elements in groups ```agda -module group-theory.powers-of-elements-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.powers-of-elements-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -11,14 +19,15 @@ open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import foundation.identity-types -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence open import foundation.universe-levels -open import group-theory.commuting-elements-groups -open import group-theory.groups -open import group-theory.homomorphisms-groups -open import group-theory.powers-of-elements-monoids +open import group-theory.commuting-elements-groups funext univalence truncations +open import group-theory.groups funext univalence truncations +open import group-theory.homomorphisms-groups funext univalence truncations +open import group-theory.powers-of-elements-monoids funext univalence truncations ```
diff --git a/src/group-theory/powers-of-elements-monoids.lagda.md b/src/group-theory/powers-of-elements-monoids.lagda.md index 66c4e4f41b..8673ac1eee 100644 --- a/src/group-theory/powers-of-elements-monoids.lagda.md +++ b/src/group-theory/powers-of-elements-monoids.lagda.md @@ -1,7 +1,15 @@ # Powers of elements in monoids ```agda -module group-theory.powers-of-elements-monoids where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.powers-of-elements-monoids + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -12,13 +20,14 @@ open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.existential-quantification -open import foundation.identity-types -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.existential-quantification funext univalence truncations +open import foundation.identity-types funext +open import foundation.propositions funext univalence open import foundation.universe-levels -open import group-theory.homomorphisms-monoids -open import group-theory.monoids +open import group-theory.homomorphisms-monoids funext univalence truncations +open import group-theory.monoids funext univalence truncations ```
diff --git a/src/group-theory/precategory-of-commutative-monoids.lagda.md b/src/group-theory/precategory-of-commutative-monoids.lagda.md index f3d5757c93..717821d092 100644 --- a/src/group-theory/precategory-of-commutative-monoids.lagda.md +++ b/src/group-theory/precategory-of-commutative-monoids.lagda.md @@ -1,20 +1,28 @@ # The precategory of commutative monoids ```agda -module group-theory.precategory-of-commutative-monoids where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.precategory-of-commutative-monoids + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.full-large-subprecategories -open import category-theory.large-precategories -open import category-theory.precategories +open import category-theory.full-large-subprecategories funext univalence truncations +open import category-theory.large-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations open import foundation.universe-levels -open import group-theory.commutative-monoids -open import group-theory.precategory-of-monoids +open import group-theory.commutative-monoids funext univalence truncations +open import group-theory.precategory-of-monoids funext univalence truncations ```
diff --git a/src/group-theory/precategory-of-concrete-groups.lagda.md b/src/group-theory/precategory-of-concrete-groups.lagda.md index 43b955bd5d..0a09c517e0 100644 --- a/src/group-theory/precategory-of-concrete-groups.lagda.md +++ b/src/group-theory/precategory-of-concrete-groups.lagda.md @@ -1,18 +1,26 @@ # The precategory of concrete groups ```agda -module group-theory.precategory-of-concrete-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.precategory-of-concrete-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.large-precategories +open import category-theory.large-precategories funext univalence truncations open import foundation.universe-levels -open import group-theory.concrete-groups -open import group-theory.homomorphisms-concrete-groups +open import group-theory.concrete-groups funext univalence truncations +open import group-theory.homomorphisms-concrete-groups funext univalence truncations ```
diff --git a/src/group-theory/precategory-of-group-actions.lagda.md b/src/group-theory/precategory-of-group-actions.lagda.md index d8fc00a1c5..466b2e056c 100644 --- a/src/group-theory/precategory-of-group-actions.lagda.md +++ b/src/group-theory/precategory-of-group-actions.lagda.md @@ -1,20 +1,28 @@ # The precategory of group actions ```agda -module group-theory.precategory-of-group-actions where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.precategory-of-group-actions + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.large-precategories -open import category-theory.precategories +open import category-theory.large-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations open import foundation.universe-levels -open import group-theory.group-actions -open import group-theory.groups -open import group-theory.homomorphisms-group-actions +open import group-theory.group-actions funext univalence truncations +open import group-theory.groups funext univalence truncations +open import group-theory.homomorphisms-group-actions funext univalence truncations ```
diff --git a/src/group-theory/precategory-of-groups.lagda.md b/src/group-theory/precategory-of-groups.lagda.md index 10f8be5a09..aa658e94db 100644 --- a/src/group-theory/precategory-of-groups.lagda.md +++ b/src/group-theory/precategory-of-groups.lagda.md @@ -1,20 +1,28 @@ # The precategory of groups ```agda -module group-theory.precategory-of-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.precategory-of-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.full-large-subprecategories -open import category-theory.large-precategories -open import category-theory.precategories +open import category-theory.full-large-subprecategories funext univalence truncations +open import category-theory.large-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations open import foundation.universe-levels -open import group-theory.groups -open import group-theory.precategory-of-semigroups +open import group-theory.groups funext univalence truncations +open import group-theory.precategory-of-semigroups funext univalence truncations ```
diff --git a/src/group-theory/precategory-of-monoids.lagda.md b/src/group-theory/precategory-of-monoids.lagda.md index a16650574c..bad4efa862 100644 --- a/src/group-theory/precategory-of-monoids.lagda.md +++ b/src/group-theory/precategory-of-monoids.lagda.md @@ -1,22 +1,30 @@ # The precategory of monoids ```agda -module group-theory.precategory-of-monoids where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.precategory-of-monoids + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.large-precategories -open import category-theory.large-subprecategories -open import category-theory.precategories +open import category-theory.large-precategories funext univalence truncations +open import category-theory.large-subprecategories funext univalence truncations +open import category-theory.precategories funext univalence truncations open import foundation.dependent-pair-types open import foundation.universe-levels -open import group-theory.homomorphisms-monoids -open import group-theory.monoids -open import group-theory.precategory-of-semigroups +open import group-theory.homomorphisms-monoids funext univalence truncations +open import group-theory.monoids funext univalence truncations +open import group-theory.precategory-of-semigroups funext univalence truncations ```
diff --git a/src/group-theory/precategory-of-orbits-monoid-actions.lagda.md b/src/group-theory/precategory-of-orbits-monoid-actions.lagda.md index 5a51488a0e..db39389d3e 100644 --- a/src/group-theory/precategory-of-orbits-monoid-actions.lagda.md +++ b/src/group-theory/precategory-of-orbits-monoid-actions.lagda.md @@ -1,27 +1,37 @@ # The precategory of orbits of a monoid action ```agda -module group-theory.precategory-of-orbits-monoid-actions where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.precategory-of-orbits-monoid-actions + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.precategories +open import category-theory.precategories funext univalence truncations -open import foundation.contractible-types +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence open import foundation.subtype-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext univalence truncations open import foundation.universe-levels -open import group-theory.monoid-actions -open import group-theory.monoids +open import group-theory.monoid-actions funext univalence truncations +open import group-theory.monoids funext univalence truncations ```
diff --git a/src/group-theory/precategory-of-semigroups.lagda.md b/src/group-theory/precategory-of-semigroups.lagda.md index 264d32e6b7..69618abf26 100644 --- a/src/group-theory/precategory-of-semigroups.lagda.md +++ b/src/group-theory/precategory-of-semigroups.lagda.md @@ -1,18 +1,26 @@ # The precategory of semigroups ```agda -module group-theory.precategory-of-semigroups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.precategory-of-semigroups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.large-precategories +open import category-theory.large-precategories funext univalence truncations open import foundation.universe-levels -open import group-theory.homomorphisms-semigroups -open import group-theory.semigroups +open import group-theory.homomorphisms-semigroups funext univalence truncations +open import group-theory.semigroups funext univalence ```
diff --git a/src/group-theory/principal-group-actions.lagda.md b/src/group-theory/principal-group-actions.lagda.md index 18aaf88ca9..d6b85061d5 100644 --- a/src/group-theory/principal-group-actions.lagda.md +++ b/src/group-theory/principal-group-actions.lagda.md @@ -1,18 +1,26 @@ # Principal group actions ```agda -module group-theory.principal-group-actions where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.principal-group-actions + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalence-extensionality +open import foundation.equivalence-extensionality funext open import foundation.universe-levels -open import group-theory.group-actions -open import group-theory.groups +open import group-theory.group-actions funext univalence truncations +open import group-theory.groups funext univalence truncations ```
diff --git a/src/group-theory/principal-torsors-concrete-groups.lagda.md b/src/group-theory/principal-torsors-concrete-groups.lagda.md index d90716ffd3..61b61c07cb 100644 --- a/src/group-theory/principal-torsors-concrete-groups.lagda.md +++ b/src/group-theory/principal-torsors-concrete-groups.lagda.md @@ -1,7 +1,15 @@ # Principal torsors of concrete groups ```agda -module group-theory.principal-torsors-concrete-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.principal-torsors-concrete-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,8 +17,8 @@ module group-theory.principal-torsors-concrete-groups where ```agda open import foundation.universe-levels -open import group-theory.concrete-group-actions -open import group-theory.concrete-groups +open import group-theory.concrete-group-actions funext univalence truncations +open import group-theory.concrete-groups funext univalence truncations ```
diff --git a/src/group-theory/products-of-elements-monoids.lagda.md b/src/group-theory/products-of-elements-monoids.lagda.md index a4712a4f13..5fc4c415bc 100644 --- a/src/group-theory/products-of-elements-monoids.lagda.md +++ b/src/group-theory/products-of-elements-monoids.lagda.md @@ -1,19 +1,27 @@ # Products of elements in a monoid ```agda -module group-theory.products-of-elements-monoids where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.products-of-elements-monoids + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import group-theory.monoids +open import group-theory.monoids funext univalence truncations -open import lists.concatenation-lists +open import lists.concatenation-lists funext univalence truncations open import lists.lists ``` diff --git a/src/group-theory/products-of-tuples-of-elements-commutative-monoids.lagda.md b/src/group-theory/products-of-tuples-of-elements-commutative-monoids.lagda.md index 120ca6b54c..cf6bd6d061 100644 --- a/src/group-theory/products-of-tuples-of-elements-commutative-monoids.lagda.md +++ b/src/group-theory/products-of-tuples-of-elements-commutative-monoids.lagda.md @@ -1,7 +1,15 @@ # Products of tuples of elements in commutative monoids ```agda -module group-theory.products-of-tuples-of-elements-commutative-monoids where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.products-of-tuples-of-elements-commutative-monoids + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,15 +17,15 @@ module group-theory.products-of-tuples-of-elements-commutative-monoids where ```agda open import elementary-number-theory.natural-numbers -open import foundation.coproduct-types -open import foundation.function-types +open import foundation.coproduct-types funext univalence truncations +open import foundation.function-types funext open import foundation.unit-type open import foundation.universe-levels -open import group-theory.commutative-monoids +open import group-theory.commutative-monoids funext univalence truncations -open import univalent-combinatorics.counting -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.counting funext univalence truncations +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/group-theory/pullbacks-subgroups.lagda.md b/src/group-theory/pullbacks-subgroups.lagda.md index 8ac1c10168..9bb80229d4 100644 --- a/src/group-theory/pullbacks-subgroups.lagda.md +++ b/src/group-theory/pullbacks-subgroups.lagda.md @@ -1,31 +1,39 @@ # Pullbacks of subgroups ```agda -module group-theory.pullbacks-subgroups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.pullbacks-subgroups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.powersets -open import foundation.pullbacks-subtypes +open import foundation.identity-types funext +open import foundation.powersets funext univalence truncations +open import foundation.pullbacks-subtypes funext univalence truncations open import foundation.universe-levels -open import group-theory.conjugation -open import group-theory.groups -open import group-theory.homomorphisms-groups -open import group-theory.normal-subgroups -open import group-theory.pullbacks-subsemigroups -open import group-theory.subgroups -open import group-theory.subsemigroups -open import group-theory.subsets-groups - -open import order-theory.commuting-squares-of-order-preserving-maps-large-posets -open import order-theory.order-preserving-maps-large-posets -open import order-theory.order-preserving-maps-large-preorders -open import order-theory.similarity-of-order-preserving-maps-large-posets +open import group-theory.conjugation funext univalence truncations +open import group-theory.groups funext univalence truncations +open import group-theory.homomorphisms-groups funext univalence truncations +open import group-theory.normal-subgroups funext univalence truncations +open import group-theory.pullbacks-subsemigroups funext univalence truncations +open import group-theory.subgroups funext univalence truncations +open import group-theory.subsemigroups funext univalence truncations +open import group-theory.subsets-groups funext univalence truncations + +open import order-theory.commuting-squares-of-order-preserving-maps-large-posets funext univalence truncations +open import order-theory.order-preserving-maps-large-posets funext univalence truncations +open import order-theory.order-preserving-maps-large-preorders funext univalence truncations +open import order-theory.similarity-of-order-preserving-maps-large-posets funext univalence truncations ```
diff --git a/src/group-theory/pullbacks-subsemigroups.lagda.md b/src/group-theory/pullbacks-subsemigroups.lagda.md index cfefc2061d..2abf126ec8 100644 --- a/src/group-theory/pullbacks-subsemigroups.lagda.md +++ b/src/group-theory/pullbacks-subsemigroups.lagda.md @@ -1,28 +1,36 @@ # Pullbacks of subsemigroups ```agda -module group-theory.pullbacks-subsemigroups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.pullbacks-subsemigroups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.identity-types -open import foundation.powersets -open import foundation.pullbacks-subtypes +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.powersets funext univalence truncations +open import foundation.pullbacks-subtypes funext univalence truncations open import foundation.universe-levels -open import group-theory.homomorphisms-semigroups -open import group-theory.semigroups -open import group-theory.subsemigroups -open import group-theory.subsets-semigroups +open import group-theory.homomorphisms-semigroups funext univalence truncations +open import group-theory.semigroups funext univalence +open import group-theory.subsemigroups funext univalence truncations +open import group-theory.subsets-semigroups funext univalence truncations -open import order-theory.commuting-squares-of-order-preserving-maps-large-posets -open import order-theory.order-preserving-maps-large-posets -open import order-theory.order-preserving-maps-large-preorders -open import order-theory.similarity-of-order-preserving-maps-large-posets +open import order-theory.commuting-squares-of-order-preserving-maps-large-posets funext univalence truncations +open import order-theory.order-preserving-maps-large-posets funext univalence truncations +open import order-theory.order-preserving-maps-large-preorders funext univalence truncations +open import order-theory.similarity-of-order-preserving-maps-large-posets funext univalence truncations ```
diff --git a/src/group-theory/quotient-groups-concrete-groups.lagda.md b/src/group-theory/quotient-groups-concrete-groups.lagda.md index f23e72c900..c733fa8b7d 100644 --- a/src/group-theory/quotient-groups-concrete-groups.lagda.md +++ b/src/group-theory/quotient-groups-concrete-groups.lagda.md @@ -1,36 +1,44 @@ # Quotient groups of concrete groups ```agda -module group-theory.quotient-groups-concrete-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.quotient-groups-concrete-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.0-connected-types -open import foundation.0-images-of-maps -open import foundation.1-types +open import foundation.0-connected-types funext univalence truncations +open import foundation.0-images-of-maps funext univalence truncations +open import foundation.1-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.identity-types -open import foundation.mere-equality -open import foundation.propositional-truncations -open import foundation.sets +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.mere-equality funext univalence truncations +open import foundation.propositional-truncations funext univalence +open import foundation.sets funext univalence open import foundation.subtype-identity-principle -open import foundation.subtypes +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels -open import group-theory.concrete-groups -open import group-theory.equivalences-concrete-group-actions -open import group-theory.mere-equivalences-concrete-group-actions -open import group-theory.normal-subgroups-concrete-groups -open import group-theory.transitive-concrete-group-actions +open import group-theory.concrete-groups funext univalence truncations +open import group-theory.equivalences-concrete-group-actions funext univalence truncations +open import group-theory.mere-equivalences-concrete-group-actions funext univalence truncations +open import group-theory.normal-subgroups-concrete-groups funext univalence truncations +open import group-theory.transitive-concrete-group-actions funext univalence truncations -open import higher-group-theory.higher-groups +open import higher-group-theory.higher-groups funext univalence truncations open import structured-types.pointed-types -open import synthetic-homotopy-theory.loop-spaces +open import synthetic-homotopy-theory.loop-spaces funext univalence truncations ```
diff --git a/src/group-theory/quotient-groups.lagda.md b/src/group-theory/quotient-groups.lagda.md index d109a8292d..e639feaf52 100644 --- a/src/group-theory/quotient-groups.lagda.md +++ b/src/group-theory/quotient-groups.lagda.md @@ -1,40 +1,50 @@ # Quotient groups ```agda -module group-theory.quotient-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.quotient-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.binary-functoriality-set-quotients -open import foundation.commuting-triangles-of-maps -open import foundation.contractible-maps -open import foundation.contractible-types +open import foundation.binary-functoriality-set-quotients funext univalence truncations +open import foundation.commuting-triangles-of-maps funext univalence +open import foundation.contractible-maps funext +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.effective-maps-equivalence-relations -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.functoriality-set-quotients -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.propositions -open import foundation.reflecting-maps-equivalence-relations -open import foundation.set-quotients -open import foundation.sets -open import foundation.subtypes -open import foundation.surjective-maps -open import foundation.universal-property-set-quotients +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.effective-maps-equivalence-relations funext univalence truncations +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.functoriality-set-quotients funext univalence truncations +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.propositions funext univalence +open import foundation.reflecting-maps-equivalence-relations funext univalence truncations +open import foundation.set-quotients funext univalence truncations +open import foundation.sets funext univalence +open import foundation.subtypes funext univalence truncations +open import foundation.surjective-maps funext univalence truncations +open import foundation.universal-property-set-quotients funext univalence truncations open import foundation.universe-levels -open import group-theory.groups -open import group-theory.homomorphisms-groups -open import group-theory.kernels-homomorphisms-groups -open import group-theory.normal-subgroups -open import group-theory.nullifying-group-homomorphisms -open import group-theory.semigroups +open import group-theory.groups funext univalence truncations +open import group-theory.homomorphisms-groups funext univalence truncations +open import group-theory.kernels-homomorphisms-groups funext univalence truncations +open import group-theory.normal-subgroups funext univalence truncations +open import group-theory.nullifying-group-homomorphisms funext univalence truncations +open import group-theory.semigroups funext univalence ```
diff --git a/src/group-theory/quotients-abelian-groups.lagda.md b/src/group-theory/quotients-abelian-groups.lagda.md index 51ce7f9b4a..6fab67dfd2 100644 --- a/src/group-theory/quotients-abelian-groups.lagda.md +++ b/src/group-theory/quotients-abelian-groups.lagda.md @@ -2,35 +2,43 @@ ```agda {-# OPTIONS --lossy-unification #-} - -module group-theory.quotients-abelian-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.quotients-abelian-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.binary-functoriality-set-quotients +open import foundation.binary-functoriality-set-quotients funext univalence truncations open import foundation.dependent-pair-types -open import foundation.effective-maps-equivalence-relations -open import foundation.equivalences -open import foundation.functoriality-set-quotients -open import foundation.identity-types -open import foundation.propositions -open import foundation.reflecting-maps-equivalence-relations -open import foundation.set-quotients -open import foundation.sets -open import foundation.surjective-maps -open import foundation.universal-property-set-quotients +open import foundation.dependent-products-propositions funext +open import foundation.effective-maps-equivalence-relations funext univalence truncations +open import foundation.equivalences funext +open import foundation.functoriality-set-quotients funext univalence truncations +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.reflecting-maps-equivalence-relations funext univalence truncations +open import foundation.set-quotients funext univalence truncations +open import foundation.sets funext univalence +open import foundation.surjective-maps funext univalence truncations +open import foundation.universal-property-set-quotients funext univalence truncations open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.groups -open import group-theory.homomorphisms-abelian-groups -open import group-theory.nullifying-group-homomorphisms -open import group-theory.quotient-groups -open import group-theory.semigroups -open import group-theory.subgroups-abelian-groups +open import group-theory.abelian-groups funext univalence truncations +open import group-theory.groups funext univalence truncations +open import group-theory.homomorphisms-abelian-groups funext univalence truncations +open import group-theory.nullifying-group-homomorphisms funext univalence truncations +open import group-theory.quotient-groups funext univalence truncations +open import group-theory.semigroups funext univalence +open import group-theory.subgroups-abelian-groups funext univalence truncations ```
diff --git a/src/group-theory/rational-commutative-monoids.lagda.md b/src/group-theory/rational-commutative-monoids.lagda.md index 2c036f47fe..834c3e5c88 100644 --- a/src/group-theory/rational-commutative-monoids.lagda.md +++ b/src/group-theory/rational-commutative-monoids.lagda.md @@ -1,7 +1,15 @@ # Rational commutative monoids ```agda -module group-theory.rational-commutative-monoids where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.rational-commutative-monoids + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,14 +18,15 @@ module group-theory.rational-commutative-monoids where open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.identity-types -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence open import foundation.universe-levels -open import group-theory.commutative-monoids -open import group-theory.monoids -open import group-theory.powers-of-elements-commutative-monoids +open import group-theory.commutative-monoids funext univalence truncations +open import group-theory.monoids funext univalence truncations +open import group-theory.powers-of-elements-commutative-monoids funext univalence truncations ```
diff --git a/src/group-theory/representations-monoids-precategories.lagda.md b/src/group-theory/representations-monoids-precategories.lagda.md index 934a1e2362..1d2eed6937 100644 --- a/src/group-theory/representations-monoids-precategories.lagda.md +++ b/src/group-theory/representations-monoids-precategories.lagda.md @@ -1,23 +1,31 @@ # Representations of monoids in precategories ```agda -module group-theory.representations-monoids-precategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.representations-monoids-precategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.endomorphisms-in-precategories -open import category-theory.functors-precategories -open import category-theory.one-object-precategories -open import category-theory.precategories +open import category-theory.endomorphisms-in-precategories funext univalence truncations +open import category-theory.functors-precategories funext univalence truncations +open import category-theory.one-object-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.unit-type open import foundation.universe-levels -open import group-theory.monoids +open import group-theory.monoids funext univalence truncations ```
diff --git a/src/group-theory/saturated-congruence-relations-commutative-monoids.lagda.md b/src/group-theory/saturated-congruence-relations-commutative-monoids.lagda.md index 52a270e3cb..9b0e7c404c 100644 --- a/src/group-theory/saturated-congruence-relations-commutative-monoids.lagda.md +++ b/src/group-theory/saturated-congruence-relations-commutative-monoids.lagda.md @@ -1,26 +1,35 @@ # Saturated congruence relations on commutative monoids ```agda -module group-theory.saturated-congruence-relations-commutative-monoids where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.saturated-congruence-relations-commutative-monoids + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.binary-relations +open import foundation.binary-relations funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalence-relations -open import foundation.equivalences +open import foundation.dependent-products-propositions funext +open import foundation.equivalence-relations funext univalence truncations +open import foundation.equivalences funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.propositions +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.propositions funext univalence open import foundation.subtype-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext univalence truncations open import foundation.universe-levels -open import group-theory.commutative-monoids -open import group-theory.congruence-relations-commutative-monoids +open import group-theory.commutative-monoids funext univalence truncations +open import group-theory.congruence-relations-commutative-monoids funext univalence truncations ```
diff --git a/src/group-theory/saturated-congruence-relations-monoids.lagda.md b/src/group-theory/saturated-congruence-relations-monoids.lagda.md index fe77217ff6..bdca18b2d0 100644 --- a/src/group-theory/saturated-congruence-relations-monoids.lagda.md +++ b/src/group-theory/saturated-congruence-relations-monoids.lagda.md @@ -1,26 +1,35 @@ # Saturated congruence relations on monoids ```agda -module group-theory.saturated-congruence-relations-monoids where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.saturated-congruence-relations-monoids + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.binary-relations +open import foundation.binary-relations funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalence-relations -open import foundation.equivalences +open import foundation.dependent-products-propositions funext +open import foundation.equivalence-relations funext univalence truncations +open import foundation.equivalences funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.propositions +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.propositions funext univalence open import foundation.subtype-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext univalence truncations open import foundation.universe-levels -open import group-theory.congruence-relations-monoids -open import group-theory.monoids +open import group-theory.congruence-relations-monoids funext univalence truncations +open import group-theory.monoids funext univalence truncations ```
diff --git a/src/group-theory/semigroups.lagda.md b/src/group-theory/semigroups.lagda.md index 4709573fcf..06bf030b81 100644 --- a/src/group-theory/semigroups.lagda.md +++ b/src/group-theory/semigroups.lagda.md @@ -1,7 +1,13 @@ # Semigroups ```agda -module group-theory.semigroups where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.semigroups + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports @@ -10,8 +16,8 @@ module group-theory.semigroups where open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.sets +open import foundation.identity-types funext +open import foundation.sets funext univalence open import foundation.universe-levels ``` diff --git a/src/group-theory/sheargroups.lagda.md b/src/group-theory/sheargroups.lagda.md index 42becd5b2b..fc14f44c93 100644 --- a/src/group-theory/sheargroups.lagda.md +++ b/src/group-theory/sheargroups.lagda.md @@ -1,16 +1,22 @@ # Sheargroups ```agda -module group-theory.sheargroups where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.sheargroups + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.sets +open import foundation.identity-types funext +open import foundation.sets funext univalence open import foundation.universe-levels ``` diff --git a/src/group-theory/shriek-concrete-group-actions.lagda.md b/src/group-theory/shriek-concrete-group-actions.lagda.md index 6e5364e97f..2291b3cbff 100644 --- a/src/group-theory/shriek-concrete-group-actions.lagda.md +++ b/src/group-theory/shriek-concrete-group-actions.lagda.md @@ -1,22 +1,30 @@ # Shriek of concrete group homomorphisms ```agda -module group-theory.shriek-concrete-group-actions where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.shriek-concrete-group-actions + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.set-truncations -open import foundation.sets +open import foundation.identity-types funext +open import foundation.set-truncations funext univalence +open import foundation.sets funext univalence open import foundation.universe-levels -open import group-theory.concrete-group-actions -open import group-theory.concrete-groups -open import group-theory.homomorphisms-concrete-groups +open import group-theory.concrete-group-actions funext univalence truncations +open import group-theory.concrete-groups funext univalence truncations +open import group-theory.homomorphisms-concrete-groups funext univalence truncations ```
diff --git a/src/group-theory/stabilizer-groups-concrete-group-actions.lagda.md b/src/group-theory/stabilizer-groups-concrete-group-actions.lagda.md index fccff9b2a3..970d4b116b 100644 --- a/src/group-theory/stabilizer-groups-concrete-group-actions.lagda.md +++ b/src/group-theory/stabilizer-groups-concrete-group-actions.lagda.md @@ -1,26 +1,34 @@ # Stabilizers of concrete group actions ```agda -module group-theory.stabilizer-groups-concrete-group-actions where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.stabilizer-groups-concrete-group-actions + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.0-connected-types +open import foundation.0-connected-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.mere-equality -open import foundation.propositional-truncations -open import foundation.sets -open import foundation.subtypes +open import foundation.function-types funext +open import foundation.mere-equality funext univalence truncations +open import foundation.propositional-truncations funext univalence +open import foundation.sets funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels -open import group-theory.concrete-group-actions -open import group-theory.concrete-groups -open import group-theory.subgroups-concrete-groups -open import group-theory.transitive-concrete-group-actions +open import group-theory.concrete-group-actions funext univalence truncations +open import group-theory.concrete-groups funext univalence truncations +open import group-theory.subgroups-concrete-groups funext univalence truncations +open import group-theory.transitive-concrete-group-actions funext univalence truncations ```
diff --git a/src/group-theory/stabilizer-groups.lagda.md b/src/group-theory/stabilizer-groups.lagda.md index 6786bf463a..a8e63662f0 100644 --- a/src/group-theory/stabilizer-groups.lagda.md +++ b/src/group-theory/stabilizer-groups.lagda.md @@ -1,18 +1,26 @@ # Stabilizer groups ```agda -module group-theory.stabilizer-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.stabilizer-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import group-theory.group-actions -open import group-theory.groups +open import group-theory.group-actions funext univalence truncations +open import group-theory.groups funext univalence truncations ```
diff --git a/src/group-theory/subgroups-abelian-groups.lagda.md b/src/group-theory/subgroups-abelian-groups.lagda.md index 61238aa5c7..2e902d02ee 100644 --- a/src/group-theory/subgroups-abelian-groups.lagda.md +++ b/src/group-theory/subgroups-abelian-groups.lagda.md @@ -1,37 +1,46 @@ # Subgroups of abelian groups ```agda -module group-theory.subgroups-abelian-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.subgroups-abelian-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.binary-relations +open import foundation.binary-relations funext univalence truncations open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalence-relations -open import foundation.equivalences -open import foundation.identity-types -open import foundation.large-binary-relations -open import foundation.propositions -open import foundation.sets +open import foundation.dependent-products-propositions funext +open import foundation.embeddings funext +open import foundation.equivalence-relations funext univalence truncations +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.large-binary-relations funext univalence truncations +open import foundation.propositions funext univalence +open import foundation.sets funext univalence open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.congruence-relations-abelian-groups -open import group-theory.congruence-relations-groups -open import group-theory.groups -open import group-theory.homomorphisms-abelian-groups -open import group-theory.normal-subgroups -open import group-theory.semigroups -open import group-theory.subgroups -open import group-theory.subsets-abelian-groups - -open import order-theory.large-posets -open import order-theory.large-preorders -open import order-theory.posets -open import order-theory.preorders +open import group-theory.abelian-groups funext univalence truncations +open import group-theory.congruence-relations-abelian-groups funext univalence truncations +open import group-theory.congruence-relations-groups funext univalence truncations +open import group-theory.groups funext univalence truncations +open import group-theory.homomorphisms-abelian-groups funext univalence truncations +open import group-theory.normal-subgroups funext univalence truncations +open import group-theory.semigroups funext univalence +open import group-theory.subgroups funext univalence truncations +open import group-theory.subsets-abelian-groups funext univalence truncations + +open import order-theory.large-posets funext univalence truncations +open import order-theory.large-preorders funext univalence truncations +open import order-theory.posets funext univalence truncations +open import order-theory.preorders funext univalence truncations ```
diff --git a/src/group-theory/subgroups-concrete-groups.lagda.md b/src/group-theory/subgroups-concrete-groups.lagda.md index eb86e36730..d2a05c0b4f 100644 --- a/src/group-theory/subgroups-concrete-groups.lagda.md +++ b/src/group-theory/subgroups-concrete-groups.lagda.md @@ -1,37 +1,46 @@ # Subgroups of concrete groups ```agda -module group-theory.subgroups-concrete-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.subgroups-concrete-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.0-connected-types -open import foundation.0-maps +open import foundation.0-connected-types funext univalence truncations +open import foundation.0-maps funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.existential-quantification -open import foundation.faithful-maps -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.existential-quantification funext univalence truncations +open import foundation.faithful-maps funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence open import foundation.structure-identity-principle -open import foundation.subtypes +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels -open import group-theory.concrete-group-actions -open import group-theory.concrete-groups -open import group-theory.equivalences-concrete-group-actions -open import group-theory.homomorphisms-concrete-groups -open import group-theory.orbits-concrete-group-actions -open import group-theory.transitive-concrete-group-actions +open import group-theory.concrete-group-actions funext univalence truncations +open import group-theory.concrete-groups funext univalence truncations +open import group-theory.equivalences-concrete-group-actions funext univalence truncations +open import group-theory.homomorphisms-concrete-groups funext univalence truncations +open import group-theory.orbits-concrete-group-actions funext univalence truncations +open import group-theory.transitive-concrete-group-actions funext univalence truncations -open import structured-types.pointed-maps +open import structured-types.pointed-maps funext univalence truncations open import structured-types.pointed-types -open import synthetic-homotopy-theory.functoriality-loop-spaces -open import synthetic-homotopy-theory.loop-spaces +open import synthetic-homotopy-theory.functoriality-loop-spaces funext univalence truncations +open import synthetic-homotopy-theory.loop-spaces funext univalence truncations ```
diff --git a/src/group-theory/subgroups-generated-by-elements-groups.lagda.md b/src/group-theory/subgroups-generated-by-elements-groups.lagda.md index fe9afdb421..a2be19b6f0 100644 --- a/src/group-theory/subgroups-generated-by-elements-groups.lagda.md +++ b/src/group-theory/subgroups-generated-by-elements-groups.lagda.md @@ -1,33 +1,41 @@ # Subgroups generated by elements of a group ```agda -module group-theory.subgroups-generated-by-elements-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.subgroups-generated-by-elements-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.group-of-integers +open import elementary-number-theory.group-of-integers funext univalence truncations open import elementary-number-theory.integers open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.identity-types -open import foundation.images-subtypes -open import foundation.logical-equivalences -open import foundation.singleton-subtypes -open import foundation.subtypes +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.images-subtypes funext univalence truncations +open import foundation.logical-equivalences funext +open import foundation.singleton-subtypes funext univalence truncations +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels -open import group-theory.free-groups-with-one-generator -open import group-theory.groups -open import group-theory.homomorphisms-groups -open import group-theory.images-of-group-homomorphisms -open import group-theory.integer-powers-of-elements-groups -open import group-theory.subgroups -open import group-theory.subgroups-generated-by-subsets-groups -open import group-theory.subsets-groups -open import group-theory.trivial-subgroups +open import group-theory.free-groups-with-one-generator funext univalence truncations +open import group-theory.groups funext univalence truncations +open import group-theory.homomorphisms-groups funext univalence truncations +open import group-theory.images-of-group-homomorphisms funext univalence truncations +open import group-theory.integer-powers-of-elements-groups funext univalence truncations +open import group-theory.subgroups funext univalence truncations +open import group-theory.subgroups-generated-by-subsets-groups funext univalence truncations +open import group-theory.subsets-groups funext univalence truncations +open import group-theory.trivial-subgroups funext univalence truncations ```
diff --git a/src/group-theory/subgroups-generated-by-families-of-elements-groups.lagda.md b/src/group-theory/subgroups-generated-by-families-of-elements-groups.lagda.md index 34c8ab61bf..3fcc672c06 100644 --- a/src/group-theory/subgroups-generated-by-families-of-elements-groups.lagda.md +++ b/src/group-theory/subgroups-generated-by-families-of-elements-groups.lagda.md @@ -1,30 +1,38 @@ # Subgroups generated by families of elements ```agda -module group-theory.subgroups-generated-by-families-of-elements-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.subgroups-generated-by-families-of-elements-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.identity-types -open import foundation.images -open import foundation.images-subtypes -open import foundation.logical-equivalences -open import foundation.propositional-truncations -open import foundation.subtypes -open import foundation.universal-property-image +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.images funext univalence truncations +open import foundation.images-subtypes funext univalence truncations +open import foundation.logical-equivalences funext +open import foundation.propositional-truncations funext univalence +open import foundation.subtypes funext univalence truncations +open import foundation.universal-property-image funext univalence truncations open import foundation.universe-levels -open import group-theory.groups -open import group-theory.homomorphisms-groups -open import group-theory.images-of-group-homomorphisms -open import group-theory.subgroups -open import group-theory.subgroups-generated-by-subsets-groups -open import group-theory.subsets-groups -open import group-theory.trivial-subgroups +open import group-theory.groups funext univalence truncations +open import group-theory.homomorphisms-groups funext univalence truncations +open import group-theory.images-of-group-homomorphisms funext univalence truncations +open import group-theory.subgroups funext univalence truncations +open import group-theory.subgroups-generated-by-subsets-groups funext univalence truncations +open import group-theory.subsets-groups funext univalence truncations +open import group-theory.trivial-subgroups funext univalence truncations ```
diff --git a/src/group-theory/subgroups-generated-by-subsets-groups.lagda.md b/src/group-theory/subgroups-generated-by-subsets-groups.lagda.md index bdcb3c854f..1314678434 100644 --- a/src/group-theory/subgroups-generated-by-subsets-groups.lagda.md +++ b/src/group-theory/subgroups-generated-by-subsets-groups.lagda.md @@ -1,52 +1,61 @@ # Subgroups generated by subsets of groups ```agda -module group-theory.subgroups-generated-by-subsets-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.subgroups-generated-by-subsets-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types -open import foundation.coproduct-types +open import foundation.cartesian-product-types funext univalence +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.fibers-of-maps -open import foundation.function-types -open import foundation.identity-types -open import foundation.images-subtypes -open import foundation.logical-equivalences -open import foundation.powersets -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.pullbacks-subtypes -open import foundation.singleton-subtypes -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.fibers-of-maps funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.images-subtypes funext univalence truncations +open import foundation.logical-equivalences funext +open import foundation.powersets funext univalence truncations +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence +open import foundation.pullbacks-subtypes funext univalence truncations +open import foundation.singleton-subtypes funext univalence truncations +open import foundation.subtypes funext univalence truncations open import foundation.unit-type open import foundation.universe-levels -open import group-theory.conjugation -open import group-theory.groups -open import group-theory.homomorphisms-groups -open import group-theory.images-of-group-homomorphisms -open import group-theory.normal-subgroups -open import group-theory.pullbacks-subgroups -open import group-theory.subgroups -open import group-theory.subsets-groups -open import group-theory.trivial-subgroups - -open import lists.concatenation-lists +open import group-theory.conjugation funext univalence truncations +open import group-theory.groups funext univalence truncations +open import group-theory.homomorphisms-groups funext univalence truncations +open import group-theory.images-of-group-homomorphisms funext univalence truncations +open import group-theory.normal-subgroups funext univalence truncations +open import group-theory.pullbacks-subgroups funext univalence truncations +open import group-theory.subgroups funext univalence truncations +open import group-theory.subsets-groups funext univalence truncations +open import group-theory.trivial-subgroups funext univalence truncations + +open import lists.concatenation-lists funext univalence truncations open import lists.lists -open import order-theory.commuting-squares-of-galois-connections-large-posets -open import order-theory.commuting-squares-of-order-preserving-maps-large-posets -open import order-theory.galois-connections-large-posets -open import order-theory.order-preserving-maps-large-posets -open import order-theory.order-preserving-maps-large-preorders -open import order-theory.similarity-of-elements-large-posets -open import order-theory.similarity-of-order-preserving-maps-large-posets +open import order-theory.commuting-squares-of-galois-connections-large-posets funext univalence truncations +open import order-theory.commuting-squares-of-order-preserving-maps-large-posets funext univalence truncations +open import order-theory.galois-connections-large-posets funext univalence truncations +open import order-theory.order-preserving-maps-large-posets funext univalence truncations +open import order-theory.order-preserving-maps-large-preorders funext univalence truncations +open import order-theory.similarity-of-elements-large-posets funext univalence truncations +open import order-theory.similarity-of-order-preserving-maps-large-posets funext univalence truncations -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/group-theory/subgroups.lagda.md b/src/group-theory/subgroups.lagda.md index 98631e94e6..22cbe4ff76 100644 --- a/src/group-theory/subgroups.lagda.md +++ b/src/group-theory/subgroups.lagda.md @@ -1,7 +1,15 @@ # Subgroups ```agda -module group-theory.subgroups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.subgroups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,41 +18,42 @@ module group-theory.subgroups where open import elementary-number-theory.integers open import elementary-number-theory.natural-numbers -open import foundation.binary-relations -open import foundation.coproduct-types +open import foundation.binary-relations funext univalence truncations +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.disjunction -open import foundation.embeddings -open import foundation.equivalence-relations -open import foundation.equivalences -open import foundation.function-types -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.large-binary-relations -open import foundation.logical-equivalences -open import foundation.powersets -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.sets +open import foundation.dependent-products-propositions funext +open import foundation.disjunction funext univalence truncations +open import foundation.embeddings funext +open import foundation.equivalence-relations funext univalence truncations +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.large-binary-relations funext univalence truncations +open import foundation.logical-equivalences funext +open import foundation.powersets funext univalence truncations +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence +open import foundation.sets funext univalence open import foundation.subtype-identity-principle -open import foundation.subtypes +open import foundation.subtypes funext univalence truncations open import foundation.transport-along-identifications open import foundation.universe-levels -open import group-theory.groups -open import group-theory.homomorphisms-groups -open import group-theory.integer-powers-of-elements-groups -open import group-theory.semigroups -open import group-theory.subsemigroups -open import group-theory.subsets-groups - -open import order-theory.large-posets -open import order-theory.large-preorders -open import order-theory.order-preserving-maps-large-posets -open import order-theory.order-preserving-maps-large-preorders -open import order-theory.posets -open import order-theory.preorders -open import order-theory.similarity-of-elements-large-posets +open import group-theory.groups funext univalence truncations +open import group-theory.homomorphisms-groups funext univalence truncations +open import group-theory.integer-powers-of-elements-groups funext univalence truncations +open import group-theory.semigroups funext univalence +open import group-theory.subsemigroups funext univalence truncations +open import group-theory.subsets-groups funext univalence truncations + +open import order-theory.large-posets funext univalence truncations +open import order-theory.large-preorders funext univalence truncations +open import order-theory.order-preserving-maps-large-posets funext univalence truncations +open import order-theory.order-preserving-maps-large-preorders funext univalence truncations +open import order-theory.posets funext univalence truncations +open import order-theory.preorders funext univalence truncations +open import order-theory.similarity-of-elements-large-posets funext univalence truncations ```
diff --git a/src/group-theory/submonoids-commutative-monoids.lagda.md b/src/group-theory/submonoids-commutative-monoids.lagda.md index 1b93a31af2..4eb08aa04a 100644 --- a/src/group-theory/submonoids-commutative-monoids.lagda.md +++ b/src/group-theory/submonoids-commutative-monoids.lagda.md @@ -1,26 +1,35 @@ # Submonoids of commutative monoids ```agda -module group-theory.submonoids-commutative-monoids where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.submonoids-commutative-monoids + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels -open import group-theory.commutative-monoids -open import group-theory.homomorphisms-commutative-monoids -open import group-theory.monoids -open import group-theory.semigroups -open import group-theory.submonoids -open import group-theory.subsets-commutative-monoids +open import group-theory.commutative-monoids funext univalence truncations +open import group-theory.homomorphisms-commutative-monoids funext univalence truncations +open import group-theory.monoids funext univalence truncations +open import group-theory.semigroups funext univalence +open import group-theory.submonoids funext univalence truncations +open import group-theory.subsets-commutative-monoids funext univalence truncations ```
diff --git a/src/group-theory/submonoids.lagda.md b/src/group-theory/submonoids.lagda.md index 4245b22e10..9a08113f5d 100644 --- a/src/group-theory/submonoids.lagda.md +++ b/src/group-theory/submonoids.lagda.md @@ -1,26 +1,35 @@ # Submonoids ```agda -module group-theory.submonoids where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.submonoids + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence open import foundation.subtype-identity-principle -open import foundation.subtypes +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels -open import group-theory.homomorphisms-monoids -open import group-theory.monoids -open import group-theory.semigroups -open import group-theory.subsets-monoids +open import group-theory.homomorphisms-monoids funext univalence truncations +open import group-theory.monoids funext univalence truncations +open import group-theory.semigroups funext univalence +open import group-theory.subsets-monoids funext univalence truncations ```
diff --git a/src/group-theory/subsemigroups.lagda.md b/src/group-theory/subsemigroups.lagda.md index f283a68db3..bfe126180e 100644 --- a/src/group-theory/subsemigroups.lagda.md +++ b/src/group-theory/subsemigroups.lagda.md @@ -1,34 +1,43 @@ # Subsemigroups ```agda -module group-theory.subsemigroups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.subsemigroups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.identity-types -open import foundation.large-binary-relations -open import foundation.powersets -open import foundation.propositions -open import foundation.sets +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.large-binary-relations funext univalence truncations +open import foundation.powersets funext univalence truncations +open import foundation.propositions funext univalence +open import foundation.sets funext univalence open import foundation.subtype-identity-principle -open import foundation.subtypes +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels -open import group-theory.homomorphisms-semigroups -open import group-theory.semigroups -open import group-theory.subsets-semigroups +open import group-theory.homomorphisms-semigroups funext univalence truncations +open import group-theory.semigroups funext univalence +open import group-theory.subsets-semigroups funext univalence truncations -open import order-theory.large-posets -open import order-theory.large-preorders -open import order-theory.order-preserving-maps-large-posets -open import order-theory.order-preserving-maps-large-preorders -open import order-theory.posets -open import order-theory.preorders +open import order-theory.large-posets funext univalence truncations +open import order-theory.large-preorders funext univalence truncations +open import order-theory.order-preserving-maps-large-posets funext univalence truncations +open import order-theory.order-preserving-maps-large-preorders funext univalence truncations +open import order-theory.posets funext univalence truncations +open import order-theory.preorders funext univalence truncations ```
diff --git a/src/group-theory/subsets-abelian-groups.lagda.md b/src/group-theory/subsets-abelian-groups.lagda.md index 98fe503199..b2ce929766 100644 --- a/src/group-theory/subsets-abelian-groups.lagda.md +++ b/src/group-theory/subsets-abelian-groups.lagda.md @@ -1,22 +1,30 @@ # Subsets of abelian groups ```agda -module group-theory.subsets-abelian-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.subsets-abelian-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.large-locale-of-subtypes -open import foundation.powersets -open import foundation.sets +open import foundation.large-locale-of-subtypes funext univalence truncations +open import foundation.powersets funext univalence truncations +open import foundation.sets funext univalence open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.subsets-groups +open import group-theory.abelian-groups funext univalence truncations +open import group-theory.subsets-groups funext univalence truncations -open import order-theory.large-locales -open import order-theory.large-posets +open import order-theory.large-locales funext univalence truncations +open import order-theory.large-posets funext univalence truncations ```
diff --git a/src/group-theory/subsets-commutative-monoids.lagda.md b/src/group-theory/subsets-commutative-monoids.lagda.md index be1275afe2..b55e1610f3 100644 --- a/src/group-theory/subsets-commutative-monoids.lagda.md +++ b/src/group-theory/subsets-commutative-monoids.lagda.md @@ -1,19 +1,28 @@ # Subsets of commutative monoids ```agda -module group-theory.subsets-commutative-monoids where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.subsets-commutative-monoids + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets +open import foundation.dependent-products-propositions funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence open import foundation.universe-levels -open import group-theory.commutative-monoids -open import group-theory.subsets-monoids +open import group-theory.commutative-monoids funext univalence truncations +open import group-theory.subsets-monoids funext univalence truncations ```
diff --git a/src/group-theory/subsets-groups.lagda.md b/src/group-theory/subsets-groups.lagda.md index 7eab7bced3..0e0c94f550 100644 --- a/src/group-theory/subsets-groups.lagda.md +++ b/src/group-theory/subsets-groups.lagda.md @@ -1,20 +1,28 @@ # Subsets of groups ```agda -module group-theory.subsets-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.subsets-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.large-locale-of-subtypes -open import foundation.sets +open import foundation.large-locale-of-subtypes funext univalence truncations +open import foundation.sets funext univalence open import foundation.universe-levels -open import group-theory.groups +open import group-theory.groups funext univalence truncations -open import order-theory.large-locales -open import order-theory.large-posets +open import order-theory.large-locales funext univalence truncations +open import order-theory.large-posets funext univalence truncations ```
diff --git a/src/group-theory/subsets-monoids.lagda.md b/src/group-theory/subsets-monoids.lagda.md index 97bb8b9059..d28ea53beb 100644 --- a/src/group-theory/subsets-monoids.lagda.md +++ b/src/group-theory/subsets-monoids.lagda.md @@ -1,19 +1,28 @@ # Subsets of monoids ```agda -module group-theory.subsets-monoids where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.subsets-monoids + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels -open import group-theory.monoids +open import group-theory.monoids funext univalence truncations ```
diff --git a/src/group-theory/subsets-semigroups.lagda.md b/src/group-theory/subsets-semigroups.lagda.md index ddfdf50d40..17b3c9e84c 100644 --- a/src/group-theory/subsets-semigroups.lagda.md +++ b/src/group-theory/subsets-semigroups.lagda.md @@ -1,24 +1,33 @@ # Subsets of semigroups ```agda -module group-theory.subsets-semigroups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.subsets-semigroups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.identity-types -open import foundation.large-locale-of-subtypes -open import foundation.powersets -open import foundation.propositions -open import foundation.sets -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.identity-types funext +open import foundation.large-locale-of-subtypes funext univalence truncations +open import foundation.powersets funext univalence truncations +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels -open import group-theory.semigroups +open import group-theory.semigroups funext univalence -open import order-theory.large-locales -open import order-theory.large-posets +open import order-theory.large-locales funext univalence truncations +open import order-theory.large-posets funext univalence truncations ```
diff --git a/src/group-theory/substitution-functor-concrete-group-actions.lagda.md b/src/group-theory/substitution-functor-concrete-group-actions.lagda.md index 80b294ad6c..7c38ebcdd3 100644 --- a/src/group-theory/substitution-functor-concrete-group-actions.lagda.md +++ b/src/group-theory/substitution-functor-concrete-group-actions.lagda.md @@ -1,7 +1,15 @@ # The substitution functor of concrete group actions ```agda -module group-theory.substitution-functor-concrete-group-actions where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.substitution-functor-concrete-group-actions + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,9 +17,9 @@ module group-theory.substitution-functor-concrete-group-actions where ```agda open import foundation.universe-levels -open import group-theory.concrete-group-actions -open import group-theory.concrete-groups -open import group-theory.homomorphisms-concrete-groups +open import group-theory.concrete-group-actions funext univalence truncations +open import group-theory.concrete-groups funext univalence truncations +open import group-theory.homomorphisms-concrete-groups funext univalence truncations ```
diff --git a/src/group-theory/substitution-functor-group-actions.lagda.md b/src/group-theory/substitution-functor-group-actions.lagda.md index d8d73e7e03..b082420710 100644 --- a/src/group-theory/substitution-functor-group-actions.lagda.md +++ b/src/group-theory/substitution-functor-group-actions.lagda.md @@ -1,31 +1,39 @@ # The substitution functor of group actions ```agda -module group-theory.substitution-functor-group-actions where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.substitution-functor-group-actions + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.functors-large-precategories +open import category-theory.functors-large-precategories funext univalence truncations open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalence-classes -open import foundation.equivalence-relations -open import foundation.existential-quantification -open import foundation.identity-types -open import foundation.propositional-truncations -open import foundation.sets +open import foundation.equivalence-classes funext univalence truncations +open import foundation.equivalence-relations funext univalence truncations +open import foundation.existential-quantification funext univalence truncations +open import foundation.identity-types funext +open import foundation.propositional-truncations funext univalence +open import foundation.sets funext univalence open import foundation.universe-levels -open import group-theory.group-actions -open import group-theory.groups -open import group-theory.homomorphisms-group-actions -open import group-theory.homomorphisms-groups -open import group-theory.precategory-of-group-actions -open import group-theory.symmetric-groups +open import group-theory.group-actions funext univalence truncations +open import group-theory.groups funext univalence truncations +open import group-theory.homomorphisms-group-actions funext univalence truncations +open import group-theory.homomorphisms-groups funext univalence truncations +open import group-theory.precategory-of-group-actions funext univalence truncations +open import group-theory.symmetric-groups funext univalence truncations ```
diff --git a/src/group-theory/surjective-group-homomorphisms.lagda.md b/src/group-theory/surjective-group-homomorphisms.lagda.md index c482bc5e50..6fac00dc4c 100644 --- a/src/group-theory/surjective-group-homomorphisms.lagda.md +++ b/src/group-theory/surjective-group-homomorphisms.lagda.md @@ -1,21 +1,30 @@ # Surjective group homomorphisms ```agda -module group-theory.surjective-group-homomorphisms where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.surjective-group-homomorphisms + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.propositions -open import foundation.surjective-maps +open import foundation.dependent-products-propositions funext +open import foundation.propositions funext univalence +open import foundation.surjective-maps funext univalence truncations open import foundation.universe-levels -open import group-theory.full-subgroups -open import group-theory.groups -open import group-theory.homomorphisms-groups -open import group-theory.images-of-group-homomorphisms -open import group-theory.surjective-semigroup-homomorphisms +open import group-theory.full-subgroups funext univalence truncations +open import group-theory.groups funext univalence truncations +open import group-theory.homomorphisms-groups funext univalence truncations +open import group-theory.images-of-group-homomorphisms funext univalence truncations +open import group-theory.surjective-semigroup-homomorphisms funext univalence truncations ```
diff --git a/src/group-theory/surjective-semigroup-homomorphisms.lagda.md b/src/group-theory/surjective-semigroup-homomorphisms.lagda.md index e112844df8..afcfe4418e 100644 --- a/src/group-theory/surjective-semigroup-homomorphisms.lagda.md +++ b/src/group-theory/surjective-semigroup-homomorphisms.lagda.md @@ -1,20 +1,29 @@ # Surjective semigroup homomorphisms ```agda -module group-theory.surjective-semigroup-homomorphisms where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.surjective-semigroup-homomorphisms + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.propositions -open import foundation.surjective-maps +open import foundation.dependent-products-propositions funext +open import foundation.propositions funext univalence +open import foundation.surjective-maps funext univalence truncations open import foundation.universe-levels -open import group-theory.full-subsemigroups -open import group-theory.homomorphisms-semigroups -open import group-theory.images-of-semigroup-homomorphisms -open import group-theory.semigroups +open import group-theory.full-subsemigroups funext univalence truncations +open import group-theory.homomorphisms-semigroups funext univalence truncations +open import group-theory.images-of-semigroup-homomorphisms funext univalence truncations +open import group-theory.semigroups funext univalence ```
diff --git a/src/group-theory/symmetric-concrete-groups.lagda.md b/src/group-theory/symmetric-concrete-groups.lagda.md index 006ef44e03..90edda4ad4 100644 --- a/src/group-theory/symmetric-concrete-groups.lagda.md +++ b/src/group-theory/symmetric-concrete-groups.lagda.md @@ -1,22 +1,30 @@ # Symmetric concrete groups ```agda -module group-theory.symmetric-concrete-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.symmetric-concrete-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.identity-types -open import foundation.mere-equality -open import foundation.sets +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.mere-equality funext univalence truncations +open import foundation.sets funext univalence open import foundation.subtype-identity-principle open import foundation.universe-levels -open import group-theory.automorphism-groups -open import group-theory.concrete-groups +open import group-theory.automorphism-groups funext univalence truncations +open import group-theory.concrete-groups funext univalence truncations ```
diff --git a/src/group-theory/symmetric-groups.lagda.md b/src/group-theory/symmetric-groups.lagda.md index bb5b38be9e..a22435d788 100644 --- a/src/group-theory/symmetric-groups.lagda.md +++ b/src/group-theory/symmetric-groups.lagda.md @@ -1,31 +1,39 @@ # Symmetric groups ```agda -module group-theory.symmetric-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.symmetric-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.automorphisms +open import foundation.automorphisms funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.identity-types -open import foundation.sets -open import foundation.subtypes +open import foundation.equivalences funext +open import foundation.function-extensionality funext +open import foundation.identity-types funext +open import foundation.sets funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels -open import group-theory.concrete-groups -open import group-theory.groups -open import group-theory.homomorphisms-groups -open import group-theory.homomorphisms-semigroups -open import group-theory.isomorphisms-groups -open import group-theory.monoids -open import group-theory.opposite-groups -open import group-theory.semigroups -open import group-theory.symmetric-concrete-groups +open import group-theory.concrete-groups funext univalence truncations +open import group-theory.groups funext univalence truncations +open import group-theory.homomorphisms-groups funext univalence truncations +open import group-theory.homomorphisms-semigroups funext univalence truncations +open import group-theory.isomorphisms-groups funext univalence truncations +open import group-theory.monoids funext univalence truncations +open import group-theory.opposite-groups funext univalence truncations +open import group-theory.semigroups funext univalence +open import group-theory.symmetric-concrete-groups funext univalence truncations ```
diff --git a/src/group-theory/torsion-elements-groups.lagda.md b/src/group-theory/torsion-elements-groups.lagda.md index 9b7a129185..46effb86d9 100644 --- a/src/group-theory/torsion-elements-groups.lagda.md +++ b/src/group-theory/torsion-elements-groups.lagda.md @@ -1,24 +1,33 @@ # Torsion elements of groups ```agda -module group-theory.torsion-elements-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.torsion-elements-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import elementary-number-theory.integers -open import elementary-number-theory.nonzero-integers +open import elementary-number-theory.nonzero-integers funext univalence truncations open import foundation.dependent-pair-types -open import foundation.existential-quantification -open import foundation.identity-types -open import foundation.propositions -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.existential-quantification funext univalence truncations +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels -open import group-theory.groups -open import group-theory.integer-powers-of-elements-groups +open import group-theory.groups funext univalence truncations +open import group-theory.integer-powers-of-elements-groups funext univalence truncations ```
diff --git a/src/group-theory/torsion-free-groups.lagda.md b/src/group-theory/torsion-free-groups.lagda.md index d7e4ed6170..553da9ce26 100644 --- a/src/group-theory/torsion-free-groups.lagda.md +++ b/src/group-theory/torsion-free-groups.lagda.md @@ -1,34 +1,44 @@ # Torsion-free groups ```agda -module group-theory.torsion-free-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.torsion-free-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.group-of-integers -open import elementary-number-theory.nonzero-integers +open import elementary-number-theory.group-of-integers funext univalence truncations +open import elementary-number-theory.nonzero-integers funext univalence truncations open import foundation.action-on-identifications-functions -open import foundation.contractible-types +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.existential-quantification +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.existential-quantification funext univalence truncations open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.propositions -open import foundation.sets -open import foundation.singleton-subtypes -open import foundation.standard-pullbacks +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.singleton-subtypes funext univalence truncations +open import foundation.standard-pullbacks funext open import foundation.universe-levels -open import group-theory.groups -open import group-theory.integer-powers-of-elements-groups -open import group-theory.orders-of-elements-groups -open import group-theory.subgroups -open import group-theory.torsion-elements-groups +open import group-theory.groups funext univalence truncations +open import group-theory.integer-powers-of-elements-groups funext univalence truncations +open import group-theory.orders-of-elements-groups funext univalence truncations +open import group-theory.subgroups funext univalence truncations +open import group-theory.torsion-elements-groups funext univalence truncations ```
diff --git a/src/group-theory/torsors.lagda.md b/src/group-theory/torsors.lagda.md index 0e1b1d1375..efc01e1b4c 100644 --- a/src/group-theory/torsors.lagda.md +++ b/src/group-theory/torsors.lagda.md @@ -1,42 +1,51 @@ # Torsors of abstract groups ```agda -module group-theory.torsors where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.torsors + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.0-connected-types +open import foundation.0-connected-types funext univalence truncations open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.mere-equality -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.retractions -open import foundation.sections -open import foundation.sets +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.mere-equality funext univalence truncations +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence +open import foundation.retractions funext +open import foundation.sections funext +open import foundation.sets funext univalence open import foundation.subtype-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext univalence truncations open import foundation.transport-along-identifications open import foundation.universe-levels -open import group-theory.concrete-groups -open import group-theory.equivalences-group-actions -open import group-theory.group-actions -open import group-theory.groups -open import group-theory.homomorphisms-groups -open import group-theory.isomorphisms-groups -open import group-theory.mere-equivalences-group-actions -open import group-theory.principal-group-actions -open import group-theory.symmetric-groups - -open import higher-group-theory.higher-groups +open import group-theory.concrete-groups funext univalence truncations +open import group-theory.equivalences-group-actions funext univalence truncations +open import group-theory.group-actions funext univalence truncations +open import group-theory.groups funext univalence truncations +open import group-theory.homomorphisms-groups funext univalence truncations +open import group-theory.isomorphisms-groups funext univalence truncations +open import group-theory.mere-equivalences-group-actions funext univalence truncations +open import group-theory.principal-group-actions funext univalence truncations +open import group-theory.symmetric-groups funext univalence truncations + +open import higher-group-theory.higher-groups funext univalence truncations ```
diff --git a/src/group-theory/transitive-concrete-group-actions.lagda.md b/src/group-theory/transitive-concrete-group-actions.lagda.md index f6af5d47b3..4208816e5f 100644 --- a/src/group-theory/transitive-concrete-group-actions.lagda.md +++ b/src/group-theory/transitive-concrete-group-actions.lagda.md @@ -1,32 +1,41 @@ # Transitive concrete group actions ```agda -module group-theory.transitive-concrete-group-actions where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.transitive-concrete-group-actions + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.1-types +open import foundation.1-types funext univalence open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.existential-quantification -open import foundation.function-types -open import foundation.identity-types -open import foundation.inhabited-types -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.sets -open import foundation.subtypes -open import foundation.surjective-maps +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.existential-quantification funext univalence truncations +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.inhabited-types funext univalence truncations +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.subtypes funext univalence truncations +open import foundation.surjective-maps funext univalence truncations open import foundation.universe-levels -open import group-theory.concrete-group-actions -open import group-theory.concrete-groups -open import group-theory.equivalences-concrete-group-actions +open import group-theory.concrete-group-actions funext univalence truncations +open import group-theory.concrete-groups funext univalence truncations +open import group-theory.equivalences-concrete-group-actions funext univalence truncations -open import higher-group-theory.transitive-higher-group-actions +open import higher-group-theory.transitive-higher-group-actions funext univalence truncations ```
diff --git a/src/group-theory/transitive-group-actions.lagda.md b/src/group-theory/transitive-group-actions.lagda.md index c8513a1bf5..0e240187f5 100644 --- a/src/group-theory/transitive-group-actions.lagda.md +++ b/src/group-theory/transitive-group-actions.lagda.md @@ -1,20 +1,29 @@ # Transitive group actions ```agda -module group-theory.transitive-group-actions where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.transitive-group-actions + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.existential-quantification -open import foundation.identity-types -open import foundation.propositions -open import foundation.surjective-maps +open import foundation.dependent-products-propositions funext +open import foundation.existential-quantification funext univalence truncations +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.surjective-maps funext univalence truncations open import foundation.universe-levels -open import group-theory.group-actions -open import group-theory.groups +open import group-theory.group-actions funext univalence truncations +open import group-theory.groups funext univalence truncations ```
diff --git a/src/group-theory/trivial-concrete-groups.lagda.md b/src/group-theory/trivial-concrete-groups.lagda.md index 0c939f55de..42b29a61c8 100644 --- a/src/group-theory/trivial-concrete-groups.lagda.md +++ b/src/group-theory/trivial-concrete-groups.lagda.md @@ -1,22 +1,33 @@ # Trivial concrete groups ```agda -module group-theory.trivial-concrete-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.trivial-concrete-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.contractible-types +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.propositions +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.propositions funext univalence +open import foundation.raising-universe-levels-unit-type open import foundation.truncation-levels open import foundation.unit-type open import foundation.universe-levels -open import group-theory.concrete-groups +open import group-theory.concrete-groups funext univalence truncations -open import higher-group-theory.trivial-higher-groups +open import higher-group-theory.trivial-higher-groups funext univalence truncations ```
diff --git a/src/group-theory/trivial-group-homomorphisms.lagda.md b/src/group-theory/trivial-group-homomorphisms.lagda.md index 3cc3b50278..acfeb81fd6 100644 --- a/src/group-theory/trivial-group-homomorphisms.lagda.md +++ b/src/group-theory/trivial-group-homomorphisms.lagda.md @@ -1,20 +1,29 @@ # Trivial group homomorphisms ```agda -module group-theory.trivial-group-homomorphisms where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.trivial-group-homomorphisms + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets +open import foundation.dependent-products-propositions funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence open import foundation.universe-levels -open import group-theory.groups -open import group-theory.homomorphisms-groups +open import group-theory.groups funext univalence truncations +open import group-theory.homomorphisms-groups funext univalence truncations ```
diff --git a/src/group-theory/trivial-groups.lagda.md b/src/group-theory/trivial-groups.lagda.md index a018e83b69..c9247a8ebc 100644 --- a/src/group-theory/trivial-groups.lagda.md +++ b/src/group-theory/trivial-groups.lagda.md @@ -1,28 +1,39 @@ # Trivial groups ```agda -module group-theory.trivial-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.trivial-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.contractible-types +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.propositions -open import foundation.raising-universe-levels +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence open import foundation.structure-identity-principle open import foundation.unit-type open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.full-subgroups -open import group-theory.groups -open import group-theory.subgroups -open import group-theory.trivial-subgroups +open import foundation-core.raising-universe-levels + +open import group-theory.abelian-groups funext univalence truncations +open import group-theory.full-subgroups funext univalence truncations +open import group-theory.groups funext univalence truncations +open import group-theory.subgroups funext univalence truncations +open import group-theory.trivial-subgroups funext univalence truncations ```
diff --git a/src/group-theory/trivial-subgroups.lagda.md b/src/group-theory/trivial-subgroups.lagda.md index e26bfde47b..a0b3ee5e9a 100644 --- a/src/group-theory/trivial-subgroups.lagda.md +++ b/src/group-theory/trivial-subgroups.lagda.md @@ -1,18 +1,26 @@ # Trivial subgroups ```agda -module group-theory.trivial-subgroups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.trivial-subgroups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import group-theory.groups -open import group-theory.subgroups +open import group-theory.groups funext univalence truncations +open import group-theory.subgroups funext univalence truncations ```
diff --git a/src/group-theory/unordered-tuples-of-elements-commutative-monoids.lagda.md b/src/group-theory/unordered-tuples-of-elements-commutative-monoids.lagda.md index 55ccfa28c6..02ac34971c 100644 --- a/src/group-theory/unordered-tuples-of-elements-commutative-monoids.lagda.md +++ b/src/group-theory/unordered-tuples-of-elements-commutative-monoids.lagda.md @@ -1,7 +1,15 @@ # Unordered tuples of elements in commutative monoids ```agda -module group-theory.unordered-tuples-of-elements-commutative-monoids where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.unordered-tuples-of-elements-commutative-monoids + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,9 +18,9 @@ module group-theory.unordered-tuples-of-elements-commutative-monoids where open import elementary-number-theory.natural-numbers open import foundation.universe-levels -open import foundation.unordered-tuples +open import foundation.unordered-tuples funext univalence truncations -open import group-theory.commutative-monoids +open import group-theory.commutative-monoids funext univalence truncations ```
diff --git a/src/group-theory/wild-representations-monoids.lagda.md b/src/group-theory/wild-representations-monoids.lagda.md index 153d5c80a5..6a4d8c1e49 100644 --- a/src/group-theory/wild-representations-monoids.lagda.md +++ b/src/group-theory/wild-representations-monoids.lagda.md @@ -1,21 +1,29 @@ # Wild representations of monoids ```agda -module group-theory.wild-representations-monoids where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module group-theory.wild-representations-monoids + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.endomorphisms -open import foundation.function-types -open import foundation.identity-types +open import foundation.endomorphisms funext univalence truncations +open import foundation.function-types funext +open import foundation.identity-types funext open import foundation.universe-levels -open import group-theory.monoids +open import group-theory.monoids funext univalence truncations -open import structured-types.morphisms-wild-monoids +open import structured-types.morphisms-wild-monoids funext univalence truncations ```
diff --git a/src/higher-group-theory.lagda.md b/src/higher-group-theory.lagda.md index 14d69b791a..05af1d9ad4 100644 --- a/src/higher-group-theory.lagda.md +++ b/src/higher-group-theory.lagda.md @@ -3,31 +3,39 @@ ## Modules in the higher group theory namespace ```agda -module higher-group-theory where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom -open import higher-group-theory.abelian-higher-groups public -open import higher-group-theory.automorphism-groups public -open import higher-group-theory.cartesian-products-higher-groups public -open import higher-group-theory.conjugation public -open import higher-group-theory.cyclic-higher-groups public -open import higher-group-theory.deloopable-groups public -open import higher-group-theory.deloopable-h-spaces public -open import higher-group-theory.deloopable-types public -open import higher-group-theory.eilenberg-mac-lane-spaces public -open import higher-group-theory.equivalences-higher-groups public -open import higher-group-theory.fixed-points-higher-group-actions public -open import higher-group-theory.free-higher-group-actions public -open import higher-group-theory.higher-group-actions public -open import higher-group-theory.higher-groups public -open import higher-group-theory.homomorphisms-higher-group-actions public -open import higher-group-theory.homomorphisms-higher-groups public -open import higher-group-theory.integers-higher-group public -open import higher-group-theory.iterated-cartesian-products-higher-groups public -open import higher-group-theory.iterated-deloopings-of-pointed-types public -open import higher-group-theory.orbits-higher-group-actions public -open import higher-group-theory.small-higher-groups public -open import higher-group-theory.subgroups-higher-groups public -open import higher-group-theory.symmetric-higher-groups public -open import higher-group-theory.transitive-higher-group-actions public -open import higher-group-theory.trivial-higher-groups public +module higher-group-theory + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where + +open import higher-group-theory.abelian-higher-groups funext univalence truncations public +open import higher-group-theory.automorphism-groups funext univalence truncations public +open import higher-group-theory.cartesian-products-higher-groups funext univalence truncations public +open import higher-group-theory.conjugation funext univalence truncations public +open import higher-group-theory.cyclic-higher-groups funext univalence truncations public +open import higher-group-theory.deloopable-groups funext univalence truncations public +open import higher-group-theory.deloopable-h-spaces funext univalence truncations public +open import higher-group-theory.deloopable-types funext univalence truncations public +open import higher-group-theory.eilenberg-mac-lane-spaces funext univalence truncations public +open import higher-group-theory.equivalences-higher-groups funext univalence truncations public +open import higher-group-theory.fixed-points-higher-group-actions funext univalence truncations public +open import higher-group-theory.free-higher-group-actions funext univalence truncations public +open import higher-group-theory.higher-group-actions funext univalence truncations public +open import higher-group-theory.higher-groups funext univalence truncations public +open import higher-group-theory.homomorphisms-higher-group-actions funext univalence truncations public +open import higher-group-theory.homomorphisms-higher-groups funext univalence truncations public +open import higher-group-theory.integers-higher-group funext univalence truncations public +open import higher-group-theory.iterated-cartesian-products-higher-groups funext univalence truncations public +open import higher-group-theory.iterated-deloopings-of-pointed-types funext univalence truncations public +open import higher-group-theory.orbits-higher-group-actions funext univalence truncations public +open import higher-group-theory.small-higher-groups funext univalence truncations public +open import higher-group-theory.subgroups-higher-groups funext univalence truncations public +open import higher-group-theory.symmetric-higher-groups funext univalence truncations public +open import higher-group-theory.transitive-higher-group-actions funext univalence truncations public +open import higher-group-theory.trivial-higher-groups funext univalence truncations public ``` diff --git a/src/higher-group-theory/abelian-higher-groups.lagda.md b/src/higher-group-theory/abelian-higher-groups.lagda.md index cdfe3e08ba..ee368631a4 100644 --- a/src/higher-group-theory/abelian-higher-groups.lagda.md +++ b/src/higher-group-theory/abelian-higher-groups.lagda.md @@ -1,26 +1,34 @@ # Abelian higher groups ```agda -module higher-group-theory.abelian-higher-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module higher-group-theory.abelian-higher-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.small-types +open import foundation.equivalences funext +open import foundation.small-types funext univalence truncations open import foundation.universe-levels -open import higher-group-theory.equivalences-higher-groups -open import higher-group-theory.higher-groups -open import higher-group-theory.small-higher-groups +open import higher-group-theory.equivalences-higher-groups funext univalence truncations +open import higher-group-theory.higher-groups funext univalence truncations +open import higher-group-theory.small-higher-groups funext univalence truncations -open import structured-types.pointed-equivalences +open import structured-types.pointed-equivalences funext univalence truncations open import structured-types.pointed-types -open import structured-types.small-pointed-types +open import structured-types.small-pointed-types funext univalence truncations -open import synthetic-homotopy-theory.connective-spectra +open import synthetic-homotopy-theory.connective-spectra funext univalence truncations ```
diff --git a/src/higher-group-theory/automorphism-groups.lagda.md b/src/higher-group-theory/automorphism-groups.lagda.md index eabdf5bf0f..06f691394d 100644 --- a/src/higher-group-theory/automorphism-groups.lagda.md +++ b/src/higher-group-theory/automorphism-groups.lagda.md @@ -1,30 +1,35 @@ # Automorphism groups ```agda -module higher-group-theory.automorphism-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module higher-group-theory.automorphism-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.0-connected-types -open import foundation.1-types -open import foundation.connected-components -open import foundation.contractible-types +open import foundation.0-connected-types funext univalence truncations +open import foundation.connected-components funext univalence truncations +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences +open import foundation.dependent-products-contractible-types funext +open import foundation.equivalences funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types -open import foundation.propositional-truncations +open import foundation.identity-types funext +open import foundation.propositional-truncations funext univalence open import foundation.subtype-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext univalence truncations open import foundation.universe-levels -open import group-theory.concrete-groups -open import group-theory.equivalences-concrete-groups - -open import higher-group-theory.equivalences-higher-groups -open import higher-group-theory.higher-groups +open import higher-group-theory.equivalences-higher-groups funext univalence truncations +open import higher-group-theory.higher-groups funext univalence truncations open import structured-types.pointed-types ``` diff --git a/src/higher-group-theory/cartesian-products-higher-groups.lagda.md b/src/higher-group-theory/cartesian-products-higher-groups.lagda.md index 2183bb2862..d86cef8efc 100644 --- a/src/higher-group-theory/cartesian-products-higher-groups.lagda.md +++ b/src/higher-group-theory/cartesian-products-higher-groups.lagda.md @@ -1,28 +1,37 @@ # Cartesian products of higher groups ```agda -module higher-group-theory.cartesian-products-higher-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module higher-group-theory.cartesian-products-higher-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.0-connected-types -open import foundation.cartesian-product-types +open import foundation.0-connected-types funext univalence truncations +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions funext open import foundation.equality-cartesian-product-types -open import foundation.equivalences -open import foundation.identity-types -open import foundation.mere-equality -open import foundation.propositions +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.mere-equality funext univalence truncations +open import foundation.propositions funext univalence open import foundation.universe-levels -open import higher-group-theory.higher-groups +open import higher-group-theory.higher-groups funext univalence truncations -open import structured-types.pointed-cartesian-product-types +open import structured-types.pointed-cartesian-product-types funext univalence truncations open import structured-types.pointed-types -open import synthetic-homotopy-theory.loop-spaces +open import synthetic-homotopy-theory.loop-spaces funext univalence truncations ```
diff --git a/src/higher-group-theory/conjugation.lagda.md b/src/higher-group-theory/conjugation.lagda.md index 66e53af615..b1862a0a93 100644 --- a/src/higher-group-theory/conjugation.lagda.md +++ b/src/higher-group-theory/conjugation.lagda.md @@ -1,22 +1,30 @@ # Conjugation in higher groups ```agda -module higher-group-theory.conjugation where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module higher-group-theory.conjugation + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.homotopies -open import foundation.identity-types +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.universe-levels -open import higher-group-theory.higher-groups -open import higher-group-theory.homomorphisms-higher-groups +open import higher-group-theory.higher-groups funext univalence truncations +open import higher-group-theory.homomorphisms-higher-groups funext univalence truncations -open import structured-types.conjugation-pointed-types +open import structured-types.conjugation-pointed-types funext univalence truncations -open import synthetic-homotopy-theory.conjugation-loops +open import synthetic-homotopy-theory.conjugation-loops funext univalence truncations ```
diff --git a/src/higher-group-theory/cyclic-higher-groups.lagda.md b/src/higher-group-theory/cyclic-higher-groups.lagda.md index d9067fb971..e138ae9908 100644 --- a/src/higher-group-theory/cyclic-higher-groups.lagda.md +++ b/src/higher-group-theory/cyclic-higher-groups.lagda.md @@ -1,19 +1,28 @@ # Cyclic higher groups ```agda -module higher-group-theory.cyclic-higher-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module higher-group-theory.cyclic-higher-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.embeddings -open import foundation.existential-quantification -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.embeddings funext +open import foundation.existential-quantification funext univalence truncations +open import foundation.propositions funext univalence open import foundation.universe-levels -open import higher-group-theory.higher-groups -open import higher-group-theory.homomorphisms-higher-groups +open import higher-group-theory.higher-groups funext univalence truncations +open import higher-group-theory.homomorphisms-higher-groups funext univalence truncations ```
diff --git a/src/higher-group-theory/deloopable-groups.lagda.md b/src/higher-group-theory/deloopable-groups.lagda.md index 45c31edf78..ad6508c4ca 100644 --- a/src/higher-group-theory/deloopable-groups.lagda.md +++ b/src/higher-group-theory/deloopable-groups.lagda.md @@ -1,7 +1,15 @@ # Deloopable groups ```agda -module higher-group-theory.deloopable-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module higher-group-theory.deloopable-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,9 +18,9 @@ module higher-group-theory.deloopable-groups where open import foundation.dependent-pair-types open import foundation.universe-levels -open import group-theory.groups +open import group-theory.groups funext univalence truncations -open import higher-group-theory.deloopable-h-spaces +open import higher-group-theory.deloopable-h-spaces funext univalence truncations ```
diff --git a/src/higher-group-theory/deloopable-h-spaces.lagda.md b/src/higher-group-theory/deloopable-h-spaces.lagda.md index 90b0d90e0c..15f84f3d77 100644 --- a/src/higher-group-theory/deloopable-h-spaces.lagda.md +++ b/src/higher-group-theory/deloopable-h-spaces.lagda.md @@ -1,7 +1,15 @@ # Deloopable H-spaces ```agda -module higher-group-theory.deloopable-h-spaces where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module higher-group-theory.deloopable-h-spaces + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,10 +18,10 @@ module higher-group-theory.deloopable-h-spaces where open import foundation.dependent-pair-types open import foundation.universe-levels -open import higher-group-theory.higher-groups +open import higher-group-theory.higher-groups funext univalence truncations -open import structured-types.equivalences-h-spaces -open import structured-types.h-spaces +open import structured-types.equivalences-h-spaces funext univalence truncations +open import structured-types.h-spaces funext univalence truncations ```
diff --git a/src/higher-group-theory/deloopable-types.lagda.md b/src/higher-group-theory/deloopable-types.lagda.md index 23e7bac773..19c3f4c108 100644 --- a/src/higher-group-theory/deloopable-types.lagda.md +++ b/src/higher-group-theory/deloopable-types.lagda.md @@ -1,24 +1,32 @@ # Deloopable types ```agda -module higher-group-theory.deloopable-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module higher-group-theory.deloopable-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.small-types +open import foundation.equivalences funext +open import foundation.small-types funext univalence truncations open import foundation.universe-levels -open import higher-group-theory.equivalences-higher-groups -open import higher-group-theory.higher-groups -open import higher-group-theory.small-higher-groups +open import higher-group-theory.equivalences-higher-groups funext univalence truncations +open import higher-group-theory.higher-groups funext univalence truncations +open import higher-group-theory.small-higher-groups funext univalence truncations -open import structured-types.pointed-equivalences +open import structured-types.pointed-equivalences funext univalence truncations open import structured-types.pointed-types -open import structured-types.small-pointed-types +open import structured-types.small-pointed-types funext univalence truncations ```
diff --git a/src/higher-group-theory/eilenberg-mac-lane-spaces.lagda.md b/src/higher-group-theory/eilenberg-mac-lane-spaces.lagda.md index 13a8cf9fab..a4cf018a73 100644 --- a/src/higher-group-theory/eilenberg-mac-lane-spaces.lagda.md +++ b/src/higher-group-theory/eilenberg-mac-lane-spaces.lagda.md @@ -1,7 +1,15 @@ # Eilenberg-Mac Lane spaces ```agda -module higher-group-theory.eilenberg-mac-lane-spaces where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module higher-group-theory.eilenberg-mac-lane-spaces + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,22 +17,23 @@ module higher-group-theory.eilenberg-mac-lane-spaces where ```agda open import elementary-number-theory.natural-numbers -open import foundation.0-connected-types -open import foundation.cartesian-product-types -open import foundation.connected-types -open import foundation.truncated-types +open import foundation.0-connected-types funext univalence truncations +open import foundation.cartesian-product-types funext univalence +open import foundation.connected-types funext univalence truncations +open import foundation.dependent-products-truncated-types funext +open import foundation.truncated-types funext univalence open import foundation.truncation-levels open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.groups +open import group-theory.abelian-groups funext univalence truncations +open import group-theory.groups funext univalence truncations -open import structured-types.equivalences-h-spaces -open import structured-types.pointed-equivalences +open import structured-types.equivalences-h-spaces funext univalence truncations +open import structured-types.pointed-equivalences funext univalence truncations open import structured-types.pointed-types -open import synthetic-homotopy-theory.iterated-loop-spaces -open import synthetic-homotopy-theory.loop-spaces +open import synthetic-homotopy-theory.iterated-loop-spaces funext univalence truncations +open import synthetic-homotopy-theory.loop-spaces funext univalence truncations ```
diff --git a/src/higher-group-theory/equivalences-higher-groups.lagda.md b/src/higher-group-theory/equivalences-higher-groups.lagda.md index c494c345cf..d46c620606 100644 --- a/src/higher-group-theory/equivalences-higher-groups.lagda.md +++ b/src/higher-group-theory/equivalences-higher-groups.lagda.md @@ -1,30 +1,38 @@ # Equivalences of higher groups ```agda -module higher-group-theory.equivalences-higher-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module higher-group-theory.equivalences-higher-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.0-connected-types +open import foundation.0-connected-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types +open import foundation.equivalences funext +open import foundation.function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.subtype-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext univalence truncations open import foundation.universe-levels -open import higher-group-theory.higher-groups -open import higher-group-theory.homomorphisms-higher-groups +open import higher-group-theory.higher-groups funext univalence truncations +open import higher-group-theory.homomorphisms-higher-groups funext univalence truncations -open import structured-types.pointed-equivalences -open import structured-types.pointed-isomorphisms +open import structured-types.pointed-equivalences funext univalence truncations +open import structured-types.pointed-isomorphisms funext univalence truncations open import structured-types.pointed-types -open import synthetic-homotopy-theory.functoriality-loop-spaces +open import synthetic-homotopy-theory.functoriality-loop-spaces funext univalence truncations ```
diff --git a/src/higher-group-theory/fixed-points-higher-group-actions.lagda.md b/src/higher-group-theory/fixed-points-higher-group-actions.lagda.md index 4dfdc5fb40..1d8e1c1428 100644 --- a/src/higher-group-theory/fixed-points-higher-group-actions.lagda.md +++ b/src/higher-group-theory/fixed-points-higher-group-actions.lagda.md @@ -1,7 +1,15 @@ # Fixed points of higher group actions ```agda -module higher-group-theory.fixed-points-higher-group-actions where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module higher-group-theory.fixed-points-higher-group-actions + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,8 +17,8 @@ module higher-group-theory.fixed-points-higher-group-actions where ```agda open import foundation.universe-levels -open import higher-group-theory.higher-group-actions -open import higher-group-theory.higher-groups +open import higher-group-theory.higher-group-actions funext univalence truncations +open import higher-group-theory.higher-groups funext univalence truncations ```
diff --git a/src/higher-group-theory/free-higher-group-actions.lagda.md b/src/higher-group-theory/free-higher-group-actions.lagda.md index ea43e3e1b2..c2b05e65bf 100644 --- a/src/higher-group-theory/free-higher-group-actions.lagda.md +++ b/src/higher-group-theory/free-higher-group-actions.lagda.md @@ -1,27 +1,36 @@ # Free higher group actions ```agda -module higher-group-theory.free-higher-group-actions where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module higher-group-theory.free-higher-group-actions + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.embeddings -open import foundation.identity-types -open import foundation.propositional-maps -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.regensburg-extension-fundamental-theorem-of-identity-types -open import foundation.sets -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.embeddings funext +open import foundation.identity-types funext +open import foundation.propositional-maps funext +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence +open import foundation.regensburg-extension-fundamental-theorem-of-identity-types funext univalence truncations +open import foundation.sets funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.transport-along-identifications open import foundation.truncation-levels open import foundation.universe-levels -open import higher-group-theory.higher-group-actions -open import higher-group-theory.higher-groups -open import higher-group-theory.orbits-higher-group-actions +open import higher-group-theory.higher-group-actions funext univalence truncations +open import higher-group-theory.higher-groups funext univalence truncations +open import higher-group-theory.orbits-higher-group-actions funext univalence truncations ```
diff --git a/src/higher-group-theory/higher-group-actions.lagda.md b/src/higher-group-theory/higher-group-actions.lagda.md index 67119d09c0..4e80bda806 100644 --- a/src/higher-group-theory/higher-group-actions.lagda.md +++ b/src/higher-group-theory/higher-group-actions.lagda.md @@ -1,17 +1,25 @@ # Higher group actions ```agda -module higher-group-theory.higher-group-actions where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module higher-group-theory.higher-group-actions + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import higher-group-theory.higher-groups +open import higher-group-theory.higher-groups funext univalence truncations ```
diff --git a/src/higher-group-theory/higher-groups.lagda.md b/src/higher-group-theory/higher-groups.lagda.md index 6102d85536..e8a7b42eef 100644 --- a/src/higher-group-theory/higher-groups.lagda.md +++ b/src/higher-group-theory/higher-groups.lagda.md @@ -1,28 +1,37 @@ # Higher groups ```agda -module higher-group-theory.higher-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module higher-group-theory.higher-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.0-connected-types +open import foundation.0-connected-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.full-subtypes -open import foundation.identity-types -open import foundation.images -open import foundation.mere-equality -open import foundation.propositional-truncations -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.full-subtypes funext univalence truncations +open import foundation.identity-types funext +open import foundation.images funext univalence truncations +open import foundation.mere-equality funext univalence truncations +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence open import foundation.unit-type open import foundation.universe-levels -open import structured-types.h-spaces +open import structured-types.h-spaces funext univalence truncations open import structured-types.pointed-types -open import synthetic-homotopy-theory.loop-spaces +open import synthetic-homotopy-theory.loop-spaces funext univalence truncations ```
diff --git a/src/higher-group-theory/homomorphisms-higher-group-actions.lagda.md b/src/higher-group-theory/homomorphisms-higher-group-actions.lagda.md index 5929ab0dbc..559d5a9701 100644 --- a/src/higher-group-theory/homomorphisms-higher-group-actions.lagda.md +++ b/src/higher-group-theory/homomorphisms-higher-group-actions.lagda.md @@ -1,22 +1,30 @@ # Homomorphisms of higher group actions ```agda -module higher-group-theory.homomorphisms-higher-group-actions where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module higher-group-theory.homomorphisms-higher-group-actions + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.equality-dependent-function-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.homotopies -open import foundation.identity-types +open import foundation.equality-dependent-function-types funext +open import foundation.equivalences funext +open import foundation.function-extensionality funext +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import higher-group-theory.higher-group-actions -open import higher-group-theory.higher-groups +open import higher-group-theory.higher-group-actions funext univalence truncations +open import higher-group-theory.higher-groups funext univalence truncations ```
diff --git a/src/higher-group-theory/homomorphisms-higher-groups.lagda.md b/src/higher-group-theory/homomorphisms-higher-groups.lagda.md index cd94013ef2..e982b71e3d 100644 --- a/src/higher-group-theory/homomorphisms-higher-groups.lagda.md +++ b/src/higher-group-theory/homomorphisms-higher-groups.lagda.md @@ -1,22 +1,30 @@ # Homomorphisms of higher groups ```agda -module higher-group-theory.homomorphisms-higher-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module higher-group-theory.homomorphisms-higher-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.equivalences -open import foundation.identity-types +open import foundation.equivalences funext +open import foundation.identity-types funext open import foundation.universe-levels -open import higher-group-theory.higher-groups +open import higher-group-theory.higher-groups funext univalence truncations -open import structured-types.pointed-homotopies -open import structured-types.pointed-maps +open import structured-types.pointed-homotopies funext univalence truncations +open import structured-types.pointed-maps funext univalence truncations -open import synthetic-homotopy-theory.functoriality-loop-spaces +open import synthetic-homotopy-theory.functoriality-loop-spaces funext univalence truncations ```
diff --git a/src/higher-group-theory/integers-higher-group.lagda.md b/src/higher-group-theory/integers-higher-group.lagda.md index 7220677f16..114f1da5fc 100644 --- a/src/higher-group-theory/integers-higher-group.lagda.md +++ b/src/higher-group-theory/integers-higher-group.lagda.md @@ -1,7 +1,15 @@ # The higher group of integers ```agda -module higher-group-theory.integers-higher-group where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module higher-group-theory.integers-higher-group + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,11 +18,11 @@ module higher-group-theory.integers-higher-group where open import foundation.dependent-pair-types open import foundation.universe-levels -open import higher-group-theory.higher-groups +open import higher-group-theory.higher-groups funext univalence truncations open import structured-types.pointed-types -open import synthetic-homotopy-theory.circle +open import synthetic-homotopy-theory.circle funext univalence truncations ```
diff --git a/src/higher-group-theory/iterated-cartesian-products-higher-groups.lagda.md b/src/higher-group-theory/iterated-cartesian-products-higher-groups.lagda.md index e9a5b7aaab..90328e664b 100644 --- a/src/higher-group-theory/iterated-cartesian-products-higher-groups.lagda.md +++ b/src/higher-group-theory/iterated-cartesian-products-higher-groups.lagda.md @@ -1,7 +1,15 @@ # Iterated cartesian products of higher groups ```agda -module higher-group-theory.iterated-cartesian-products-higher-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module higher-group-theory.iterated-cartesian-products-higher-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,30 +17,33 @@ module higher-group-theory.iterated-cartesian-products-higher-groups where ```agda open import elementary-number-theory.natural-numbers -open import foundation.0-connected-types -open import foundation.contractible-types -open import foundation.coproduct-types +open import foundation.0-connected-types funext univalence truncations +open import foundation.contractible-types funext univalence +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-cartesian-product-types -open import foundation.identity-types -open import foundation.iterated-cartesian-product-types -open import foundation.mere-equality -open import foundation.propositions -open import foundation.sets +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.identity-types funext +open import foundation.iterated-cartesian-product-types funext univalence truncations +open import foundation.mere-equality funext univalence truncations +open import foundation.propositions funext univalence +open import foundation.raising-universe-levels-unit-type +open import foundation.sets funext univalence open import foundation.unit-type open import foundation.universe-levels -open import higher-group-theory.cartesian-products-higher-groups -open import higher-group-theory.higher-groups -open import higher-group-theory.trivial-higher-groups +open import higher-group-theory.cartesian-products-higher-groups funext univalence truncations +open import higher-group-theory.higher-groups funext univalence truncations +open import higher-group-theory.trivial-higher-groups funext univalence truncations open import structured-types.pointed-types -open import synthetic-homotopy-theory.loop-spaces +open import synthetic-homotopy-theory.loop-spaces funext univalence truncations -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/higher-group-theory/iterated-deloopings-of-pointed-types.lagda.md b/src/higher-group-theory/iterated-deloopings-of-pointed-types.lagda.md index d5f051b7fd..c66681691a 100644 --- a/src/higher-group-theory/iterated-deloopings-of-pointed-types.lagda.md +++ b/src/higher-group-theory/iterated-deloopings-of-pointed-types.lagda.md @@ -1,7 +1,15 @@ # Iterated deloopings of pointed types ```agda -module higher-group-theory.iterated-deloopings-of-pointed-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module higher-group-theory.iterated-deloopings-of-pointed-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,16 +17,16 @@ module higher-group-theory.iterated-deloopings-of-pointed-types where ```agda open import elementary-number-theory.natural-numbers -open import foundation.cartesian-product-types -open import foundation.connected-types +open import foundation.cartesian-product-types funext univalence +open import foundation.connected-types funext univalence truncations open import foundation.dependent-pair-types open import foundation.truncation-levels open import foundation.universe-levels -open import structured-types.pointed-equivalences +open import structured-types.pointed-equivalences funext univalence truncations open import structured-types.pointed-types -open import synthetic-homotopy-theory.iterated-loop-spaces +open import synthetic-homotopy-theory.iterated-loop-spaces funext univalence truncations ```
diff --git a/src/higher-group-theory/orbits-higher-group-actions.lagda.md b/src/higher-group-theory/orbits-higher-group-actions.lagda.md index 69003ac59b..bdb1462613 100644 --- a/src/higher-group-theory/orbits-higher-group-actions.lagda.md +++ b/src/higher-group-theory/orbits-higher-group-actions.lagda.md @@ -1,7 +1,15 @@ # Orbits of higher group actions ```agda -module higher-group-theory.orbits-higher-group-actions where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module higher-group-theory.orbits-higher-group-actions + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,8 +18,8 @@ module higher-group-theory.orbits-higher-group-actions where open import foundation.dependent-pair-types open import foundation.universe-levels -open import higher-group-theory.higher-group-actions -open import higher-group-theory.higher-groups +open import higher-group-theory.higher-group-actions funext univalence truncations +open import higher-group-theory.higher-groups funext univalence truncations ```
diff --git a/src/higher-group-theory/small-higher-groups.lagda.md b/src/higher-group-theory/small-higher-groups.lagda.md index 0252d1093d..8b22786df8 100644 --- a/src/higher-group-theory/small-higher-groups.lagda.md +++ b/src/higher-group-theory/small-higher-groups.lagda.md @@ -1,32 +1,41 @@ # Small ∞-groups ```agda -module higher-group-theory.small-higher-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module higher-group-theory.small-higher-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.0-connected-types +open import foundation.0-connected-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.identity-types -open import foundation.images -open import foundation.locally-small-types -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.replacement -open import foundation.small-types +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.images funext univalence truncations +open import foundation.locally-small-types funext univalence truncations +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence +open import foundation.replacement funext univalence truncations +open import foundation.small-types funext univalence truncations open import foundation.type-arithmetic-dependent-pair-types open import foundation.unit-type open import foundation.universe-levels -open import higher-group-theory.equivalences-higher-groups -open import higher-group-theory.higher-groups +open import higher-group-theory.equivalences-higher-groups funext univalence truncations +open import higher-group-theory.higher-groups funext univalence truncations -open import structured-types.pointed-equivalences +open import structured-types.pointed-equivalences funext univalence truncations open import structured-types.pointed-types -open import structured-types.small-pointed-types +open import structured-types.small-pointed-types funext univalence truncations ```
diff --git a/src/higher-group-theory/subgroups-higher-groups.lagda.md b/src/higher-group-theory/subgroups-higher-groups.lagda.md index 14e6b1ebce..123590b49f 100644 --- a/src/higher-group-theory/subgroups-higher-groups.lagda.md +++ b/src/higher-group-theory/subgroups-higher-groups.lagda.md @@ -1,20 +1,28 @@ # Subgroups of higher groups ```agda -module higher-group-theory.subgroups-higher-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module higher-group-theory.subgroups-higher-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.0-connected-types -open import foundation.cartesian-product-types +open import foundation.0-connected-types funext univalence truncations +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.sets +open import foundation.function-types funext +open import foundation.sets funext univalence open import foundation.universe-levels -open import higher-group-theory.higher-groups +open import higher-group-theory.higher-groups funext univalence truncations open import structured-types.pointed-types ``` diff --git a/src/higher-group-theory/symmetric-higher-groups.lagda.md b/src/higher-group-theory/symmetric-higher-groups.lagda.md index 9af7adc4fe..8b7eff4943 100644 --- a/src/higher-group-theory/symmetric-higher-groups.lagda.md +++ b/src/higher-group-theory/symmetric-higher-groups.lagda.md @@ -1,19 +1,27 @@ # Symmetric higher groups ```agda -module higher-group-theory.symmetric-higher-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module higher-group-theory.symmetric-higher-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.0-connected-types -open import foundation.connected-components-universes +open import foundation.0-connected-types funext univalence truncations +open import foundation.connected-components-universes funext univalence truncations open import foundation.dependent-pair-types -open import foundation.mere-equivalences +open import foundation.mere-equivalences funext univalence truncations open import foundation.universe-levels -open import higher-group-theory.higher-groups +open import higher-group-theory.higher-groups funext univalence truncations open import structured-types.pointed-types ``` diff --git a/src/higher-group-theory/transitive-higher-group-actions.lagda.md b/src/higher-group-theory/transitive-higher-group-actions.lagda.md index a6a4b3f711..83ecac6255 100644 --- a/src/higher-group-theory/transitive-higher-group-actions.lagda.md +++ b/src/higher-group-theory/transitive-higher-group-actions.lagda.md @@ -1,26 +1,35 @@ # Transitive higher group actions ```agda -module higher-group-theory.transitive-higher-group-actions where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module higher-group-theory.transitive-higher-group-actions + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.0-connected-types +open import foundation.0-connected-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.inhabited-types -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.regensburg-extension-fundamental-theorem-of-identity-types -open import foundation.surjective-maps +open import foundation.dependent-products-propositions funext +open import foundation.identity-types funext +open import foundation.inhabited-types funext univalence truncations +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence +open import foundation.regensburg-extension-fundamental-theorem-of-identity-types funext univalence truncations +open import foundation.surjective-maps funext univalence truncations open import foundation.transport-along-identifications open import foundation.universe-levels -open import higher-group-theory.higher-group-actions -open import higher-group-theory.higher-groups -open import higher-group-theory.orbits-higher-group-actions +open import higher-group-theory.higher-group-actions funext univalence truncations +open import higher-group-theory.higher-groups funext univalence truncations +open import higher-group-theory.orbits-higher-group-actions funext univalence truncations ```
diff --git a/src/higher-group-theory/trivial-higher-groups.lagda.md b/src/higher-group-theory/trivial-higher-groups.lagda.md index 18edbed574..e1e3f11898 100644 --- a/src/higher-group-theory/trivial-higher-groups.lagda.md +++ b/src/higher-group-theory/trivial-higher-groups.lagda.md @@ -1,20 +1,31 @@ # Trivial higher groups ```agda -module higher-group-theory.trivial-higher-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module higher-group-theory.trivial-higher-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.0-connected-types -open import foundation.contractible-types +open import foundation.0-connected-types funext univalence truncations +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.propositions +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.propositions funext univalence +open import foundation.raising-universe-levels-unit-type open import foundation.unit-type open import foundation.universe-levels -open import higher-group-theory.higher-groups +open import higher-group-theory.higher-groups funext univalence truncations ```
diff --git a/src/linear-algebra.lagda.md b/src/linear-algebra.lagda.md index 883be1c3fa..8fd89fbcfb 100644 --- a/src/linear-algebra.lagda.md +++ b/src/linear-algebra.lagda.md @@ -3,24 +3,32 @@ ## Modules in the linear algebra namespace ```agda -module linear-algebra where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom -open import linear-algebra.constant-matrices public -open import linear-algebra.constant-vectors public -open import linear-algebra.diagonal-matrices-on-rings public -open import linear-algebra.functoriality-matrices public -open import linear-algebra.functoriality-vectors public -open import linear-algebra.matrices public -open import linear-algebra.matrices-on-rings public +module linear-algebra + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where + +open import linear-algebra.constant-matrices funext univalence truncations public +open import linear-algebra.constant-vectors funext univalence truncations public +open import linear-algebra.diagonal-matrices-on-rings funext univalence truncations public +open import linear-algebra.functoriality-matrices funext univalence truncations public +open import linear-algebra.functoriality-vectors funext univalence truncations public +open import linear-algebra.matrices funext univalence truncations public +open import linear-algebra.matrices-on-rings funext univalence truncations public open import linear-algebra.multiplication-matrices public -open import linear-algebra.scalar-multiplication-matrices public -open import linear-algebra.scalar-multiplication-vectors public -open import linear-algebra.scalar-multiplication-vectors-on-rings public -open import linear-algebra.transposition-matrices public -open import linear-algebra.vectors public -open import linear-algebra.vectors-on-commutative-rings public -open import linear-algebra.vectors-on-commutative-semirings public -open import linear-algebra.vectors-on-euclidean-domains public -open import linear-algebra.vectors-on-rings public -open import linear-algebra.vectors-on-semirings public +open import linear-algebra.scalar-multiplication-matrices funext univalence truncations public +open import linear-algebra.scalar-multiplication-vectors funext univalence truncations public +open import linear-algebra.scalar-multiplication-vectors-on-rings funext univalence truncations public +open import linear-algebra.transposition-matrices funext univalence truncations public +open import linear-algebra.vectors funext univalence truncations public +open import linear-algebra.vectors-on-commutative-rings funext univalence truncations public +open import linear-algebra.vectors-on-commutative-semirings funext univalence truncations public +open import linear-algebra.vectors-on-euclidean-domains funext univalence truncations public +open import linear-algebra.vectors-on-rings funext univalence truncations public +open import linear-algebra.vectors-on-semirings funext univalence truncations public ``` diff --git a/src/linear-algebra/constant-matrices.lagda.md b/src/linear-algebra/constant-matrices.lagda.md index 03b95489d8..c64d8e2c75 100644 --- a/src/linear-algebra/constant-matrices.lagda.md +++ b/src/linear-algebra/constant-matrices.lagda.md @@ -1,7 +1,15 @@ # Constant matrices ```agda -module linear-algebra.constant-matrices where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module linear-algebra.constant-matrices + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -11,8 +19,8 @@ open import elementary-number-theory.natural-numbers open import foundation.universe-levels -open import linear-algebra.constant-vectors -open import linear-algebra.matrices +open import linear-algebra.constant-vectors funext univalence truncations +open import linear-algebra.matrices funext univalence truncations ```
diff --git a/src/linear-algebra/constant-vectors.lagda.md b/src/linear-algebra/constant-vectors.lagda.md index 11b8372bc9..c3b3e6b564 100644 --- a/src/linear-algebra/constant-vectors.lagda.md +++ b/src/linear-algebra/constant-vectors.lagda.md @@ -1,7 +1,15 @@ # Diagonal vectors ```agda -module linear-algebra.constant-vectors where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module linear-algebra.constant-vectors + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -11,7 +19,7 @@ open import elementary-number-theory.natural-numbers open import foundation.universe-levels -open import linear-algebra.vectors +open import linear-algebra.vectors funext univalence truncations ```
diff --git a/src/linear-algebra/diagonal-matrices-on-rings.lagda.md b/src/linear-algebra/diagonal-matrices-on-rings.lagda.md index c15d89761a..2415218f8c 100644 --- a/src/linear-algebra/diagonal-matrices-on-rings.lagda.md +++ b/src/linear-algebra/diagonal-matrices-on-rings.lagda.md @@ -1,7 +1,15 @@ # Diagonal matrices on rings ```agda -module linear-algebra.diagonal-matrices-on-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module linear-algebra.diagonal-matrices-on-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -11,13 +19,13 @@ open import elementary-number-theory.natural-numbers open import foundation.universe-levels -open import linear-algebra.constant-vectors -open import linear-algebra.functoriality-vectors -open import linear-algebra.matrices-on-rings -open import linear-algebra.vectors -open import linear-algebra.vectors-on-rings +open import linear-algebra.constant-vectors funext univalence truncations +open import linear-algebra.functoriality-vectors funext univalence truncations +open import linear-algebra.matrices-on-rings funext univalence truncations +open import linear-algebra.vectors funext univalence truncations +open import linear-algebra.vectors-on-rings funext univalence truncations -open import ring-theory.rings +open import ring-theory.rings funext univalence truncations ```
diff --git a/src/linear-algebra/functoriality-matrices.lagda.md b/src/linear-algebra/functoriality-matrices.lagda.md index 1c0b419bd0..68b717b8bd 100644 --- a/src/linear-algebra/functoriality-matrices.lagda.md +++ b/src/linear-algebra/functoriality-matrices.lagda.md @@ -1,7 +1,15 @@ # Functoriality of the type of matrices ```agda -module linear-algebra.functoriality-matrices where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module linear-algebra.functoriality-matrices + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -11,8 +19,8 @@ open import elementary-number-theory.natural-numbers open import foundation.universe-levels -open import linear-algebra.functoriality-vectors -open import linear-algebra.matrices +open import linear-algebra.functoriality-vectors funext univalence truncations +open import linear-algebra.matrices funext univalence truncations ```
diff --git a/src/linear-algebra/functoriality-vectors.lagda.md b/src/linear-algebra/functoriality-vectors.lagda.md index 61c74c2380..c13c3d82e6 100644 --- a/src/linear-algebra/functoriality-vectors.lagda.md +++ b/src/linear-algebra/functoriality-vectors.lagda.md @@ -1,7 +1,15 @@ # Functoriality of the type of vectors ```agda -module linear-algebra.functoriality-vectors where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module linear-algebra.functoriality-vectors + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -11,17 +19,15 @@ open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-binary-functions open import foundation.dependent-pair-types -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.postcomposition-functions +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.postcomposition-functions funext open import foundation.universe-levels -open import foundation.whiskering-homotopies-composition -open import linear-algebra.vectors +open import linear-algebra.vectors funext univalence truncations -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/linear-algebra/matrices-on-rings.lagda.md b/src/linear-algebra/matrices-on-rings.lagda.md index e14bfa5210..02456493fe 100644 --- a/src/linear-algebra/matrices-on-rings.lagda.md +++ b/src/linear-algebra/matrices-on-rings.lagda.md @@ -1,7 +1,15 @@ # Matrices on rings ```agda -module linear-algebra.matrices-on-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module linear-algebra.matrices-on-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,16 +18,16 @@ module linear-algebra.matrices-on-rings where open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-binary-functions -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import linear-algebra.constant-matrices -open import linear-algebra.functoriality-matrices -open import linear-algebra.matrices -open import linear-algebra.vectors -open import linear-algebra.vectors-on-rings +open import linear-algebra.constant-matrices funext univalence truncations +open import linear-algebra.functoriality-matrices funext univalence truncations +open import linear-algebra.matrices funext univalence truncations +open import linear-algebra.vectors funext univalence truncations +open import linear-algebra.vectors-on-rings funext univalence truncations -open import ring-theory.rings +open import ring-theory.rings funext univalence truncations ```
diff --git a/src/linear-algebra/matrices.lagda.md b/src/linear-algebra/matrices.lagda.md index f95efc19d8..6d3e481c22 100644 --- a/src/linear-algebra/matrices.lagda.md +++ b/src/linear-algebra/matrices.lagda.md @@ -1,7 +1,15 @@ # Matrices ```agda -module linear-algebra.matrices where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module linear-algebra.matrices + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,13 +18,14 @@ module linear-algebra.matrices where open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-binary-functions -open import foundation.contractible-types +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.dependent-products-contractible-types funext +open import foundation.identity-types funext open import foundation.universe-levels -open import linear-algebra.functoriality-vectors -open import linear-algebra.vectors +open import linear-algebra.functoriality-vectors funext univalence truncations +open import linear-algebra.vectors funext univalence truncations ```
diff --git a/src/linear-algebra/scalar-multiplication-matrices.lagda.md b/src/linear-algebra/scalar-multiplication-matrices.lagda.md index 460f312973..d528635def 100644 --- a/src/linear-algebra/scalar-multiplication-matrices.lagda.md +++ b/src/linear-algebra/scalar-multiplication-matrices.lagda.md @@ -1,7 +1,15 @@ # Scalar multiplication on matrices ```agda -module linear-algebra.scalar-multiplication-matrices where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module linear-algebra.scalar-multiplication-matrices + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -11,8 +19,8 @@ open import elementary-number-theory.natural-numbers open import foundation.universe-levels -open import linear-algebra.matrices -open import linear-algebra.scalar-multiplication-vectors +open import linear-algebra.matrices funext univalence truncations +open import linear-algebra.scalar-multiplication-vectors funext univalence truncations ```
diff --git a/src/linear-algebra/scalar-multiplication-vectors-on-rings.lagda.md b/src/linear-algebra/scalar-multiplication-vectors-on-rings.lagda.md index b4d616f839..ab6f5a310c 100644 --- a/src/linear-algebra/scalar-multiplication-vectors-on-rings.lagda.md +++ b/src/linear-algebra/scalar-multiplication-vectors-on-rings.lagda.md @@ -1,7 +1,15 @@ # Scalar multiplication of vectors on rings ```agda -module linear-algebra.scalar-multiplication-vectors-on-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module linear-algebra.scalar-multiplication-vectors-on-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -11,18 +19,18 @@ open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-binary-functions open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import group-theory.endomorphism-rings-abelian-groups -open import group-theory.homomorphisms-abelian-groups +open import group-theory.endomorphism-rings-abelian-groups funext univalence truncations +open import group-theory.homomorphisms-abelian-groups funext univalence truncations -open import linear-algebra.vectors -open import linear-algebra.vectors-on-rings +open import linear-algebra.vectors funext univalence truncations +open import linear-algebra.vectors-on-rings funext univalence truncations -open import ring-theory.homomorphisms-rings -open import ring-theory.modules-rings -open import ring-theory.rings +open import ring-theory.homomorphisms-rings funext univalence truncations +open import ring-theory.modules-rings funext univalence truncations +open import ring-theory.rings funext univalence truncations ```
diff --git a/src/linear-algebra/scalar-multiplication-vectors.lagda.md b/src/linear-algebra/scalar-multiplication-vectors.lagda.md index b6f55dd1cd..97c2c4a54c 100644 --- a/src/linear-algebra/scalar-multiplication-vectors.lagda.md +++ b/src/linear-algebra/scalar-multiplication-vectors.lagda.md @@ -1,7 +1,15 @@ # Scalar multiplication of vectors ```agda -module linear-algebra.scalar-multiplication-vectors where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module linear-algebra.scalar-multiplication-vectors + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -11,8 +19,8 @@ open import elementary-number-theory.natural-numbers open import foundation.universe-levels -open import linear-algebra.functoriality-vectors -open import linear-algebra.vectors +open import linear-algebra.functoriality-vectors funext univalence truncations +open import linear-algebra.vectors funext univalence truncations ```
diff --git a/src/linear-algebra/transposition-matrices.lagda.md b/src/linear-algebra/transposition-matrices.lagda.md index c46fe91ff2..542fbf8ff6 100644 --- a/src/linear-algebra/transposition-matrices.lagda.md +++ b/src/linear-algebra/transposition-matrices.lagda.md @@ -1,7 +1,15 @@ # Transposition of matrices ```agda -module linear-algebra.transposition-matrices where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module linear-algebra.transposition-matrices + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -11,12 +19,12 @@ open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import linear-algebra.functoriality-vectors -open import linear-algebra.matrices -open import linear-algebra.vectors +open import linear-algebra.functoriality-vectors funext univalence truncations +open import linear-algebra.matrices funext univalence truncations +open import linear-algebra.vectors funext univalence truncations ```
diff --git a/src/linear-algebra/vectors-on-commutative-rings.lagda.md b/src/linear-algebra/vectors-on-commutative-rings.lagda.md index 83724fd171..54ee8a539b 100644 --- a/src/linear-algebra/vectors-on-commutative-rings.lagda.md +++ b/src/linear-algebra/vectors-on-commutative-rings.lagda.md @@ -1,25 +1,33 @@ # Vectors on commutative rings ```agda -module linear-algebra.vectors-on-commutative-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module linear-algebra.vectors-on-commutative-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import commutative-algebra.commutative-rings +open import commutative-algebra.commutative-rings funext univalence truncations open import elementary-number-theory.natural-numbers -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import group-theory.commutative-monoids -open import group-theory.monoids -open import group-theory.semigroups +open import group-theory.commutative-monoids funext univalence truncations +open import group-theory.monoids funext univalence truncations +open import group-theory.semigroups funext univalence -open import linear-algebra.constant-vectors -open import linear-algebra.vectors-on-rings +open import linear-algebra.constant-vectors funext univalence truncations +open import linear-algebra.vectors-on-rings funext univalence truncations ```
diff --git a/src/linear-algebra/vectors-on-commutative-semirings.lagda.md b/src/linear-algebra/vectors-on-commutative-semirings.lagda.md index 37cfe9c5b2..d7e572df0f 100644 --- a/src/linear-algebra/vectors-on-commutative-semirings.lagda.md +++ b/src/linear-algebra/vectors-on-commutative-semirings.lagda.md @@ -1,25 +1,33 @@ # Vectors on commutative semirings ```agda -module linear-algebra.vectors-on-commutative-semirings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module linear-algebra.vectors-on-commutative-semirings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import commutative-algebra.commutative-semirings +open import commutative-algebra.commutative-semirings funext univalence truncations open import elementary-number-theory.natural-numbers -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import group-theory.commutative-monoids -open import group-theory.monoids -open import group-theory.semigroups +open import group-theory.commutative-monoids funext univalence truncations +open import group-theory.monoids funext univalence truncations +open import group-theory.semigroups funext univalence -open import linear-algebra.constant-vectors -open import linear-algebra.vectors-on-semirings +open import linear-algebra.constant-vectors funext univalence truncations +open import linear-algebra.vectors-on-semirings funext univalence truncations ```
diff --git a/src/linear-algebra/vectors-on-euclidean-domains.lagda.md b/src/linear-algebra/vectors-on-euclidean-domains.lagda.md index 63019ac835..b15a3ef71f 100644 --- a/src/linear-algebra/vectors-on-euclidean-domains.lagda.md +++ b/src/linear-algebra/vectors-on-euclidean-domains.lagda.md @@ -1,32 +1,40 @@ # Vectors on euclidean domains ```agda -module linear-algebra.vectors-on-euclidean-domains where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module linear-algebra.vectors-on-euclidean-domains + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import commutative-algebra.euclidean-domains +open import commutative-algebra.euclidean-domains funext univalence truncations open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-binary-functions open import foundation.dependent-pair-types -open import foundation.function-extensionality -open import foundation.identity-types +open import foundation.function-extensionality funext +open import foundation.identity-types funext open import foundation.unital-binary-operations open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.commutative-monoids -open import group-theory.groups -open import group-theory.monoids -open import group-theory.semigroups +open import group-theory.abelian-groups funext univalence truncations +open import group-theory.commutative-monoids funext univalence truncations +open import group-theory.groups funext univalence truncations +open import group-theory.monoids funext univalence truncations +open import group-theory.semigroups funext univalence -open import linear-algebra.constant-vectors -open import linear-algebra.functoriality-vectors -open import linear-algebra.vectors +open import linear-algebra.constant-vectors funext univalence truncations +open import linear-algebra.functoriality-vectors funext univalence truncations +open import linear-algebra.vectors funext univalence truncations ```
diff --git a/src/linear-algebra/vectors-on-rings.lagda.md b/src/linear-algebra/vectors-on-rings.lagda.md index fbeb4ee829..466509e729 100644 --- a/src/linear-algebra/vectors-on-rings.lagda.md +++ b/src/linear-algebra/vectors-on-rings.lagda.md @@ -1,7 +1,15 @@ # Vectors on rings ```agda -module linear-algebra.vectors-on-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module linear-algebra.vectors-on-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -11,22 +19,22 @@ open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-binary-functions open import foundation.dependent-pair-types -open import foundation.function-extensionality -open import foundation.identity-types +open import foundation.function-extensionality funext +open import foundation.identity-types funext open import foundation.unital-binary-operations open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.commutative-monoids -open import group-theory.groups -open import group-theory.monoids -open import group-theory.semigroups +open import group-theory.abelian-groups funext univalence truncations +open import group-theory.commutative-monoids funext univalence truncations +open import group-theory.groups funext univalence truncations +open import group-theory.monoids funext univalence truncations +open import group-theory.semigroups funext univalence -open import linear-algebra.constant-vectors -open import linear-algebra.functoriality-vectors -open import linear-algebra.vectors +open import linear-algebra.constant-vectors funext univalence truncations +open import linear-algebra.functoriality-vectors funext univalence truncations +open import linear-algebra.vectors funext univalence truncations -open import ring-theory.rings +open import ring-theory.rings funext univalence truncations ```
diff --git a/src/linear-algebra/vectors-on-semirings.lagda.md b/src/linear-algebra/vectors-on-semirings.lagda.md index c66387088a..c9bb1f1860 100644 --- a/src/linear-algebra/vectors-on-semirings.lagda.md +++ b/src/linear-algebra/vectors-on-semirings.lagda.md @@ -1,7 +1,15 @@ # Vectors on semirings ```agda -module linear-algebra.vectors-on-semirings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module linear-algebra.vectors-on-semirings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -11,19 +19,19 @@ open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-binary-functions open import foundation.dependent-pair-types -open import foundation.function-extensionality -open import foundation.identity-types +open import foundation.function-extensionality funext +open import foundation.identity-types funext open import foundation.universe-levels -open import group-theory.commutative-monoids -open import group-theory.monoids -open import group-theory.semigroups +open import group-theory.commutative-monoids funext univalence truncations +open import group-theory.monoids funext univalence truncations +open import group-theory.semigroups funext univalence -open import linear-algebra.constant-vectors -open import linear-algebra.functoriality-vectors -open import linear-algebra.vectors +open import linear-algebra.constant-vectors funext univalence truncations +open import linear-algebra.functoriality-vectors funext univalence truncations +open import linear-algebra.vectors funext univalence truncations -open import ring-theory.semirings +open import ring-theory.semirings funext univalence truncations ```
diff --git a/src/linear-algebra/vectors.lagda.md b/src/linear-algebra/vectors.lagda.md index a870ba74c9..b9f463b036 100644 --- a/src/linear-algebra/vectors.lagda.md +++ b/src/linear-algebra/vectors.lagda.md @@ -1,7 +1,15 @@ # Vectors ```agda -module linear-algebra.vectors where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module linear-algebra.vectors + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,27 +18,31 @@ module linear-algebra.vectors where open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types -open import foundation.contractible-types -open import foundation.coproduct-types +open import foundation.cartesian-product-types funext univalence +open import foundation.contractible-types funext univalence +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.raising-universe-levels -open import foundation.sets +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-truncated-types funext +open import foundation.equality-dependent-pair-types funext +open import foundation.equivalences funext +open import foundation.function-extensionality funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.raising-universe-levels-unit-type +open import foundation.sets funext univalence open import foundation.transport-along-identifications -open import foundation.truncated-types +open import foundation.truncated-types funext univalence open import foundation.truncation-levels open import foundation.unit-type open import foundation.universe-levels open import foundation.whiskering-higher-homotopies-composition -open import univalent-combinatorics.involution-standard-finite-types -open import univalent-combinatorics.standard-finite-types +open import foundation-core.raising-universe-levels + +open import univalent-combinatorics.involution-standard-finite-types funext univalence truncations +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/lists.lagda.md b/src/lists.lagda.md index 0263108995..80e76a8003 100644 --- a/src/lists.lagda.md +++ b/src/lists.lagda.md @@ -3,24 +3,33 @@ ## Modules in the lists namespace ```agda -module lists where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom -open import lists.arrays public -open import lists.concatenation-lists public -open import lists.flattening-lists public -open import lists.functoriality-lists public +module lists + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where + +open import lists.arrays funext univalence truncations public +open import lists.concatenation-lists funext univalence truncations public +open import lists.equality-lists funext univalence truncations public +open import lists.flattening-lists funext univalence truncations public +open import lists.functoriality-lists funext univalence truncations public open import lists.lists public -open import lists.lists-discrete-types public -open import lists.permutation-lists public -open import lists.permutation-vectors public -open import lists.predicates-on-lists public -open import lists.quicksort-lists public -open import lists.reversing-lists public -open import lists.sort-by-insertion-lists public -open import lists.sort-by-insertion-vectors public -open import lists.sorted-lists public -open import lists.sorted-vectors public -open import lists.sorting-algorithms-lists public -open import lists.sorting-algorithms-vectors public -open import lists.universal-property-lists-wild-monoids public +open import lists.lists-discrete-types funext univalence truncations public +open import lists.permutation-lists funext univalence truncations public +open import lists.permutation-vectors funext univalence truncations public +open import lists.predicates-on-lists funext univalence public +open import lists.quicksort-lists funext univalence truncations public +open import lists.reversing-lists funext univalence truncations public +open import lists.sort-by-insertion-lists funext univalence truncations public +open import lists.sort-by-insertion-vectors funext univalence truncations public +open import lists.sorted-lists funext univalence truncations public +open import lists.sorted-vectors funext univalence truncations public +open import lists.sorting-algorithms-lists funext univalence truncations public +open import lists.sorting-algorithms-vectors funext univalence truncations public +open import lists.universal-property-lists-wild-monoids funext univalence truncations public ``` diff --git a/src/lists/arrays.lagda.md b/src/lists/arrays.lagda.md index 054ea39af4..f2ea3b61ac 100644 --- a/src/lists/arrays.lagda.md +++ b/src/lists/arrays.lagda.md @@ -1,7 +1,15 @@ # Arrays ```agda -module lists.arrays where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module lists.arrays + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,24 +18,25 @@ module lists.arrays where open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.coproduct-types +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.equality-dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.empty-types funext univalence truncations +open import foundation.equality-dependent-pair-types funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence open import foundation.unit-type open import foundation.universe-levels -open import linear-algebra.vectors +open import linear-algebra.vectors funext univalence truncations open import lists.lists -open import univalent-combinatorics.involution-standard-finite-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.involution-standard-finite-types funext univalence truncations +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/lists/concatenation-lists.lagda.md b/src/lists/concatenation-lists.lagda.md index 1face70497..45cfd83362 100644 --- a/src/lists/concatenation-lists.lagda.md +++ b/src/lists/concatenation-lists.lagda.md @@ -1,7 +1,15 @@ # Concatenation of lists ```agda -module lists.concatenation-lists where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module lists.concatenation-lists + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -12,13 +20,14 @@ open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.identity-types -open import foundation.sets +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.sets funext univalence open import foundation.universe-levels -open import group-theory.monoids +open import group-theory.monoids funext univalence truncations +open import lists.equality-lists funext univalence truncations open import lists.lists ``` diff --git a/src/lists/equality-lists.lagda.md b/src/lists/equality-lists.lagda.md new file mode 100644 index 0000000000..c53e1a7c46 --- /dev/null +++ b/src/lists/equality-lists.lagda.md @@ -0,0 +1,159 @@ +# Equality of lists + +```agda +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module lists.equality-lists + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where +``` + +
Imports + +```agda +open import elementary-number-theory.natural-numbers + +open import foundation.action-on-higher-identifications-functions funext +open import foundation.action-on-identifications-functions +open import foundation.cartesian-product-types funext univalence +open import foundation.contractible-types funext univalence +open import foundation.coproduct-types funext univalence truncations +open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-truncated-types funext +open import foundation.empty-types funext univalence truncations +open import foundation.equality-dependent-pair-types funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.negation funext +open import foundation.raising-universe-levels-unit-type +open import foundation.sets funext univalence +open import foundation.torsorial-type-families funext univalence truncations +open import foundation.truncated-types funext univalence +open import foundation.truncation-levels +open import foundation.unit-type +open import foundation.universe-levels + +open import foundation-core.homotopies +open import foundation-core.identity-types +open import foundation-core.maybe +open import foundation-core.raising-universe-levels + +open import lists.lists +``` + +
+ +## Properties + +### Characterizing the identity type of lists + +```agda +Eq-list : {l1 : Level} {A : UU l1} → list A → list A → UU l1 +Eq-list {l1} nil nil = raise-unit l1 +Eq-list {l1} nil (cons x l') = raise-empty l1 +Eq-list {l1} (cons x l) nil = raise-empty l1 +Eq-list {l1} (cons x l) (cons x' l') = (Id x x') × Eq-list l l' + +refl-Eq-list : {l1 : Level} {A : UU l1} (l : list A) → Eq-list l l +refl-Eq-list nil = raise-star +refl-Eq-list (cons x l) = pair refl (refl-Eq-list l) + +Eq-eq-list : + {l1 : Level} {A : UU l1} (l l' : list A) → Id l l' → Eq-list l l' +Eq-eq-list l .l refl = refl-Eq-list l + +eq-Eq-list : + {l1 : Level} {A : UU l1} (l l' : list A) → Eq-list l l' → Id l l' +eq-Eq-list nil nil (map-raise star) = refl +eq-Eq-list nil (cons x l') (map-raise f) = ex-falso f +eq-Eq-list (cons x l) nil (map-raise f) = ex-falso f +eq-Eq-list (cons x l) (cons .x l') (pair refl e) = + ap (cons x) (eq-Eq-list l l' e) + +square-eq-Eq-list : + {l1 : Level} {A : UU l1} {x : A} {l l' : list A} (p : Id l l') → + Id + ( Eq-eq-list (cons x l) (cons x l') (ap (cons x) p)) + ( pair refl (Eq-eq-list l l' p)) +square-eq-Eq-list refl = refl + +is-section-eq-Eq-list : + {l1 : Level} {A : UU l1} (l l' : list A) (e : Eq-list l l') → + Id (Eq-eq-list l l' (eq-Eq-list l l' e)) e +is-section-eq-Eq-list nil nil e = eq-is-contr is-contr-raise-unit +is-section-eq-Eq-list nil (cons x l') e = ex-falso (is-empty-raise-empty e) +is-section-eq-Eq-list (cons x l) nil e = ex-falso (is-empty-raise-empty e) +is-section-eq-Eq-list (cons x l) (cons .x l') (pair refl e) = + ( square-eq-Eq-list (eq-Eq-list l l' e)) ∙ + ( eq-pair-eq-fiber (is-section-eq-Eq-list l l' e)) + +eq-Eq-refl-Eq-list : + {l1 : Level} {A : UU l1} (l : list A) → + Id (eq-Eq-list l l (refl-Eq-list l)) refl +eq-Eq-refl-Eq-list nil = refl +eq-Eq-refl-Eq-list (cons x l) = ap² (cons x) (eq-Eq-refl-Eq-list l) + +is-retraction-eq-Eq-list : + {l1 : Level} {A : UU l1} (l l' : list A) (p : Id l l') → + Id (eq-Eq-list l l' (Eq-eq-list l l' p)) p +is-retraction-eq-Eq-list nil .nil refl = refl +is-retraction-eq-Eq-list (cons x l) .(cons x l) refl = + eq-Eq-refl-Eq-list (cons x l) + +is-equiv-Eq-eq-list : + {l1 : Level} {A : UU l1} (l l' : list A) → is-equiv (Eq-eq-list l l') +is-equiv-Eq-eq-list l l' = + is-equiv-is-invertible + ( eq-Eq-list l l') + ( is-section-eq-Eq-list l l') + ( is-retraction-eq-Eq-list l l') + +equiv-Eq-list : + {l1 : Level} {A : UU l1} (l l' : list A) → Id l l' ≃ Eq-list l l' +equiv-Eq-list l l' = + pair (Eq-eq-list l l') (is-equiv-Eq-eq-list l l') + +is-torsorial-Eq-list : + {l1 : Level} {A : UU l1} (l : list A) → + is-torsorial (Eq-list l) +is-torsorial-Eq-list {A = A} l = + is-contr-equiv' + ( Σ (list A) (Id l)) + ( equiv-tot (equiv-Eq-list l)) + ( is-torsorial-Id l) + +is-trunc-Eq-list : + (k : 𝕋) {l : Level} {A : UU l} → is-trunc (succ-𝕋 (succ-𝕋 k)) A → + (l l' : list A) → is-trunc (succ-𝕋 k) (Eq-list l l') +is-trunc-Eq-list k H nil nil = + is-trunc-is-contr (succ-𝕋 k) is-contr-raise-unit +is-trunc-Eq-list k H nil (cons x l') = + is-trunc-is-empty k is-empty-raise-empty +is-trunc-Eq-list k H (cons x l) nil = + is-trunc-is-empty k is-empty-raise-empty +is-trunc-Eq-list k H (cons x l) (cons y l') = + is-trunc-product (succ-𝕋 k) (H x y) (is-trunc-Eq-list k H l l') + +is-trunc-list : + (k : 𝕋) {l : Level} {A : UU l} → is-trunc (succ-𝕋 (succ-𝕋 k)) A → + is-trunc (succ-𝕋 (succ-𝕋 k)) (list A) +is-trunc-list k H l l' = + is-trunc-equiv + ( succ-𝕋 k) + ( Eq-list l l') + ( equiv-Eq-list l l') + ( is-trunc-Eq-list k H l l') + +is-set-list : + {l : Level} {A : UU l} → is-set A → is-set (list A) +is-set-list = is-trunc-list neg-two-𝕋 + +list-Set : {l : Level} → Set l → Set l +list-Set A = pair (list (type-Set A)) (is-set-list (is-set-type-Set A)) +``` diff --git a/src/lists/flattening-lists.lagda.md b/src/lists/flattening-lists.lagda.md index 3534e0b657..3d29cd7d27 100644 --- a/src/lists/flattening-lists.lagda.md +++ b/src/lists/flattening-lists.lagda.md @@ -1,21 +1,29 @@ # Flattening of lists ```agda -module lists.flattening-lists where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module lists.flattening-lists + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.sums-of-natural-numbers +open import elementary-number-theory.sums-of-natural-numbers funext univalence truncations open import foundation.action-on-identifications-functions -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import lists.concatenation-lists -open import lists.functoriality-lists +open import lists.concatenation-lists funext univalence truncations +open import lists.functoriality-lists funext univalence truncations open import lists.lists ``` diff --git a/src/lists/functoriality-lists.lagda.md b/src/lists/functoriality-lists.lagda.md index 5fca45b262..0ef95d7220 100644 --- a/src/lists/functoriality-lists.lagda.md +++ b/src/lists/functoriality-lists.lagda.md @@ -1,30 +1,40 @@ # Functoriality of the list operation ```agda -module lists.functoriality-lists where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module lists.functoriality-lists + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.equality-natural-numbers +open import elementary-number-theory.equality-natural-numbers funext univalence truncations open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.equality-dependent-pair-types funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence open import foundation.transport-along-identifications open import foundation.universe-levels -open import linear-algebra.functoriality-vectors -open import linear-algebra.vectors +open import linear-algebra.functoriality-vectors funext univalence truncations +open import linear-algebra.vectors funext univalence truncations -open import lists.arrays -open import lists.concatenation-lists +open import lists.arrays funext univalence truncations +open import lists.concatenation-lists funext univalence truncations +open import lists.equality-lists funext univalence truncations open import lists.lists ``` diff --git a/src/lists/lists-discrete-types.lagda.md b/src/lists/lists-discrete-types.lagda.md index d0b8cd7b4b..26c643d666 100644 --- a/src/lists/lists-discrete-types.lagda.md +++ b/src/lists/lists-discrete-types.lagda.md @@ -1,25 +1,36 @@ # Lists of elements in discrete types ```agda -module lists.lists-discrete-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module lists.lists-discrete-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.booleans -open import foundation.cartesian-product-types -open import foundation.coproduct-types -open import foundation.decidable-equality -open import foundation.decidable-types +open import foundation.booleans funext univalence truncations +open import foundation.cartesian-product-types funext univalence +open import foundation.coproduct-types funext univalence truncations +open import foundation.decidable-equality funext univalence truncations +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.function-types -open import foundation.identity-types -open import foundation.raising-universe-levels +open import foundation.empty-types funext univalence truncations +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.raising-universe-levels-unit-type open import foundation.unit-type open import foundation.universe-levels +open import foundation-core.raising-universe-levels + +open import lists.equality-lists funext univalence truncations open import lists.lists ``` diff --git a/src/lists/lists.lagda.md b/src/lists/lists.lagda.md index dfa10f3084..e9a1e4c030 100644 --- a/src/lists/lists.lagda.md +++ b/src/lists/lists.lagda.md @@ -9,28 +9,19 @@ module lists.lists where ```agda open import elementary-number-theory.natural-numbers -open import foundation.action-on-higher-identifications-functions -open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types -open import foundation.contractible-types -open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.equality-dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.maybe -open import foundation.negation -open import foundation.raising-universe-levels -open import foundation.sets -open import foundation.torsorial-type-families -open import foundation.truncated-types -open import foundation.truncation-levels open import foundation.unit-type open import foundation.universe-levels + +open import foundation-core.cartesian-product-types +open import foundation-core.coproduct-types +open import foundation-core.empty-types +open import foundation-core.equivalences +open import foundation-core.function-types +open import foundation-core.homotopies +open import foundation-core.identity-types +open import foundation-core.maybe +open import foundation-core.negation ```
@@ -161,113 +152,6 @@ tail-is-nonnil-list l p = pr2 (pr1 (is-cons-is-nonnil-list l p)) ``` -### Characterizing the identity type of lists - -```agda -Eq-list : {l1 : Level} {A : UU l1} → list A → list A → UU l1 -Eq-list {l1} nil nil = raise-unit l1 -Eq-list {l1} nil (cons x l') = raise-empty l1 -Eq-list {l1} (cons x l) nil = raise-empty l1 -Eq-list {l1} (cons x l) (cons x' l') = (Id x x') × Eq-list l l' - -refl-Eq-list : {l1 : Level} {A : UU l1} (l : list A) → Eq-list l l -refl-Eq-list nil = raise-star -refl-Eq-list (cons x l) = pair refl (refl-Eq-list l) - -Eq-eq-list : - {l1 : Level} {A : UU l1} (l l' : list A) → Id l l' → Eq-list l l' -Eq-eq-list l .l refl = refl-Eq-list l - -eq-Eq-list : - {l1 : Level} {A : UU l1} (l l' : list A) → Eq-list l l' → Id l l' -eq-Eq-list nil nil (map-raise star) = refl -eq-Eq-list nil (cons x l') (map-raise f) = ex-falso f -eq-Eq-list (cons x l) nil (map-raise f) = ex-falso f -eq-Eq-list (cons x l) (cons .x l') (pair refl e) = - ap (cons x) (eq-Eq-list l l' e) - -square-eq-Eq-list : - {l1 : Level} {A : UU l1} {x : A} {l l' : list A} (p : Id l l') → - Id - ( Eq-eq-list (cons x l) (cons x l') (ap (cons x) p)) - ( pair refl (Eq-eq-list l l' p)) -square-eq-Eq-list refl = refl - -is-section-eq-Eq-list : - {l1 : Level} {A : UU l1} (l l' : list A) (e : Eq-list l l') → - Id (Eq-eq-list l l' (eq-Eq-list l l' e)) e -is-section-eq-Eq-list nil nil e = eq-is-contr is-contr-raise-unit -is-section-eq-Eq-list nil (cons x l') e = ex-falso (is-empty-raise-empty e) -is-section-eq-Eq-list (cons x l) nil e = ex-falso (is-empty-raise-empty e) -is-section-eq-Eq-list (cons x l) (cons .x l') (pair refl e) = - ( square-eq-Eq-list (eq-Eq-list l l' e)) ∙ - ( eq-pair-eq-fiber (is-section-eq-Eq-list l l' e)) - -eq-Eq-refl-Eq-list : - {l1 : Level} {A : UU l1} (l : list A) → - Id (eq-Eq-list l l (refl-Eq-list l)) refl -eq-Eq-refl-Eq-list nil = refl -eq-Eq-refl-Eq-list (cons x l) = ap² (cons x) (eq-Eq-refl-Eq-list l) - -is-retraction-eq-Eq-list : - {l1 : Level} {A : UU l1} (l l' : list A) (p : Id l l') → - Id (eq-Eq-list l l' (Eq-eq-list l l' p)) p -is-retraction-eq-Eq-list nil .nil refl = refl -is-retraction-eq-Eq-list (cons x l) .(cons x l) refl = - eq-Eq-refl-Eq-list (cons x l) - -is-equiv-Eq-eq-list : - {l1 : Level} {A : UU l1} (l l' : list A) → is-equiv (Eq-eq-list l l') -is-equiv-Eq-eq-list l l' = - is-equiv-is-invertible - ( eq-Eq-list l l') - ( is-section-eq-Eq-list l l') - ( is-retraction-eq-Eq-list l l') - -equiv-Eq-list : - {l1 : Level} {A : UU l1} (l l' : list A) → Id l l' ≃ Eq-list l l' -equiv-Eq-list l l' = - pair (Eq-eq-list l l') (is-equiv-Eq-eq-list l l') - -is-torsorial-Eq-list : - {l1 : Level} {A : UU l1} (l : list A) → - is-torsorial (Eq-list l) -is-torsorial-Eq-list {A = A} l = - is-contr-equiv' - ( Σ (list A) (Id l)) - ( equiv-tot (equiv-Eq-list l)) - ( is-torsorial-Id l) - -is-trunc-Eq-list : - (k : 𝕋) {l : Level} {A : UU l} → is-trunc (succ-𝕋 (succ-𝕋 k)) A → - (l l' : list A) → is-trunc (succ-𝕋 k) (Eq-list l l') -is-trunc-Eq-list k H nil nil = - is-trunc-is-contr (succ-𝕋 k) is-contr-raise-unit -is-trunc-Eq-list k H nil (cons x l') = - is-trunc-is-empty k is-empty-raise-empty -is-trunc-Eq-list k H (cons x l) nil = - is-trunc-is-empty k is-empty-raise-empty -is-trunc-Eq-list k H (cons x l) (cons y l') = - is-trunc-product (succ-𝕋 k) (H x y) (is-trunc-Eq-list k H l l') - -is-trunc-list : - (k : 𝕋) {l : Level} {A : UU l} → is-trunc (succ-𝕋 (succ-𝕋 k)) A → - is-trunc (succ-𝕋 (succ-𝕋 k)) (list A) -is-trunc-list k H l l' = - is-trunc-equiv - ( succ-𝕋 k) - ( Eq-list l l') - ( equiv-Eq-list l l') - ( is-trunc-Eq-list k H l l') - -is-set-list : - {l : Level} {A : UU l} → is-set A → is-set (list A) -is-set-list = is-trunc-list neg-two-𝕋 - -list-Set : {l : Level} → Set l → Set l -list-Set A = pair (list (type-Set A)) (is-set-list (is-set-type-Set A)) -``` - ### The length operation behaves well with respect to the other list operations ```agda diff --git a/src/lists/permutation-lists.lagda.md b/src/lists/permutation-lists.lagda.md index 26ca630086..03fc227b69 100644 --- a/src/lists/permutation-lists.lagda.md +++ b/src/lists/permutation-lists.lagda.md @@ -1,32 +1,41 @@ # Permutations of lists ```agda -module lists.permutation-lists where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module lists.permutation-lists + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.equality-natural-numbers +open import elementary-number-theory.equality-natural-numbers funext univalence truncations open import elementary-number-theory.natural-numbers -open import finite-group-theory.permutations-standard-finite-types +open import finite-group-theory.permutations-standard-finite-types funext univalence truncations open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types -open import foundation.identity-types -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.equality-dependent-pair-types funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence open import foundation.transport-along-identifications open import foundation.universe-levels -open import linear-algebra.functoriality-vectors -open import linear-algebra.vectors +open import linear-algebra.functoriality-vectors funext univalence truncations +open import linear-algebra.vectors funext univalence truncations -open import lists.arrays -open import lists.functoriality-lists +open import lists.arrays funext univalence truncations +open import lists.functoriality-lists funext univalence truncations open import lists.lists -open import lists.permutation-vectors +open import lists.permutation-vectors funext univalence truncations ```
diff --git a/src/lists/permutation-vectors.lagda.md b/src/lists/permutation-vectors.lagda.md index 4099f1bfe0..0c6164cb89 100644 --- a/src/lists/permutation-vectors.lagda.md +++ b/src/lists/permutation-vectors.lagda.md @@ -1,7 +1,15 @@ # Permutations of vectors ```agda -module lists.permutation-vectors where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module lists.permutation-vectors + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,29 +17,29 @@ module lists.permutation-vectors where ```agda open import elementary-number-theory.natural-numbers -open import finite-group-theory.permutations-standard-finite-types -open import finite-group-theory.transpositions-standard-finite-types +open import finite-group-theory.permutations-standard-finite-types funext univalence truncations +open import finite-group-theory.transpositions-standard-finite-types funext univalence truncations open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types -open import foundation.coproduct-types +open import foundation.cartesian-product-types funext univalence +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalence-extensionality -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-coproduct-types -open import foundation.identity-types -open import foundation.negated-equality +open import foundation.equivalence-extensionality funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-coproduct-types funext univalence truncations +open import foundation.identity-types funext +open import foundation.negated-equality funext univalence truncations open import foundation.transport-along-identifications open import foundation.universe-levels -open import linear-algebra.functoriality-vectors -open import linear-algebra.vectors +open import linear-algebra.functoriality-vectors funext univalence truncations +open import linear-algebra.vectors funext univalence truncations -open import lists.arrays +open import lists.arrays funext univalence truncations open import lists.lists -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/lists/predicates-on-lists.lagda.md b/src/lists/predicates-on-lists.lagda.md index 4d52edb669..f969b4387b 100644 --- a/src/lists/predicates-on-lists.lagda.md +++ b/src/lists/predicates-on-lists.lagda.md @@ -1,13 +1,21 @@ # Predicates on lists ```agda -module lists.predicates-on-lists where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module lists.predicates-on-lists + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.propositions funext univalence +open import foundation.raising-universe-levels-unit-type open import foundation.unit-type open import foundation.universe-levels diff --git a/src/lists/quicksort-lists.lagda.md b/src/lists/quicksort-lists.lagda.md index 0acbdc4224..66deca8be8 100644 --- a/src/lists/quicksort-lists.lagda.md +++ b/src/lists/quicksort-lists.lagda.md @@ -1,25 +1,33 @@ # Quicksort for lists ```agda -module lists.quicksort-lists where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module lists.quicksort-lists + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.inequality-natural-numbers funext univalence truncations open import elementary-number-theory.natural-numbers -open import elementary-number-theory.strong-induction-natural-numbers +open import elementary-number-theory.strong-induction-natural-numbers funext univalence truncations -open import foundation.coproduct-types -open import foundation.identity-types +open import foundation.coproduct-types funext univalence truncations +open import foundation.identity-types funext open import foundation.unit-type open import foundation.universe-levels -open import lists.concatenation-lists +open import lists.concatenation-lists funext univalence truncations open import lists.lists -open import order-theory.decidable-total-orders +open import order-theory.decidable-total-orders funext univalence truncations ```
diff --git a/src/lists/reversing-lists.lagda.md b/src/lists/reversing-lists.lagda.md index 551bed29c5..d0f9b6bb53 100644 --- a/src/lists/reversing-lists.lagda.md +++ b/src/lists/reversing-lists.lagda.md @@ -1,7 +1,15 @@ # Reversing lists ```agda -module lists.reversing-lists where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module lists.reversing-lists + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,13 +18,13 @@ module lists.reversing-lists where open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.function-types -open import foundation.identity-types +open import foundation.function-types funext +open import foundation.identity-types funext open import foundation.universe-levels -open import lists.concatenation-lists -open import lists.flattening-lists -open import lists.functoriality-lists +open import lists.concatenation-lists funext univalence truncations +open import lists.flattening-lists funext univalence truncations +open import lists.functoriality-lists funext univalence truncations open import lists.lists ``` diff --git a/src/lists/sort-by-insertion-lists.lagda.md b/src/lists/sort-by-insertion-lists.lagda.md index c14433df58..74f8e14eb7 100644 --- a/src/lists/sort-by-insertion-lists.lagda.md +++ b/src/lists/sort-by-insertion-lists.lagda.md @@ -1,26 +1,34 @@ # Sort by insertion for lists ```agda -module lists.sort-by-insertion-lists where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module lists.sort-by-insertion-lists + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import finite-group-theory.permutations-standard-finite-types +open import finite-group-theory.permutations-standard-finite-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import lists.arrays +open import lists.arrays funext univalence truncations open import lists.lists -open import lists.permutation-lists -open import lists.sort-by-insertion-vectors -open import lists.sorted-lists -open import lists.sorting-algorithms-lists +open import lists.permutation-lists funext univalence truncations +open import lists.sort-by-insertion-vectors funext univalence truncations +open import lists.sorted-lists funext univalence truncations +open import lists.sorting-algorithms-lists funext univalence truncations -open import order-theory.decidable-total-orders +open import order-theory.decidable-total-orders funext univalence truncations ```
diff --git a/src/lists/sort-by-insertion-vectors.lagda.md b/src/lists/sort-by-insertion-vectors.lagda.md index 56d1870c3a..1d489cb819 100644 --- a/src/lists/sort-by-insertion-vectors.lagda.md +++ b/src/lists/sort-by-insertion-vectors.lagda.md @@ -1,7 +1,15 @@ # Sort by insertion for vectors ```agda -module lists.sort-by-insertion-vectors where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module lists.sort-by-insertion-vectors + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,26 +17,27 @@ module lists.sort-by-insertion-vectors where ```agda open import elementary-number-theory.natural-numbers -open import finite-group-theory.permutations-standard-finite-types -open import finite-group-theory.transpositions-standard-finite-types +open import finite-group-theory.permutations-standard-finite-types funext univalence truncations +open import finite-group-theory.transpositions-standard-finite-types funext univalence truncations open import foundation.action-on-identifications-functions -open import foundation.coproduct-types +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.functoriality-coproduct-types -open import foundation.identity-types +open import foundation.equivalences funext +open import foundation.functoriality-coproduct-types funext univalence truncations +open import foundation.identity-types funext +open import foundation.raising-universe-levels-unit-type open import foundation.transport-along-identifications open import foundation.unit-type open import foundation.universe-levels -open import linear-algebra.vectors +open import linear-algebra.vectors funext univalence truncations -open import lists.permutation-vectors -open import lists.sorted-vectors -open import lists.sorting-algorithms-vectors +open import lists.permutation-vectors funext univalence truncations +open import lists.sorted-vectors funext univalence truncations +open import lists.sorting-algorithms-vectors funext univalence truncations -open import order-theory.decidable-total-orders +open import order-theory.decidable-total-orders funext univalence truncations ```
diff --git a/src/lists/sorted-lists.lagda.md b/src/lists/sorted-lists.lagda.md index dbd5f1f37e..38e52e5c33 100644 --- a/src/lists/sorted-lists.lagda.md +++ b/src/lists/sorted-lists.lagda.md @@ -1,7 +1,15 @@ # Sorted lists ```agda -module lists.sorted-lists where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module lists.sorted-lists + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,17 +18,19 @@ module lists.sorted-lists where open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.propositions funext univalence +open import foundation.raising-universe-levels-unit-type open import foundation.unit-type open import foundation.universe-levels -open import linear-algebra.vectors +open import linear-algebra.vectors funext univalence truncations -open import lists.arrays +open import lists.arrays funext univalence truncations open import lists.lists -open import lists.sorted-vectors +open import lists.sorted-vectors funext univalence truncations -open import order-theory.decidable-total-orders +open import order-theory.decidable-total-orders funext univalence truncations ```
diff --git a/src/lists/sorted-vectors.lagda.md b/src/lists/sorted-vectors.lagda.md index dbb2353d4f..14a254a0dc 100644 --- a/src/lists/sorted-vectors.lagda.md +++ b/src/lists/sorted-vectors.lagda.md @@ -1,7 +1,15 @@ # Sorted vectors ```agda -module lists.sorted-vectors where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module lists.sorted-vectors + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,23 +17,25 @@ module lists.sorted-vectors where ```agda open import elementary-number-theory.natural-numbers -open import finite-group-theory.permutations-standard-finite-types +open import finite-group-theory.permutations-standard-finite-types funext univalence truncations -open import foundation.coproduct-types +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.propositions funext univalence +open import foundation.raising-universe-levels-unit-type open import foundation.unit-type open import foundation.universe-levels -open import linear-algebra.vectors +open import linear-algebra.vectors funext univalence truncations -open import lists.permutation-vectors +open import lists.permutation-vectors funext univalence truncations -open import order-theory.decidable-total-orders +open import order-theory.decidable-total-orders funext univalence truncations -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/lists/sorting-algorithms-lists.lagda.md b/src/lists/sorting-algorithms-lists.lagda.md index 14b5f6541e..a6159eac36 100644 --- a/src/lists/sorting-algorithms-lists.lagda.md +++ b/src/lists/sorting-algorithms-lists.lagda.md @@ -1,7 +1,15 @@ # Sorting algorithms for lists ```agda -module lists.sorting-algorithms-lists where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module lists.sorting-algorithms-lists + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,22 +17,22 @@ module lists.sorting-algorithms-lists where ```agda open import elementary-number-theory.natural-numbers -open import finite-group-theory.permutations-standard-finite-types +open import finite-group-theory.permutations-standard-finite-types funext univalence truncations -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import linear-algebra.vectors +open import linear-algebra.vectors funext univalence truncations -open import lists.arrays +open import lists.arrays funext univalence truncations open import lists.lists -open import lists.permutation-lists -open import lists.sorted-lists -open import lists.sorting-algorithms-vectors +open import lists.permutation-lists funext univalence truncations +open import lists.sorted-lists funext univalence truncations +open import lists.sorting-algorithms-vectors funext univalence truncations -open import order-theory.decidable-total-orders +open import order-theory.decidable-total-orders funext univalence truncations ```
diff --git a/src/lists/sorting-algorithms-vectors.lagda.md b/src/lists/sorting-algorithms-vectors.lagda.md index 029591d5fb..ce0eea6f2d 100644 --- a/src/lists/sorting-algorithms-vectors.lagda.md +++ b/src/lists/sorting-algorithms-vectors.lagda.md @@ -1,7 +1,15 @@ # Sorting algorithms for vectors ```agda -module lists.sorting-algorithms-vectors where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module lists.sorting-algorithms-vectors + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,19 +17,19 @@ module lists.sorting-algorithms-vectors where ```agda open import elementary-number-theory.natural-numbers -open import finite-group-theory.permutations-standard-finite-types +open import finite-group-theory.permutations-standard-finite-types funext univalence truncations -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import linear-algebra.vectors +open import linear-algebra.vectors funext univalence truncations -open import lists.permutation-vectors -open import lists.sorted-vectors +open import lists.permutation-vectors funext univalence truncations +open import lists.sorted-vectors funext univalence truncations -open import order-theory.decidable-total-orders +open import order-theory.decidable-total-orders funext univalence truncations ```
diff --git a/src/lists/universal-property-lists-wild-monoids.lagda.md b/src/lists/universal-property-lists-wild-monoids.lagda.md index 67c4735fec..c2508d85c8 100644 --- a/src/lists/universal-property-lists-wild-monoids.lagda.md +++ b/src/lists/universal-property-lists-wild-monoids.lagda.md @@ -1,7 +1,15 @@ # The universal property of lists with respect to wild monoids ```agda -module lists.universal-property-lists-wild-monoids where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module lists.universal-property-lists-wild-monoids + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,22 +17,22 @@ module lists.universal-property-lists-wild-monoids where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.unit-type open import foundation.universe-levels open import foundation.whiskering-higher-homotopies-composition -open import group-theory.homomorphisms-semigroups +open import group-theory.homomorphisms-semigroups funext univalence truncations -open import lists.concatenation-lists +open import lists.concatenation-lists funext univalence truncations open import lists.lists -open import structured-types.h-spaces -open import structured-types.morphisms-h-spaces -open import structured-types.morphisms-wild-monoids -open import structured-types.pointed-maps +open import structured-types.h-spaces funext univalence truncations +open import structured-types.morphisms-h-spaces funext univalence truncations +open import structured-types.morphisms-wild-monoids funext univalence truncations +open import structured-types.pointed-maps funext univalence truncations open import structured-types.pointed-types -open import structured-types.wild-monoids +open import structured-types.wild-monoids funext univalence truncations ```
diff --git a/src/literature.lagda.md b/src/literature.lagda.md index 97fa876ae4..50ff8c4841 100644 --- a/src/literature.lagda.md +++ b/src/literature.lagda.md @@ -7,14 +7,22 @@ ## Modules in the literature namespace ```agda -module literature where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom -open import literature.100-theorems public -open import literature.1000plus-theorems public -open import literature.idempotents-in-intensional-type-theory public -open import literature.introduction-to-homotopy-type-theory public -open import literature.oeis public -open import literature.sequential-colimits-in-homotopy-type-theory public +module literature + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where + +open import literature.100-theorems funext univalence truncations public +open import literature.1000plus-theorems funext univalence truncations public +open import literature.idempotents-in-intensional-type-theory funext univalence truncations public +open import literature.introduction-to-homotopy-type-theory funext univalence truncations public +open import literature.oeis funext univalence truncations public +open import literature.sequential-colimits-in-homotopy-type-theory funext univalence truncations public ``` ## References diff --git a/src/literature/100-theorems.lagda.md b/src/literature/100-theorems.lagda.md index a7891c065f..d6d0060c2f 100644 --- a/src/literature/100-theorems.lagda.md +++ b/src/literature/100-theorems.lagda.md @@ -6,7 +6,15 @@ This file records formalized results from {{#cite 100theorems}} ```agda -module literature.100-theorems where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module literature.100-theorems + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ``` ## The list @@ -16,7 +24,7 @@ module literature.100-theorems where **Author:** [Fredrik Bakke](https://www.ntnu.edu/employees/fredrik.bakke) ```agda -open import elementary-number-theory.rational-numbers using +open import elementary-number-theory.rational-numbers funext univalence truncations using ( is-countable-ℚ) ``` @@ -25,7 +33,7 @@ open import elementary-number-theory.rational-numbers using **Author:** [Egbert Rijke](https://egbertrijke.github.io) ```agda -open import elementary-number-theory.infinitude-of-primes using +open import elementary-number-theory.infinitude-of-primes funext univalence truncations using ( infinitude-of-primes-ℕ) ``` @@ -40,7 +48,7 @@ hence we refer to the generalization as the Cantor-Schröder-Bernstein-Escardó theorem. ```agda -open import foundation.cantor-schroder-bernstein-escardo using +open import foundation.cantor-schroder-bernstein-escardo funext univalence truncations using ( Cantor-Schröder-Bernstein-Escardó ; Cantor-Schröder-Bernstein) ``` @@ -50,17 +58,17 @@ open import foundation.cantor-schroder-bernstein-escardo using **Author:** [Egbert Rijke](https://egbertrijke.github.io) ```agda -open import commutative-algebra.binomial-theorem-commutative-rings using +open import commutative-algebra.binomial-theorem-commutative-rings funext univalence truncations using ( binomial-theorem-Commutative-Ring) -open import commutative-algebra.binomial-theorem-commutative-semirings using +open import commutative-algebra.binomial-theorem-commutative-semirings funext univalence truncations using ( binomial-theorem-Commutative-Semiring) -open import ring-theory.binomial-theorem-rings using +open import ring-theory.binomial-theorem-rings funext univalence truncations using ( binomial-theorem-Ring) -open import ring-theory.binomial-theorem-semirings using +open import ring-theory.binomial-theorem-semirings funext univalence truncations using ( binomial-theorem-Semiring) -open import elementary-number-theory.binomial-theorem-integers using +open import elementary-number-theory.binomial-theorem-integers funext univalence truncations using ( binomial-theorem-ℤ) -open import elementary-number-theory.binomial-theorem-natural-numbers using +open import elementary-number-theory.binomial-theorem-natural-numbers funext univalence truncations using ( binomial-theorem-ℕ) ``` @@ -69,7 +77,7 @@ open import elementary-number-theory.binomial-theorem-natural-numbers using **Author:** [Egbert Rijke](https://egbertrijke.github.io) ```agda -open import univalent-combinatorics.decidable-subtypes using +open import univalent-combinatorics.decidable-subtypes funext univalence truncations using ( number-of-elements-decidable-subtype-is-finite) ``` @@ -78,7 +86,7 @@ open import univalent-combinatorics.decidable-subtypes using **Author:** [Egbert Rijke](https://egbertrijke.github.io) ```agda -open import univalent-combinatorics.binomial-types using +open import univalent-combinatorics.binomial-types funext univalence truncations using ( has-cardinality-binomial-type) ``` @@ -91,9 +99,9 @@ while the linked theorems are formalizations of Bezout's lemma, even though these are different statements. ```agda -open import elementary-number-theory.bezouts-lemma-integers using +open import elementary-number-theory.bezouts-lemma-integers funext univalence truncations using ( bezouts-lemma-ℤ) -open import elementary-number-theory.bezouts-lemma-natural-numbers using +open import elementary-number-theory.bezouts-lemma-natural-numbers funext univalence truncations using ( bezouts-lemma-ℕ) ``` @@ -102,7 +110,7 @@ open import elementary-number-theory.bezouts-lemma-natural-numbers using **Author:** [Egbert Rijke](https://egbertrijke.github.io) ```agda -open import foundation.cantors-theorem using +open import foundation.cantors-theorem funext univalence truncations using ( theorem-Cantor) ``` @@ -130,7 +138,7 @@ open import elementary-number-theory.natural-numbers using **Author:** [Victor Blanchi](https://github.com/VictorBlanchi) ```agda -open import elementary-number-theory.fundamental-theorem-of-arithmetic using +open import elementary-number-theory.fundamental-theorem-of-arithmetic funext univalence truncations using ( fundamental-theorem-arithmetic-list-ℕ) ``` @@ -139,7 +147,7 @@ open import elementary-number-theory.fundamental-theorem-of-arithmetic using **Author:** [malarbol](https://github.com/malarbol) ```agda -open import real-numbers.metric-space-of-real-numbers using +open import real-numbers.metric-space-of-real-numbers funext univalence truncations using ( is-triangular-premetric-leq-ℝ) ``` diff --git a/src/literature/1000plus-theorems.lagda.md b/src/literature/1000plus-theorems.lagda.md index 2257a9effc..7301bbe215 100644 --- a/src/literature/1000plus-theorems.lagda.md +++ b/src/literature/1000plus-theorems.lagda.md @@ -9,7 +9,15 @@ theorems in mathematics that have their own Wikipedia entry. We welcome any contribution to this list! ```agda -module literature.1000plus-theorems where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module literature.1000plus-theorems + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ``` ## Formalized theorems @@ -21,9 +29,9 @@ The theorems are ordered alphabetically, omitting definite articles ("the"). **Author:** [Bryan Lu](https://blu-bird.github.io) ```agda -open import elementary-number-theory.bezouts-lemma-integers using +open import elementary-number-theory.bezouts-lemma-integers funext univalence truncations using ( bezouts-lemma-ℤ) -open import elementary-number-theory.bezouts-lemma-natural-numbers using +open import elementary-number-theory.bezouts-lemma-natural-numbers funext univalence truncations using ( bezouts-lemma-ℕ) ``` @@ -32,17 +40,17 @@ open import elementary-number-theory.bezouts-lemma-natural-numbers using **Author:** [Egbert Rijke](https://egbertrijke.github.io) ```agda -open import commutative-algebra.binomial-theorem-commutative-rings using +open import commutative-algebra.binomial-theorem-commutative-rings funext univalence truncations using ( binomial-theorem-Commutative-Ring) -open import commutative-algebra.binomial-theorem-commutative-semirings using +open import commutative-algebra.binomial-theorem-commutative-semirings funext univalence truncations using ( binomial-theorem-Commutative-Semiring) -open import ring-theory.binomial-theorem-rings using +open import ring-theory.binomial-theorem-rings funext univalence truncations using ( binomial-theorem-Ring) -open import ring-theory.binomial-theorem-semirings using +open import ring-theory.binomial-theorem-semirings funext univalence truncations using ( binomial-theorem-Semiring) -open import elementary-number-theory.binomial-theorem-integers using +open import elementary-number-theory.binomial-theorem-integers funext univalence truncations using ( binomial-theorem-ℤ) -open import elementary-number-theory.binomial-theorem-natural-numbers using +open import elementary-number-theory.binomial-theorem-natural-numbers funext univalence truncations using ( binomial-theorem-ℕ) ``` @@ -57,7 +65,7 @@ hence we refer to the generalization as the Cantor-Schröder-Bernstein-Escardó theorem. ```agda -open import foundation.cantor-schroder-bernstein-escardo using +open import foundation.cantor-schroder-bernstein-escardo funext univalence truncations using ( Cantor-Schröder-Bernstein-Escardó ; Cantor-Schröder-Bernstein) ``` @@ -67,7 +75,7 @@ open import foundation.cantor-schroder-bernstein-escardo using **Author:** [Egbert Rijke](https://egbertrijke.github.io) ```agda -open import foundation.cantors-theorem using +open import foundation.cantors-theorem funext univalence truncations using ( theorem-Cantor) ``` @@ -76,7 +84,7 @@ open import foundation.cantors-theorem using **Author:** [Egbert Rijke](https://egbertrijke.github.io) ```agda -open import group-theory.cayleys-theorem using +open import group-theory.cayleys-theorem funext univalence truncations using ( Cayleys-theorem) ``` @@ -85,7 +93,7 @@ open import group-theory.cayleys-theorem using **Author:** [Fredrik Bakke](https://www.ntnu.edu/employees/fredrik.bakke) ```agda -open import foundation.diaconescus-theorem using +open import foundation.diaconescus-theorem funext univalence truncations using ( theorem-Diaconescu) ``` @@ -94,7 +102,7 @@ open import foundation.diaconescus-theorem using **Author:** [Egbert Rijke](https://egbertrijke.github.io) ```agda -open import elementary-number-theory.infinitude-of-primes using +open import elementary-number-theory.infinitude-of-primes funext univalence truncations using ( infinitude-of-primes-ℕ) ``` @@ -103,7 +111,7 @@ open import elementary-number-theory.infinitude-of-primes using **Author:** [Victor Blanchi](https://github.com/VictorBlanchi) ```agda -open import elementary-number-theory.fundamental-theorem-of-arithmetic using +open import elementary-number-theory.fundamental-theorem-of-arithmetic funext univalence truncations using ( fundamental-theorem-arithmetic-list-ℕ) ``` @@ -112,7 +120,7 @@ open import elementary-number-theory.fundamental-theorem-of-arithmetic using **Author:** [Egbert Rijke](https://egbertrijke.github.io) ```agda -open import foundation.fundamental-theorem-of-equivalence-relations using +open import foundation.fundamental-theorem-of-equivalence-relations funext univalence truncations using ( equiv-equivalence-relation-partition) ``` @@ -121,10 +129,10 @@ open import foundation.fundamental-theorem-of-equivalence-relations using **Author:** [Fredrik Bakke](https://www.ntnu.edu/employees/fredrik.bakke) ```agda -open import domain-theory.kleenes-fixed-point-theorem-posets using +open import domain-theory.kleenes-fixed-point-theorem-posets funext univalence truncations using ( is-least-fixed-point-theorem-kleene-hom-Poset ; is-least-fixed-point-theorem-kleene-Poset) -open import domain-theory.kleenes-fixed-point-theorem-omega-complete-posets using +open import domain-theory.kleenes-fixed-point-theorem-omega-complete-posets funext univalence truncations using ( is-least-fixed-point-theorem-kleene-hom-ω-Complete-Poset ; is-least-fixed-point-theorem-kleene-ω-Complete-Poset) ``` @@ -134,7 +142,7 @@ open import domain-theory.kleenes-fixed-point-theorem-omega-complete-posets usin **Author:** [Fredrik Bakke](https://www.ntnu.edu/employees/fredrik.bakke) ```agda -open import order-theory.knaster-tarski-fixed-point-theorem using +open import order-theory.knaster-tarski-fixed-point-theorem funext univalence truncations using ( least-fixed-point-knaster-tarski-Inflattice ; greatest-fixed-point-knaster-tarski-Suplattice) ``` @@ -144,7 +152,7 @@ open import order-theory.knaster-tarski-fixed-point-theorem using **Author:** [Egbert Rijke](https://egbertrijke.github.io) ```agda -open import foundation.lawveres-fixed-point-theorem using +open import foundation.lawveres-fixed-point-theorem funext univalence truncations using ( fixed-point-theorem-Lawvere) ``` @@ -153,9 +161,9 @@ open import foundation.lawveres-fixed-point-theorem using **Author:** [Emily Riehl](https://emilyriehl.github.io/) ```agda -open import category-theory.yoneda-lemma-categories using +open import category-theory.yoneda-lemma-categories funext univalence truncations using ( lemma-yoneda-Category) -open import category-theory.yoneda-lemma-precategories using +open import category-theory.yoneda-lemma-precategories funext univalence truncations using ( lemma-yoneda-Precategory) ``` diff --git a/src/literature/idempotents-in-intensional-type-theory.lagda.md b/src/literature/idempotents-in-intensional-type-theory.lagda.md index 448cd6e695..56abeef25f 100644 --- a/src/literature/idempotents-in-intensional-type-theory.lagda.md +++ b/src/literature/idempotents-in-intensional-type-theory.lagda.md @@ -4,7 +4,15 @@ This file collects references to formalization of constructions and theorems from {{#cite Shu17}}. ```agda -module literature.idempotents-in-intensional-type-theory where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module literature.idempotents-in-intensional-type-theory + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ``` ## 1 Introduction @@ -13,11 +21,11 @@ The introduction section gives an introduction to the problem at hand and motivates its study in univalent foundations. ```agda -open import group-theory.groups using +open import group-theory.groups funext univalence truncations using ( Group ) -open import higher-group-theory.higher-groups using +open import higher-group-theory.higher-groups funext univalence truncations using ( ∞-Group ) ``` @@ -27,11 +35,11 @@ open import higher-group-theory.higher-groups using The second section introduces basic notions from homotopy type theory. ```agda -open import foundation.dependent-function-types -- "dependent products" +open import foundation.dependent-function-types funext univalence -- "dependent products" open import foundation.dependent-pair-types -- "dependent sums" -open import foundation.identity-types using +open import foundation.identity-types funext using ( _＝_ -- "identity type, its elements are paths" ; refl -- "the canonical elements of the identity types" ; concat -- "transitivity of paths" @@ -67,7 +75,7 @@ open import foundation-core.sets using ; is-set -- all identity types are propositions ) -open import foundation.homotopies using +open import foundation.homotopies funext using ( _~_ -- "homotopy" ; nat-htpy -- "naturality of homotopies" ) @@ -78,32 +86,32 @@ given in the article: an equivalence is a function equipped with a left inverse and a right inverse. ```agda -open import foundation.equivalences using +open import foundation.equivalences funext using ( is-equiv -- "type of equivalence proofs" ; equiv -- "type of equivalences" ; is-property-is-equiv -- "the type of equivalence proofs is a mere proposition" ) -open import foundation.function-extensionality using +open import foundation.function-extensionality funext using ( funext -- "the function extensionality axiom" ) -open import foundation.univalence using +open import foundation.univalence funext univalence using ( equiv-eq -- "the canonical map `(A ＝ B) → (A ≃ B)`" ; univalence -- "the univalence axiom" ) -open import foundation.propositional-truncations using +open import foundation.propositional-truncations funext univalence using ( ║_║₋₁ -- "propositional truncation" ; unit-trunc-Prop -- "the map `A → ║ A ║₋₁`" ; universal-property-trunc-Prop -- "the universal property of propositional truncation" ) -open import foundation.mere-equivalences using +open import foundation.mere-equivalences funext univalence truncations using ( mere-equiv -- "merely equivalent" ) -open import foundation.univalence-implies-function-extensionality using +open import foundation.univalence-implies-function-extensionality funext univalence truncations using ( funext-univalence -- "univalence implies function extensionality" ) @@ -127,11 +135,11 @@ We reserve the terminology "a coherent idempotent" for what in the article is referred to as "a (fully coherent) idempotent". ```agda -open import foundation.endomorphisms using +open import foundation.endomorphisms funext univalence truncations using ( endo -- "endofunction" ) -open import foundation.idempotent-maps using +open import foundation.idempotent-maps funext using ( is-idempotent -- "idempotency witness" ; idempotent-map -- "pre-idempotent (map)" ) @@ -140,12 +148,12 @@ open import foundation.idempotent-maps using **Definition 3.2.** Retracts and splittings. ```agda -open import foundation.retracts-of-types using +open import foundation.retracts-of-types funext univalence using ( retracts -- "retracts of a type" ; retract -- "type of retracts between two types" ) -open import foundation.split-idempotent-maps using +open import foundation.split-idempotent-maps funext univalence truncations using ( is-split-idempotent -- "splitting of an endofunction" ) ``` @@ -153,7 +161,7 @@ open import foundation.split-idempotent-maps using **Lemma 3.3.** If $f$ has a splitting, then it is pre-idempotent. ```agda -open import foundation.split-idempotent-maps using +open import foundation.split-idempotent-maps funext univalence truncations using ( is-idempotent-is-split-idempotent ) ``` @@ -162,7 +170,7 @@ open import foundation.split-idempotent-maps using equivalence. ```agda -open import foundation.split-idempotent-maps using +open import foundation.split-idempotent-maps funext univalence truncations using ( essentially-unique-splitting-type-is-split-idempotent ) ``` @@ -173,7 +181,7 @@ The library's preferred terminology for "a quasi-idempotent" is "a quasicoherent idempotent". ```agda -open import foundation.quasicoherently-idempotent-maps using +open import foundation.quasicoherently-idempotent-maps funext univalence truncations using ( is-quasicoherently-idempotent -- "the type of witnesses of quasi-idempotence" ; quasicoherently-idempotent-map -- "the type of quasi-idempotents" ) @@ -182,7 +190,7 @@ open import foundation.quasicoherently-idempotent-maps using **Lemma 3.6.** If $f$ has a splitting, then it is a quasi-idempotent. ```agda -open import foundation.split-idempotent-maps using +open import foundation.split-idempotent-maps funext univalence truncations using ( is-quasicoherently-idempotent-is-split-idempotent ) ``` @@ -191,7 +199,7 @@ open import foundation.split-idempotent-maps using splitting. ```agda -open import foundation.split-idempotent-maps using +open import foundation.split-idempotent-maps funext univalence truncations using ( is-split-idempotent-is-idempotent-is-set ) ``` @@ -204,12 +212,12 @@ open import foundation.split-idempotent-maps using splitting. ```agda -open import foundation.weakly-constant-maps using +open import foundation.weakly-constant-maps funext using ( is-weakly-constant -- "the type of witnesses that a map is weakly constant" ; weakly-constant-map -- "the type of weakly constant maps" ) -open import foundation.split-idempotent-maps using +open import foundation.split-idempotent-maps funext univalence truncations using ( is-split-idempotent-is-weakly-constant-is-idempotent ) ``` @@ -219,12 +227,12 @@ is an embedding if and only if it is pre-idempotent and the type $f(x) = x$ admits a weakly constant endofunction for all $x$. ```agda -open import foundation.sections using +open import foundation.sections funext using ( is-section -- "the type of witnesses that a map is a section to a map" ; section -- "the type of sections of a map" ) -open import foundation.embeddings using +open import foundation.embeddings funext using ( is-emb -- "the type of witnesses that a map is an embedding" ; _↪_ -- "the type of embeddings between two types" ) @@ -254,7 +262,7 @@ a coherent system of idempotence data. **Definition 4.2.** The Cantor space. ```agda -open import set-theory.cantor-space using +open import set-theory.cantor-space funext univalence truncations using ( cantor-space -- "C" ) ``` @@ -268,7 +276,7 @@ open import set-theory.cantor-space using **Definition 4.5.** $B\operatorname{Aut}({-})$. ```agda -open import foundation.connected-components-universes using +open import foundation.connected-components-universes funext univalence truncations using ( component-UU -- "BAut(-)" ) ``` @@ -300,11 +308,11 @@ quasi-idempotent map splits. Sequential colimits of types. ```agda -open import synthetic-homotopy-theory.sequential-diagrams using +open import synthetic-homotopy-theory.sequential-diagrams funext univalence using ( sequential-diagram ) -open import synthetic-homotopy-theory.sequential-colimits using +open import synthetic-homotopy-theory.sequential-colimits funext univalence truncations using ( standard-sequential-colimit ) ``` @@ -312,11 +320,11 @@ open import synthetic-homotopy-theory.sequential-colimits using Sequential limits of types. ```agda -open import foundation.inverse-sequential-diagrams using +open import foundation.inverse-sequential-diagrams funext univalence truncations using ( inverse-sequential-diagram ) -open import foundation.sequential-limits using +open import foundation.sequential-limits funext univalence truncations using ( standard-sequential-limit ) ``` @@ -329,7 +337,7 @@ inverse sequential diagrams rather than those that are constantly $f$. Also note that compared to the paper, the coherences in the formalization are transposed. ```agda -open import foundation.sequential-limits using +open import foundation.sequential-limits funext univalence truncations using ( Eq-standard-sequential-limit -- observational equality on standard sequential limits ; extensionality-standard-sequential-limit ) @@ -338,7 +346,7 @@ open import foundation.sequential-limits using **Theorem 5.3.** Assuming function extensionality, any quasi-idempotent splits. ```agda -open import foundation.split-idempotent-maps using +open import foundation.split-idempotent-maps funext univalence truncations using ( is-split-idempotent-is-quasicoherently-idempotent ) ``` @@ -346,7 +354,7 @@ open import foundation.split-idempotent-maps using **Remark 5.4.** Components of the construction. ```agda -open import foundation.split-idempotent-maps using +open import foundation.split-idempotent-maps funext univalence truncations using ( inverse-sequential-diagram-splitting-type-is-quasicoherently-idempotent' ; splitting-type-is-quasicoherently-idempotent' ; inclusion-splitting-type-is-quasicoherently-idempotent' @@ -367,7 +375,7 @@ quasi-idempotence. **Lemma 6.3.** Characterization of the identity types of retract formation. ```agda -open import foundation.retracts-of-types using +open import foundation.retracts-of-types funext univalence using ( equiv-retracts -- observational equality on retracts ; extensionality-retracts ) @@ -398,7 +406,7 @@ definition of coherently idempotent maps is given. **Definition 9.1.** (Fully coherent) idempotents. ```agda -open import foundation.coherently-idempotent-maps using +open import foundation.coherently-idempotent-maps funext univalence truncations using ( is-coherently-idempotent -- "type of (fully coherent) idempotence witnesses" ) ``` diff --git a/src/literature/introduction-to-homotopy-type-theory.lagda.md b/src/literature/introduction-to-homotopy-type-theory.lagda.md index 73694d20ac..a604dcc5d5 100644 --- a/src/literature/introduction-to-homotopy-type-theory.lagda.md +++ b/src/literature/introduction-to-homotopy-type-theory.lagda.md @@ -4,7 +4,15 @@ This file collects references to formalization of constructions, propositions, theorems and exercises from {{#cite Rij22}}. ```agda -module literature.introduction-to-homotopy-type-theory where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module literature.introduction-to-homotopy-type-theory + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where open import foundation.universe-levels ``` @@ -37,7 +45,7 @@ open import elementary-number-theory.addition-natural-numbers using ### 3.3 Pattern matching ```agda -open import elementary-number-theory.fibonacci-sequence using +open import elementary-number-theory.fibonacci-sequence funext univalence truncations using ( Fibonacci-ℕ) ``` @@ -51,16 +59,16 @@ open import elementary-number-theory.multiplication-natural-numbers using ( mul-ℕ ; _*ℕ_) -- (b) -open import elementary-number-theory.exponentiation-natural-numbers using +open import elementary-number-theory.exponentiation-natural-numbers funext univalence truncations using ( exp-ℕ) ``` **Exercise 3.2.** Minimum and maximum. ```agda -open import elementary-number-theory.minimum-natural-numbers using +open import elementary-number-theory.minimum-natural-numbers funext univalence truncations using ( min-ℕ) -open import elementary-number-theory.maximum-natural-numbers using +open import elementary-number-theory.maximum-natural-numbers funext univalence truncations using ( max-ℕ) ``` @@ -72,14 +80,14 @@ open import elementary-number-theory.triangular-numbers using ( triangular-number-ℕ) -- (b) -open import elementary-number-theory.factorials using +open import elementary-number-theory.factorials funext univalence truncations using ( factorial-ℕ) ``` **Exercise 3.4.** Binomial coefficients. ```agda -open import elementary-number-theory.binomial-coefficients using +open import elementary-number-theory.binomial-coefficients funext univalence truncations using ( binomial-coefficient-ℕ ; is-zero-binomial-coefficient-ℕ) ``` @@ -88,7 +96,7 @@ open import elementary-number-theory.binomial-coefficients using numbers. ```agda -open import elementary-number-theory.fibonacci-sequence using +open import elementary-number-theory.fibonacci-sequence funext univalence truncations using ( Fibo) ``` @@ -106,7 +114,7 @@ swapping operation `(m, 0) ↦ (m, 1) ; (m, 1) ↦ (m + 1, 0)`, using the same encoding of pairs with functions as the definition of the Fibonacci sequence. ```agda -open import elementary-number-theory.fibonacci-sequence using +open import elementary-number-theory.fibonacci-sequence funext univalence truncations using ( shift-one ; shift-two) div-two-induction-step : (ℕ → ℕ) → (ℕ → ℕ) @@ -154,7 +162,7 @@ open import foundation.unit-type using **Definition 4.3.1.** The empty type. ```agda -open import foundation.empty-types using +open import foundation.empty-types funext univalence truncations using ( empty -- ∅ ; ind-empty ; ex-falso) @@ -163,16 +171,16 @@ open import foundation.empty-types using **Definition 4.3.2.** Negation of types. ```agda -open import foundation.negation using +open import foundation.negation funext using ( ¬_) -open import foundation.empty-types using +open import foundation.empty-types funext univalence truncations using ( is-empty) ``` **Proposition 4.3.4** Contrapositives. ```agda -open import foundation.negation using +open import foundation.negation funext using ( map-neg) ``` @@ -181,7 +189,7 @@ open import foundation.negation using **Definition 4.4.1.** Coproducts of types. ```agda -open import foundation.coproduct-types using +open import foundation.coproduct-types funext univalence truncations using ( _+_ ; inl ; inr @@ -192,7 +200,7 @@ open import foundation.coproduct-types using **Remark 4.4.2.** Coproducts of functions. ```agda -open import foundation.functoriality-coproduct-types using +open import foundation.functoriality-coproduct-types funext univalence truncations using ( map-coproduct -- f + g : A + B → A' + B' ) ``` @@ -200,7 +208,7 @@ open import foundation.functoriality-coproduct-types using **Proposition 4.4.3.** Projections from coproducts with an empty type. ```agda -open import foundation.type-arithmetic-empty-type using +open import foundation.type-arithmetic-empty-type funext univalence truncations using ( map-right-unit-law-coproduct-is-empty -- is-empty B → (A + B) → A ) ``` @@ -266,7 +274,7 @@ open import foundation.dependent-pair-types using **Definition 4.6.4.** The cartesian product. ```agda -open import foundation.cartesian-product-types using +open import foundation.cartesian-product-types funext univalence using ( _×_ ; ind-product) ``` @@ -282,35 +290,35 @@ open import elementary-number-theory.integers using ( pred-ℤ) -- (b) -open import elementary-number-theory.addition-integers using +open import elementary-number-theory.addition-integers funext univalence truncations using ( add-ℤ) open import elementary-number-theory.integers using ( neg-ℤ) -- (c) -open import elementary-number-theory.multiplication-integers using +open import elementary-number-theory.multiplication-integers funext univalence truncations using ( mul-ℤ) ``` **Exercise 4.2.** Boolean negation, conjunction and disjunction. ```agda -open import foundation.booleans using +open import foundation.booleans funext univalence truncations using ( bool ; false ; true ; ind-bool) -- (a) -open import foundation.booleans using +open import foundation.booleans funext univalence truncations using ( neg-bool) -- (b) -open import foundation.booleans using +open import foundation.booleans funext univalence truncations using ( conjunction-bool) -- (c) -open import foundation.booleans using +open import foundation.booleans funext univalence truncations using ( disjunction-bool) ``` @@ -321,18 +329,18 @@ Note that we call bi-implications _logical equivalences_ in the library. A type `X` for which we can show `¬¬X` is called _irrefutable_. ```agda -open import foundation.logical-equivalences using +open import foundation.logical-equivalences funext using ( _↔_) -- (a) _ : {l : Level} (P : UU l) → ¬ (P × ¬ P) _ = λ P (p , np) → np p -open import foundation.negation using +open import foundation.negation funext using ( no-fixed-points-neg -- ¬(P ↔ ¬P) ) -- (b) -open import foundation.double-negation using +open import foundation.double-negation funext univalence truncations using ( ¬¬_ ; intro-double-negation -- P → ¬¬P ; map-double-negation -- (P → Q) → (¬¬P → ¬¬Q) @@ -340,17 +348,17 @@ open import foundation.double-negation using ) -- (c) -open import foundation.double-negation using +open import foundation.double-negation funext univalence truncations using ( double-negation-double-negation-elim -- ¬¬(¬¬P → P) ; double-negation-Peirces-law -- ¬¬(((P → Q) → P) → P) ; double-negation-linearity-implication -- ¬¬((P → Q) + (Q → P)) ) -open import foundation.irrefutable-propositions using +open import foundation.irrefutable-propositions funext univalence truncations using ( is-irrefutable-is-decidable -- ¬¬(P + ¬P) ) -- (d) -open import foundation.decidable-types using +open import foundation.decidable-types funext univalence truncations using ( double-negation-elim-is-decidable -- (P + ¬P) → (¬¬P → P) ) @@ -366,7 +374,7 @@ _ = ( λ (p : P) → nqp (λ _ → p)) -- (e) -open import logic.double-negation-elimination using +open import logic.double-negation-elimination funext univalence truncations using ( double-negation-elim-neg -- ¬¬(¬ P) → P ; double-negation-elim-exp-neg-neg -- ¬¬(P → ¬¬Q) → (P → ¬¬Q) ; double-negation-elim-product @@ -382,7 +390,7 @@ _ = ( double-negation-elim-neg (¬ Q)) -- (f) -open import foundation.irrefutable-propositions using +open import foundation.irrefutable-propositions funext univalence truncations using ( is-irrefutable-product -- ¬¬A → ¬¬B → ¬¬(A × B) ) @@ -427,7 +435,7 @@ open import lists.lists using ( fold-list) -- (c) -open import lists.functoriality-lists using +open import lists.functoriality-lists funext univalence truncations using ( map-list) -- (d) @@ -435,21 +443,21 @@ open import lists.lists using ( length-list) -- (e) -open import elementary-number-theory.sums-of-natural-numbers using +open import elementary-number-theory.sums-of-natural-numbers funext univalence truncations using ( sum-list-ℕ) -open import elementary-number-theory.products-of-natural-numbers using +open import elementary-number-theory.products-of-natural-numbers funext univalence truncations using ( product-list-ℕ) -- (f) -open import lists.concatenation-lists using +open import lists.concatenation-lists funext univalence truncations using ( concat-list) -- (g) -open import lists.flattening-lists using +open import lists.flattening-lists funext univalence truncations using ( flatten-list) -- (h) -open import lists.reversing-lists using +open import lists.reversing-lists funext univalence truncations using ( reverse-list) ``` @@ -460,7 +468,7 @@ open import lists.reversing-lists using **Definition 5.1.1.** The identity type. ```agda -open import foundation.identity-types using +open import foundation.identity-types funext using ( _＝_ ; Id ; refl ; ind-Id) @@ -471,21 +479,21 @@ open import foundation.identity-types using **Definition 5.2.1.** Concatenation of identifications. ```agda -open import foundation.identity-types using +open import foundation.identity-types funext using ( concat ; _∙_) ``` **Definition 5.2.2.** Inverse operation. ```agda -open import foundation.identity-types using +open import foundation.identity-types funext using ( inv) ``` **Definition 5.2.4.** Associator. ```agda -open import foundation.identity-types using +open import foundation.identity-types funext using ( assoc -- (p ∙ q) ∙ r = p ∙ (q ∙ r) ) ``` @@ -493,7 +501,7 @@ open import foundation.identity-types using **Definition 5.2.5.** Unit law operations. ```agda -open import foundation.identity-types using +open import foundation.identity-types funext using ( left-unit -- refl ∙ p = p ; right-unit -- p ∙ refl = p ) @@ -502,7 +510,7 @@ open import foundation.identity-types using **Definition 5.2.5.** Inverse law operations. ```agda -open import foundation.identity-types using +open import foundation.identity-types funext using ( left-inv -- inv p ∙ p = refl ; right-inv -- p ∙ inv p = refl ) @@ -554,9 +562,10 @@ open import foundation.action-on-identifications-dependent-functions using **Proposition 5.5.1.** Contractibility of singletons. ```agda -open import foundation.torsorial-type-families using +open import foundation.torsorial-type-families funext univalence truncations using ( is-torsorial-Id) -open import foundation.contractible-types using +open import foundation.contractible-types funext univalence +open import foundation.dependent-products-contractible-types funext using ( eq-is-contr') _ : {l : Level} {A : UU l} (a : A) (y : Σ A (λ x → a ＝ x)) → (a , refl) ＝ y @@ -604,7 +613,7 @@ open import elementary-number-theory.addition-natural-numbers using **Exercise 5.1.** Distributivity of inversion over concatenation. ```agda -open import foundation.identity-types using +open import foundation.identity-types funext using ( distributive-inv-concat -- inv (p ∙ q) = inv q ∙ inv p ) ``` @@ -612,7 +621,7 @@ open import foundation.identity-types using **Exercise 5.2.** Transposing concatenation. ```agda -open import foundation.identity-types using +open import foundation.identity-types funext using ( left-transpose-eq-concat -- (p ∙ q = r) → (q = inv p ∙ r) ; right-transpose-eq-concat -- (p ∙ q = r) → (p = r ∙ inv q) ) @@ -621,14 +630,14 @@ open import foundation.identity-types using **Exercise 5.3.** Path lifting. ```agda -open import foundation.equality-dependent-pair-types using +open import foundation.equality-dependent-pair-types funext using ( eq-pair-eq-base) ``` **Exercise 5.4.** Mac Lane pentagon. ```agda -open import foundation.identity-types using +open import foundation.identity-types funext using ( mac-lane-pentagon) ``` @@ -677,13 +686,13 @@ open import elementary-number-theory.integers using ```agda -- (a) -open import elementary-number-theory.addition-integers using +open import elementary-number-theory.addition-integers funext univalence truncations using ( left-unit-law-add-ℤ -- 0 + x = x ; right-unit-law-add-ℤ -- x + 0 = x ) -- (b) -open import elementary-number-theory.addition-integers using +open import elementary-number-theory.addition-integers funext univalence truncations using ( left-predecessor-law-add-ℤ -- pred x + y = pred (x + y) ; right-predecessor-law-add-ℤ -- x + pred y = pred (x + y) ; left-successor-law-add-ℤ -- succ x + y = succ (x + y) @@ -691,13 +700,13 @@ open import elementary-number-theory.addition-integers using ) -- (c) -open import elementary-number-theory.addition-integers using +open import elementary-number-theory.addition-integers funext univalence truncations using ( associative-add-ℤ -- (x + y) + z = x + (y + z) ; commutative-add-ℤ -- x + y = y + x ) -- (d) -open import elementary-number-theory.addition-integers using +open import elementary-number-theory.addition-integers funext univalence truncations using ( left-inverse-law-add-ℤ -- (-x) + x = 0 ; right-inverse-law-add-ℤ -- x + (-x) = 0 ) @@ -707,7 +716,7 @@ open import elementary-number-theory.addition-integers using ```agda -- (a) -open import elementary-number-theory.multiplication-integers using +open import elementary-number-theory.multiplication-integers funext univalence truncations using ( left-zero-law-mul-ℤ -- 0 * x = x ; right-zero-law-mul-ℤ -- x * 0 = x ; left-unit-law-mul-ℤ -- 1 * x = x @@ -715,7 +724,7 @@ open import elementary-number-theory.multiplication-integers using ) -- (b) -open import elementary-number-theory.multiplication-integers using +open import elementary-number-theory.multiplication-integers funext univalence truncations using ( left-predecessor-law-mul-ℤ' -- pred x * y = x * y - y ; right-predecessor-law-mul-ℤ' -- x * pred y = x * y - x ; left-successor-law-mul-ℤ' -- succ x * y = x * y + y @@ -723,13 +732,13 @@ open import elementary-number-theory.multiplication-integers using ) -- (c) -open import elementary-number-theory.multiplication-integers using +open import elementary-number-theory.multiplication-integers funext univalence truncations using ( left-distributive-mul-add-ℤ -- x * (y + z) = x * y + x * z ; right-distributive-mul-add-ℤ -- (x + y) * z = x * z + y * z ) -- (d) -open import elementary-number-theory.multiplication-integers using +open import elementary-number-theory.multiplication-integers funext univalence truncations using ( associative-mul-ℤ -- (x * y) * z = x * (y * z) ; commutative-mul-ℤ -- x * y = y * x ) @@ -786,7 +795,7 @@ open import foundation.universe-levels using **Remark 6.2.4.** Inclusions into the successor universe. ```agda -open import foundation.raising-universe-levels using +open import foundation-core.raising-universe-levels using ( raise) _ : (l : Level) → UU l → UU (lsuc l) @@ -811,14 +820,14 @@ unrelated, Agda considers them equal. Other universe equalities may be found in **Definition 6.3.1.** Observational equality of ℕ. ```agda -open import elementary-number-theory.equality-natural-numbers using +open import elementary-number-theory.equality-natural-numbers funext univalence truncations using ( Eq-ℕ) ``` **Lemma 6.3.2.** Observational equality of ℕ is reflexive. ```agda -open import elementary-number-theory.equality-natural-numbers using +open import elementary-number-theory.equality-natural-numbers funext univalence truncations using ( refl-Eq-ℕ) ``` @@ -826,7 +835,7 @@ open import elementary-number-theory.equality-natural-numbers using identifications. ```agda -open import elementary-number-theory.equality-natural-numbers using +open import elementary-number-theory.equality-natural-numbers funext univalence truncations using ( Eq-eq-ℕ ; eq-Eq-ℕ) @@ -923,11 +932,11 @@ open import elementary-number-theory.multiplication-natural-numbers using ```agda -- (a) -open import foundation.booleans using +open import foundation.booleans funext univalence truncations using ( Eq-bool) -- (b) -open import foundation.booleans using +open import foundation.booleans funext univalence truncations using ( Eq-eq-bool ; eq-Eq-bool) @@ -935,7 +944,7 @@ _ : (x y : bool) → (x ＝ y) ↔ Eq-bool x y _ = λ x y → (Eq-eq-bool , eq-Eq-bool) -- (c) -open import foundation.booleans using +open import foundation.booleans funext univalence truncations using ( neq-neg-bool -- b ≠ neg-bool b ) _ : ¬ (false ＝ true) @@ -945,22 +954,22 @@ _ = neq-neg-bool false **Exercise 6.3.** Standard linear order on ℕ. ```agda -open import elementary-number-theory.inequality-natural-numbers using +open import elementary-number-theory.inequality-natural-numbers funext univalence truncations using ( _≤-ℕ_) -- (a) -open import elementary-number-theory.inequality-natural-numbers using +open import elementary-number-theory.inequality-natural-numbers funext univalence truncations using ( refl-leq-ℕ ; antisymmetric-leq-ℕ ; transitive-leq-ℕ) -- (b) -open import elementary-number-theory.inequality-natural-numbers using +open import elementary-number-theory.inequality-natural-numbers funext univalence truncations using ( linear-leq-ℕ -- (m ≤ n) + (n ≤ m) ) -- (c) -open import elementary-number-theory.inequality-natural-numbers using +open import elementary-number-theory.inequality-natural-numbers funext univalence truncations using ( preserves-leq-left-add-ℕ ; reflects-leq-left-add-ℕ) @@ -969,7 +978,7 @@ _ = λ m n k → (preserves-leq-left-add-ℕ k m n , reflects-leq-left-add-ℕ k m n) -- (d) -open import elementary-number-theory.inequality-natural-numbers using +open import elementary-number-theory.inequality-natural-numbers funext univalence truncations using ( preserves-leq-left-mul-ℕ ; reflects-order-mul-ℕ) @@ -979,10 +988,10 @@ _ = (preserves-leq-left-mul-ℕ (succ-ℕ k) m n , reflects-order-mul-ℕ k m n) -- (e) -open import elementary-number-theory.minimum-natural-numbers using +open import elementary-number-theory.minimum-natural-numbers funext univalence truncations using ( is-greatest-lower-bound-min-ℕ -- (k ≤ min m n) ↔ (k ≤ m) × (k ≤ n) ) -open import elementary-number-theory.maximum-natural-numbers using +open import elementary-number-theory.maximum-natural-numbers funext univalence truncations using ( is-least-upper-bound-max-ℕ -- (max m n ≤ k) ↔ (m ≤ k) × (n ≤ k) ) ``` @@ -990,23 +999,23 @@ open import elementary-number-theory.maximum-natural-numbers using **Exercise 6.4.** Standard strict order on ℕ. ```agda -open import elementary-number-theory.strict-inequality-natural-numbers using +open import elementary-number-theory.strict-inequality-natural-numbers funext univalence truncations using ( _<-ℕ_) -- (a) -open import elementary-number-theory.strict-inequality-natural-numbers using +open import elementary-number-theory.strict-inequality-natural-numbers funext univalence truncations using ( anti-reflexive-le-ℕ ; antisymmetric-le-ℕ ; transitive-le-ℕ) -- (b) -open import elementary-number-theory.strict-inequality-natural-numbers using +open import elementary-number-theory.strict-inequality-natural-numbers funext univalence truncations using ( succ-le-ℕ -- n < n + 1 ; preserves-le-succ-ℕ -- m < n → m < n + 1 ) -- (c) -open import elementary-number-theory.strict-inequality-natural-numbers using +open import elementary-number-theory.strict-inequality-natural-numbers funext univalence truncations using ( leq-succ-le-ℕ ; le-leq-succ-ℕ ; contradiction-le-ℕ @@ -1022,11 +1031,11 @@ _ = λ m n → contradiction-le-ℕ m n , le-not-leq-ℕ m n **Exercise 6.5.** Distance function on ℕ. ```agda -open import elementary-number-theory.distance-natural-numbers using +open import elementary-number-theory.distance-natural-numbers funext univalence truncations using ( dist-ℕ) -- (a) -open import elementary-number-theory.distance-natural-numbers using +open import elementary-number-theory.distance-natural-numbers funext univalence truncations using ( dist-eq-ℕ ; eq-dist-ℕ ; symmetric-dist-ℕ -- dist m n = dist n m @@ -1039,13 +1048,13 @@ _ = λ m n → (dist-eq-ℕ m n , eq-dist-ℕ m n) -- TODO: b -- (c) -open import elementary-number-theory.distance-natural-numbers using +open import elementary-number-theory.distance-natural-numbers funext univalence truncations using ( translation-invariant-dist-ℕ -- dist (a + m) (a + n) = dist m n ; left-distributive-mul-dist-ℕ' -- dist (k * m) (k * n) = k * (dist m n) ) -- (d) -open import elementary-number-theory.distance-natural-numbers using +open import elementary-number-theory.distance-natural-numbers funext univalence truncations using ( is-additive-right-inverse-dist-ℕ -- x + dist x y = y for x ≤ y ) ``` @@ -1053,7 +1062,7 @@ open import elementary-number-theory.distance-natural-numbers using **Exercise 6.6.** The absolute value function. ```agda -open import elementary-number-theory.absolute-value-integers using +open import elementary-number-theory.absolute-value-integers funext univalence truncations using ( abs-ℤ ; eq-abs-ℤ ; abs-eq-ℤ @@ -1075,14 +1084,14 @@ Note that the library's division relation uses the property `k * d = n`, as opposed to the book's `d * k = n`. ```agda -open import elementary-number-theory.divisibility-natural-numbers using +open import elementary-number-theory.divisibility-natural-numbers funext univalence truncations using ( div-ℕ) ``` **Example 7.1.4.** Divisibility by one. ```agda -open import elementary-number-theory.divisibility-natural-numbers using +open import elementary-number-theory.divisibility-natural-numbers funext univalence truncations using ( div-one-ℕ -- 1 | x ) ``` @@ -1091,7 +1100,7 @@ open import elementary-number-theory.divisibility-natural-numbers using ```agda -open import elementary-number-theory.divisibility-natural-numbers using +open import elementary-number-theory.divisibility-natural-numbers funext univalence truncations using ( div-add-ℕ -- d | x → d | y → d | (x + y) ) ``` @@ -1103,7 +1112,7 @@ The other other two claims are shown in Exercise [7.1](#exercise-7.1). **Definition 7.2.1.** Typal binary relations. ```agda -open import foundation.binary-relations using +open import foundation.binary-relations funext univalence truncations using ( Relation ; is-reflexive ; is-symmetric @@ -1114,14 +1123,14 @@ open import foundation.binary-relations using **Definition 7.2.2.** Congruence relations on ℕ. ```agda -open import elementary-number-theory.congruence-natural-numbers using +open import elementary-number-theory.congruence-natural-numbers funext univalence truncations using ( _≡_mod_) ``` **Example 7.2.3.** The modulus is congruent to zero. ```agda -open import elementary-number-theory.congruence-natural-numbers using +open import elementary-number-theory.congruence-natural-numbers funext univalence truncations using ( cong-zero-ℕ -- k ≡ 0 mod k ) ``` @@ -1129,7 +1138,7 @@ open import elementary-number-theory.congruence-natural-numbers using **Proposition 7.2.4.** Congruence modulo `k` is an equivalence relation. ```agda -open import elementary-number-theory.congruence-natural-numbers using +open import elementary-number-theory.congruence-natural-numbers funext univalence truncations using ( refl-cong-ℕ ; symmetric-cong-ℕ ; transitive-cong-ℕ) @@ -1143,7 +1152,7 @@ The point `⋆` is called `neg-one-Fin` because it represents the element `k - 1 under the inclusion into ℕ. ```agda -open import univalent-combinatorics.standard-finite-types using +open import univalent-combinatorics.standard-finite-types funext univalence truncations using ( Fin ; inl-Fin -- inclusion Fin k → Fin (k + 1) ; neg-one-Fin -- point Fin (k + 1) @@ -1153,14 +1162,14 @@ open import univalent-combinatorics.standard-finite-types using **Definition 7.3.4.** Inclusion into ℕ. ```agda -open import univalent-combinatorics.standard-finite-types using +open import univalent-combinatorics.standard-finite-types funext univalence truncations using ( nat-Fin) ``` **Lemma 7.3.5.** The inclusion into ℕ is bounded. ```agda -open import univalent-combinatorics.standard-finite-types using +open import univalent-combinatorics.standard-finite-types funext univalence truncations using ( strict-upper-bound-nat-Fin -- ι x < k ) ``` @@ -1168,7 +1177,7 @@ open import univalent-combinatorics.standard-finite-types using **Proposition 7.3.6.** The inclusion into ℕ is injective. ```agda -open import univalent-combinatorics.standard-finite-types using +open import univalent-combinatorics.standard-finite-types funext univalence truncations using ( is-injective-nat-Fin) ``` @@ -1184,7 +1193,7 @@ open import foundation.split-surjective-maps using **Definition 7.4.2.** Zero and successor on standard finite types. ```agda -open import univalent-combinatorics.standard-finite-types using +open import univalent-combinatorics.standard-finite-types funext univalence truncations using ( zero-Fin ; skip-zero-Fin ; succ-Fin) @@ -1193,7 +1202,7 @@ open import univalent-combinatorics.standard-finite-types using **Definition 7.4.3.** The surjection from ℕ into standard finite types. ```agda -open import elementary-number-theory.modular-arithmetic-standard-finite-types using +open import elementary-number-theory.modular-arithmetic-standard-finite-types funext univalence truncations using ( mod-succ-ℕ -- [-]ₖ₊₁ ) ``` @@ -1201,11 +1210,11 @@ open import elementary-number-theory.modular-arithmetic-standard-finite-types us **Lemma 7.4.4.** Preservation of zero and successor `mod k`. ```agda -open import univalent-combinatorics.standard-finite-types using +open import univalent-combinatorics.standard-finite-types funext univalence truncations using ( is-zero-nat-zero-Fin -- ι(zero) = 0 ; nat-skip-zero-Fin -- ι(skip-zero x) = ι(x) + 1 ) -open import elementary-number-theory.modular-arithmetic-standard-finite-types using +open import elementary-number-theory.modular-arithmetic-standard-finite-types funext univalence truncations using ( cong-nat-succ-Fin -- ι(succ x) ≡ ι(x) + 1 mod k ) ``` @@ -1213,7 +1222,7 @@ open import elementary-number-theory.modular-arithmetic-standard-finite-types us **Proposition 7.4.5.** ```agda -open import elementary-number-theory.modular-arithmetic-standard-finite-types using +open import elementary-number-theory.modular-arithmetic-standard-finite-types funext univalence truncations using ( cong-nat-mod-succ-ℕ -- ι[x]ₖ₊₁ ≡ x mod (k + 1) ) ``` @@ -1221,14 +1230,14 @@ open import elementary-number-theory.modular-arithmetic-standard-finite-types us **Proposition 7.4.6.** ```agda -open import elementary-number-theory.divisibility-natural-numbers using +open import elementary-number-theory.divisibility-natural-numbers funext univalence truncations using ( is-zero-div-ℕ ; div-is-zero-ℕ) _ : (d x : ℕ) → x <-ℕ d → div-ℕ d x ↔ (x ＝ 0) _ = λ d x x ```agda -open import elementary-number-theory.divisibility-natural-numbers using +open import elementary-number-theory.divisibility-natural-numbers funext univalence truncations using ( div-right-summand-ℕ -- d | x → d | x + y → d | y ; div-left-summand-ℕ -- d | y → d | x + y → d | x ) @@ -1325,7 +1334,7 @@ open import elementary-number-theory.divisibility-natural-numbers using **Exercise 7.2.** Divisibility is a partial order. ```agda -open import elementary-number-theory.divisibility-natural-numbers using +open import elementary-number-theory.divisibility-natural-numbers funext univalence truncations using ( refl-div-ℕ ; antisymmetric-div-ℕ ; transitive-div-ℕ) @@ -1334,25 +1343,25 @@ open import elementary-number-theory.divisibility-natural-numbers using **Exercise 7.3.** `n!` is divisible by all `0 < x ≤ n` ```agda -open import elementary-number-theory.factorials using +open import elementary-number-theory.factorials funext univalence truncations using ( div-factorial-ℕ) ``` **Exercise 7.4.** The successor on `Fin (k + 1)` adds one. ```agda -open import elementary-number-theory.modular-arithmetic-standard-finite-types using +open import elementary-number-theory.modular-arithmetic-standard-finite-types funext univalence truncations using ( is-add-one-succ-Fin') ``` **Exercise 7.5.** Observational equality of `Fin k`. ```agda -open import univalent-combinatorics.equality-standard-finite-types using +open import univalent-combinatorics.equality-standard-finite-types funext univalence truncations using ( Eq-Fin) -- (a) -open import univalent-combinatorics.equality-standard-finite-types using +open import univalent-combinatorics.equality-standard-finite-types funext univalence truncations using ( Eq-Fin-eq ; eq-Eq-Fin) @@ -1360,22 +1369,22 @@ _ : (k : ℕ) → {x y : Fin k} → (x ＝ y) ↔ Eq-Fin k x y _ = λ k → (Eq-Fin-eq k , eq-Eq-Fin k) -- (b) -open import univalent-combinatorics.standard-finite-types using +open import univalent-combinatorics.standard-finite-types funext univalence truncations using ( is-injective-inl-Fin) -- (c) -open import univalent-combinatorics.standard-finite-types using +open import univalent-combinatorics.standard-finite-types funext univalence truncations using ( neq-zero-succ-Fin) -- (d) -open import univalent-combinatorics.standard-finite-types using +open import univalent-combinatorics.standard-finite-types funext univalence truncations using ( is-injective-succ-Fin) ``` **Exercise 7.6.** The predecessor function on `Fin k`. ```agda -open import univalent-combinatorics.standard-finite-types using +open import univalent-combinatorics.standard-finite-types funext univalence truncations using ( neg-two-Fin ; skip-neg-two-Fin ; pred-Fin @@ -1387,11 +1396,11 @@ open import univalent-combinatorics.standard-finite-types using **Exercise 7.7.** Classical finite types. ```agda -open import univalent-combinatorics.classical-finite-types using +open import univalent-combinatorics.classical-finite-types funext univalence truncations using ( classical-Fin) -- (a) -open import univalent-combinatorics.classical-finite-types using +open import univalent-combinatorics.classical-finite-types funext univalence truncations using ( Eq-classical-Fin ; Eq-eq-classical-Fin ; eq-Eq-classical-Fin) @@ -1400,7 +1409,7 @@ _ : (k : ℕ) → (x y : classical-Fin k) → (x ＝ y) ↔ Eq-classical-Fin k x _ = λ k x y → (Eq-eq-classical-Fin k x y , eq-Eq-classical-Fin k x y) -- (b) -open import univalent-combinatorics.classical-finite-types using +open import univalent-combinatorics.classical-finite-types funext univalence truncations using ( classical-standard-Fin -- ι ; standard-classical-Fin -- α ; is-section-classical-standard-Fin -- α (ι x) = x @@ -1411,21 +1420,21 @@ open import univalent-combinatorics.classical-finite-types using **Exercise 7.8.** Multiplication on `ℤ/(k + 1)`. ```agda -open import elementary-number-theory.modular-arithmetic-standard-finite-types using +open import elementary-number-theory.modular-arithmetic-standard-finite-types funext univalence truncations using ( mul-Fin) -- (a) -open import elementary-number-theory.modular-arithmetic-standard-finite-types using +open import elementary-number-theory.modular-arithmetic-standard-finite-types funext univalence truncations using ( cong-mul-Fin -- ι(x * y) ≡ ι x * ι y mod (k + 1) ) -- (b) -open import elementary-number-theory.congruence-natural-numbers using +open import elementary-number-theory.congruence-natural-numbers funext univalence truncations using ( congruence-mul-ℕ -- x ≡ x' → y ≡ y' → (x * y) ≡ (x' * y') ) -- (c) -open import elementary-number-theory.modular-arithmetic-standard-finite-types using +open import elementary-number-theory.modular-arithmetic-standard-finite-types funext univalence truncations using ( associative-mul-Fin -- (x * y) * z = x * (y * z) ; commutative-mul-Fin -- x * y = y * x ; left-unit-law-mul-Fin -- 1 * x = x @@ -1439,7 +1448,7 @@ open import elementary-number-theory.modular-arithmetic-standard-finite-types us ```agda -- (a) -open import elementary-number-theory.euclidean-division-natural-numbers using +open import elementary-number-theory.euclidean-division-natural-numbers funext univalence truncations using ( euclidean-division-ℕ) -- TODO: b @@ -1448,21 +1457,21 @@ open import elementary-number-theory.euclidean-division-natural-numbers using **Exercise 7.10.** `k`-ary natural numbers. ```agda -open import elementary-number-theory.finitary-natural-numbers using +open import elementary-number-theory.finitary-natural-numbers funext univalence truncations using ( based-ℕ -- ℕₖ ; convert-based-ℕ -- fₖ ) -- (a) -open import elementary-number-theory.finitary-natural-numbers using +open import elementary-number-theory.finitary-natural-numbers funext univalence truncations using ( is-empty-based-zero-ℕ) -- (b) -open import elementary-number-theory.finitary-natural-numbers using +open import elementary-number-theory.finitary-natural-numbers funext univalence truncations using ( is-injective-convert-based-ℕ) -- (c) -open import elementary-number-theory.finitary-natural-numbers using +open import elementary-number-theory.finitary-natural-numbers funext univalence truncations using ( inv-convert-based-ℕ -- gₖ ; is-section-inv-convert-based-ℕ -- fₖ₊₁ (gₖ n) = n ; is-retraction-inv-convert-based-ℕ -- gₖ (fₖ₊₁ x) = x @@ -1476,14 +1485,14 @@ open import elementary-number-theory.finitary-natural-numbers using **Definition 8.1.1.** Decidable types. ```agda -open import foundation.decidable-types using +open import foundation.decidable-types funext univalence truncations using ( is-decidable) ``` **Example 8.1.2.** The unit type and the empty type are decidable ```agda -open import foundation.decidable-types using +open import foundation.decidable-types funext univalence truncations using ( is-decidable-unit ; is-decidable-empty) ``` @@ -1491,7 +1500,7 @@ open import foundation.decidable-types using **Example 8.1.3.** Decidability of coproducts, products and functions. ```agda -open import foundation.decidable-types using +open import foundation.decidable-types funext univalence truncations using ( is-decidable-coproduct -- if A and B are decidable, then A + B is decidable ; is-decidable-product -- if A and B are decidable, then A × B is decidable ; is-decidable-function-type -- if A and B are decidable, then A → B is decidable @@ -1502,18 +1511,18 @@ open import foundation.decidable-types using **Example 8.1.4.** Decidability of observational equality and inequality on ℕ. ```agda -open import elementary-number-theory.equality-natural-numbers using +open import elementary-number-theory.equality-natural-numbers funext univalence truncations using ( is-decidable-Eq-ℕ) -open import elementary-number-theory.inequality-natural-numbers using +open import elementary-number-theory.inequality-natural-numbers funext univalence truncations using ( is-decidable-leq-ℕ) -open import elementary-number-theory.strict-inequality-natural-numbers using +open import elementary-number-theory.strict-inequality-natural-numbers funext univalence truncations using ( is-decidable-le-ℕ) ``` **Definition 8.1.5.** Decidable equality. ```agda -open import foundation.decidable-equality using +open import foundation.decidable-equality funext univalence truncations using ( has-decidable-equality) ``` @@ -1521,21 +1530,21 @@ open import foundation.decidable-equality using equivalent. ```agda -open import foundation.decidable-types using +open import foundation.decidable-types funext univalence truncations using ( is-decidable-iff') ``` **Proposition 8.1.7.** Equality on ℕ is decidable. ```agda -open import elementary-number-theory.equality-natural-numbers using +open import elementary-number-theory.equality-natural-numbers funext univalence truncations using ( has-decidable-equality-ℕ) ``` **Proposition 8.1.8.** Equality on `Fin k` is decidable. ```agda -open import univalent-combinatorics.equality-standard-finite-types using +open import univalent-combinatorics.equality-standard-finite-types funext univalence truncations using ( is-decidable-Eq-Fin ; has-decidable-equality-Fin) ``` @@ -1543,7 +1552,7 @@ open import univalent-combinatorics.equality-standard-finite-types using **Theorem 8.1.9.** Divisibility is decidable. ```agda -open import elementary-number-theory.modular-arithmetic-standard-finite-types using +open import elementary-number-theory.modular-arithmetic-standard-finite-types funext univalence truncations using ( is-decidable-div-ℕ) ``` @@ -1556,7 +1565,7 @@ Instead we use Agda's `with` abstraction to do case analysis on the result of `is-decidable-div-ℕ 2 n`, as explained in Remark 8.2.2. ```agda -open import elementary-number-theory.collatz-conjecture using +open import elementary-number-theory.collatz-conjecture funext univalence truncations using ( collatz) ``` @@ -1564,7 +1573,7 @@ open import elementary-number-theory.collatz-conjecture using assumptions. ```agda -open import foundation.decidable-types using +open import foundation.decidable-types funext univalence truncations using ( is-decidable-product' ; is-decidable-function-type') ``` @@ -1572,14 +1581,14 @@ open import foundation.decidable-types using **Proposition 8.2.4.** ```agda -open import elementary-number-theory.decidable-types using +open import elementary-number-theory.decidable-types funext univalence truncations using ( is-decidable-Π-ℕ) ``` **Corollary 8.2.5.** ```agda -open import elementary-number-theory.decidable-types using +open import elementary-number-theory.decidable-types funext univalence truncations using ( is-decidable-bounded-Π-ℕ) ``` @@ -1588,18 +1597,18 @@ open import elementary-number-theory.decidable-types using **Definition 8.3.1.** Bounds for families over ℕ. ```agda -open import elementary-number-theory.lower-bounds-natural-numbers using +open import elementary-number-theory.lower-bounds-natural-numbers funext univalence truncations using ( is-lower-bound-ℕ) -open import elementary-number-theory.upper-bounds-natural-numbers using +open import elementary-number-theory.upper-bounds-natural-numbers funext univalence truncations using ( is-upper-bound-ℕ) -open import elementary-number-theory.well-ordering-principle-natural-numbers using +open import elementary-number-theory.well-ordering-principle-natural-numbers funext univalence truncations using ( minimal-element-ℕ) ``` **Theorem 8.3.2.** Well-ordering principle of ℕ. ```agda -open import elementary-number-theory.well-ordering-principle-natural-numbers using +open import elementary-number-theory.well-ordering-principle-natural-numbers funext univalence truncations using ( well-ordering-principle-ℕ) ``` @@ -1608,49 +1617,49 @@ open import elementary-number-theory.well-ordering-principle-natural-numbers usi **Definition 8.4.1.** The type of greatest common divisors. ```agda -open import elementary-number-theory.greatest-common-divisor-natural-numbers using +open import elementary-number-theory.greatest-common-divisor-natural-numbers funext univalence truncations using ( is-gcd-ℕ) ``` **Proposition 8.4.2.** Uniqueness of the greatest common divisor. ```agda -open import elementary-number-theory.greatest-common-divisor-natural-numbers using +open import elementary-number-theory.greatest-common-divisor-natural-numbers funext univalence truncations using ( uniqueness-is-gcd-ℕ) ``` **Definition 8.4.3.** Multiples of the greatest common divisor. ```agda -open import elementary-number-theory.greatest-common-divisor-natural-numbers using +open import elementary-number-theory.greatest-common-divisor-natural-numbers funext univalence truncations using ( is-multiple-of-gcd-ℕ) ``` **Proposition 8.4.4.** Decidability of multiples of the greatest common divisor. ```agda -open import elementary-number-theory.greatest-common-divisor-natural-numbers using +open import elementary-number-theory.greatest-common-divisor-natural-numbers funext univalence truncations using ( is-decidable-is-multiple-of-gcd-ℕ) ``` **Lemma 8.4.5.** `a + b` is a multiple of `gcd(a, b)`. ```agda -open import elementary-number-theory.greatest-common-divisor-natural-numbers using +open import elementary-number-theory.greatest-common-divisor-natural-numbers funext univalence truncations using ( sum-is-multiple-of-gcd-ℕ) ``` **Definition 8.4.6.** The greatest common divisor. ```agda -open import elementary-number-theory.greatest-common-divisor-natural-numbers using +open import elementary-number-theory.greatest-common-divisor-natural-numbers funext univalence truncations using ( gcd-ℕ) ``` **Lemma 8.4.7.** `gcd(a, b)` is zero if and only if `a + b` = 0. ```agda -open import elementary-number-theory.greatest-common-divisor-natural-numbers using +open import elementary-number-theory.greatest-common-divisor-natural-numbers funext univalence truncations using ( is-zero-gcd-ℕ ; is-zero-add-is-zero-gcd-ℕ) @@ -1661,7 +1670,7 @@ _ = λ a b → (is-zero-add-is-zero-gcd-ℕ a b , is-zero-gcd-ℕ a b) **Theorem 8.4.8.** `gcd(a, b)` is a greatest common divisor. ```agda -open import elementary-number-theory.greatest-common-divisor-natural-numbers using +open import elementary-number-theory.greatest-common-divisor-natural-numbers funext univalence truncations using ( is-gcd-gcd-ℕ) ``` @@ -1670,44 +1679,44 @@ open import elementary-number-theory.greatest-common-divisor-natural-numbers usi **Definition 8.5.1.** Proper divisors and primes. ```agda -open import elementary-number-theory.proper-divisors-natural-numbers using +open import elementary-number-theory.proper-divisors-natural-numbers funext univalence truncations using ( is-proper-divisor-ℕ) -open import elementary-number-theory.prime-numbers using +open import elementary-number-theory.prime-numbers funext univalence truncations using ( is-prime-ℕ) ``` **Proposition 8.5.2.** Being a prime is decidable. ```agda -open import elementary-number-theory.prime-numbers using +open import elementary-number-theory.prime-numbers funext univalence truncations using ( is-decidable-is-prime-ℕ) ``` **Definition 8.5.3.** Sieve of Erathostenes. ```agda -open import elementary-number-theory.sieve-of-eratosthenes using +open import elementary-number-theory.sieve-of-eratosthenes funext univalence truncations using ( in-sieve-of-eratosthenes-ℕ) ``` **Lemma 8.5.4.** Being in the sieve of Erathostenes is decidable. ```agda -open import elementary-number-theory.sieve-of-eratosthenes using +open import elementary-number-theory.sieve-of-eratosthenes funext univalence truncations using ( is-decidable-in-sieve-of-eratosthenes-ℕ) ``` **Lemma 8.5.5.** `n! + 1` is above `n` in the sieve. ```agda -open import elementary-number-theory.sieve-of-eratosthenes using +open import elementary-number-theory.sieve-of-eratosthenes funext univalence truncations using ( in-sieve-of-eratosthenes-succ-factorial-ℕ) ``` **Theorem 8.5.6.** Infinitude of primes. ```agda -open import elementary-number-theory.infinitude-of-primes using +open import elementary-number-theory.infinitude-of-primes funext univalence truncations using ( infinitude-of-primes-ℕ) ``` @@ -1716,14 +1725,14 @@ open import elementary-number-theory.infinitude-of-primes using **Definition 8.6.1.** Booleanization. ```agda -open import reflection.boolean-reflection using +open import reflection.boolean-reflection funext univalence truncations using ( booleanization) ``` **Theorem 8.6.2.** Boolean reflection principle. ```agda -open import reflection.boolean-reflection using +open import reflection.boolean-reflection funext univalence truncations using ( boolean-reflection -- reflect ) @@ -1737,22 +1746,22 @@ _ = boolean-reflection (is-decidable-is-prime-ℕ 37) refl ```agda -- (a) -open import elementary-number-theory.goldbach-conjecture using +open import elementary-number-theory.goldbach-conjecture funext univalence truncations using ( Goldbach-conjecture) -- (b) -open import elementary-number-theory.twin-prime-conjecture using +open import elementary-number-theory.twin-prime-conjecture funext univalence truncations using ( twin-prime-conjecture) -- (c) -open import elementary-number-theory.collatz-conjecture using +open import elementary-number-theory.collatz-conjecture funext univalence truncations using ( Collatz-conjecture) ``` **Exercise 8.2.** `is-decidable` is idempotent. ```agda -open import foundation.decidable-types using +open import foundation.decidable-types funext univalence truncations using ( idempotent-is-decidable -- is-decidable (is-decidable P) → is-decidable P ) ``` @@ -1760,7 +1769,7 @@ open import foundation.decidable-types using **Exercise 8.3.** Markov's principle over finite types. ```agda -open import elementary-number-theory.well-ordering-principle-standard-finite-types using +open import elementary-number-theory.well-ordering-principle-standard-finite-types funext univalence truncations using ( exists-not-not-for-all-Fin -- ¬((x : Fin k) → P x) → Σ (x : Fin k) ¬(P x) ) ``` @@ -1768,7 +1777,7 @@ open import elementary-number-theory.well-ordering-principle-standard-finite-typ **Exercise 8.4.** Prime functions. ```agda -open import elementary-number-theory.infinitude-of-primes using +open import elementary-number-theory.infinitude-of-primes funext univalence truncations using ( prime-ℕ -- n-th prime ; prime-counting-ℕ -- number of primes less than or equal `n` ) @@ -1782,7 +1791,7 @@ TODO decidable equality, assuming the other factor is pointed. ```agda -open import foundation.decidable-equality using +open import foundation.decidable-equality funext univalence truncations using ( has-decidable-equality-product' ; has-decidable-equality-left-factor ; has-decidable-equality-right-factor) @@ -1797,7 +1806,7 @@ _ = has-decidable-equality-left-factor eqAB , has-decidable-equality-right-factor eqAB) -open import foundation.decidable-equality using +open import foundation.decidable-equality funext univalence truncations using ( has-decidable-equality-product) ``` @@ -1809,11 +1818,11 @@ and `B : 𝒱` aren't assumed to be in the same universe, then we need to raise identity type of `A`, the identity type of `B`, and the empty type to `𝒰 ⊔ 𝒱`. ```agda -open import foundation.equality-coproduct-types using +open import foundation.equality-coproduct-types funext univalence truncations using ( Eq-coproduct) -- (a) -open import foundation.equality-coproduct-types using +open import foundation.equality-coproduct-types funext univalence truncations using ( Eq-eq-coproduct ; eq-Eq-coproduct) @@ -1823,7 +1832,7 @@ _ : _ = λ x y → (Eq-eq-coproduct x y , eq-Eq-coproduct x y) -- (b) -open import foundation.decidable-equality using +open import foundation.decidable-equality funext univalence truncations using ( has-decidable-equality-coproduct ; has-decidable-equality-left-summand ; has-decidable-equality-right-summand) @@ -1838,14 +1847,14 @@ _ = has-decidable-equality-left-summand eqAB , has-decidable-equality-right-summand eqAB) -open import elementary-number-theory.equality-integers using +open import elementary-number-theory.equality-integers funext univalence truncations using ( has-decidable-equality-ℤ) ``` **Exercise 8.8.** Decidable equality in dependent pair types. ```agda -open import foundation.decidable-equality using +open import foundation.decidable-equality funext univalence truncations using ( has-decidable-equality-Σ ; has-decidable-equality-fiber-has-decidable-equality-Σ) @@ -1858,7 +1867,7 @@ _ = has-decidable-equality-Σ eqA , has-decidable-equality-fiber-has-decidable-equality-Σ eqA -open import foundation.decidable-equality using +open import foundation.decidable-equality funext univalence truncations using ( has-decidable-equality-base-has-decidable-equality-Σ) ``` @@ -1866,7 +1875,7 @@ open import foundation.decidable-equality using of `Fin k` ```agda -open import univalent-combinatorics.decidable-dependent-function-types using +open import univalent-combinatorics.decidable-dependent-function-types funext univalence truncations using ( is-decidable-Π-Fin) -- TODO: b @@ -1880,7 +1889,7 @@ TODO **Exercise 8.11.** Bézout's identity. ```agda -open import elementary-number-theory.bezouts-lemma-natural-numbers using +open import elementary-number-theory.bezouts-lemma-natural-numbers funext univalence truncations using ( is-decidable-is-distance-between-multiples-ℕ --^ Σ (k : ℕ) Σ (l : ℕ) dist(k*x, l*x) = z is decidable ; minimal-positive-distance-x-coeff @@ -1901,18 +1910,18 @@ _ = **Exercise 8.12.** Prime factor decomposition. ```agda -open import elementary-number-theory.fundamental-theorem-of-arithmetic using +open import elementary-number-theory.fundamental-theorem-of-arithmetic funext univalence truncations using ( nat-least-nontrivial-divisor-ℕ -- for every 1 < n a number... ; is-prime-least-nontrivial-divisor-ℕ -- which is a prime... ; div-least-nontrivial-divisor-ℕ -- and divides n ) -open import elementary-number-theory.fundamental-theorem-of-arithmetic using +open import elementary-number-theory.fundamental-theorem-of-arithmetic funext univalence truncations using ( list-fundamental-theorem-arithmetic-ℕ -- for every 1 < n a list of numbers... ; is-sorted-list-fundamental-theorem-arithmetic-ℕ -- which is sorted... ; is-prime-list-fundamental-theorem-arithmetic-ℕ -- only contains primes... ; is-decomposition-list-fundamental-theorem-arithmetic-ℕ -- and multiplies up to n ) -open import elementary-number-theory.fundamental-theorem-of-arithmetic using +open import elementary-number-theory.fundamental-theorem-of-arithmetic funext univalence truncations using ( eq-prime-decomposition-list-ℕ -- prime decompositions of a fixed number are equal ) ``` @@ -1928,7 +1937,7 @@ TODO. **Exercise 8.15.** The cofibonacci sequenece. ```agda -open import elementary-number-theory.cofibonacci using +open import elementary-number-theory.cofibonacci funext univalence truncations using ( cofibonacci ; forward-is-left-adjoint-cofibonacci) diff --git a/src/literature/oeis.lagda.md b/src/literature/oeis.lagda.md index 9ecf4af942..1eddd56857 100644 --- a/src/literature/oeis.lagda.md +++ b/src/literature/oeis.lagda.md @@ -4,16 +4,24 @@ This file records formalized sequences of the [Online Encyclopedia of Integer Sequences](https://oeis.org) {{#cite oeis}}. ```agda -module literature.oeis where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module literature.oeis + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.exponentiation-natural-numbers +open import elementary-number-theory.exponentiation-natural-numbers funext univalence truncations open import elementary-number-theory.natural-numbers -open import foundation.function-types +open import foundation.function-types funext ```
@@ -23,14 +31,14 @@ open import foundation.function-types ### [A000001](https://oeis.org/A000001) The number of groups of order `n` ```agda -open import finite-group-theory.finite-groups using +open import finite-group-theory.finite-groups funext univalence truncations using ( number-of-groups-of-order) ``` ### [A000002](https://oeis.org/A000002) The Kolakoski sequence ```agda -open import elementary-number-theory.kolakoski-sequence using +open import elementary-number-theory.kolakoski-sequence funext univalence truncations using ( kolakoski) ``` @@ -52,7 +60,7 @@ A000007 (succ-ℕ _) = 0 ### [A000010](https://oeis.org/A000010) Euler's totient function ```agda -open import elementary-number-theory.eulers-totient-function using +open import elementary-number-theory.eulers-totient-function funext univalence truncations using ( eulers-totient-function-relatively-prime) ``` @@ -73,21 +81,21 @@ A000027 = succ-ℕ ### [A000040](https://oeis.org/A000040) The prime numbers ```agda -open import elementary-number-theory.infinitude-of-primes using +open import elementary-number-theory.infinitude-of-primes funext univalence truncations using ( prime-ℕ) ``` ### [A000045](https://oeis.org/A000045) The Fibonacci sequence ```agda -open import elementary-number-theory.fibonacci-sequence using +open import elementary-number-theory.fibonacci-sequence funext univalence truncations using ( Fibonacci-ℕ) ``` ### [A000058](https://oeis.org/A000058) Sylvester's sequence ```agda -open import elementary-number-theory.sylvesters-sequence using +open import elementary-number-theory.sylvesters-sequence funext univalence truncations using ( sylvesters-sequence-ℕ) ``` @@ -101,28 +109,28 @@ A000079 = exp-ℕ 2 ### [A000108](https://oeis.org/A000108) The Catalan numbers ```agda -open import elementary-number-theory.catalan-numbers using +open import elementary-number-theory.catalan-numbers funext univalence truncations using ( catalan-numbers) ``` ### [A000110](https://oeis.org/A000110) The Bell numbers ```agda -open import elementary-number-theory.bell-numbers using +open import elementary-number-theory.bell-numbers funext univalence truncations using ( bell-number-ℕ) ``` ### [A000142](https://oeis.org/A000142) Factorials ```agda -open import elementary-number-theory.factorials using +open import elementary-number-theory.factorials funext univalence truncations using ( factorial-ℕ) ``` ### [A000215](https://oeis.org/A000215) The Fermat numbers ```agda -open import elementary-number-theory.fermat-numbers using +open import elementary-number-theory.fermat-numbers funext univalence truncations using ( fermat-number-ℕ) ``` @@ -136,28 +144,28 @@ A000244 = exp-ℕ 3 ### [A000720](https://oeis.org/A000720) The prime counting function ```agda -open import elementary-number-theory.infinitude-of-primes using +open import elementary-number-theory.infinitude-of-primes funext univalence truncations using ( prime-counting-ℕ) ``` ### [A000945](https://oeis.org/A000945) The Euclid–Mullin sequence ```agda -open import elementary-number-theory.euclid-mullin-sequence using +open import elementary-number-theory.euclid-mullin-sequence funext univalence truncations using ( euclid-mullin-ℕ) ``` ### [A001175](https://oeis.org/A001175) Pisano periods ```agda -open import elementary-number-theory.pisano-periods using +open import elementary-number-theory.pisano-periods funext univalence truncations using ( pisano-period) ``` ### [A001177](https://oeis.org/A001177) The cofibonacci sequence ```agda -open import elementary-number-theory.cofibonacci using +open import elementary-number-theory.cofibonacci funext univalence truncations using ( cofibonacci) ``` @@ -171,21 +179,21 @@ A001477 = id ### [A003090](https://oeis.org/A003090) The number of main classes of Latin squares of order `n` ```agda -open import univalent-combinatorics.main-classes-of-latin-squares using +open import univalent-combinatorics.main-classes-of-latin-squares funext univalence truncations using ( number-of-main-classes-of-Latin-squares-of-order) ``` ### [A006369](https://oeis.org/A006369) Collatz' bijection ```agda -open import elementary-number-theory.collatz-bijection using +open import elementary-number-theory.collatz-bijection funext univalence truncations using ( map-collatz-bijection) ``` ### [A027851](https://oeis.org/A027851) The number of semigroups of order `n` up to isomorphism ```agda -open import finite-group-theory.finite-semigroups using +open import finite-group-theory.finite-semigroups funext univalence truncations using ( number-of-semigroups-of-order) ``` @@ -199,7 +207,7 @@ open import elementary-number-theory.ackermann-function using ### [A058129](https://oeis.org/A058129) The number of monoids of order `n` up to isomorphism ```agda -open import finite-group-theory.finite-monoids using +open import finite-group-theory.finite-monoids funext univalence truncations using ( number-of-monoids-of-order) ``` diff --git a/src/literature/sequential-colimits-in-homotopy-type-theory.lagda.md b/src/literature/sequential-colimits-in-homotopy-type-theory.lagda.md index 34e5e2e86f..87d46f80b0 100644 --- a/src/literature/sequential-colimits-in-homotopy-type-theory.lagda.md +++ b/src/literature/sequential-colimits-in-homotopy-type-theory.lagda.md @@ -4,7 +4,15 @@ This file collects references to formalization of constructions and theorems from {{#cite SvDR20}}. ```agda -module literature.sequential-colimits-in-homotopy-type-theory where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module literature.sequential-colimits-in-homotopy-type-theory + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ``` ## 2 Homotopy Type Theory @@ -16,7 +24,7 @@ import below for completeness. open import foundation.universe-levels using ( UU ) -open import foundation.identity-types using +open import foundation.identity-types funext using ( Id -- "path" ; refl -- "constant path" ; inv -- "inverse path" @@ -26,20 +34,20 @@ open import foundation.identity-types using open import foundation.action-on-identifications-functions using ( ap -- "functions respect paths" ) -open import foundation.homotopies using +open import foundation.homotopies funext using ( _~_ -- "homotopy" ) -open import foundation.equivalences using +open import foundation.equivalences funext using ( equiv -- "equivalence" ) -open import foundation.univalence using +open import foundation.univalence funext univalence using ( univalence -- "the univalence axiom" ; map-eq -- "function p̅ associated to a path" ) -open import foundation.function-extensionality using +open import foundation.function-extensionality funext using ( funext -- "the function extensionality axiom" ) -open import foundation.fibers-of-maps using +open import foundation.fibers-of-maps funext using ( fiber -- "the homotopy fiber of a function" ) open import foundation.transport-along-identifications using @@ -48,21 +56,22 @@ open import foundation.transport-along-identifications using open import foundation.action-on-identifications-dependent-functions using ( apd -- "dependent functions respect paths" ) -open import foundation.truncated-types using +open import foundation.truncated-types funext univalence +open import foundation.dependent-products-truncated-types funext using ( is-trunc -- "`n`-truncated types" ) -open import foundation.truncations using +open import foundation.truncations funext univalence truncations using ( trunc -- "the `n`-truncation of a type" ; unit-trunc -- "the unit map into a type's `n`-truncation" ; is-truncation-trunc -- "precomposing by the unit is an equivalence" ) -open import foundation.connected-types using +open import foundation.connected-types funext univalence truncations using ( is-connected -- "`n`-connected types" ) -open import foundation.truncated-maps using +open import foundation.truncated-maps funext using ( is-trunc-map -- "`n`-truncated functions" ) -open import foundation.connected-maps using +open import foundation.connected-maps funext univalence truncations using ( is-connected-map -- "`n`-connected functions" ) ``` @@ -77,7 +86,7 @@ sequential colimits, and defines lifts of elements in a sequential diagram. **Definition 3.1.** Sequences. ```agda -open import synthetic-homotopy-theory.sequential-diagrams using +open import synthetic-homotopy-theory.sequential-diagrams funext univalence using ( sequential-diagram ) ``` @@ -96,7 +105,7 @@ universal property, and results about the standard construction of colimits are obtained by specialization to the canonical cocone. ```agda -open import synthetic-homotopy-theory.sequential-colimits using +open import synthetic-homotopy-theory.sequential-colimits funext univalence truncations using ( standard-sequential-colimit -- the canonical colimit type ; map-cocone-standard-sequential-colimit -- "the canonical injection" ; coherence-cocone-standard-sequential-colimit -- "the glue" @@ -112,7 +121,7 @@ colimit is specified by the type `htpy-out-of-standard-sequential-colimit`, which we can then turn into a proper homotopy. ```agda -open import synthetic-homotopy-theory.sequential-colimits using +open import synthetic-homotopy-theory.sequential-colimits funext univalence truncations using ( htpy-out-of-standard-sequential-colimit -- data of a homotopy ; htpy-htpy-out-of-standard-sequential-colimit -- "data of a homotopy induces a homotopy" ) @@ -125,12 +134,12 @@ We call natural transformations _morphisms of sequential diagrams_, and natural equivalences _equivalences of sequential diagrams_. ```agda -open import synthetic-homotopy-theory.morphisms-sequential-diagrams using +open import synthetic-homotopy-theory.morphisms-sequential-diagrams funext univalence truncations using ( hom-sequential-diagram -- "natural transformation" ; id-hom-sequential-diagram -- "identity natural transformation" ; comp-hom-sequential-diagram -- "composition of natural transformations" ) -open import synthetic-homotopy-theory.equivalences-sequential-diagrams using +open import synthetic-homotopy-theory.equivalences-sequential-diagrams funext univalence truncations using ( equiv-sequential-diagram -- "natural equivalence" ) ``` @@ -138,7 +147,7 @@ open import synthetic-homotopy-theory.equivalences-sequential-diagrams using **Lemma 3.5.** Functoriality of the Sequential Colimit. ```agda -open import synthetic-homotopy-theory.functoriality-sequential-colimits using +open import synthetic-homotopy-theory.functoriality-sequential-colimits funext univalence truncations using ( map-hom-standard-sequential-colimit -- "a natural transformation induces a map" ; preserves-id-map-hom-standard-sequential-colimit -- "1∞ ~ id(A∞)" ; preserves-comp-map-hom-standard-sequential-colimit -- "(σ ∘ τ)∞ ~ σ∞ ∘ τ∞" @@ -160,7 +169,7 @@ property of a colimit of `A`. Specializing to the standard sequential colimit, we get and equivalence `A[k]∞ ≃ A∞`. ```agda -open import synthetic-homotopy-theory.shifts-sequential-diagrams using +open import synthetic-homotopy-theory.shifts-sequential-diagrams funext univalence truncations using ( compute-sequential-colimit-shift-sequential-diagram -- "A[k]∞ ≃ A∞" ) compute-sequential-colimit-shift-sequential-diagram-once = @@ -181,7 +190,7 @@ The paper defines fibered sequences as a family over the total space **Definition 4.1.** Fibered sequences. Equifibered sequences. ```agda -open import synthetic-homotopy-theory.dependent-sequential-diagrams using +open import synthetic-homotopy-theory.dependent-sequential-diagrams funext univalence using ( dependent-sequential-diagram -- "A sequence (B, b) fibered over (A, a)" ) ``` @@ -199,7 +208,7 @@ because it characterizes families over a sequential colimit. **Definition 4.3.** Σ of a fibered sequence. ```agda -open import synthetic-homotopy-theory.total-sequential-diagrams using +open import synthetic-homotopy-theory.total-sequential-diagrams funext univalence truncations using ( total-sequential-diagram -- "Σ (A, a) (B, b)" ; pr1-total-sequential-diagram -- "the canonical projection" ) diff --git a/src/logic.lagda.md b/src/logic.lagda.md index 840556f77d..37fcbe1e5b 100644 --- a/src/logic.lagda.md +++ b/src/logic.lagda.md @@ -3,22 +3,30 @@ ## Modules in the logic namespace ```agda -module logic where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom -open import logic.complements-de-morgan-subtypes public -open import logic.complements-decidable-subtypes public -open import logic.complements-double-negation-stable-subtypes public -open import logic.de-morgan-embeddings public -open import logic.de-morgan-maps public -open import logic.de-morgan-propositions public -open import logic.de-morgan-subtypes public -open import logic.de-morgan-types public -open import logic.de-morgans-law public -open import logic.double-negation-eliminating-maps public -open import logic.double-negation-elimination public -open import logic.double-negation-stable-embeddings public -open import logic.double-negation-stable-subtypes public -open import logic.functoriality-existential-quantification public -open import logic.markovian-types public -open import logic.markovs-principle public +module logic + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where + +open import logic.complements-de-morgan-subtypes funext univalence truncations public +open import logic.complements-decidable-subtypes funext univalence truncations public +open import logic.complements-double-negation-stable-subtypes funext univalence truncations public +open import logic.de-morgan-embeddings funext univalence truncations public +open import logic.de-morgan-maps funext univalence truncations public +open import logic.de-morgan-propositions funext univalence truncations public +open import logic.de-morgan-subtypes funext univalence truncations public +open import logic.de-morgan-types funext univalence truncations public +open import logic.de-morgans-law funext univalence truncations public +open import logic.double-negation-eliminating-maps funext univalence truncations public +open import logic.double-negation-elimination funext univalence truncations public +open import logic.double-negation-stable-embeddings funext univalence truncations public +open import logic.double-negation-stable-subtypes funext univalence truncations public +open import logic.functoriality-existential-quantification funext univalence truncations public +open import logic.markovian-types funext univalence truncations public +open import logic.markovs-principle funext univalence truncations public ``` diff --git a/src/logic/complements-de-morgan-subtypes.lagda.md b/src/logic/complements-de-morgan-subtypes.lagda.md index fbfe0b0e4a..6a889c8e35 100644 --- a/src/logic/complements-de-morgan-subtypes.lagda.md +++ b/src/logic/complements-de-morgan-subtypes.lagda.md @@ -1,31 +1,39 @@ # Complements of De Morgan subtypes ```agda -module logic.complements-de-morgan-subtypes where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module logic.complements-de-morgan-subtypes + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.complements-subtypes -open import foundation.decidable-subtypes +open import foundation.complements-subtypes funext univalence truncations +open import foundation.decidable-subtypes funext univalence truncations open import foundation.dependent-pair-types -open import foundation.double-negation -open import foundation.full-subtypes -open import foundation.involutions -open import foundation.negation -open import foundation.postcomposition-functions -open import foundation.powersets -open import foundation.propositional-truncations -open import foundation.subtypes -open import foundation.unions-subtypes +open import foundation.double-negation funext univalence truncations +open import foundation.full-subtypes funext univalence truncations +open import foundation.involutions funext univalence +open import foundation.negation funext +open import foundation.postcomposition-functions funext +open import foundation.powersets funext univalence truncations +open import foundation.propositional-truncations funext univalence +open import foundation.subtypes funext univalence truncations +open import foundation.unions-subtypes funext univalence truncations open import foundation.universe-levels open import foundation-core.function-types -open import logic.complements-decidable-subtypes -open import logic.de-morgan-propositions -open import logic.de-morgan-subtypes +open import logic.complements-decidable-subtypes funext univalence truncations +open import logic.de-morgan-propositions funext univalence truncations +open import logic.de-morgan-subtypes funext univalence truncations ```
diff --git a/src/logic/complements-decidable-subtypes.lagda.md b/src/logic/complements-decidable-subtypes.lagda.md index ae2a775f33..ad8bf92967 100644 --- a/src/logic/complements-decidable-subtypes.lagda.md +++ b/src/logic/complements-decidable-subtypes.lagda.md @@ -1,33 +1,41 @@ # Complements of decidable subtypes ```agda -module logic.complements-decidable-subtypes where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module logic.complements-decidable-subtypes + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.complements-subtypes -open import foundation.coproduct-types -open import foundation.decidable-propositions -open import foundation.decidable-subtypes -open import foundation.decidable-types +open import foundation.complements-subtypes funext univalence truncations +open import foundation.coproduct-types funext univalence truncations +open import foundation.decidable-propositions funext univalence truncations +open import foundation.decidable-subtypes funext univalence truncations +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.double-negation-stable-propositions +open import foundation.double-negation-stable-propositions funext univalence truncations open import foundation.evaluation-functions -open import foundation.full-subtypes -open import foundation.involutions -open import foundation.negation -open import foundation.postcomposition-functions -open import foundation.powersets -open import foundation.propositional-truncations -open import foundation.unions-subtypes +open import foundation.full-subtypes funext univalence truncations +open import foundation.involutions funext univalence +open import foundation.negation funext +open import foundation.postcomposition-functions funext +open import foundation.powersets funext univalence truncations +open import foundation.propositional-truncations funext univalence +open import foundation.unions-subtypes funext univalence truncations open import foundation.universe-levels open import foundation-core.function-types -open import foundation-core.subtypes +open import foundation-core.subtypes funext -open import logic.double-negation-stable-subtypes +open import logic.double-negation-stable-subtypes funext univalence truncations ```
diff --git a/src/logic/complements-double-negation-stable-subtypes.lagda.md b/src/logic/complements-double-negation-stable-subtypes.lagda.md index e4ba546190..55e0606901 100644 --- a/src/logic/complements-double-negation-stable-subtypes.lagda.md +++ b/src/logic/complements-double-negation-stable-subtypes.lagda.md @@ -1,28 +1,36 @@ # Complements of double negation stable subtypes ```agda -module logic.complements-double-negation-stable-subtypes where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module logic.complements-double-negation-stable-subtypes + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.double-negation -open import foundation.double-negation-stable-propositions -open import foundation.full-subtypes -open import foundation.involutions -open import foundation.negation -open import foundation.postcomposition-functions -open import foundation.powersets -open import foundation.propositional-truncations -open import foundation.subtypes -open import foundation.unions-subtypes +open import foundation.double-negation funext univalence truncations +open import foundation.double-negation-stable-propositions funext univalence truncations +open import foundation.full-subtypes funext univalence truncations +open import foundation.involutions funext univalence +open import foundation.negation funext +open import foundation.postcomposition-functions funext +open import foundation.powersets funext univalence truncations +open import foundation.propositional-truncations funext univalence +open import foundation.subtypes funext univalence truncations +open import foundation.unions-subtypes funext univalence truncations open import foundation.universe-levels open import foundation-core.function-types -open import logic.double-negation-stable-subtypes +open import logic.double-negation-stable-subtypes funext univalence truncations ```
diff --git a/src/logic/de-morgan-embeddings.lagda.md b/src/logic/de-morgan-embeddings.lagda.md index 3391dea43b..60cc6ced01 100644 --- a/src/logic/de-morgan-embeddings.lagda.md +++ b/src/logic/de-morgan-embeddings.lagda.md @@ -1,35 +1,44 @@ # De Morgan embeddings ```agda -module logic.de-morgan-embeddings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module logic.de-morgan-embeddings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cartesian-morphisms-arrows -open import foundation.decidable-embeddings -open import foundation.decidable-maps -open import foundation.decidable-propositions -open import foundation.decidable-types +open import foundation.cartesian-morphisms-arrows funext univalence truncations +open import foundation.decidable-embeddings funext univalence truncations +open import foundation.decidable-maps funext univalence truncations +open import foundation.decidable-propositions funext univalence truncations +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.fibers-of-maps -open import foundation.functoriality-cartesian-product-types -open import foundation.functoriality-coproduct-types +open import foundation.dependent-products-propositions funext +open import foundation.embeddings funext +open import foundation.fibers-of-maps funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.functoriality-coproduct-types funext univalence truncations open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopy-induction -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.negation -open import foundation.propositional-maps -open import foundation.propositions -open import foundation.retracts-of-maps +open import foundation.homotopy-induction funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.negation funext +open import foundation.propositional-maps funext +open import foundation.propositions funext univalence +open import foundation.retracts-of-maps funext univalence open import foundation.subtype-identity-principle open import foundation.type-arithmetic-dependent-pair-types open import foundation.unit-type -open import foundation.universal-property-equivalences +open import foundation.universal-property-equivalences funext open import foundation.universe-levels open import foundation-core.cartesian-product-types @@ -42,11 +51,11 @@ open import foundation-core.homotopies open import foundation-core.injective-maps open import foundation-core.torsorial-type-families -open import logic.de-morgan-maps -open import logic.de-morgan-propositions -open import logic.de-morgan-types -open import logic.double-negation-eliminating-maps -open import logic.double-negation-elimination +open import logic.de-morgan-maps funext univalence truncations +open import logic.de-morgan-propositions funext univalence truncations +open import logic.de-morgan-types funext univalence truncations +open import logic.double-negation-eliminating-maps funext univalence truncations +open import logic.double-negation-elimination funext univalence truncations ```
diff --git a/src/logic/de-morgan-maps.lagda.md b/src/logic/de-morgan-maps.lagda.md index 17b5a68d6e..1a536521d0 100644 --- a/src/logic/de-morgan-maps.lagda.md +++ b/src/logic/de-morgan-maps.lagda.md @@ -1,7 +1,15 @@ # De Morgan maps ```agda -module logic.de-morgan-maps where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module logic.de-morgan-maps + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,28 +18,29 @@ module logic.de-morgan-maps where open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.cartesian-morphisms-arrows -open import foundation.coproduct-types -open import foundation.decidable-equality -open import foundation.decidable-maps -open import foundation.decidable-types +open import foundation.cartesian-morphisms-arrows funext univalence truncations +open import foundation.coproduct-types funext univalence truncations +open import foundation.decidable-equality funext univalence truncations +open import foundation.decidable-maps funext univalence truncations +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.double-negation -open import foundation.embeddings -open import foundation.empty-types -open import foundation.existential-quantification -open import foundation.functoriality-cartesian-product-types -open import foundation.functoriality-coproduct-types -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.negation -open import foundation.propositions -open import foundation.retractions -open import foundation.retracts-of-maps -open import foundation.retracts-of-types +open import foundation.dependent-products-propositions funext +open import foundation.double-negation funext univalence truncations +open import foundation.embeddings funext +open import foundation.empty-types funext univalence truncations +open import foundation.existential-quantification funext univalence truncations +open import foundation.functoriality-cartesian-product-types funext +open import foundation.functoriality-coproduct-types funext univalence truncations +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.negation funext +open import foundation.propositions funext univalence +open import foundation.retractions funext +open import foundation.retracts-of-maps funext univalence +open import foundation.retracts-of-types funext univalence open import foundation.transport-along-identifications open import foundation.unit-type -open import foundation.universal-property-equivalences +open import foundation.universal-property-equivalences funext open import foundation.universe-levels open import foundation-core.contractible-maps @@ -41,10 +50,10 @@ open import foundation-core.function-types open import foundation-core.functoriality-dependent-pair-types open import foundation-core.homotopies -open import logic.de-morgan-types -open import logic.de-morgans-law -open import logic.double-negation-eliminating-maps -open import logic.double-negation-elimination +open import logic.de-morgan-types funext univalence truncations +open import logic.de-morgans-law funext univalence truncations +open import logic.double-negation-eliminating-maps funext univalence truncations +open import logic.double-negation-elimination funext univalence truncations ```
diff --git a/src/logic/de-morgan-propositions.lagda.md b/src/logic/de-morgan-propositions.lagda.md index 5ca81ba117..8eeb904564 100644 --- a/src/logic/de-morgan-propositions.lagda.md +++ b/src/logic/de-morgan-propositions.lagda.md @@ -1,43 +1,53 @@ # De Morgan propositions ```agda -module logic.de-morgan-propositions where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module logic.de-morgan-propositions + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.cartesian-product-types -open import foundation.conjunction -open import foundation.contractible-types -open import foundation.coproduct-types -open import foundation.decidable-types +open import foundation.cartesian-product-types funext univalence +open import foundation.conjunction funext univalence truncations +open import foundation.contractible-types funext univalence +open import foundation.coproduct-types funext univalence truncations +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.disjunction -open import foundation.double-negation -open import foundation.embeddings -open import foundation.empty-types -open import foundation.equivalences +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.disjunction funext univalence truncations +open import foundation.double-negation funext univalence truncations +open import foundation.embeddings funext +open import foundation.empty-types funext univalence truncations +open import foundation.equivalences funext open import foundation.evaluation-functions -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.identity-types -open import foundation.irrefutable-propositions -open import foundation.logical-equivalences -open import foundation.negation -open import foundation.propositional-extensionality -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.retracts-of-types -open import foundation.sets -open import foundation.subtypes +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.identity-types funext +open import foundation.irrefutable-propositions funext univalence truncations +open import foundation.logical-equivalences funext +open import foundation.negation funext +open import foundation.propositional-extensionality funext univalence truncations +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence +open import foundation.retracts-of-types funext univalence +open import foundation.sets funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.transport-along-identifications open import foundation.universe-levels -open import foundation-core.decidable-propositions +open import foundation-core.decidable-propositions funext univalence truncations -open import logic.de-morgan-types -open import logic.de-morgans-law +open import logic.de-morgan-types funext univalence truncations +open import logic.de-morgans-law funext univalence truncations ```
diff --git a/src/logic/de-morgan-subtypes.lagda.md b/src/logic/de-morgan-subtypes.lagda.md index 8981009f85..e68c0b8fdc 100644 --- a/src/logic/de-morgan-subtypes.lagda.md +++ b/src/logic/de-morgan-subtypes.lagda.md @@ -1,24 +1,33 @@ # De Morgan subtypes ```agda -module logic.de-morgan-subtypes where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module logic.de-morgan-subtypes + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.1-types -open import foundation.coproduct-types +open import foundation.1-types funext univalence +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types -open import foundation.functoriality-cartesian-product-types -open import foundation.functoriality-dependent-pair-types -open import foundation.logical-equivalences -open import foundation.propositional-maps -open import foundation.sets -open import foundation.structured-type-duality -open import foundation.subtypes -open import foundation.type-theoretic-principle-of-choice +open import foundation.dependent-products-propositions funext +open import foundation.equality-dependent-function-types funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.logical-equivalences funext +open import foundation.propositional-maps funext +open import foundation.sets funext univalence +open import foundation.structured-type-duality funext univalence truncations +open import foundation.subtypes funext univalence truncations +open import foundation.type-theoretic-principle-of-choice funext open import foundation.universe-levels open import foundation-core.embeddings @@ -31,10 +40,10 @@ open import foundation-core.propositions open import foundation-core.truncated-types open import foundation-core.truncation-levels -open import logic.de-morgan-embeddings -open import logic.de-morgan-maps -open import logic.de-morgan-propositions -open import logic.de-morgan-types +open import logic.de-morgan-embeddings funext univalence truncations +open import logic.de-morgan-maps funext univalence truncations +open import logic.de-morgan-propositions funext univalence truncations +open import logic.de-morgan-types funext univalence truncations ```
diff --git a/src/logic/de-morgan-types.lagda.md b/src/logic/de-morgan-types.lagda.md index a87cd18593..76e0af3857 100644 --- a/src/logic/de-morgan-types.lagda.md +++ b/src/logic/de-morgan-types.lagda.md @@ -1,40 +1,50 @@ # De Morgan types ```agda -module logic.de-morgan-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module logic.de-morgan-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.cartesian-product-types -open import foundation.conjunction -open import foundation.contractible-types -open import foundation.coproduct-types -open import foundation.decidable-types +open import foundation.cartesian-product-types funext univalence +open import foundation.conjunction funext univalence truncations +open import foundation.contractible-types funext univalence +open import foundation.coproduct-types funext univalence truncations +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.disjunction -open import foundation.double-negation -open import foundation.empty-types +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.disjunction funext univalence truncations +open import foundation.double-negation funext univalence truncations +open import foundation.empty-types funext univalence truncations open import foundation.evaluation-functions -open import foundation.function-types -open import foundation.identity-types -open import foundation.irrefutable-propositions -open import foundation.logical-equivalences -open import foundation.negation -open import foundation.precomposition-functions -open import foundation.propositional-truncations -open import foundation.retracts-of-types +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.irrefutable-propositions funext univalence truncations +open import foundation.logical-equivalences funext +open import foundation.negation funext +open import foundation.precomposition-functions funext +open import foundation.propositional-truncations funext univalence +open import foundation.retracts-of-types funext univalence open import foundation.truncation-levels -open import foundation.truncations +open import foundation.truncations funext univalence truncations open import foundation.unit-type open import foundation.universe-levels -open import foundation-core.decidable-propositions +open import foundation-core.decidable-propositions funext univalence truncations open import foundation-core.equivalences open import foundation-core.propositions -open import logic.de-morgans-law +open import logic.de-morgans-law funext univalence truncations ```
diff --git a/src/logic/de-morgans-law.lagda.md b/src/logic/de-morgans-law.lagda.md index b680aef549..89e256159c 100644 --- a/src/logic/de-morgans-law.lagda.md +++ b/src/logic/de-morgans-law.lagda.md @@ -1,30 +1,39 @@ # De Morgan's law ```agda -module logic.de-morgans-law where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module logic.de-morgans-law + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.cartesian-product-types -open import foundation.conjunction -open import foundation.coproduct-types -open import foundation.decidable-types +open import foundation.cartesian-product-types funext univalence +open import foundation.conjunction funext univalence truncations +open import foundation.coproduct-types funext univalence truncations +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.disjunction -open import foundation.double-negation -open import foundation.empty-types +open import foundation.dependent-products-propositions funext +open import foundation.disjunction funext univalence truncations +open import foundation.double-negation funext univalence truncations +open import foundation.empty-types funext univalence truncations open import foundation.evaluation-functions -open import foundation.function-types -open import foundation.logical-equivalences -open import foundation.negation +open import foundation.function-types funext +open import foundation.logical-equivalences funext +open import foundation.negation funext open import foundation.universe-levels -open import foundation-core.decidable-propositions +open import foundation-core.decidable-propositions funext univalence truncations open import foundation-core.propositions -open import univalent-combinatorics.2-element-types +open import univalent-combinatorics.2-element-types funext univalence truncations ```
diff --git a/src/logic/double-negation-eliminating-maps.lagda.md b/src/logic/double-negation-eliminating-maps.lagda.md index 836e3191e1..dd43302f51 100644 --- a/src/logic/double-negation-eliminating-maps.lagda.md +++ b/src/logic/double-negation-eliminating-maps.lagda.md @@ -1,28 +1,36 @@ # Double negation eliminating maps ```agda -module logic.double-negation-eliminating-maps where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module logic.double-negation-eliminating-maps + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cartesian-morphisms-arrows -open import foundation.coproduct-types -open import foundation.decidable-equality -open import foundation.decidable-maps -open import foundation.decidable-types +open import foundation.cartesian-morphisms-arrows funext univalence truncations +open import foundation.coproduct-types funext univalence truncations +open import foundation.decidable-equality funext univalence truncations +open import foundation.decidable-maps funext univalence truncations +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.double-negation -open import foundation.empty-types -open import foundation.functoriality-cartesian-product-types -open import foundation.functoriality-coproduct-types -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.retractions -open import foundation.retracts-of-maps -open import foundation.retracts-of-types +open import foundation.double-negation funext univalence truncations +open import foundation.empty-types funext univalence truncations +open import foundation.functoriality-cartesian-product-types funext +open import foundation.functoriality-coproduct-types funext univalence truncations +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.retractions funext +open import foundation.retracts-of-maps funext univalence +open import foundation.retracts-of-types funext univalence open import foundation.transport-along-identifications open import foundation.universe-levels @@ -33,7 +41,7 @@ open import foundation-core.function-types open import foundation-core.functoriality-dependent-pair-types open import foundation-core.homotopies -open import logic.double-negation-elimination +open import logic.double-negation-elimination funext univalence truncations ```
diff --git a/src/logic/double-negation-elimination.lagda.md b/src/logic/double-negation-elimination.lagda.md index 1acfd21ebb..8431b818f9 100644 --- a/src/logic/double-negation-elimination.lagda.md +++ b/src/logic/double-negation-elimination.lagda.md @@ -1,27 +1,36 @@ # Double negation elimination ```agda -module logic.double-negation-elimination where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module logic.double-negation-elimination + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.cartesian-product-types -open import foundation.coproduct-types -open import foundation.decidable-types +open import foundation.cartesian-product-types funext univalence +open import foundation.coproduct-types funext univalence truncations +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.double-negation +open import foundation.dependent-products-propositions funext +open import foundation.double-negation funext univalence truncations open import foundation.evaluation-functions -open import foundation.hilberts-epsilon-operators -open import foundation.logical-equivalences -open import foundation.retracts-of-types +open import foundation.hilberts-epsilon-operators funext univalence truncations +open import foundation.logical-equivalences funext +open import foundation.retracts-of-types funext univalence open import foundation.transport-along-identifications open import foundation.unit-type open import foundation.universe-levels open import foundation-core.contractible-types -open import foundation-core.decidable-propositions +open import foundation-core.decidable-propositions funext univalence truncations open import foundation-core.empty-types open import foundation-core.equivalences open import foundation-core.function-types diff --git a/src/logic/double-negation-stable-embeddings.lagda.md b/src/logic/double-negation-stable-embeddings.lagda.md index 4e6a207085..fb9dee71b0 100644 --- a/src/logic/double-negation-stable-embeddings.lagda.md +++ b/src/logic/double-negation-stable-embeddings.lagda.md @@ -1,36 +1,45 @@ # Double negation stable embeddings ```agda -module logic.double-negation-stable-embeddings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module logic.double-negation-stable-embeddings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cartesian-morphisms-arrows -open import foundation.decidable-embeddings -open import foundation.decidable-maps -open import foundation.decidable-propositions -open import foundation.decidable-types +open import foundation.cartesian-morphisms-arrows funext univalence truncations +open import foundation.decidable-embeddings funext univalence truncations +open import foundation.decidable-maps funext univalence truncations +open import foundation.decidable-propositions funext univalence truncations +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.double-negation-stable-propositions -open import foundation.embeddings -open import foundation.fibers-of-maps -open import foundation.functoriality-cartesian-product-types -open import foundation.functoriality-coproduct-types +open import foundation.dependent-products-propositions funext +open import foundation.double-negation-stable-propositions funext univalence truncations +open import foundation.embeddings funext +open import foundation.fibers-of-maps funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.functoriality-coproduct-types funext univalence truncations open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopy-induction -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.negation -open import foundation.propositional-maps -open import foundation.propositions -open import foundation.retracts-of-maps +open import foundation.homotopy-induction funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.negation funext +open import foundation.propositional-maps funext +open import foundation.propositions funext univalence +open import foundation.retracts-of-maps funext univalence open import foundation.subtype-identity-principle open import foundation.type-arithmetic-dependent-pair-types open import foundation.unit-type -open import foundation.universal-property-equivalences +open import foundation.universal-property-equivalences funext open import foundation.universe-levels open import foundation-core.cartesian-product-types @@ -43,8 +52,8 @@ open import foundation-core.homotopies open import foundation-core.injective-maps open import foundation-core.torsorial-type-families -open import logic.double-negation-eliminating-maps -open import logic.double-negation-elimination +open import logic.double-negation-eliminating-maps funext univalence truncations +open import logic.double-negation-elimination funext univalence truncations ```
diff --git a/src/logic/double-negation-stable-subtypes.lagda.md b/src/logic/double-negation-stable-subtypes.lagda.md index 6614510a1b..ad65a767d0 100644 --- a/src/logic/double-negation-stable-subtypes.lagda.md +++ b/src/logic/double-negation-stable-subtypes.lagda.md @@ -1,26 +1,35 @@ # Double negation stable subtypes ```agda -module logic.double-negation-stable-subtypes where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module logic.double-negation-stable-subtypes + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.1-types -open import foundation.coproduct-types +open import foundation.1-types funext univalence +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.double-negation-stable-propositions -open import foundation.equality-dependent-function-types -open import foundation.functoriality-cartesian-product-types -open import foundation.functoriality-dependent-function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.logical-equivalences -open import foundation.propositional-maps -open import foundation.sets -open import foundation.structured-type-duality -open import foundation.subtypes -open import foundation.type-theoretic-principle-of-choice +open import foundation.dependent-products-propositions funext +open import foundation.double-negation-stable-propositions funext univalence truncations +open import foundation.equality-dependent-function-types funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.functoriality-dependent-function-types funext univalence +open import foundation.functoriality-dependent-pair-types funext +open import foundation.logical-equivalences funext +open import foundation.propositional-maps funext +open import foundation.sets funext univalence +open import foundation.structured-type-duality funext univalence truncations +open import foundation.subtypes funext univalence truncations +open import foundation.type-theoretic-principle-of-choice funext open import foundation.universe-levels open import foundation-core.embeddings @@ -34,9 +43,9 @@ open import foundation-core.transport-along-identifications open import foundation-core.truncated-types open import foundation-core.truncation-levels -open import logic.double-negation-eliminating-maps -open import logic.double-negation-elimination -open import logic.double-negation-stable-embeddings +open import logic.double-negation-eliminating-maps funext univalence truncations +open import logic.double-negation-elimination funext univalence truncations +open import logic.double-negation-stable-embeddings funext univalence truncations ```
diff --git a/src/logic/functoriality-existential-quantification.lagda.md b/src/logic/functoriality-existential-quantification.lagda.md index 30953b6729..93d69746a3 100644 --- a/src/logic/functoriality-existential-quantification.lagda.md +++ b/src/logic/functoriality-existential-quantification.lagda.md @@ -1,13 +1,21 @@ # Functoriality of existential quantification ```agda -module logic.functoriality-existential-quantification where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module logic.functoriality-existential-quantification + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.existential-quantification +open import foundation.existential-quantification funext univalence truncations open import foundation.universe-levels open import foundation-core.function-types diff --git a/src/logic/markovian-types.lagda.md b/src/logic/markovian-types.lagda.md index 54b779cddd..136503e369 100644 --- a/src/logic/markovian-types.lagda.md +++ b/src/logic/markovian-types.lagda.md @@ -1,7 +1,15 @@ # Markovian types ```agda -module logic.markovian-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module logic.markovian-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,22 +17,23 @@ module logic.markovian-types where ```agda open import elementary-number-theory.natural-numbers -open import foundation.booleans -open import foundation.decidable-subtypes +open import foundation.decidable-subtypes funext univalence truncations open import foundation.dependent-pair-types -open import foundation.disjunction -open import foundation.existential-quantification -open import foundation.function-types -open import foundation.inhabited-types -open import foundation.negation -open import foundation.universal-quantification +open import foundation.dependent-products-propositions funext +open import foundation.disjunction funext univalence truncations +open import foundation.existential-quantification funext univalence truncations +open import foundation.function-types funext +open import foundation.inhabited-types funext univalence truncations +open import foundation.negation funext +open import foundation.universal-quantification funext univalence truncations open import foundation.universe-levels +open import foundation-core.booleans open import foundation-core.identity-types open import foundation-core.propositions open import foundation-core.sets -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
@@ -41,8 +50,8 @@ then there is an element of `A` that is ### The predicate of being Markovian -We phrase the condition using the [type of booleans](foundation.booleans.md) so -that the predicate is small. +We phrase the condition using the +[type of booleans](foundation-core.booleans.md) so that the predicate is small. ```agda is-markovian : {l : Level} → UU l → UU l diff --git a/src/logic/markovs-principle.lagda.md b/src/logic/markovs-principle.lagda.md index 51ef1a407f..7c6277d7fe 100644 --- a/src/logic/markovs-principle.lagda.md +++ b/src/logic/markovs-principle.lagda.md @@ -1,7 +1,15 @@ # Markov's principle ```agda -module logic.markovs-principle where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module logic.markovs-principle + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,24 +17,24 @@ module logic.markovs-principle where ```agda open import elementary-number-theory.natural-numbers -open import foundation.booleans -open import foundation.decidable-subtypes +open import foundation.decidable-subtypes funext univalence truncations open import foundation.dependent-pair-types -open import foundation.disjunction -open import foundation.existential-quantification -open import foundation.function-types -open import foundation.inhabited-types -open import foundation.negation -open import foundation.universal-quantification +open import foundation.disjunction funext univalence truncations +open import foundation.existential-quantification funext univalence truncations +open import foundation.function-types funext +open import foundation.inhabited-types funext univalence truncations +open import foundation.negation funext +open import foundation.universal-quantification funext univalence truncations open import foundation.universe-levels +open import foundation-core.booleans open import foundation-core.identity-types open import foundation-core.propositions open import foundation-core.sets -open import logic.markovian-types +open import logic.markovian-types funext univalence truncations -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/metric-spaces.lagda.md b/src/metric-spaces.lagda.md index b9016b2906..582b960669 100644 --- a/src/metric-spaces.lagda.md +++ b/src/metric-spaces.lagda.md @@ -43,52 +43,60 @@ property of **indistinguishability of identicals** ## Modules in the metric spaces namespace ```agda -module metric-spaces where - -open import metric-spaces.category-of-metric-spaces-and-isometries public -open import metric-spaces.category-of-metric-spaces-and-short-functions public -open import metric-spaces.cauchy-approximations-metric-spaces public -open import metric-spaces.cauchy-approximations-premetric-spaces public -open import metric-spaces.cauchy-sequences-complete-metric-spaces public -open import metric-spaces.cauchy-sequences-metric-spaces public -open import metric-spaces.closed-premetric-structures public -open import metric-spaces.complete-metric-spaces public -open import metric-spaces.convergent-cauchy-approximations-metric-spaces public -open import metric-spaces.dependent-products-metric-spaces public -open import metric-spaces.discrete-premetric-structures public -open import metric-spaces.equality-of-metric-spaces public -open import metric-spaces.equality-of-premetric-spaces public -open import metric-spaces.extensional-premetric-structures public -open import metric-spaces.functions-metric-spaces public -open import metric-spaces.functor-category-set-functions-isometry-metric-spaces public -open import metric-spaces.functor-category-short-isometry-metric-spaces public -open import metric-spaces.induced-premetric-structures-on-preimages public -open import metric-spaces.isometric-equivalences-premetric-spaces public -open import metric-spaces.isometries-metric-spaces public -open import metric-spaces.isometries-premetric-spaces public -open import metric-spaces.limits-of-cauchy-approximations-in-premetric-spaces public -open import metric-spaces.metric-space-of-cauchy-approximations-in-a-metric-space public -open import metric-spaces.metric-space-of-convergent-cauchy-approximations-in-a-metric-space public -open import metric-spaces.metric-space-of-rational-numbers public -open import metric-spaces.metric-space-of-rational-numbers-with-open-neighborhoods public -open import metric-spaces.metric-spaces public -open import metric-spaces.metric-structures public -open import metric-spaces.monotonic-premetric-structures public -open import metric-spaces.ordering-premetric-structures public -open import metric-spaces.precategory-of-metric-spaces-and-functions public -open import metric-spaces.precategory-of-metric-spaces-and-isometries public -open import metric-spaces.precategory-of-metric-spaces-and-short-functions public -open import metric-spaces.premetric-spaces public -open import metric-spaces.premetric-structures public -open import metric-spaces.pseudometric-spaces public -open import metric-spaces.pseudometric-structures public -open import metric-spaces.reflexive-premetric-structures public -open import metric-spaces.saturated-metric-spaces public -open import metric-spaces.short-functions-metric-spaces public -open import metric-spaces.short-functions-premetric-spaces public -open import metric-spaces.subspaces-metric-spaces public -open import metric-spaces.symmetric-premetric-structures public -open import metric-spaces.triangular-premetric-structures public +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module metric-spaces + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where + +open import metric-spaces.category-of-metric-spaces-and-isometries funext univalence truncations public +open import metric-spaces.category-of-metric-spaces-and-short-functions funext univalence truncations public +open import metric-spaces.cauchy-approximations-metric-spaces funext univalence truncations public +open import metric-spaces.cauchy-approximations-premetric-spaces funext univalence truncations public +open import metric-spaces.cauchy-sequences-complete-metric-spaces funext univalence truncations public +open import metric-spaces.cauchy-sequences-metric-spaces funext univalence truncations public +open import metric-spaces.closed-premetric-structures funext univalence truncations public +open import metric-spaces.complete-metric-spaces funext univalence truncations public +open import metric-spaces.convergent-cauchy-approximations-metric-spaces funext univalence truncations public +open import metric-spaces.dependent-products-metric-spaces funext univalence truncations public +open import metric-spaces.discrete-premetric-structures funext univalence truncations public +open import metric-spaces.equality-of-metric-spaces funext univalence truncations public +open import metric-spaces.equality-of-premetric-spaces funext univalence truncations public +open import metric-spaces.extensional-premetric-structures funext univalence truncations public +open import metric-spaces.functions-metric-spaces funext univalence truncations public +open import metric-spaces.functor-category-set-functions-isometry-metric-spaces funext univalence truncations public +open import metric-spaces.functor-category-short-isometry-metric-spaces funext univalence truncations public +open import metric-spaces.induced-premetric-structures-on-preimages funext univalence truncations public +open import metric-spaces.isometric-equivalences-premetric-spaces funext univalence truncations public +open import metric-spaces.isometries-metric-spaces funext univalence truncations public +open import metric-spaces.isometries-premetric-spaces funext univalence truncations public +open import metric-spaces.limits-of-cauchy-approximations-in-premetric-spaces funext univalence truncations public +open import metric-spaces.metric-space-of-cauchy-approximations-in-a-metric-space funext univalence truncations public +open import metric-spaces.metric-space-of-convergent-cauchy-approximations-in-a-metric-space funext univalence truncations public +open import metric-spaces.metric-space-of-rational-numbers funext univalence truncations public +open import metric-spaces.metric-space-of-rational-numbers-with-open-neighborhoods funext univalence truncations public +open import metric-spaces.metric-spaces funext univalence truncations public +open import metric-spaces.metric-structures funext univalence truncations public +open import metric-spaces.monotonic-premetric-structures funext univalence truncations public +open import metric-spaces.ordering-premetric-structures funext univalence truncations public +open import metric-spaces.precategory-of-metric-spaces-and-functions funext univalence truncations public +open import metric-spaces.precategory-of-metric-spaces-and-isometries funext univalence truncations public +open import metric-spaces.precategory-of-metric-spaces-and-short-functions funext univalence truncations public +open import metric-spaces.premetric-spaces funext univalence truncations public +open import metric-spaces.premetric-structures funext univalence truncations public +open import metric-spaces.pseudometric-spaces funext univalence truncations public +open import metric-spaces.pseudometric-structures funext univalence truncations public +open import metric-spaces.reflexive-premetric-structures funext univalence truncations public +open import metric-spaces.saturated-metric-spaces funext univalence truncations public +open import metric-spaces.short-functions-metric-spaces funext univalence truncations public +open import metric-spaces.short-functions-premetric-spaces funext univalence truncations public +open import metric-spaces.subspaces-metric-spaces funext univalence truncations public +open import metric-spaces.symmetric-premetric-structures funext univalence truncations public +open import metric-spaces.triangular-premetric-structures funext univalence truncations public ``` ## References diff --git a/src/metric-spaces/category-of-metric-spaces-and-isometries.lagda.md b/src/metric-spaces/category-of-metric-spaces-and-isometries.lagda.md index 33740c7c95..1466bd15e5 100644 --- a/src/metric-spaces/category-of-metric-spaces-and-isometries.lagda.md +++ b/src/metric-spaces/category-of-metric-spaces-and-isometries.lagda.md @@ -1,25 +1,34 @@ # The category of metric spaces and isometries ```agda -module metric-spaces.category-of-metric-spaces-and-isometries where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module metric-spaces.category-of-metric-spaces-and-isometries + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.isomorphisms-in-precategories +open import category-theory.categories funext univalence truncations +open import category-theory.isomorphisms-in-precategories funext univalence truncations -open import foundation.contractible-types +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.functoriality-dependent-pair-types +open import foundation.dependent-products-contractible-types funext +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext univalence truncations open import foundation.universe-levels -open import metric-spaces.equality-of-metric-spaces -open import metric-spaces.metric-spaces -open import metric-spaces.precategory-of-metric-spaces-and-isometries +open import metric-spaces.equality-of-metric-spaces funext univalence truncations +open import metric-spaces.metric-spaces funext univalence truncations +open import metric-spaces.precategory-of-metric-spaces-and-isometries funext univalence truncations ```
diff --git a/src/metric-spaces/category-of-metric-spaces-and-short-functions.lagda.md b/src/metric-spaces/category-of-metric-spaces-and-short-functions.lagda.md index 64d510500c..769564a71e 100644 --- a/src/metric-spaces/category-of-metric-spaces-and-short-functions.lagda.md +++ b/src/metric-spaces/category-of-metric-spaces-and-short-functions.lagda.md @@ -1,25 +1,34 @@ # The category of metric spaces and short maps ```agda -module metric-spaces.category-of-metric-spaces-and-short-functions where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module metric-spaces.category-of-metric-spaces-and-short-functions + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.isomorphisms-in-precategories +open import category-theory.categories funext univalence truncations +open import category-theory.isomorphisms-in-precategories funext univalence truncations -open import foundation.contractible-types +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.functoriality-dependent-pair-types +open import foundation.dependent-products-contractible-types funext +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext univalence truncations open import foundation.universe-levels -open import metric-spaces.equality-of-metric-spaces -open import metric-spaces.metric-spaces -open import metric-spaces.precategory-of-metric-spaces-and-short-functions +open import metric-spaces.equality-of-metric-spaces funext univalence truncations +open import metric-spaces.metric-spaces funext univalence truncations +open import metric-spaces.precategory-of-metric-spaces-and-short-functions funext univalence truncations ```
diff --git a/src/metric-spaces/cauchy-approximations-metric-spaces.lagda.md b/src/metric-spaces/cauchy-approximations-metric-spaces.lagda.md index 1b5a1f41c2..cad097ac2f 100644 --- a/src/metric-spaces/cauchy-approximations-metric-spaces.lagda.md +++ b/src/metric-spaces/cauchy-approximations-metric-spaces.lagda.md @@ -1,26 +1,35 @@ # Cauchy approximations in metric spaces ```agda -module metric-spaces.cauchy-approximations-metric-spaces where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module metric-spaces.cauchy-approximations-metric-spaces + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.positive-rational-numbers +open import elementary-number-theory.positive-rational-numbers funext univalence truncations -open import foundation.binary-relations +open import foundation.binary-relations funext univalence truncations open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.transport-along-identifications open import foundation.universe-levels -open import metric-spaces.cauchy-approximations-premetric-spaces -open import metric-spaces.limits-of-cauchy-approximations-in-premetric-spaces -open import metric-spaces.metric-spaces +open import metric-spaces.cauchy-approximations-premetric-spaces funext univalence truncations +open import metric-spaces.limits-of-cauchy-approximations-in-premetric-spaces funext univalence truncations +open import metric-spaces.metric-spaces funext univalence truncations ```
diff --git a/src/metric-spaces/cauchy-approximations-premetric-spaces.lagda.md b/src/metric-spaces/cauchy-approximations-premetric-spaces.lagda.md index c33d16562a..020a5bdfa1 100644 --- a/src/metric-spaces/cauchy-approximations-premetric-spaces.lagda.md +++ b/src/metric-spaces/cauchy-approximations-premetric-spaces.lagda.md @@ -1,27 +1,32 @@ # Cauchy approximations in premetric spaces ```agda -module metric-spaces.cauchy-approximations-premetric-spaces where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module metric-spaces.cauchy-approximations-premetric-spaces + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.positive-rational-numbers +open import elementary-number-theory.positive-rational-numbers funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.propositions -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels -open import metric-spaces.premetric-spaces -open import metric-spaces.short-functions-premetric-spaces +open import metric-spaces.premetric-spaces funext univalence truncations +open import metric-spaces.short-functions-premetric-spaces funext univalence truncations ```
diff --git a/src/metric-spaces/cauchy-sequences-complete-metric-spaces.lagda.md b/src/metric-spaces/cauchy-sequences-complete-metric-spaces.lagda.md index 7a77f2ac4e..e4d5a0abad 100644 --- a/src/metric-spaces/cauchy-sequences-complete-metric-spaces.lagda.md +++ b/src/metric-spaces/cauchy-sequences-complete-metric-spaces.lagda.md @@ -2,22 +2,29 @@ ```agda {-# OPTIONS --lossy-unification #-} - -module metric-spaces.cauchy-sequences-complete-metric-spaces where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module metric-spaces.cauchy-sequences-complete-metric-spaces + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.functoriality-dependent-pair-types +open import foundation.functoriality-dependent-pair-types funext open import foundation.universe-levels -open import metric-spaces.cauchy-approximations-metric-spaces -open import metric-spaces.cauchy-sequences-metric-spaces -open import metric-spaces.complete-metric-spaces -open import metric-spaces.convergent-cauchy-approximations-metric-spaces -open import metric-spaces.metric-spaces +open import metric-spaces.cauchy-approximations-metric-spaces funext univalence truncations +open import metric-spaces.cauchy-sequences-metric-spaces funext univalence truncations +open import metric-spaces.complete-metric-spaces funext univalence truncations +open import metric-spaces.convergent-cauchy-approximations-metric-spaces funext univalence truncations +open import metric-spaces.metric-spaces funext univalence truncations ```
diff --git a/src/metric-spaces/cauchy-sequences-metric-spaces.lagda.md b/src/metric-spaces/cauchy-sequences-metric-spaces.lagda.md index 2b923f6d47..d74fb76f6d 100644 --- a/src/metric-spaces/cauchy-sequences-metric-spaces.lagda.md +++ b/src/metric-spaces/cauchy-sequences-metric-spaces.lagda.md @@ -2,37 +2,44 @@ ```agda {-# OPTIONS --lossy-unification #-} - -module metric-spaces.cauchy-sequences-metric-spaces where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module metric-spaces.cauchy-sequences-metric-spaces + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.addition-rational-numbers -open import elementary-number-theory.archimedean-property-positive-rational-numbers -open import elementary-number-theory.inequality-natural-numbers -open import elementary-number-theory.inequality-rational-numbers -open import elementary-number-theory.maximum-natural-numbers -open import elementary-number-theory.multiplicative-group-of-positive-rational-numbers +open import elementary-number-theory.addition-rational-numbers funext univalence truncations +open import elementary-number-theory.archimedean-property-positive-rational-numbers funext univalence truncations +open import elementary-number-theory.inequality-natural-numbers funext univalence truncations +open import elementary-number-theory.inequality-rational-numbers funext univalence truncations +open import elementary-number-theory.maximum-natural-numbers funext univalence truncations +open import elementary-number-theory.multiplicative-group-of-positive-rational-numbers funext univalence truncations open import elementary-number-theory.natural-numbers -open import elementary-number-theory.nonzero-natural-numbers -open import elementary-number-theory.positive-rational-numbers -open import elementary-number-theory.strict-inequality-rational-numbers -open import elementary-number-theory.unit-fractions-rational-numbers +open import elementary-number-theory.nonzero-natural-numbers funext univalence truncations +open import elementary-number-theory.positive-rational-numbers funext univalence truncations +open import elementary-number-theory.strict-inequality-rational-numbers funext univalence truncations +open import elementary-number-theory.unit-fractions-rational-numbers funext univalence truncations open import foundation.action-on-identifications-functions open import foundation.binary-transport -open import foundation.coproduct-types +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.propositions +open import foundation.identity-types funext +open import foundation.propositions funext univalence open import foundation.transport-along-identifications open import foundation.universe-levels -open import metric-spaces.cauchy-approximations-metric-spaces -open import metric-spaces.limits-of-cauchy-approximations-in-premetric-spaces -open import metric-spaces.metric-spaces +open import metric-spaces.cauchy-approximations-metric-spaces funext univalence truncations +open import metric-spaces.limits-of-cauchy-approximations-in-premetric-spaces funext univalence truncations +open import metric-spaces.metric-spaces funext univalence truncations ```
diff --git a/src/metric-spaces/closed-premetric-structures.lagda.md b/src/metric-spaces/closed-premetric-structures.lagda.md index 8bf46dea34..69e5379228 100644 --- a/src/metric-spaces/closed-premetric-structures.lagda.md +++ b/src/metric-spaces/closed-premetric-structures.lagda.md @@ -1,41 +1,50 @@ # Closed premetric structures ```agda -module metric-spaces.closed-premetric-structures where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module metric-spaces.closed-premetric-structures + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.addition-rational-numbers -open import elementary-number-theory.positive-rational-numbers -open import elementary-number-theory.strict-inequality-rational-numbers +open import elementary-number-theory.addition-rational-numbers funext univalence truncations +open import elementary-number-theory.positive-rational-numbers funext univalence truncations +open import elementary-number-theory.strict-inequality-rational-numbers funext univalence truncations open import foundation.action-on-identifications-functions -open import foundation.binary-relations +open import foundation.binary-relations funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-types +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.function-extensionality funext +open import foundation.function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.propositional-extensionality -open import foundation.propositions -open import foundation.sets -open import foundation.subtypes -open import foundation.torsorial-type-families +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.propositional-extensionality funext univalence truncations +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.subtypes funext univalence truncations +open import foundation.torsorial-type-families funext univalence truncations open import foundation.transport-along-identifications -open import foundation.univalence +open import foundation.univalence funext univalence open import foundation.universe-levels -open import metric-spaces.extensional-premetric-structures -open import metric-spaces.monotonic-premetric-structures -open import metric-spaces.ordering-premetric-structures -open import metric-spaces.premetric-structures -open import metric-spaces.reflexive-premetric-structures -open import metric-spaces.symmetric-premetric-structures -open import metric-spaces.triangular-premetric-structures +open import metric-spaces.extensional-premetric-structures funext univalence truncations +open import metric-spaces.monotonic-premetric-structures funext univalence truncations +open import metric-spaces.ordering-premetric-structures funext univalence truncations +open import metric-spaces.premetric-structures funext univalence truncations +open import metric-spaces.reflexive-premetric-structures funext univalence truncations +open import metric-spaces.symmetric-premetric-structures funext univalence truncations +open import metric-spaces.triangular-premetric-structures funext univalence truncations ```
diff --git a/src/metric-spaces/complete-metric-spaces.lagda.md b/src/metric-spaces/complete-metric-spaces.lagda.md index 1cb1c38a3a..458b61aa4f 100644 --- a/src/metric-spaces/complete-metric-spaces.lagda.md +++ b/src/metric-spaces/complete-metric-spaces.lagda.md @@ -1,22 +1,31 @@ # Complete metric spaces ```agda -module metric-spaces.complete-metric-spaces where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module metric-spaces.complete-metric-spaces + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.positive-rational-numbers +open import elementary-number-theory.positive-rational-numbers funext univalence truncations open import foundation.dependent-pair-types -open import foundation.propositions -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.propositions funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels -open import metric-spaces.cauchy-approximations-metric-spaces -open import metric-spaces.convergent-cauchy-approximations-metric-spaces -open import metric-spaces.metric-spaces +open import metric-spaces.cauchy-approximations-metric-spaces funext univalence truncations +open import metric-spaces.convergent-cauchy-approximations-metric-spaces funext univalence truncations +open import metric-spaces.metric-spaces funext univalence truncations ```
diff --git a/src/metric-spaces/convergent-cauchy-approximations-metric-spaces.lagda.md b/src/metric-spaces/convergent-cauchy-approximations-metric-spaces.lagda.md index f8ade7ad4b..e6ff718e15 100644 --- a/src/metric-spaces/convergent-cauchy-approximations-metric-spaces.lagda.md +++ b/src/metric-spaces/convergent-cauchy-approximations-metric-spaces.lagda.md @@ -1,22 +1,31 @@ # Convergent Cauchy approximations in metric spaces ```agda -module metric-spaces.convergent-cauchy-approximations-metric-spaces where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module metric-spaces.convergent-cauchy-approximations-metric-spaces + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.positive-rational-numbers +open import elementary-number-theory.positive-rational-numbers funext univalence truncations open import foundation.dependent-pair-types -open import foundation.propositions -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.propositions funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels -open import metric-spaces.cauchy-approximations-metric-spaces -open import metric-spaces.limits-of-cauchy-approximations-in-premetric-spaces -open import metric-spaces.metric-spaces +open import metric-spaces.cauchy-approximations-metric-spaces funext univalence truncations +open import metric-spaces.limits-of-cauchy-approximations-in-premetric-spaces funext univalence truncations +open import metric-spaces.metric-spaces funext univalence truncations ```
diff --git a/src/metric-spaces/dependent-products-metric-spaces.lagda.md b/src/metric-spaces/dependent-products-metric-spaces.lagda.md index 9114877759..27ed6f4152 100644 --- a/src/metric-spaces/dependent-products-metric-spaces.lagda.md +++ b/src/metric-spaces/dependent-products-metric-spaces.lagda.md @@ -1,28 +1,37 @@ # Dependent products of metric spaces ```agda -module metric-spaces.dependent-products-metric-spaces where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module metric-spaces.dependent-products-metric-spaces + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-extensionality -open import foundation.propositions -open import foundation.sets +open import foundation.dependent-products-propositions funext +open import foundation.function-extensionality funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence open import foundation.universe-levels -open import metric-spaces.extensional-premetric-structures -open import metric-spaces.metric-spaces -open import metric-spaces.metric-structures -open import metric-spaces.monotonic-premetric-structures -open import metric-spaces.premetric-structures -open import metric-spaces.pseudometric-structures -open import metric-spaces.reflexive-premetric-structures -open import metric-spaces.short-functions-metric-spaces -open import metric-spaces.symmetric-premetric-structures -open import metric-spaces.triangular-premetric-structures +open import metric-spaces.extensional-premetric-structures funext univalence truncations +open import metric-spaces.metric-spaces funext univalence truncations +open import metric-spaces.metric-structures funext univalence truncations +open import metric-spaces.monotonic-premetric-structures funext univalence truncations +open import metric-spaces.premetric-structures funext univalence truncations +open import metric-spaces.pseudometric-structures funext univalence truncations +open import metric-spaces.reflexive-premetric-structures funext univalence truncations +open import metric-spaces.short-functions-metric-spaces funext univalence truncations +open import metric-spaces.symmetric-premetric-structures funext univalence truncations +open import metric-spaces.triangular-premetric-structures funext univalence truncations ```
diff --git a/src/metric-spaces/discrete-premetric-structures.lagda.md b/src/metric-spaces/discrete-premetric-structures.lagda.md index e7611f1876..f8fc6208fe 100644 --- a/src/metric-spaces/discrete-premetric-structures.lagda.md +++ b/src/metric-spaces/discrete-premetric-structures.lagda.md @@ -1,40 +1,38 @@ # Discrete premetric structures ```agda -module metric-spaces.discrete-premetric-structures where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module metric-spaces.discrete-premetric-structures + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.positive-rational-numbers +open import elementary-number-theory.positive-rational-numbers funext univalence truncations -open import foundation.action-on-identifications-functions -open import foundation.binary-relations -open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.propositional-extensionality -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.sets -open import foundation.subtypes -open import foundation.torsorial-type-families -open import foundation.transport-along-identifications -open import foundation.univalence +open import foundation.dependent-products-propositions funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels -open import metric-spaces.extensional-premetric-structures -open import metric-spaces.monotonic-premetric-structures -open import metric-spaces.premetric-structures -open import metric-spaces.reflexive-premetric-structures -open import metric-spaces.symmetric-premetric-structures -open import metric-spaces.triangular-premetric-structures +open import metric-spaces.extensional-premetric-structures funext univalence truncations +open import metric-spaces.premetric-structures funext univalence truncations +open import metric-spaces.reflexive-premetric-structures funext univalence truncations +open import metric-spaces.symmetric-premetric-structures funext univalence truncations +open import metric-spaces.triangular-premetric-structures funext univalence truncations ```
diff --git a/src/metric-spaces/equality-of-metric-spaces.lagda.md b/src/metric-spaces/equality-of-metric-spaces.lagda.md index 9e6b49a73c..b035908558 100644 --- a/src/metric-spaces/equality-of-metric-spaces.lagda.md +++ b/src/metric-spaces/equality-of-metric-spaces.lagda.md @@ -1,27 +1,37 @@ # Equality of metric spaces ```agda -module metric-spaces.equality-of-metric-spaces where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module metric-spaces.equality-of-metric-spaces + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.contractible-types +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.subtypes -open import foundation.torsorial-type-families +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.subtypes funext univalence truncations +open import foundation.torsorial-type-families funext univalence truncations open import foundation.universe-levels -open import metric-spaces.equality-of-premetric-spaces -open import metric-spaces.isometric-equivalences-premetric-spaces -open import metric-spaces.metric-spaces -open import metric-spaces.premetric-spaces +open import metric-spaces.equality-of-premetric-spaces funext univalence truncations +open import metric-spaces.isometric-equivalences-premetric-spaces funext univalence truncations +open import metric-spaces.metric-spaces funext univalence truncations +open import metric-spaces.premetric-spaces funext univalence truncations ```
diff --git a/src/metric-spaces/equality-of-premetric-spaces.lagda.md b/src/metric-spaces/equality-of-premetric-spaces.lagda.md index bf75c6dad0..3aa02935e8 100644 --- a/src/metric-spaces/equality-of-premetric-spaces.lagda.md +++ b/src/metric-spaces/equality-of-premetric-spaces.lagda.md @@ -1,7 +1,15 @@ # Equality of premetric spaces ```agda -module metric-spaces.equality-of-premetric-spaces where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module metric-spaces.equality-of-premetric-spaces + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,23 +17,25 @@ module metric-spaces.equality-of-premetric-spaces where ```agda open import foundation.action-on-identifications-functions open import foundation.binary-transport -open import foundation.contractible-types +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types -open import foundation.equivalences -open import foundation.functoriality-dependent-pair-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.propositions -open import foundation.subtypes -open import foundation.torsorial-type-families +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.equality-dependent-pair-types funext +open import foundation.equivalences funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.propositions funext univalence +open import foundation.subtypes funext univalence truncations +open import foundation.torsorial-type-families funext univalence truncations open import foundation.transport-along-identifications -open import foundation.univalence +open import foundation.univalence funext univalence open import foundation.universe-levels -open import metric-spaces.isometries-premetric-spaces -open import metric-spaces.premetric-spaces -open import metric-spaces.premetric-structures +open import metric-spaces.isometries-premetric-spaces funext univalence truncations +open import metric-spaces.premetric-spaces funext univalence truncations +open import metric-spaces.premetric-structures funext univalence truncations ```
diff --git a/src/metric-spaces/extensional-premetric-structures.lagda.md b/src/metric-spaces/extensional-premetric-structures.lagda.md index 0e614ca440..fbf8dcadd2 100644 --- a/src/metric-spaces/extensional-premetric-structures.lagda.md +++ b/src/metric-spaces/extensional-premetric-structures.lagda.md @@ -1,28 +1,37 @@ # Extensional premetric structures on types ```agda -module metric-spaces.extensional-premetric-structures where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module metric-spaces.extensional-premetric-structures + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.positive-rational-numbers +open import elementary-number-theory.positive-rational-numbers funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets -open import foundation.subtypes -open import foundation.torsorial-type-families +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.subtypes funext univalence truncations +open import foundation.torsorial-type-families funext univalence truncations open import foundation.transport-along-identifications open import foundation.universe-levels -open import metric-spaces.premetric-structures -open import metric-spaces.reflexive-premetric-structures +open import metric-spaces.premetric-structures funext univalence truncations +open import metric-spaces.reflexive-premetric-structures funext univalence truncations ```
diff --git a/src/metric-spaces/functions-metric-spaces.lagda.md b/src/metric-spaces/functions-metric-spaces.lagda.md index 2c95ab35af..2017f87b70 100644 --- a/src/metric-spaces/functions-metric-spaces.lagda.md +++ b/src/metric-spaces/functions-metric-spaces.lagda.md @@ -1,19 +1,27 @@ # Functions between metric spaces ```agda -module metric-spaces.functions-metric-spaces where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module metric-spaces.functions-metric-spaces + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.sets +open import foundation.function-types funext +open import foundation.sets funext univalence open import foundation.universe-levels -open import metric-spaces.metric-spaces -open import metric-spaces.premetric-spaces +open import metric-spaces.metric-spaces funext univalence truncations +open import metric-spaces.premetric-spaces funext univalence truncations ```
diff --git a/src/metric-spaces/functor-category-set-functions-isometry-metric-spaces.lagda.md b/src/metric-spaces/functor-category-set-functions-isometry-metric-spaces.lagda.md index deb9612d34..bb4da6d1b5 100644 --- a/src/metric-spaces/functor-category-set-functions-isometry-metric-spaces.lagda.md +++ b/src/metric-spaces/functor-category-set-functions-isometry-metric-spaces.lagda.md @@ -1,35 +1,35 @@ # The functor from the precategory of metric spaces and isometries to the precategory of sets ```agda -module metric-spaces.functor-category-set-functions-isometry-metric-spaces where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module metric-spaces.functor-category-set-functions-isometry-metric-spaces + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.conservative-functors-precategories -open import category-theory.faithful-functors-precategories -open import category-theory.functors-precategories -open import category-theory.isomorphisms-in-precategories -open import category-theory.maps-precategories -open import category-theory.precategories - -open import foundation.category-of-sets +open import category-theory.conservative-functors-precategories funext univalence truncations +open import category-theory.faithful-functors-precategories funext univalence truncations +open import category-theory.functors-precategories funext univalence truncations + +open import foundation.category-of-sets funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.isomorphisms-of-sets -open import foundation.subtypes +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.isomorphisms-of-sets funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels -open import metric-spaces.category-of-metric-spaces-and-isometries -open import metric-spaces.isometries-metric-spaces -open import metric-spaces.metric-spaces -open import metric-spaces.precategory-of-metric-spaces-and-isometries +open import metric-spaces.isometries-metric-spaces funext univalence truncations +open import metric-spaces.metric-spaces funext univalence truncations +open import metric-spaces.precategory-of-metric-spaces-and-isometries funext univalence truncations ```
diff --git a/src/metric-spaces/functor-category-short-isometry-metric-spaces.lagda.md b/src/metric-spaces/functor-category-short-isometry-metric-spaces.lagda.md index efc5aa2595..620648994b 100644 --- a/src/metric-spaces/functor-category-short-isometry-metric-spaces.lagda.md +++ b/src/metric-spaces/functor-category-short-isometry-metric-spaces.lagda.md @@ -1,32 +1,32 @@ # The inclusion of isometries into the category of metric spaces and short maps ```agda -module metric-spaces.functor-category-short-isometry-metric-spaces where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module metric-spaces.functor-category-short-isometry-metric-spaces + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.conservative-functors-precategories -open import category-theory.faithful-functors-precategories -open import category-theory.functors-precategories -open import category-theory.isomorphisms-in-precategories -open import category-theory.maps-precategories -open import category-theory.precategories -open import category-theory.split-essentially-surjective-functors-precategories +open import category-theory.conservative-functors-precategories funext univalence truncations +open import category-theory.faithful-functors-precategories funext univalence truncations +open import category-theory.functors-precategories funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.identity-types +open import foundation.equivalences funext +open import foundation.identity-types funext open import foundation.universe-levels -open import metric-spaces.isometries-metric-spaces -open import metric-spaces.precategory-of-metric-spaces-and-isometries -open import metric-spaces.precategory-of-metric-spaces-and-short-functions -open import metric-spaces.short-functions-metric-spaces +open import metric-spaces.precategory-of-metric-spaces-and-isometries funext univalence truncations +open import metric-spaces.precategory-of-metric-spaces-and-short-functions funext univalence truncations +open import metric-spaces.short-functions-metric-spaces funext univalence truncations ```
diff --git a/src/metric-spaces/induced-premetric-structures-on-preimages.lagda.md b/src/metric-spaces/induced-premetric-structures-on-preimages.lagda.md index 880bd2efd8..f7c29eeb56 100644 --- a/src/metric-spaces/induced-premetric-structures-on-preimages.lagda.md +++ b/src/metric-spaces/induced-premetric-structures-on-preimages.lagda.md @@ -1,25 +1,33 @@ # Induced premetric structures on preimages ```agda -module metric-spaces.induced-premetric-structures-on-preimages where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module metric-spaces.induced-premetric-structures-on-preimages + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.positive-rational-numbers +open import elementary-number-theory.positive-rational-numbers funext univalence truncations -open import foundation.function-types -open import foundation.identity-types -open import foundation.injective-maps +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.injective-maps funext open import foundation.universe-levels -open import metric-spaces.extensional-premetric-structures -open import metric-spaces.monotonic-premetric-structures -open import metric-spaces.premetric-structures -open import metric-spaces.reflexive-premetric-structures -open import metric-spaces.symmetric-premetric-structures -open import metric-spaces.triangular-premetric-structures +open import metric-spaces.extensional-premetric-structures funext univalence truncations +open import metric-spaces.monotonic-premetric-structures funext univalence truncations +open import metric-spaces.premetric-structures funext univalence truncations +open import metric-spaces.reflexive-premetric-structures funext univalence truncations +open import metric-spaces.symmetric-premetric-structures funext univalence truncations +open import metric-spaces.triangular-premetric-structures funext univalence truncations ```
diff --git a/src/metric-spaces/isometric-equivalences-premetric-spaces.lagda.md b/src/metric-spaces/isometric-equivalences-premetric-spaces.lagda.md index 34c143ce20..c7ed7f9641 100644 --- a/src/metric-spaces/isometric-equivalences-premetric-spaces.lagda.md +++ b/src/metric-spaces/isometric-equivalences-premetric-spaces.lagda.md @@ -1,31 +1,41 @@ # Isometric equivalences between premetric spaces ```agda -module metric-spaces.isometric-equivalences-premetric-spaces where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module metric-spaces.isometric-equivalences-premetric-spaces + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.contractible-types +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.subtypes -open import foundation.torsorial-type-families +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.function-extensionality funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.subtypes funext univalence truncations +open import foundation.torsorial-type-families funext univalence truncations open import foundation.transport-along-identifications open import foundation.type-arithmetic-dependent-pair-types -open import foundation.univalence +open import foundation.univalence funext univalence open import foundation.universe-levels -open import metric-spaces.equality-of-premetric-spaces -open import metric-spaces.isometries-premetric-spaces -open import metric-spaces.premetric-spaces +open import metric-spaces.equality-of-premetric-spaces funext univalence truncations +open import metric-spaces.isometries-premetric-spaces funext univalence truncations +open import metric-spaces.premetric-spaces funext univalence truncations ```
diff --git a/src/metric-spaces/isometries-metric-spaces.lagda.md b/src/metric-spaces/isometries-metric-spaces.lagda.md index 5078244b1f..9960550fb1 100644 --- a/src/metric-spaces/isometries-metric-spaces.lagda.md +++ b/src/metric-spaces/isometries-metric-spaces.lagda.md @@ -1,35 +1,44 @@ # Isometries between metric spaces ```agda -module metric-spaces.isometries-metric-spaces where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module metric-spaces.isometries-metric-spaces + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.positive-rational-numbers +open import elementary-number-theory.positive-rational-numbers funext univalence truncations open import foundation.binary-transport open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalences -open import foundation.existential-quantification -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.propositional-truncations -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.existential-quantification funext univalence truncations +open import foundation.function-extensionality funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence open import foundation.sequences -open import foundation.sets -open import foundation.subtypes -open import foundation.univalence +open import foundation.sets funext univalence +open import foundation.subtypes funext univalence truncations +open import foundation.univalence funext univalence open import foundation.universe-levels -open import metric-spaces.functions-metric-spaces -open import metric-spaces.isometries-premetric-spaces -open import metric-spaces.metric-spaces +open import metric-spaces.functions-metric-spaces funext univalence truncations +open import metric-spaces.isometries-premetric-spaces funext univalence truncations +open import metric-spaces.metric-spaces funext univalence truncations ```
diff --git a/src/metric-spaces/isometries-premetric-spaces.lagda.md b/src/metric-spaces/isometries-premetric-spaces.lagda.md index 6b3812351b..91e39e1cd9 100644 --- a/src/metric-spaces/isometries-premetric-spaces.lagda.md +++ b/src/metric-spaces/isometries-premetric-spaces.lagda.md @@ -1,30 +1,39 @@ # Isometries between premetric spaces ```agda -module metric-spaces.isometries-premetric-spaces where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module metric-spaces.isometries-premetric-spaces + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.positive-rational-numbers +open import elementary-number-theory.positive-rational-numbers funext univalence truncations open import foundation.binary-transport open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.logical-equivalences -open import foundation.propositions -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.function-extensionality funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.logical-equivalences funext +open import foundation.propositions funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels -open import metric-spaces.extensional-premetric-structures -open import metric-spaces.premetric-spaces +open import metric-spaces.extensional-premetric-structures funext univalence truncations +open import metric-spaces.premetric-spaces funext univalence truncations ```
diff --git a/src/metric-spaces/limits-of-cauchy-approximations-in-premetric-spaces.lagda.md b/src/metric-spaces/limits-of-cauchy-approximations-in-premetric-spaces.lagda.md index a3a62b7f90..0901e9afec 100644 --- a/src/metric-spaces/limits-of-cauchy-approximations-in-premetric-spaces.lagda.md +++ b/src/metric-spaces/limits-of-cauchy-approximations-in-premetric-spaces.lagda.md @@ -1,32 +1,33 @@ # Limits of Cauchy approximations in premetric spaces ```agda -module metric-spaces.limits-of-cauchy-approximations-in-premetric-spaces where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module metric-spaces.limits-of-cauchy-approximations-in-premetric-spaces + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.positive-rational-numbers - -open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.propositions -open import foundation.subtypes +open import elementary-number-theory.positive-rational-numbers funext univalence truncations + +open import foundation.dependent-products-propositions funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence open import foundation.transport-along-identifications open import foundation.universe-levels -open import metric-spaces.cauchy-approximations-premetric-spaces -open import metric-spaces.extensional-premetric-structures -open import metric-spaces.premetric-spaces -open import metric-spaces.short-functions-premetric-spaces -open import metric-spaces.symmetric-premetric-structures -open import metric-spaces.triangular-premetric-structures +open import metric-spaces.cauchy-approximations-premetric-spaces funext univalence truncations +open import metric-spaces.extensional-premetric-structures funext univalence truncations +open import metric-spaces.premetric-spaces funext univalence truncations +open import metric-spaces.symmetric-premetric-structures funext univalence truncations +open import metric-spaces.triangular-premetric-structures funext univalence truncations ```
diff --git a/src/metric-spaces/metric-space-of-cauchy-approximations-in-a-metric-space.lagda.md b/src/metric-spaces/metric-space-of-cauchy-approximations-in-a-metric-space.lagda.md index dc0c9c9e53..b880bcabd0 100644 --- a/src/metric-spaces/metric-space-of-cauchy-approximations-in-a-metric-space.lagda.md +++ b/src/metric-spaces/metric-space-of-cauchy-approximations-in-a-metric-space.lagda.md @@ -1,20 +1,28 @@ # The metric space of cauchy approximations in a metric space ```agda -module metric-spaces.metric-space-of-cauchy-approximations-in-a-metric-space where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module metric-spaces.metric-space-of-cauchy-approximations-in-a-metric-space + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.positive-rational-numbers +open import elementary-number-theory.positive-rational-numbers funext univalence truncations open import foundation.universe-levels -open import metric-spaces.cauchy-approximations-metric-spaces -open import metric-spaces.dependent-products-metric-spaces -open import metric-spaces.metric-spaces -open import metric-spaces.subspaces-metric-spaces +open import metric-spaces.cauchy-approximations-metric-spaces funext univalence truncations +open import metric-spaces.dependent-products-metric-spaces funext univalence truncations +open import metric-spaces.metric-spaces funext univalence truncations +open import metric-spaces.subspaces-metric-spaces funext univalence truncations ```
diff --git a/src/metric-spaces/metric-space-of-convergent-cauchy-approximations-in-a-metric-space.lagda.md b/src/metric-spaces/metric-space-of-convergent-cauchy-approximations-in-a-metric-space.lagda.md index 07c23b1fdf..a440fd546f 100644 --- a/src/metric-spaces/metric-space-of-convergent-cauchy-approximations-in-a-metric-space.lagda.md +++ b/src/metric-spaces/metric-space-of-convergent-cauchy-approximations-in-a-metric-space.lagda.md @@ -1,7 +1,15 @@ # The metric space of convergent cauchy approximations in a metric space ```agda -module metric-spaces.metric-space-of-convergent-cauchy-approximations-in-a-metric-space where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module metric-spaces.metric-space-of-convergent-cauchy-approximations-in-a-metric-space + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,10 +17,10 @@ module metric-spaces.metric-space-of-convergent-cauchy-approximations-in-a-metri ```agda open import foundation.universe-levels -open import metric-spaces.convergent-cauchy-approximations-metric-spaces -open import metric-spaces.metric-space-of-cauchy-approximations-in-a-metric-space -open import metric-spaces.metric-spaces -open import metric-spaces.subspaces-metric-spaces +open import metric-spaces.convergent-cauchy-approximations-metric-spaces funext univalence truncations +open import metric-spaces.metric-space-of-cauchy-approximations-in-a-metric-space funext univalence truncations +open import metric-spaces.metric-spaces funext univalence truncations +open import metric-spaces.subspaces-metric-spaces funext univalence truncations ```
diff --git a/src/metric-spaces/metric-space-of-rational-numbers-with-open-neighborhoods.lagda.md b/src/metric-spaces/metric-space-of-rational-numbers-with-open-neighborhoods.lagda.md index 5f2525fef2..0cedf01468 100644 --- a/src/metric-spaces/metric-space-of-rational-numbers-with-open-neighborhoods.lagda.md +++ b/src/metric-spaces/metric-space-of-rational-numbers-with-open-neighborhoods.lagda.md @@ -2,41 +2,49 @@ ```agda {-# OPTIONS --lossy-unification #-} - -module metric-spaces.metric-space-of-rational-numbers-with-open-neighborhoods where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module metric-spaces.metric-space-of-rational-numbers-with-open-neighborhoods + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.addition-rational-numbers -open import elementary-number-theory.difference-rational-numbers -open import elementary-number-theory.inequality-rational-numbers -open import elementary-number-theory.positive-rational-numbers -open import elementary-number-theory.rational-numbers -open import elementary-number-theory.strict-inequality-rational-numbers +open import elementary-number-theory.addition-rational-numbers funext univalence truncations +open import elementary-number-theory.difference-rational-numbers funext univalence truncations +open import elementary-number-theory.inequality-rational-numbers funext univalence truncations +open import elementary-number-theory.positive-rational-numbers funext univalence truncations +open import elementary-number-theory.rational-numbers funext univalence truncations +open import elementary-number-theory.strict-inequality-rational-numbers funext univalence truncations open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.identity-types -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.empty-types funext univalence truncations +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence open import foundation.transport-along-identifications open import foundation.universe-levels -open import metric-spaces.extensional-premetric-structures -open import metric-spaces.metric-spaces -open import metric-spaces.metric-structures -open import metric-spaces.monotonic-premetric-structures -open import metric-spaces.premetric-spaces -open import metric-spaces.premetric-structures -open import metric-spaces.pseudometric-structures -open import metric-spaces.reflexive-premetric-structures -open import metric-spaces.symmetric-premetric-structures -open import metric-spaces.triangular-premetric-structures +open import metric-spaces.extensional-premetric-structures funext univalence truncations +open import metric-spaces.metric-spaces funext univalence truncations +open import metric-spaces.metric-structures funext univalence truncations +open import metric-spaces.monotonic-premetric-structures funext univalence truncations +open import metric-spaces.premetric-spaces funext univalence truncations +open import metric-spaces.premetric-structures funext univalence truncations +open import metric-spaces.pseudometric-structures funext univalence truncations +open import metric-spaces.reflexive-premetric-structures funext univalence truncations +open import metric-spaces.symmetric-premetric-structures funext univalence truncations +open import metric-spaces.triangular-premetric-structures funext univalence truncations ```
diff --git a/src/metric-spaces/metric-space-of-rational-numbers.lagda.md b/src/metric-spaces/metric-space-of-rational-numbers.lagda.md index 8ad75841c4..af3178f2b3 100644 --- a/src/metric-spaces/metric-space-of-rational-numbers.lagda.md +++ b/src/metric-spaces/metric-space-of-rational-numbers.lagda.md @@ -2,50 +2,58 @@ ```agda {-# OPTIONS --lossy-unification #-} - -module metric-spaces.metric-space-of-rational-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module metric-spaces.metric-space-of-rational-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.addition-rational-numbers -open import elementary-number-theory.difference-rational-numbers -open import elementary-number-theory.inequality-rational-numbers -open import elementary-number-theory.positive-rational-numbers -open import elementary-number-theory.rational-numbers -open import elementary-number-theory.strict-inequality-rational-numbers +open import elementary-number-theory.addition-rational-numbers funext univalence truncations +open import elementary-number-theory.difference-rational-numbers funext univalence truncations +open import elementary-number-theory.inequality-rational-numbers funext univalence truncations +open import elementary-number-theory.positive-rational-numbers funext univalence truncations +open import elementary-number-theory.rational-numbers funext univalence truncations +open import elementary-number-theory.strict-inequality-rational-numbers funext univalence truncations open import foundation.action-on-identifications-functions open import foundation.binary-transport -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.diagonal-maps-cartesian-products-of-types -open import foundation.empty-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-cartesian-product-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.diagonal-maps-cartesian-products-of-types funext univalence +open import foundation.empty-types funext univalence truncations +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.propositions funext univalence open import foundation.transport-along-identifications open import foundation.universe-levels -open import metric-spaces.cauchy-approximations-metric-spaces -open import metric-spaces.convergent-cauchy-approximations-metric-spaces -open import metric-spaces.extensional-premetric-structures -open import metric-spaces.isometries-metric-spaces -open import metric-spaces.limits-of-cauchy-approximations-in-premetric-spaces -open import metric-spaces.metric-spaces -open import metric-spaces.metric-structures -open import metric-spaces.monotonic-premetric-structures -open import metric-spaces.premetric-spaces -open import metric-spaces.premetric-structures -open import metric-spaces.pseudometric-structures -open import metric-spaces.reflexive-premetric-structures -open import metric-spaces.saturated-metric-spaces -open import metric-spaces.symmetric-premetric-structures -open import metric-spaces.triangular-premetric-structures +open import metric-spaces.cauchy-approximations-metric-spaces funext univalence truncations +open import metric-spaces.convergent-cauchy-approximations-metric-spaces funext univalence truncations +open import metric-spaces.extensional-premetric-structures funext univalence truncations +open import metric-spaces.isometries-metric-spaces funext univalence truncations +open import metric-spaces.limits-of-cauchy-approximations-in-premetric-spaces funext univalence truncations +open import metric-spaces.metric-spaces funext univalence truncations +open import metric-spaces.metric-structures funext univalence truncations +open import metric-spaces.monotonic-premetric-structures funext univalence truncations +open import metric-spaces.premetric-spaces funext univalence truncations +open import metric-spaces.premetric-structures funext univalence truncations +open import metric-spaces.pseudometric-structures funext univalence truncations +open import metric-spaces.reflexive-premetric-structures funext univalence truncations +open import metric-spaces.saturated-metric-spaces funext univalence truncations +open import metric-spaces.symmetric-premetric-structures funext univalence truncations +open import metric-spaces.triangular-premetric-structures funext univalence truncations ```
diff --git a/src/metric-spaces/metric-spaces.lagda.md b/src/metric-spaces/metric-spaces.lagda.md index 27701dbe35..8be6017f7c 100644 --- a/src/metric-spaces/metric-spaces.lagda.md +++ b/src/metric-spaces/metric-spaces.lagda.md @@ -1,36 +1,45 @@ # Metric spaces ```agda -module metric-spaces.metric-spaces where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module metric-spaces.metric-spaces + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.positive-rational-numbers +open import elementary-number-theory.positive-rational-numbers funext univalence truncations -open import foundation.binary-relations +open import foundation.binary-relations funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels -open import metric-spaces.extensional-premetric-structures -open import metric-spaces.metric-structures -open import metric-spaces.monotonic-premetric-structures -open import metric-spaces.premetric-spaces -open import metric-spaces.premetric-structures -open import metric-spaces.pseudometric-spaces -open import metric-spaces.pseudometric-structures -open import metric-spaces.reflexive-premetric-structures -open import metric-spaces.symmetric-premetric-structures -open import metric-spaces.triangular-premetric-structures +open import metric-spaces.extensional-premetric-structures funext univalence truncations +open import metric-spaces.metric-structures funext univalence truncations +open import metric-spaces.monotonic-premetric-structures funext univalence truncations +open import metric-spaces.premetric-spaces funext univalence truncations +open import metric-spaces.premetric-structures funext univalence truncations +open import metric-spaces.pseudometric-spaces funext univalence truncations +open import metric-spaces.pseudometric-structures funext univalence truncations +open import metric-spaces.reflexive-premetric-structures funext univalence truncations +open import metric-spaces.symmetric-premetric-structures funext univalence truncations +open import metric-spaces.triangular-premetric-structures funext univalence truncations ```
diff --git a/src/metric-spaces/metric-structures.lagda.md b/src/metric-spaces/metric-structures.lagda.md index 0839f2efae..d572ebe102 100644 --- a/src/metric-spaces/metric-structures.lagda.md +++ b/src/metric-spaces/metric-structures.lagda.md @@ -1,27 +1,36 @@ # Metric structures ```agda -module metric-spaces.metric-structures where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module metric-spaces.metric-structures + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.logical-equivalences -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.function-types funext +open import foundation.logical-equivalences funext +open import foundation.propositions funext univalence open import foundation.universe-levels -open import metric-spaces.closed-premetric-structures -open import metric-spaces.extensional-premetric-structures -open import metric-spaces.monotonic-premetric-structures -open import metric-spaces.ordering-premetric-structures -open import metric-spaces.premetric-structures -open import metric-spaces.pseudometric-structures -open import metric-spaces.reflexive-premetric-structures -open import metric-spaces.symmetric-premetric-structures -open import metric-spaces.triangular-premetric-structures +open import metric-spaces.closed-premetric-structures funext univalence truncations +open import metric-spaces.extensional-premetric-structures funext univalence truncations +open import metric-spaces.monotonic-premetric-structures funext univalence truncations +open import metric-spaces.ordering-premetric-structures funext univalence truncations +open import metric-spaces.premetric-structures funext univalence truncations +open import metric-spaces.pseudometric-structures funext univalence truncations +open import metric-spaces.reflexive-premetric-structures funext univalence truncations +open import metric-spaces.symmetric-premetric-structures funext univalence truncations +open import metric-spaces.triangular-premetric-structures funext univalence truncations ```
diff --git a/src/metric-spaces/monotonic-premetric-structures.lagda.md b/src/metric-spaces/monotonic-premetric-structures.lagda.md index d495f3087d..ce2b2b41f6 100644 --- a/src/metric-spaces/monotonic-premetric-structures.lagda.md +++ b/src/metric-spaces/monotonic-premetric-structures.lagda.md @@ -1,18 +1,27 @@ # Monotonic premetric structures on types ```agda -module metric-spaces.monotonic-premetric-structures where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module metric-spaces.monotonic-premetric-structures + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.positive-rational-numbers +open import elementary-number-theory.positive-rational-numbers funext univalence truncations -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.propositions funext univalence open import foundation.universe-levels -open import metric-spaces.premetric-structures +open import metric-spaces.premetric-structures funext univalence truncations ```
diff --git a/src/metric-spaces/ordering-premetric-structures.lagda.md b/src/metric-spaces/ordering-premetric-structures.lagda.md index 9d31996995..7add37a1c2 100644 --- a/src/metric-spaces/ordering-premetric-structures.lagda.md +++ b/src/metric-spaces/ordering-premetric-structures.lagda.md @@ -1,25 +1,34 @@ # The poset of premetric structures on a type ```agda -module metric-spaces.ordering-premetric-structures where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module metric-spaces.ordering-premetric-structures + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.positive-rational-numbers +open import elementary-number-theory.positive-rational-numbers funext univalence truncations -open import foundation.binary-relations +open import foundation.binary-relations funext univalence truncations open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.identity-types -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence open import foundation.universe-levels -open import metric-spaces.premetric-structures +open import metric-spaces.premetric-structures funext univalence truncations -open import order-theory.posets -open import order-theory.preorders +open import order-theory.posets funext univalence truncations +open import order-theory.preorders funext univalence truncations ```
diff --git a/src/metric-spaces/precategory-of-metric-spaces-and-functions.lagda.md b/src/metric-spaces/precategory-of-metric-spaces-and-functions.lagda.md index 0ad621c3a1..36e06dd6cc 100644 --- a/src/metric-spaces/precategory-of-metric-spaces-and-functions.lagda.md +++ b/src/metric-spaces/precategory-of-metric-spaces-and-functions.lagda.md @@ -1,20 +1,28 @@ # The precategory of metric spaces and functions ```agda -module metric-spaces.precategory-of-metric-spaces-and-functions where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module metric-spaces.precategory-of-metric-spaces-and-functions + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.precategories +open import category-theory.precategories funext univalence truncations -open import foundation.function-types -open import foundation.identity-types +open import foundation.function-types funext +open import foundation.identity-types funext open import foundation.universe-levels -open import metric-spaces.functions-metric-spaces -open import metric-spaces.metric-spaces +open import metric-spaces.functions-metric-spaces funext univalence truncations +open import metric-spaces.metric-spaces funext univalence truncations ```
diff --git a/src/metric-spaces/precategory-of-metric-spaces-and-isometries.lagda.md b/src/metric-spaces/precategory-of-metric-spaces-and-isometries.lagda.md index 9f8d292f56..c2b0bdaa0a 100644 --- a/src/metric-spaces/precategory-of-metric-spaces-and-isometries.lagda.md +++ b/src/metric-spaces/precategory-of-metric-spaces-and-isometries.lagda.md @@ -1,36 +1,37 @@ # The precategory of metric spaces and isometries ```agda -module metric-spaces.precategory-of-metric-spaces-and-isometries where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module metric-spaces.precategory-of-metric-spaces-and-isometries + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.isomorphisms-in-precategories -open import category-theory.precategories +open import category-theory.isomorphisms-in-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations open import foundation.action-on-identifications-functions -open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.propositions -open import foundation.subtypes -open import foundation.torsorial-type-families -open import foundation.transport-along-identifications +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.logical-equivalences funext open import foundation.type-arithmetic-cartesian-product-types open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels -open import metric-spaces.equality-of-metric-spaces -open import metric-spaces.functions-metric-spaces -open import metric-spaces.isometries-metric-spaces -open import metric-spaces.metric-spaces +open import metric-spaces.equality-of-metric-spaces funext univalence truncations +open import metric-spaces.functions-metric-spaces funext univalence truncations +open import metric-spaces.isometries-metric-spaces funext univalence truncations +open import metric-spaces.metric-spaces funext univalence truncations ```
diff --git a/src/metric-spaces/precategory-of-metric-spaces-and-short-functions.lagda.md b/src/metric-spaces/precategory-of-metric-spaces-and-short-functions.lagda.md index 1133d2e084..147ead9a05 100644 --- a/src/metric-spaces/precategory-of-metric-spaces-and-short-functions.lagda.md +++ b/src/metric-spaces/precategory-of-metric-spaces-and-short-functions.lagda.md @@ -1,37 +1,40 @@ # The precategory of metric spaces and short functions ```agda -module metric-spaces.precategory-of-metric-spaces-and-short-functions where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module metric-spaces.precategory-of-metric-spaces-and-short-functions + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.isomorphisms-in-precategories -open import category-theory.precategories +open import category-theory.isomorphisms-in-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations open import foundation.action-on-identifications-functions open import foundation.binary-transport -open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.propositions -open import foundation.torsorial-type-families +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.logical-equivalences funext +open import foundation.propositions funext univalence open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels -open import metric-spaces.equality-of-metric-spaces -open import metric-spaces.functions-metric-spaces -open import metric-spaces.isometric-equivalences-premetric-spaces -open import metric-spaces.isometries-metric-spaces -open import metric-spaces.metric-spaces -open import metric-spaces.precategory-of-metric-spaces-and-isometries -open import metric-spaces.short-functions-metric-spaces +open import metric-spaces.equality-of-metric-spaces funext univalence truncations +open import metric-spaces.functions-metric-spaces funext univalence truncations +open import metric-spaces.isometric-equivalences-premetric-spaces funext univalence truncations +open import metric-spaces.isometries-metric-spaces funext univalence truncations +open import metric-spaces.metric-spaces funext univalence truncations +open import metric-spaces.short-functions-metric-spaces funext univalence truncations ```
diff --git a/src/metric-spaces/premetric-spaces.lagda.md b/src/metric-spaces/premetric-spaces.lagda.md index edc68f4a20..52ab74ffd0 100644 --- a/src/metric-spaces/premetric-spaces.lagda.md +++ b/src/metric-spaces/premetric-spaces.lagda.md @@ -1,26 +1,35 @@ # Premetric spaces ```agda -module metric-spaces.premetric-spaces where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module metric-spaces.premetric-spaces + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.positive-rational-numbers +open import elementary-number-theory.positive-rational-numbers funext univalence truncations open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.function-types funext +open import foundation.propositions funext univalence open import foundation.universe-levels -open import metric-spaces.discrete-premetric-structures -open import metric-spaces.extensional-premetric-structures -open import metric-spaces.monotonic-premetric-structures -open import metric-spaces.premetric-structures -open import metric-spaces.reflexive-premetric-structures -open import metric-spaces.symmetric-premetric-structures -open import metric-spaces.triangular-premetric-structures +open import metric-spaces.discrete-premetric-structures funext univalence truncations +open import metric-spaces.extensional-premetric-structures funext univalence truncations +open import metric-spaces.monotonic-premetric-structures funext univalence truncations +open import metric-spaces.premetric-structures funext univalence truncations +open import metric-spaces.reflexive-premetric-structures funext univalence truncations +open import metric-spaces.symmetric-premetric-structures funext univalence truncations +open import metric-spaces.triangular-premetric-structures funext univalence truncations ```
diff --git a/src/metric-spaces/premetric-structures.lagda.md b/src/metric-spaces/premetric-structures.lagda.md index 1efac73fa8..e28c3f156f 100644 --- a/src/metric-spaces/premetric-structures.lagda.md +++ b/src/metric-spaces/premetric-structures.lagda.md @@ -1,32 +1,41 @@ # Premetric structures on types ```agda -module metric-spaces.premetric-structures where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module metric-spaces.premetric-structures + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.positive-rational-numbers +open import elementary-number-theory.positive-rational-numbers funext univalence truncations -open import foundation.binary-relations +open import foundation.binary-relations funext univalence truncations open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.equivalences -open import foundation.existential-quantification -open import foundation.function-extensionality -open import foundation.function-types +open import foundation.dependent-products-propositions funext +open import foundation.empty-types funext univalence truncations +open import foundation.equivalences funext +open import foundation.existential-quantification funext univalence truncations +open import foundation.function-extensionality funext +open import foundation.function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.negation -open import foundation.propositional-extensionality -open import foundation.propositions -open import foundation.sets -open import foundation.subtypes -open import foundation.torsorial-type-families +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.negation funext +open import foundation.propositional-extensionality funext univalence truncations +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.subtypes funext univalence truncations +open import foundation.torsorial-type-families funext univalence truncations open import foundation.transport-along-identifications -open import foundation.univalence +open import foundation.univalence funext univalence open import foundation.universe-levels ``` diff --git a/src/metric-spaces/pseudometric-spaces.lagda.md b/src/metric-spaces/pseudometric-spaces.lagda.md index 1504bef0ae..f722b1dc34 100644 --- a/src/metric-spaces/pseudometric-spaces.lagda.md +++ b/src/metric-spaces/pseudometric-spaces.lagda.md @@ -1,30 +1,39 @@ # Pseudometric spaces ```agda -module metric-spaces.pseudometric-spaces where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module metric-spaces.pseudometric-spaces + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.binary-relations +open import foundation.binary-relations funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalence-relations -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.equivalence-relations funext univalence truncations +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels -open import metric-spaces.discrete-premetric-structures -open import metric-spaces.extensional-premetric-structures -open import metric-spaces.monotonic-premetric-structures -open import metric-spaces.premetric-spaces -open import metric-spaces.premetric-structures -open import metric-spaces.pseudometric-structures -open import metric-spaces.reflexive-premetric-structures -open import metric-spaces.symmetric-premetric-structures -open import metric-spaces.triangular-premetric-structures +open import metric-spaces.discrete-premetric-structures funext univalence truncations +open import metric-spaces.extensional-premetric-structures funext univalence truncations +open import metric-spaces.monotonic-premetric-structures funext univalence truncations +open import metric-spaces.premetric-spaces funext univalence truncations +open import metric-spaces.premetric-structures funext univalence truncations +open import metric-spaces.pseudometric-structures funext univalence truncations +open import metric-spaces.reflexive-premetric-structures funext univalence truncations +open import metric-spaces.symmetric-premetric-structures funext univalence truncations +open import metric-spaces.triangular-premetric-structures funext univalence truncations ```
diff --git a/src/metric-spaces/pseudometric-structures.lagda.md b/src/metric-spaces/pseudometric-structures.lagda.md index fb0476457b..e6e6869aea 100644 --- a/src/metric-spaces/pseudometric-structures.lagda.md +++ b/src/metric-spaces/pseudometric-structures.lagda.md @@ -1,25 +1,34 @@ # Pseudometric structures on a type ```agda -module metric-spaces.pseudometric-structures where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module metric-spaces.pseudometric-structures + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence open import foundation.universe-levels -open import metric-spaces.closed-premetric-structures -open import metric-spaces.discrete-premetric-structures -open import metric-spaces.extensional-premetric-structures -open import metric-spaces.monotonic-premetric-structures -open import metric-spaces.premetric-structures -open import metric-spaces.reflexive-premetric-structures -open import metric-spaces.symmetric-premetric-structures -open import metric-spaces.triangular-premetric-structures +open import metric-spaces.closed-premetric-structures funext univalence truncations +open import metric-spaces.discrete-premetric-structures funext univalence truncations +open import metric-spaces.extensional-premetric-structures funext univalence truncations +open import metric-spaces.monotonic-premetric-structures funext univalence truncations +open import metric-spaces.premetric-structures funext univalence truncations +open import metric-spaces.reflexive-premetric-structures funext univalence truncations +open import metric-spaces.symmetric-premetric-structures funext univalence truncations +open import metric-spaces.triangular-premetric-structures funext univalence truncations ```
diff --git a/src/metric-spaces/reflexive-premetric-structures.lagda.md b/src/metric-spaces/reflexive-premetric-structures.lagda.md index 5bb77664f7..ddba4791fa 100644 --- a/src/metric-spaces/reflexive-premetric-structures.lagda.md +++ b/src/metric-spaces/reflexive-premetric-structures.lagda.md @@ -1,28 +1,37 @@ # Reflexive premetric structures on types ```agda -module metric-spaces.reflexive-premetric-structures where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module metric-spaces.reflexive-premetric-structures + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.positive-rational-numbers +open import elementary-number-theory.positive-rational-numbers funext univalence truncations -open import foundation.binary-relations +open import foundation.binary-relations funext univalence truncations open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.equivalences -open import foundation.existential-quantification -open import foundation.function-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.negation -open import foundation.propositions -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.empty-types funext univalence truncations +open import foundation.equivalences funext +open import foundation.existential-quantification funext univalence truncations +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.negation funext +open import foundation.propositions funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels -open import metric-spaces.premetric-structures +open import metric-spaces.premetric-structures funext univalence truncations ```
diff --git a/src/metric-spaces/saturated-metric-spaces.lagda.md b/src/metric-spaces/saturated-metric-spaces.lagda.md index f4d759453b..31fd1230b5 100644 --- a/src/metric-spaces/saturated-metric-spaces.lagda.md +++ b/src/metric-spaces/saturated-metric-spaces.lagda.md @@ -1,33 +1,42 @@ # Saturated metric spaces ```agda -module metric-spaces.saturated-metric-spaces where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module metric-spaces.saturated-metric-spaces + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.positive-rational-numbers +open import elementary-number-theory.positive-rational-numbers funext univalence truncations -open import foundation.binary-relations +open import foundation.binary-relations funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.propositions -open import foundation.sets -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels -open import metric-spaces.closed-premetric-structures -open import metric-spaces.functions-metric-spaces -open import metric-spaces.metric-spaces -open import metric-spaces.metric-structures -open import metric-spaces.premetric-spaces -open import metric-spaces.premetric-structures -open import metric-spaces.short-functions-metric-spaces +open import metric-spaces.closed-premetric-structures funext univalence truncations +open import metric-spaces.functions-metric-spaces funext univalence truncations +open import metric-spaces.metric-spaces funext univalence truncations +open import metric-spaces.metric-structures funext univalence truncations +open import metric-spaces.premetric-spaces funext univalence truncations +open import metric-spaces.premetric-structures funext univalence truncations +open import metric-spaces.short-functions-metric-spaces funext univalence truncations ```
diff --git a/src/metric-spaces/short-functions-metric-spaces.lagda.md b/src/metric-spaces/short-functions-metric-spaces.lagda.md index bab344ebbb..eaeb79e4a7 100644 --- a/src/metric-spaces/short-functions-metric-spaces.lagda.md +++ b/src/metric-spaces/short-functions-metric-spaces.lagda.md @@ -1,32 +1,41 @@ # Short functions between metric spaces ```agda -module metric-spaces.short-functions-metric-spaces where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module metric-spaces.short-functions-metric-spaces + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.positive-rational-numbers +open import elementary-number-theory.positive-rational-numbers funext univalence truncations open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.propositional-truncations -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.function-extensionality funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence open import foundation.sequences -open import foundation.sets -open import foundation.subtypes +open import foundation.sets funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels -open import metric-spaces.functions-metric-spaces -open import metric-spaces.isometries-metric-spaces -open import metric-spaces.metric-spaces -open import metric-spaces.short-functions-premetric-spaces +open import metric-spaces.functions-metric-spaces funext univalence truncations +open import metric-spaces.isometries-metric-spaces funext univalence truncations +open import metric-spaces.metric-spaces funext univalence truncations +open import metric-spaces.short-functions-premetric-spaces funext univalence truncations ```
diff --git a/src/metric-spaces/short-functions-premetric-spaces.lagda.md b/src/metric-spaces/short-functions-premetric-spaces.lagda.md index f719e1acfc..2cccf33128 100644 --- a/src/metric-spaces/short-functions-premetric-spaces.lagda.md +++ b/src/metric-spaces/short-functions-premetric-spaces.lagda.md @@ -1,31 +1,40 @@ # Short functions between premetric spaces ```agda -module metric-spaces.short-functions-premetric-spaces where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module metric-spaces.short-functions-premetric-spaces + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.positive-rational-numbers +open import elementary-number-theory.positive-rational-numbers funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.existential-quantification -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.propositional-truncations -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.existential-quantification funext univalence truncations +open import foundation.function-extensionality funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence open import foundation.sequences -open import foundation.sets -open import foundation.subtypes +open import foundation.sets funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels -open import metric-spaces.isometries-premetric-spaces -open import metric-spaces.premetric-spaces +open import metric-spaces.isometries-premetric-spaces funext univalence truncations +open import metric-spaces.premetric-spaces funext univalence truncations ```
diff --git a/src/metric-spaces/subspaces-metric-spaces.lagda.md b/src/metric-spaces/subspaces-metric-spaces.lagda.md index 0b5765b507..75c9fb0de0 100644 --- a/src/metric-spaces/subspaces-metric-spaces.lagda.md +++ b/src/metric-spaces/subspaces-metric-spaces.lagda.md @@ -1,28 +1,36 @@ # Subspaces of metric spaces ```agda -module metric-spaces.subspaces-metric-spaces where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module metric-spaces.subspaces-metric-spaces + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.logical-equivalences -open import foundation.subtypes +open import foundation.logical-equivalences funext +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels -open import metric-spaces.extensional-premetric-structures -open import metric-spaces.functions-metric-spaces -open import metric-spaces.isometries-metric-spaces -open import metric-spaces.metric-spaces -open import metric-spaces.metric-structures -open import metric-spaces.monotonic-premetric-structures -open import metric-spaces.premetric-structures -open import metric-spaces.pseudometric-structures -open import metric-spaces.reflexive-premetric-structures -open import metric-spaces.symmetric-premetric-structures -open import metric-spaces.triangular-premetric-structures +open import metric-spaces.extensional-premetric-structures funext univalence truncations +open import metric-spaces.functions-metric-spaces funext univalence truncations +open import metric-spaces.isometries-metric-spaces funext univalence truncations +open import metric-spaces.metric-spaces funext univalence truncations +open import metric-spaces.metric-structures funext univalence truncations +open import metric-spaces.monotonic-premetric-structures funext univalence truncations +open import metric-spaces.premetric-structures funext univalence truncations +open import metric-spaces.pseudometric-structures funext univalence truncations +open import metric-spaces.reflexive-premetric-structures funext univalence truncations +open import metric-spaces.symmetric-premetric-structures funext univalence truncations +open import metric-spaces.triangular-premetric-structures funext univalence truncations ```
diff --git a/src/metric-spaces/symmetric-premetric-structures.lagda.md b/src/metric-spaces/symmetric-premetric-structures.lagda.md index 86d360e6a2..29db29d8b2 100644 --- a/src/metric-spaces/symmetric-premetric-structures.lagda.md +++ b/src/metric-spaces/symmetric-premetric-structures.lagda.md @@ -1,22 +1,31 @@ # Symmetric premetric structures on types ```agda -module metric-spaces.symmetric-premetric-structures where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module metric-spaces.symmetric-premetric-structures + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.positive-rational-numbers - -open import foundation.binary-relations -open import foundation.existential-quantification -open import foundation.function-types -open import foundation.identity-types -open import foundation.propositions +open import elementary-number-theory.positive-rational-numbers funext univalence truncations + +open import foundation.binary-relations funext univalence truncations +open import foundation.dependent-products-propositions funext +open import foundation.existential-quantification funext univalence truncations +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence open import foundation.universe-levels -open import metric-spaces.premetric-structures +open import metric-spaces.premetric-structures funext univalence truncations ```
diff --git a/src/metric-spaces/triangular-premetric-structures.lagda.md b/src/metric-spaces/triangular-premetric-structures.lagda.md index 98b2b7c42a..5ed5ffade7 100644 --- a/src/metric-spaces/triangular-premetric-structures.lagda.md +++ b/src/metric-spaces/triangular-premetric-structures.lagda.md @@ -1,24 +1,33 @@ # Triangular premetric structures on types ```agda -module metric-spaces.triangular-premetric-structures where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module metric-spaces.triangular-premetric-structures + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.positive-rational-numbers +open import elementary-number-theory.positive-rational-numbers funext univalence truncations -open import foundation.binary-relations -open import foundation.function-types -open import foundation.identity-types -open import foundation.propositions +open import foundation.binary-relations funext univalence truncations +open import foundation.dependent-products-propositions funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence open import foundation.transport-along-identifications open import foundation.universe-levels -open import metric-spaces.monotonic-premetric-structures -open import metric-spaces.premetric-structures -open import metric-spaces.reflexive-premetric-structures +open import metric-spaces.monotonic-premetric-structures funext univalence truncations +open import metric-spaces.premetric-structures funext univalence truncations +open import metric-spaces.reflexive-premetric-structures funext univalence truncations ```
diff --git a/src/modal-type-theory.lagda.md b/src/modal-type-theory.lagda.md index e9f60ad038..872a5334ed 100644 --- a/src/modal-type-theory.lagda.md +++ b/src/modal-type-theory.lagda.md @@ -20,29 +20,37 @@ _cohesive_ structure. ## Modules in the modal type theory namespace ```agda -module modal-type-theory where - -open import modal-type-theory.action-on-homotopies-flat-modality public -open import modal-type-theory.action-on-identifications-crisp-functions public -open import modal-type-theory.action-on-identifications-flat-modality public -open import modal-type-theory.crisp-cartesian-product-types public -open import modal-type-theory.crisp-coproduct-types public -open import modal-type-theory.crisp-dependent-function-types public -open import modal-type-theory.crisp-dependent-pair-types public -open import modal-type-theory.crisp-function-types public -open import modal-type-theory.crisp-identity-types public -open import modal-type-theory.crisp-law-of-excluded-middle public -open import modal-type-theory.crisp-pullbacks public +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module modal-type-theory + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where + +open import modal-type-theory.action-on-homotopies-flat-modality funext univalence public +open import modal-type-theory.action-on-identifications-crisp-functions funext univalence public +open import modal-type-theory.action-on-identifications-flat-modality funext univalence public +open import modal-type-theory.crisp-cartesian-product-types funext univalence truncations public +open import modal-type-theory.crisp-coproduct-types funext univalence truncations public +open import modal-type-theory.crisp-dependent-function-types funext univalence public +open import modal-type-theory.crisp-dependent-pair-types funext univalence truncations public +open import modal-type-theory.crisp-function-types funext univalence public +open import modal-type-theory.crisp-identity-types funext univalence public +open import modal-type-theory.crisp-law-of-excluded-middle funext univalence truncations public +open import modal-type-theory.crisp-pullbacks funext univalence truncations public open import modal-type-theory.crisp-types public -open import modal-type-theory.dependent-universal-property-flat-discrete-crisp-types public -open import modal-type-theory.flat-discrete-crisp-types public -open import modal-type-theory.flat-modality public -open import modal-type-theory.flat-sharp-adjunction public -open import modal-type-theory.functoriality-flat-modality public -open import modal-type-theory.functoriality-sharp-modality public -open import modal-type-theory.sharp-codiscrete-maps public -open import modal-type-theory.sharp-codiscrete-types public -open import modal-type-theory.sharp-modality public -open import modal-type-theory.transport-along-crisp-identifications public -open import modal-type-theory.universal-property-flat-discrete-crisp-types public +open import modal-type-theory.dependent-universal-property-flat-discrete-crisp-types funext public +open import modal-type-theory.flat-discrete-crisp-types funext univalence truncations public +open import modal-type-theory.flat-modality funext public +open import modal-type-theory.flat-sharp-adjunction funext univalence truncations public +open import modal-type-theory.functoriality-flat-modality funext univalence public +open import modal-type-theory.functoriality-sharp-modality funext univalence truncations public +open import modal-type-theory.sharp-codiscrete-maps funext univalence truncations public +open import modal-type-theory.sharp-codiscrete-types funext univalence truncations public +open import modal-type-theory.sharp-modality funext univalence truncations public +open import modal-type-theory.transport-along-crisp-identifications funext univalence public +open import modal-type-theory.universal-property-flat-discrete-crisp-types funext univalence truncations public ``` diff --git a/src/modal-type-theory/action-on-homotopies-flat-modality.lagda.md b/src/modal-type-theory/action-on-homotopies-flat-modality.lagda.md index 248652177b..49d931713d 100644 --- a/src/modal-type-theory/action-on-homotopies-flat-modality.lagda.md +++ b/src/modal-type-theory/action-on-homotopies-flat-modality.lagda.md @@ -2,20 +2,25 @@ ```agda {-# OPTIONS --cohesion --flat-split #-} +open import foundation-core.univalence +open import foundation.function-extensionality-axiom -module modal-type-theory.action-on-homotopies-flat-modality where +module modal-type-theory.action-on-homotopies-flat-modality + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda -open import foundation.homotopies -open import foundation.identity-types +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.universe-levels -open import modal-type-theory.action-on-identifications-flat-modality -open import modal-type-theory.flat-modality -open import modal-type-theory.functoriality-flat-modality +open import modal-type-theory.action-on-identifications-flat-modality funext univalence +open import modal-type-theory.flat-modality funext +open import modal-type-theory.functoriality-flat-modality funext univalence ```
diff --git a/src/modal-type-theory/action-on-identifications-crisp-functions.lagda.md b/src/modal-type-theory/action-on-identifications-crisp-functions.lagda.md index 085fda16e2..cb21b3b661 100644 --- a/src/modal-type-theory/action-on-identifications-crisp-functions.lagda.md +++ b/src/modal-type-theory/action-on-identifications-crisp-functions.lagda.md @@ -2,8 +2,13 @@ ```agda {-# OPTIONS --cohesion --flat-split #-} +open import foundation-core.univalence +open import foundation.function-extensionality-axiom -module modal-type-theory.action-on-identifications-crisp-functions where +module modal-type-theory.action-on-identifications-crisp-functions + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports @@ -13,7 +18,7 @@ open import foundation.universe-levels open import foundation-core.identity-types -open import modal-type-theory.crisp-identity-types +open import modal-type-theory.crisp-identity-types funext univalence ```
diff --git a/src/modal-type-theory/action-on-identifications-flat-modality.lagda.md b/src/modal-type-theory/action-on-identifications-flat-modality.lagda.md index 4f878208a8..0b9f51e1a1 100644 --- a/src/modal-type-theory/action-on-identifications-flat-modality.lagda.md +++ b/src/modal-type-theory/action-on-identifications-flat-modality.lagda.md @@ -2,20 +2,25 @@ ```agda {-# OPTIONS --cohesion --flat-split #-} +open import foundation-core.univalence +open import foundation.function-extensionality-axiom -module modal-type-theory.action-on-identifications-flat-modality where +module modal-type-theory.action-on-identifications-flat-modality + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import modal-type-theory.action-on-identifications-crisp-functions -open import modal-type-theory.crisp-identity-types -open import modal-type-theory.flat-modality +open import modal-type-theory.action-on-identifications-crisp-functions funext univalence +open import modal-type-theory.crisp-identity-types funext univalence +open import modal-type-theory.flat-modality funext ```
diff --git a/src/modal-type-theory/crisp-cartesian-product-types.lagda.md b/src/modal-type-theory/crisp-cartesian-product-types.lagda.md index 000d78c746..d9f66a0889 100644 --- a/src/modal-type-theory/crisp-cartesian-product-types.lagda.md +++ b/src/modal-type-theory/crisp-cartesian-product-types.lagda.md @@ -2,28 +2,35 @@ ```agda {-# OPTIONS --cohesion --flat-split #-} - -module modal-type-theory.crisp-cartesian-product-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module modal-type-theory.crisp-cartesian-product-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-cartesian-product-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.inhabited-types -open import foundation.propositional-truncations -open import foundation.retractions -open import foundation.sections +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.inhabited-types funext univalence truncations +open import foundation.propositional-truncations funext univalence +open import foundation.retractions funext +open import foundation.sections funext open import foundation.universe-levels -open import modal-type-theory.flat-discrete-crisp-types -open import modal-type-theory.flat-modality +open import modal-type-theory.flat-discrete-crisp-types funext univalence truncations +open import modal-type-theory.flat-modality funext ```
diff --git a/src/modal-type-theory/crisp-coproduct-types.lagda.md b/src/modal-type-theory/crisp-coproduct-types.lagda.md index 1fc84587d7..f944e87ba2 100644 --- a/src/modal-type-theory/crisp-coproduct-types.lagda.md +++ b/src/modal-type-theory/crisp-coproduct-types.lagda.md @@ -2,26 +2,33 @@ ```agda {-# OPTIONS --cohesion --flat-split #-} - -module modal-type-theory.crisp-coproduct-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module modal-type-theory.crisp-coproduct-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.coproduct-types +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-coproduct-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.retractions -open import foundation.sections +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-coproduct-types funext univalence truncations +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.retractions funext +open import foundation.sections funext open import foundation.universe-levels -open import modal-type-theory.flat-discrete-crisp-types -open import modal-type-theory.flat-modality +open import modal-type-theory.flat-discrete-crisp-types funext univalence truncations +open import modal-type-theory.flat-modality funext ```
diff --git a/src/modal-type-theory/crisp-dependent-function-types.lagda.md b/src/modal-type-theory/crisp-dependent-function-types.lagda.md index a5034fb664..0671da5be0 100644 --- a/src/modal-type-theory/crisp-dependent-function-types.lagda.md +++ b/src/modal-type-theory/crisp-dependent-function-types.lagda.md @@ -2,24 +2,29 @@ ```agda {-# OPTIONS --cohesion --flat-split #-} +open import foundation-core.univalence +open import foundation.function-extensionality-axiom -module modal-type-theory.crisp-dependent-function-types where +module modal-type-theory.crisp-dependent-function-types + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.identity-types -open import foundation.retractions -open import foundation.sections +open import foundation.equivalences funext +open import foundation.function-extensionality funext +open import foundation.identity-types funext +open import foundation.retractions funext +open import foundation.sections funext open import foundation.universe-levels -open import modal-type-theory.action-on-identifications-flat-modality -open import modal-type-theory.flat-modality -open import modal-type-theory.functoriality-flat-modality +open import modal-type-theory.action-on-identifications-flat-modality funext univalence +open import modal-type-theory.flat-modality funext +open import modal-type-theory.functoriality-flat-modality funext univalence ```
diff --git a/src/modal-type-theory/crisp-dependent-pair-types.lagda.md b/src/modal-type-theory/crisp-dependent-pair-types.lagda.md index 962a9f0762..ed35c3c1a7 100644 --- a/src/modal-type-theory/crisp-dependent-pair-types.lagda.md +++ b/src/modal-type-theory/crisp-dependent-pair-types.lagda.md @@ -2,26 +2,33 @@ ```agda {-# OPTIONS --cohesion --flat-split #-} - -module modal-type-theory.crisp-dependent-pair-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module modal-type-theory.crisp-dependent-pair-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.retractions -open import foundation.sections +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.retractions funext +open import foundation.sections funext open import foundation.universe-levels -open import modal-type-theory.flat-discrete-crisp-types -open import modal-type-theory.flat-modality -open import modal-type-theory.functoriality-flat-modality +open import modal-type-theory.flat-discrete-crisp-types funext univalence truncations +open import modal-type-theory.flat-modality funext +open import modal-type-theory.functoriality-flat-modality funext univalence ```
diff --git a/src/modal-type-theory/crisp-function-types.lagda.md b/src/modal-type-theory/crisp-function-types.lagda.md index 57b0ed3e46..631be9cc7a 100644 --- a/src/modal-type-theory/crisp-function-types.lagda.md +++ b/src/modal-type-theory/crisp-function-types.lagda.md @@ -2,26 +2,31 @@ ```agda {-# OPTIONS --cohesion --flat-split #-} +open import foundation-core.univalence +open import foundation.function-extensionality-axiom -module modal-type-theory.crisp-function-types where +module modal-type-theory.crisp-function-types + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.identity-types -open import foundation.postcomposition-functions -open import foundation.retractions -open import foundation.sections +open import foundation.equivalences funext +open import foundation.function-extensionality funext +open import foundation.identity-types funext +open import foundation.postcomposition-functions funext +open import foundation.retractions funext +open import foundation.sections funext open import foundation.universe-levels -open import modal-type-theory.action-on-identifications-flat-modality -open import modal-type-theory.crisp-dependent-function-types -open import modal-type-theory.flat-modality -open import modal-type-theory.functoriality-flat-modality +open import modal-type-theory.action-on-identifications-flat-modality funext univalence +open import modal-type-theory.crisp-dependent-function-types funext univalence +open import modal-type-theory.flat-modality funext +open import modal-type-theory.functoriality-flat-modality funext univalence ```
diff --git a/src/modal-type-theory/crisp-identity-types.lagda.md b/src/modal-type-theory/crisp-identity-types.lagda.md index adffea8d96..14ff0cfc25 100644 --- a/src/modal-type-theory/crisp-identity-types.lagda.md +++ b/src/modal-type-theory/crisp-identity-types.lagda.md @@ -2,23 +2,28 @@ ```agda {-# OPTIONS --cohesion --flat-split #-} +open import foundation-core.univalence +open import foundation.function-extensionality-axiom -module modal-type-theory.crisp-identity-types where +module modal-type-theory.crisp-identity-types + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.retractions -open import foundation.retracts-of-types -open import foundation.sections +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.retractions funext +open import foundation.retracts-of-types funext univalence +open import foundation.sections funext open import foundation.universe-levels -open import modal-type-theory.flat-modality +open import modal-type-theory.flat-modality funext ```
diff --git a/src/modal-type-theory/crisp-law-of-excluded-middle.lagda.md b/src/modal-type-theory/crisp-law-of-excluded-middle.lagda.md index 52f9b9c10f..7df60a57fe 100644 --- a/src/modal-type-theory/crisp-law-of-excluded-middle.lagda.md +++ b/src/modal-type-theory/crisp-law-of-excluded-middle.lagda.md @@ -2,18 +2,25 @@ ```agda {-# OPTIONS --cohesion --flat-split #-} - -module modal-type-theory.crisp-law-of-excluded-middle where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module modal-type-theory.crisp-law-of-excluded-middle + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.decidable-types +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types open import foundation.universe-levels -open import foundation-core.decidable-propositions +open import foundation-core.decidable-propositions funext univalence truncations open import foundation-core.propositions ``` diff --git a/src/modal-type-theory/crisp-pullbacks.lagda.md b/src/modal-type-theory/crisp-pullbacks.lagda.md index d0e87ca486..fa4d97d8e9 100644 --- a/src/modal-type-theory/crisp-pullbacks.lagda.md +++ b/src/modal-type-theory/crisp-pullbacks.lagda.md @@ -2,34 +2,41 @@ ```agda {-# OPTIONS --cohesion --flat-split #-} - -module modal-type-theory.crisp-pullbacks where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module modal-type-theory.crisp-pullbacks + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cones-over-cospan-diagrams +open import foundation.cones-over-cospan-diagrams funext open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-pullbacks -open import foundation.homotopies -open import foundation.identity-types +open import foundation.equality-dependent-pair-types funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-pullbacks funext univalence truncations +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.morphisms-cospan-diagrams -open import foundation.pullbacks -open import foundation.standard-pullbacks +open import foundation.pullbacks funext univalence truncations +open import foundation.standard-pullbacks funext open import foundation.universe-levels -open import modal-type-theory.action-on-identifications-crisp-functions -open import modal-type-theory.action-on-identifications-flat-modality -open import modal-type-theory.crisp-dependent-pair-types -open import modal-type-theory.crisp-identity-types -open import modal-type-theory.flat-discrete-crisp-types -open import modal-type-theory.flat-modality -open import modal-type-theory.functoriality-flat-modality +open import modal-type-theory.action-on-identifications-crisp-functions funext univalence +open import modal-type-theory.action-on-identifications-flat-modality funext univalence +open import modal-type-theory.crisp-dependent-pair-types funext univalence truncations +open import modal-type-theory.crisp-identity-types funext univalence +open import modal-type-theory.flat-discrete-crisp-types funext univalence truncations +open import modal-type-theory.flat-modality funext +open import modal-type-theory.functoriality-flat-modality funext univalence ```
diff --git a/src/modal-type-theory/dependent-universal-property-flat-discrete-crisp-types.lagda.md b/src/modal-type-theory/dependent-universal-property-flat-discrete-crisp-types.lagda.md index 1754d487ba..51556595b2 100644 --- a/src/modal-type-theory/dependent-universal-property-flat-discrete-crisp-types.lagda.md +++ b/src/modal-type-theory/dependent-universal-property-flat-discrete-crisp-types.lagda.md @@ -2,17 +2,20 @@ ```agda {-# OPTIONS --cohesion --flat-split #-} +open import foundation.function-extensionality-axiom -module modal-type-theory.dependent-universal-property-flat-discrete-crisp-types where +module modal-type-theory.dependent-universal-property-flat-discrete-crisp-types + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.equivalences +open import foundation.equivalences funext open import foundation.universe-levels -open import modal-type-theory.flat-modality +open import modal-type-theory.flat-modality funext ```
diff --git a/src/modal-type-theory/flat-discrete-crisp-types.lagda.md b/src/modal-type-theory/flat-discrete-crisp-types.lagda.md index 5bf37687fc..031f266c5b 100644 --- a/src/modal-type-theory/flat-discrete-crisp-types.lagda.md +++ b/src/modal-type-theory/flat-discrete-crisp-types.lagda.md @@ -2,8 +2,15 @@ ```agda {-# OPTIONS --cohesion --flat-split #-} - -module modal-type-theory.flat-discrete-crisp-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module modal-type-theory.flat-discrete-crisp-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -12,24 +19,25 @@ module modal-type-theory.flat-discrete-crisp-types where open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.booleans +open import foundation.booleans funext univalence truncations open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.empty-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.propositions -open import foundation.retractions -open import foundation.sections +open import foundation.dependent-products-propositions funext +open import foundation.embeddings funext +open import foundation.empty-types funext univalence truncations +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.retractions funext +open import foundation.sections funext open import foundation.unit-type open import foundation.universe-levels -open import modal-type-theory.action-on-homotopies-flat-modality -open import modal-type-theory.crisp-identity-types -open import modal-type-theory.flat-modality -open import modal-type-theory.functoriality-flat-modality +open import modal-type-theory.action-on-homotopies-flat-modality funext univalence +open import modal-type-theory.crisp-identity-types funext univalence +open import modal-type-theory.flat-modality funext +open import modal-type-theory.functoriality-flat-modality funext univalence ```
diff --git a/src/modal-type-theory/flat-modality.lagda.md b/src/modal-type-theory/flat-modality.lagda.md index 10318f9d11..04ce309fe6 100644 --- a/src/modal-type-theory/flat-modality.lagda.md +++ b/src/modal-type-theory/flat-modality.lagda.md @@ -2,18 +2,21 @@ ```agda {-# OPTIONS --cohesion --flat-split #-} +open import foundation.function-extensionality-axiom -module modal-type-theory.flat-modality where +module modal-type-theory.flat-modality + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.identity-types -open import foundation.retractions -open import foundation.sections +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.retractions funext +open import foundation.sections funext open import foundation.universe-levels ``` diff --git a/src/modal-type-theory/flat-sharp-adjunction.lagda.md b/src/modal-type-theory/flat-sharp-adjunction.lagda.md index f3cd07d5ef..a371ebc155 100644 --- a/src/modal-type-theory/flat-sharp-adjunction.lagda.md +++ b/src/modal-type-theory/flat-sharp-adjunction.lagda.md @@ -2,27 +2,34 @@ ```agda {-# OPTIONS --cohesion --flat-split #-} - -module modal-type-theory.flat-sharp-adjunction where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module modal-type-theory.flat-sharp-adjunction + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.identity-types -open import foundation.retractions -open import foundation.sections +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.retractions funext +open import foundation.sections funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import modal-type-theory.action-on-identifications-flat-modality -open import modal-type-theory.flat-modality -open import modal-type-theory.functoriality-flat-modality -open import modal-type-theory.sharp-codiscrete-types -open import modal-type-theory.sharp-modality +open import modal-type-theory.action-on-identifications-flat-modality funext univalence +open import modal-type-theory.flat-modality funext +open import modal-type-theory.functoriality-flat-modality funext univalence +open import modal-type-theory.sharp-codiscrete-types funext univalence truncations +open import modal-type-theory.sharp-modality funext univalence truncations ```
diff --git a/src/modal-type-theory/functoriality-flat-modality.lagda.md b/src/modal-type-theory/functoriality-flat-modality.lagda.md index 150a1c469e..09cd2350eb 100644 --- a/src/modal-type-theory/functoriality-flat-modality.lagda.md +++ b/src/modal-type-theory/functoriality-flat-modality.lagda.md @@ -2,25 +2,30 @@ ```agda {-# OPTIONS --cohesion --flat-split #-} +open import foundation-core.univalence +open import foundation.function-extensionality-axiom -module modal-type-theory.functoriality-flat-modality where +module modal-type-theory.functoriality-flat-modality + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.retractions -open import foundation.retracts-of-types -open import foundation.sections +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.retractions funext +open import foundation.retracts-of-types funext univalence +open import foundation.sections funext open import foundation.universe-levels -open import modal-type-theory.action-on-identifications-flat-modality -open import modal-type-theory.flat-modality +open import modal-type-theory.action-on-identifications-flat-modality funext univalence +open import modal-type-theory.flat-modality funext ```
diff --git a/src/modal-type-theory/functoriality-sharp-modality.lagda.md b/src/modal-type-theory/functoriality-sharp-modality.lagda.md index 673562dad9..90e5bb9622 100644 --- a/src/modal-type-theory/functoriality-sharp-modality.lagda.md +++ b/src/modal-type-theory/functoriality-sharp-modality.lagda.md @@ -2,8 +2,15 @@ ```agda {-# OPTIONS --cohesion --flat-split #-} +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom -module modal-type-theory.functoriality-sharp-modality where +module modal-type-theory.functoriality-sharp-modality + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -11,17 +18,17 @@ module modal-type-theory.functoriality-sharp-modality where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.locally-small-types +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.locally-small-types funext univalence truncations open import foundation.universe-levels -open import modal-type-theory.sharp-modality +open import modal-type-theory.sharp-modality funext univalence truncations -open import orthogonal-factorization-systems.locally-small-modal-operators -open import orthogonal-factorization-systems.modal-induction -open import orthogonal-factorization-systems.modal-subuniverse-induction +open import orthogonal-factorization-systems.locally-small-modal-operators funext univalence truncations +open import orthogonal-factorization-systems.modal-induction funext univalence truncations +open import orthogonal-factorization-systems.modal-subuniverse-induction funext univalence truncations ```
diff --git a/src/modal-type-theory/sharp-codiscrete-maps.lagda.md b/src/modal-type-theory/sharp-codiscrete-maps.lagda.md index b6f62e6748..7df414a0a2 100644 --- a/src/modal-type-theory/sharp-codiscrete-maps.lagda.md +++ b/src/modal-type-theory/sharp-codiscrete-maps.lagda.md @@ -2,18 +2,26 @@ ```agda {-# OPTIONS --cohesion --flat-split #-} - -module modal-type-theory.sharp-codiscrete-maps where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module modal-type-theory.sharp-codiscrete-maps + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.fibers-of-maps -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.fibers-of-maps funext +open import foundation.propositions funext univalence open import foundation.universe-levels -open import modal-type-theory.sharp-codiscrete-types +open import modal-type-theory.sharp-codiscrete-types funext univalence truncations ```
diff --git a/src/modal-type-theory/sharp-codiscrete-types.lagda.md b/src/modal-type-theory/sharp-codiscrete-types.lagda.md index 0eb4a695fb..5ca1421c8f 100644 --- a/src/modal-type-theory/sharp-codiscrete-types.lagda.md +++ b/src/modal-type-theory/sharp-codiscrete-types.lagda.md @@ -2,8 +2,15 @@ ```agda {-# OPTIONS --cohesion --flat-split #-} - -module modal-type-theory.sharp-codiscrete-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module modal-type-theory.sharp-codiscrete-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -11,19 +18,19 @@ module modal-type-theory.sharp-codiscrete-types where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.transport-along-equivalences +open import foundation.dependent-products-propositions funext +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.transport-along-equivalences funext univalence open import foundation.universe-levels -open import modal-type-theory.sharp-modality +open import modal-type-theory.sharp-modality funext univalence truncations -open import orthogonal-factorization-systems.higher-modalities -open import orthogonal-factorization-systems.modal-operators +open import orthogonal-factorization-systems.higher-modalities funext univalence truncations +open import orthogonal-factorization-systems.modal-operators funext univalence truncations ```
diff --git a/src/modal-type-theory/sharp-modality.lagda.md b/src/modal-type-theory/sharp-modality.lagda.md index 3dba911431..0d6ea97322 100644 --- a/src/modal-type-theory/sharp-modality.lagda.md +++ b/src/modal-type-theory/sharp-modality.lagda.md @@ -2,8 +2,15 @@ ```agda {-# OPTIONS --cohesion --flat-split #-} - -module modal-type-theory.sharp-modality where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module modal-type-theory.sharp-modality + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -11,15 +18,15 @@ module modal-type-theory.sharp-modality where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.locally-small-types +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.locally-small-types funext univalence truncations open import foundation.universe-levels -open import orthogonal-factorization-systems.locally-small-modal-operators -open import orthogonal-factorization-systems.modal-induction -open import orthogonal-factorization-systems.modal-subuniverse-induction +open import orthogonal-factorization-systems.locally-small-modal-operators funext univalence truncations +open import orthogonal-factorization-systems.modal-induction funext univalence truncations +open import orthogonal-factorization-systems.modal-subuniverse-induction funext univalence truncations ```
diff --git a/src/modal-type-theory/transport-along-crisp-identifications.lagda.md b/src/modal-type-theory/transport-along-crisp-identifications.lagda.md index 3405430500..8cce9f17ef 100644 --- a/src/modal-type-theory/transport-along-crisp-identifications.lagda.md +++ b/src/modal-type-theory/transport-along-crisp-identifications.lagda.md @@ -2,19 +2,24 @@ ```agda {-# OPTIONS --cohesion --flat-split #-} +open import foundation-core.univalence +open import foundation.function-extensionality-axiom -module modal-type-theory.transport-along-crisp-identifications where +module modal-type-theory.transport-along-crisp-identifications + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.function-types -open import foundation.identity-types +open import foundation.function-types funext +open import foundation.identity-types funext open import foundation.universe-levels -open import modal-type-theory.crisp-identity-types +open import modal-type-theory.crisp-identity-types funext univalence ```
diff --git a/src/modal-type-theory/universal-property-flat-discrete-crisp-types.lagda.md b/src/modal-type-theory/universal-property-flat-discrete-crisp-types.lagda.md index 63e293c714..d9c850ee27 100644 --- a/src/modal-type-theory/universal-property-flat-discrete-crisp-types.lagda.md +++ b/src/modal-type-theory/universal-property-flat-discrete-crisp-types.lagda.md @@ -2,8 +2,15 @@ ```agda {-# OPTIONS --cohesion --flat-split #-} - -module modal-type-theory.universal-property-flat-discrete-crisp-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module modal-type-theory.universal-property-flat-discrete-crisp-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -11,19 +18,19 @@ module modal-type-theory.universal-property-flat-discrete-crisp-types where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.identity-types -open import foundation.postcomposition-functions -open import foundation.universal-property-equivalences +open import foundation.equivalences funext +open import foundation.function-extensionality funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.postcomposition-functions funext +open import foundation.universal-property-equivalences funext open import foundation.universe-levels -open import modal-type-theory.action-on-identifications-crisp-functions -open import modal-type-theory.crisp-function-types -open import modal-type-theory.flat-discrete-crisp-types -open import modal-type-theory.flat-modality -open import modal-type-theory.functoriality-flat-modality +open import modal-type-theory.action-on-identifications-crisp-functions funext univalence +open import modal-type-theory.crisp-function-types funext univalence +open import modal-type-theory.flat-discrete-crisp-types funext univalence truncations +open import modal-type-theory.flat-modality funext +open import modal-type-theory.functoriality-flat-modality funext univalence ```
diff --git a/src/order-theory.lagda.md b/src/order-theory.lagda.md index 5d93468b21..6141bfecbf 100644 --- a/src/order-theory.lagda.md +++ b/src/order-theory.lagda.md @@ -3,141 +3,149 @@ ## Modules in the order theory namespace ```agda -module order-theory where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom -open import order-theory.accessible-elements-relations public -open import order-theory.bottom-elements-large-posets public -open import order-theory.bottom-elements-posets public -open import order-theory.bottom-elements-preorders public -open import order-theory.chains-posets public -open import order-theory.chains-preorders public -open import order-theory.closure-operators-large-locales public -open import order-theory.closure-operators-large-posets public -open import order-theory.commuting-squares-of-galois-connections-large-posets public -open import order-theory.commuting-squares-of-order-preserving-maps-large-posets public -open import order-theory.coverings-locales public -open import order-theory.decidable-posets public -open import order-theory.decidable-preorders public -open import order-theory.decidable-subposets public -open import order-theory.decidable-subpreorders public -open import order-theory.decidable-total-orders public -open import order-theory.decidable-total-preorders public -open import order-theory.deflationary-maps-posets public -open import order-theory.deflationary-maps-preorders public -open import order-theory.dependent-products-large-frames public -open import order-theory.dependent-products-large-inflattices public -open import order-theory.dependent-products-large-locales public -open import order-theory.dependent-products-large-meet-semilattices public -open import order-theory.dependent-products-large-posets public -open import order-theory.dependent-products-large-preorders public -open import order-theory.dependent-products-large-suplattices public -open import order-theory.distributive-lattices public -open import order-theory.finite-coverings-locales public -open import order-theory.finite-posets public -open import order-theory.finite-preorders public -open import order-theory.finite-total-orders public -open import order-theory.finitely-graded-posets public -open import order-theory.frames public -open import order-theory.galois-connections public -open import order-theory.galois-connections-large-posets public -open import order-theory.greatest-lower-bounds-large-posets public -open import order-theory.greatest-lower-bounds-posets public -open import order-theory.homomorphisms-frames public -open import order-theory.homomorphisms-large-frames public -open import order-theory.homomorphisms-large-locales public -open import order-theory.homomorphisms-large-meet-semilattices public -open import order-theory.homomorphisms-large-suplattices public -open import order-theory.homomorphisms-meet-semilattices public -open import order-theory.homomorphisms-meet-suplattices public -open import order-theory.homomorphisms-suplattices public -open import order-theory.ideals-preorders public -open import order-theory.incidence-algebras public -open import order-theory.inflationary-maps-posets public -open import order-theory.inflationary-maps-preorders public -open import order-theory.inflattices public -open import order-theory.inhabited-chains-posets public -open import order-theory.inhabited-chains-preorders public -open import order-theory.inhabited-finite-total-orders public -open import order-theory.interval-subposets public -open import order-theory.join-preserving-maps-posets public -open import order-theory.join-semilattices public -open import order-theory.knaster-tarski-fixed-point-theorem public -open import order-theory.large-frames public -open import order-theory.large-inflattices public -open import order-theory.large-join-semilattices public -open import order-theory.large-locales public -open import order-theory.large-meet-semilattices public -open import order-theory.large-meet-subsemilattices public -open import order-theory.large-posets public -open import order-theory.large-preorders public -open import order-theory.large-quotient-locales public -open import order-theory.large-subframes public -open import order-theory.large-subposets public -open import order-theory.large-subpreorders public -open import order-theory.large-subsuplattices public -open import order-theory.large-suplattices public -open import order-theory.lattices public -open import order-theory.least-upper-bounds-large-posets public -open import order-theory.least-upper-bounds-posets public -open import order-theory.locales public -open import order-theory.locally-finite-posets public -open import order-theory.lower-bounds-large-posets public -open import order-theory.lower-bounds-posets public -open import order-theory.lower-sets-large-posets public -open import order-theory.lower-types-preorders public -open import order-theory.maximal-chains-posets public -open import order-theory.maximal-chains-preorders public -open import order-theory.meet-semilattices public -open import order-theory.meet-suplattices public -open import order-theory.nuclei-large-locales public -open import order-theory.opposite-large-posets public -open import order-theory.opposite-large-preorders public -open import order-theory.opposite-posets public -open import order-theory.opposite-preorders public -open import order-theory.order-preserving-maps-large-posets public -open import order-theory.order-preserving-maps-large-preorders public -open import order-theory.order-preserving-maps-posets public -open import order-theory.order-preserving-maps-preorders public -open import order-theory.ordinals public -open import order-theory.posets public -open import order-theory.powers-of-large-locales public -open import order-theory.precategory-of-decidable-total-orders public -open import order-theory.precategory-of-finite-posets public -open import order-theory.precategory-of-finite-total-orders public -open import order-theory.precategory-of-inhabited-finite-total-orders public -open import order-theory.precategory-of-posets public -open import order-theory.precategory-of-total-orders public -open import order-theory.preorders public -open import order-theory.principal-lower-sets-large-posets public -open import order-theory.principal-upper-sets-large-posets public -open import order-theory.reflective-galois-connections-large-posets public -open import order-theory.resizing-posets public -open import order-theory.resizing-preorders public -open import order-theory.resizing-suplattices public -open import order-theory.similarity-of-elements-large-posets public -open import order-theory.similarity-of-elements-large-preorders public -open import order-theory.similarity-of-order-preserving-maps-large-posets public -open import order-theory.similarity-of-order-preserving-maps-large-preorders public -open import order-theory.strict-order-preserving-maps public -open import order-theory.strict-preorders public -open import order-theory.strictly-inflationary-maps-strict-preorders public -open import order-theory.strictly-preordered-sets public -open import order-theory.subposets public -open import order-theory.subpreorders public -open import order-theory.suplattices public -open import order-theory.supremum-preserving-maps-posets public -open import order-theory.top-elements-large-posets public -open import order-theory.top-elements-posets public -open import order-theory.top-elements-preorders public -open import order-theory.total-orders public -open import order-theory.total-preorders public -open import order-theory.transitive-well-founded-relations public -open import order-theory.transposition-inequalities-along-order-preserving-retractions-posets public -open import order-theory.transposition-inequalities-along-sections-of-order-preserving-maps-posets public -open import order-theory.upper-bounds-chains-posets public -open import order-theory.upper-bounds-large-posets public -open import order-theory.upper-bounds-posets public -open import order-theory.upper-sets-large-posets public -open import order-theory.well-founded-relations public -open import order-theory.zorns-lemma public +module order-theory + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where + +open import order-theory.accessible-elements-relations funext univalence truncations public +open import order-theory.bottom-elements-large-posets funext univalence truncations public +open import order-theory.bottom-elements-posets funext univalence truncations public +open import order-theory.bottom-elements-preorders funext univalence truncations public +open import order-theory.chains-posets funext univalence truncations public +open import order-theory.chains-preorders funext univalence truncations public +open import order-theory.closure-operators-large-locales funext univalence truncations public +open import order-theory.closure-operators-large-posets funext univalence truncations public +open import order-theory.commuting-squares-of-galois-connections-large-posets funext univalence truncations public +open import order-theory.commuting-squares-of-order-preserving-maps-large-posets funext univalence truncations public +open import order-theory.coverings-locales funext univalence truncations public +open import order-theory.decidable-posets funext univalence truncations public +open import order-theory.decidable-preorders funext univalence truncations public +open import order-theory.decidable-subposets funext univalence truncations public +open import order-theory.decidable-subpreorders funext univalence truncations public +open import order-theory.decidable-total-orders funext univalence truncations public +open import order-theory.decidable-total-preorders funext univalence truncations public +open import order-theory.deflationary-maps-posets funext univalence truncations public +open import order-theory.deflationary-maps-preorders funext univalence truncations public +open import order-theory.dependent-products-large-frames funext univalence truncations public +open import order-theory.dependent-products-large-inflattices funext univalence truncations public +open import order-theory.dependent-products-large-locales funext univalence truncations public +open import order-theory.dependent-products-large-meet-semilattices funext univalence truncations public +open import order-theory.dependent-products-large-posets funext univalence truncations public +open import order-theory.dependent-products-large-preorders funext univalence truncations public +open import order-theory.dependent-products-large-suplattices funext univalence truncations public +open import order-theory.distributive-lattices funext univalence truncations public +open import order-theory.finite-coverings-locales funext univalence truncations public +open import order-theory.finite-posets funext univalence truncations public +open import order-theory.finite-preorders funext univalence truncations public +open import order-theory.finite-total-orders funext univalence truncations public +open import order-theory.finitely-graded-posets funext univalence truncations public +open import order-theory.frames funext univalence truncations public +open import order-theory.galois-connections funext univalence truncations public +open import order-theory.galois-connections-large-posets funext univalence truncations public +open import order-theory.greatest-lower-bounds-large-posets funext univalence truncations public +open import order-theory.greatest-lower-bounds-posets funext univalence truncations public +open import order-theory.homomorphisms-frames funext univalence truncations public +open import order-theory.homomorphisms-large-frames funext univalence truncations public +open import order-theory.homomorphisms-large-locales funext univalence truncations public +open import order-theory.homomorphisms-large-meet-semilattices funext univalence truncations public +open import order-theory.homomorphisms-large-suplattices funext univalence truncations public +open import order-theory.homomorphisms-meet-semilattices funext univalence truncations public +open import order-theory.homomorphisms-meet-suplattices funext univalence truncations public +open import order-theory.homomorphisms-suplattices funext univalence truncations public +open import order-theory.ideals-preorders funext univalence truncations public +open import order-theory.incidence-algebras funext univalence truncations public +open import order-theory.inflationary-maps-posets funext univalence truncations public +open import order-theory.inflationary-maps-preorders funext univalence truncations public +open import order-theory.inflattices funext univalence truncations public +open import order-theory.inhabited-chains-posets funext univalence truncations public +open import order-theory.inhabited-chains-preorders funext univalence truncations public +open import order-theory.inhabited-finite-total-orders funext univalence truncations public +open import order-theory.interval-subposets funext univalence truncations public +open import order-theory.join-preserving-maps-posets funext univalence truncations public +open import order-theory.join-semilattices funext univalence truncations public +open import order-theory.knaster-tarski-fixed-point-theorem funext univalence truncations public +open import order-theory.large-frames funext univalence truncations public +open import order-theory.large-inflattices funext univalence truncations public +open import order-theory.large-join-semilattices funext univalence truncations public +open import order-theory.large-locales funext univalence truncations public +open import order-theory.large-meet-semilattices funext univalence truncations public +open import order-theory.large-meet-subsemilattices funext univalence truncations public +open import order-theory.large-posets funext univalence truncations public +open import order-theory.large-preorders funext univalence truncations public +open import order-theory.large-quotient-locales funext univalence truncations public +open import order-theory.large-subframes funext univalence truncations public +open import order-theory.large-subposets funext univalence truncations public +open import order-theory.large-subpreorders funext univalence truncations public +open import order-theory.large-subsuplattices funext univalence truncations public +open import order-theory.large-suplattices funext univalence truncations public +open import order-theory.lattices funext univalence truncations public +open import order-theory.least-upper-bounds-large-posets funext univalence truncations public +open import order-theory.least-upper-bounds-posets funext univalence truncations public +open import order-theory.locales funext univalence truncations public +open import order-theory.locally-finite-posets funext univalence truncations public +open import order-theory.lower-bounds-large-posets funext univalence truncations public +open import order-theory.lower-bounds-posets funext univalence truncations public +open import order-theory.lower-sets-large-posets funext univalence truncations public +open import order-theory.lower-types-preorders funext univalence truncations public +open import order-theory.maximal-chains-posets funext univalence truncations public +open import order-theory.maximal-chains-preorders funext univalence truncations public +open import order-theory.meet-semilattices funext univalence truncations public +open import order-theory.meet-suplattices funext univalence truncations public +open import order-theory.nuclei-large-locales funext univalence truncations public +open import order-theory.opposite-large-posets funext univalence truncations public +open import order-theory.opposite-large-preorders funext univalence truncations public +open import order-theory.opposite-posets funext univalence truncations public +open import order-theory.opposite-preorders funext univalence truncations public +open import order-theory.order-preserving-maps-large-posets funext univalence truncations public +open import order-theory.order-preserving-maps-large-preorders funext univalence truncations public +open import order-theory.order-preserving-maps-posets funext univalence truncations public +open import order-theory.order-preserving-maps-preorders funext univalence truncations public +open import order-theory.ordinals funext univalence truncations public +open import order-theory.posets funext univalence truncations public +open import order-theory.powers-of-large-locales funext univalence truncations public +open import order-theory.precategory-of-decidable-total-orders funext univalence truncations public +open import order-theory.precategory-of-finite-posets funext univalence truncations public +open import order-theory.precategory-of-finite-total-orders funext univalence truncations public +open import order-theory.precategory-of-inhabited-finite-total-orders funext univalence truncations public +open import order-theory.precategory-of-posets funext univalence truncations public +open import order-theory.precategory-of-total-orders funext univalence truncations public +open import order-theory.preorders funext univalence truncations public +open import order-theory.principal-lower-sets-large-posets funext univalence truncations public +open import order-theory.principal-upper-sets-large-posets funext univalence truncations public +open import order-theory.reflective-galois-connections-large-posets funext univalence truncations public +open import order-theory.resizing-posets funext univalence truncations public +open import order-theory.resizing-preorders funext univalence truncations public +open import order-theory.resizing-suplattices funext univalence truncations public +open import order-theory.similarity-of-elements-large-posets funext univalence truncations public +open import order-theory.similarity-of-elements-large-preorders funext univalence truncations public +open import order-theory.similarity-of-order-preserving-maps-large-posets funext univalence truncations public +open import order-theory.similarity-of-order-preserving-maps-large-preorders funext univalence truncations public +open import order-theory.strict-order-preserving-maps funext univalence truncations public +open import order-theory.strict-preorders funext univalence truncations public +open import order-theory.strictly-inflationary-maps-strict-preorders funext univalence truncations public +open import order-theory.strictly-preordered-sets funext univalence truncations public +open import order-theory.subposets funext univalence truncations public +open import order-theory.subpreorders funext univalence truncations public +open import order-theory.suplattices funext univalence truncations public +open import order-theory.supremum-preserving-maps-posets funext univalence truncations public +open import order-theory.top-elements-large-posets funext univalence truncations public +open import order-theory.top-elements-posets funext univalence truncations public +open import order-theory.top-elements-preorders funext univalence truncations public +open import order-theory.total-orders funext univalence truncations public +open import order-theory.total-preorders funext univalence truncations public +open import order-theory.transitive-well-founded-relations funext univalence truncations public +open import order-theory.transposition-inequalities-along-order-preserving-retractions-posets funext univalence truncations public +open import order-theory.transposition-inequalities-along-sections-of-order-preserving-maps-posets funext univalence truncations public +open import order-theory.upper-bounds-chains-posets funext univalence truncations public +open import order-theory.upper-bounds-large-posets funext univalence truncations public +open import order-theory.upper-bounds-posets funext univalence truncations public +open import order-theory.upper-sets-large-posets funext univalence truncations public +open import order-theory.well-founded-relations funext univalence truncations public +open import order-theory.zorns-lemma funext univalence truncations public ``` diff --git a/src/order-theory/accessible-elements-relations.lagda.md b/src/order-theory/accessible-elements-relations.lagda.md index a6b6863dca..f3ccf76782 100644 --- a/src/order-theory/accessible-elements-relations.lagda.md +++ b/src/order-theory/accessible-elements-relations.lagda.md @@ -1,16 +1,24 @@ # Accessible elements with respect to relations ```agda -module order-theory.accessible-elements-relations where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.accessible-elements-relations + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.binary-relations +open import foundation.binary-relations funext univalence truncations open import foundation.dependent-pair-types -open import foundation.function-extensionality +open import foundation.function-extensionality funext open import foundation.universe-levels open import foundation-core.negation diff --git a/src/order-theory/bottom-elements-large-posets.lagda.md b/src/order-theory/bottom-elements-large-posets.lagda.md index 76262a6702..d4fe894d5b 100644 --- a/src/order-theory/bottom-elements-large-posets.lagda.md +++ b/src/order-theory/bottom-elements-large-posets.lagda.md @@ -1,7 +1,15 @@ # Bottom elements in large posets ```agda -module order-theory.bottom-elements-large-posets where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.bottom-elements-large-posets + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,8 +17,8 @@ module order-theory.bottom-elements-large-posets where ```agda open import foundation.universe-levels -open import order-theory.dependent-products-large-posets -open import order-theory.large-posets +open import order-theory.dependent-products-large-posets funext univalence truncations +open import order-theory.large-posets funext univalence truncations ```
diff --git a/src/order-theory/bottom-elements-posets.lagda.md b/src/order-theory/bottom-elements-posets.lagda.md index 19f835b65c..3982c74350 100644 --- a/src/order-theory/bottom-elements-posets.lagda.md +++ b/src/order-theory/bottom-elements-posets.lagda.md @@ -1,19 +1,28 @@ # Bottom elements in posets ```agda -module order-theory.bottom-elements-posets where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.bottom-elements-posets + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.propositions -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.propositions funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels -open import order-theory.bottom-elements-preorders -open import order-theory.posets +open import order-theory.bottom-elements-preorders funext univalence truncations +open import order-theory.posets funext univalence truncations ```
diff --git a/src/order-theory/bottom-elements-preorders.lagda.md b/src/order-theory/bottom-elements-preorders.lagda.md index 5d5c0f1b8b..3268073ad4 100644 --- a/src/order-theory/bottom-elements-preorders.lagda.md +++ b/src/order-theory/bottom-elements-preorders.lagda.md @@ -1,17 +1,26 @@ # Bottom elements in preorders ```agda -module order-theory.bottom-elements-preorders where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.bottom-elements-preorders + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.propositions funext univalence open import foundation.universe-levels -open import order-theory.preorders +open import order-theory.preorders funext univalence truncations ```
diff --git a/src/order-theory/chains-posets.lagda.md b/src/order-theory/chains-posets.lagda.md index 404b506ee9..c87c808b43 100644 --- a/src/order-theory/chains-posets.lagda.md +++ b/src/order-theory/chains-posets.lagda.md @@ -1,29 +1,38 @@ # Chains in posets ```agda -module order-theory.chains-posets where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.chains-posets + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.coproduct-types +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.disjunction -open import foundation.existential-quantification -open import foundation.function-types -open import foundation.identity-types -open import foundation.images -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.disjunction funext univalence truncations +open import foundation.existential-quantification funext univalence truncations +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.images funext univalence truncations +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels -open import order-theory.chains-preorders -open import order-theory.order-preserving-maps-posets -open import order-theory.posets -open import order-theory.subposets -open import order-theory.total-orders +open import order-theory.chains-preorders funext univalence truncations +open import order-theory.order-preserving-maps-posets funext univalence truncations +open import order-theory.posets funext univalence truncations +open import order-theory.subposets funext univalence truncations +open import order-theory.total-orders funext univalence truncations ```
diff --git a/src/order-theory/chains-preorders.lagda.md b/src/order-theory/chains-preorders.lagda.md index 65c1ad4c19..8c8840bc25 100644 --- a/src/order-theory/chains-preorders.lagda.md +++ b/src/order-theory/chains-preorders.lagda.md @@ -1,20 +1,29 @@ # Chains in preorders ```agda -module order-theory.chains-preorders where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.chains-preorders + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.propositions -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.propositions funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels -open import order-theory.preorders -open import order-theory.subpreorders -open import order-theory.total-preorders +open import order-theory.preorders funext univalence truncations +open import order-theory.subpreorders funext univalence truncations +open import order-theory.total-preorders funext univalence truncations ```
diff --git a/src/order-theory/closure-operators-large-locales.lagda.md b/src/order-theory/closure-operators-large-locales.lagda.md index 3bc839becd..70b5f9715c 100644 --- a/src/order-theory/closure-operators-large-locales.lagda.md +++ b/src/order-theory/closure-operators-large-locales.lagda.md @@ -1,7 +1,15 @@ # Closure operators on large locales ```agda -module order-theory.closure-operators-large-locales where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.closure-operators-large-locales + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,26 +17,27 @@ module order-theory.closure-operators-large-locales where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.identity-types -open import foundation.large-binary-relations -open import foundation.logical-equivalences -open import foundation.propositions -open import foundation.sets -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.large-binary-relations funext univalence truncations +open import foundation.logical-equivalences funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels -open import order-theory.closure-operators-large-posets -open import order-theory.large-frames -open import order-theory.large-locales -open import order-theory.large-meet-semilattices -open import order-theory.large-meet-subsemilattices -open import order-theory.large-posets -open import order-theory.large-subposets -open import order-theory.large-subpreorders -open import order-theory.large-suplattices -open import order-theory.least-upper-bounds-large-posets -open import order-theory.order-preserving-maps-large-posets +open import order-theory.closure-operators-large-posets funext univalence truncations +open import order-theory.large-frames funext univalence truncations +open import order-theory.large-locales funext univalence truncations +open import order-theory.large-meet-semilattices funext univalence truncations +open import order-theory.large-meet-subsemilattices funext univalence truncations +open import order-theory.large-posets funext univalence truncations +open import order-theory.large-subposets funext univalence truncations +open import order-theory.large-subpreorders funext univalence truncations +open import order-theory.large-suplattices funext univalence truncations +open import order-theory.least-upper-bounds-large-posets funext univalence truncations +open import order-theory.order-preserving-maps-large-posets funext univalence truncations ```
diff --git a/src/order-theory/closure-operators-large-posets.lagda.md b/src/order-theory/closure-operators-large-posets.lagda.md index edc0a558e9..5a2dc0a26f 100644 --- a/src/order-theory/closure-operators-large-posets.lagda.md +++ b/src/order-theory/closure-operators-large-posets.lagda.md @@ -1,22 +1,31 @@ # Closure operators on large posets ```agda -module order-theory.closure-operators-large-posets where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.closure-operators-large-posets + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.identity-types -open import foundation.large-binary-relations -open import foundation.propositions -open import foundation.sets +open import foundation.dependent-products-propositions funext +open import foundation.identity-types funext +open import foundation.large-binary-relations funext univalence truncations +open import foundation.propositions funext univalence +open import foundation.sets funext univalence open import foundation.universe-levels -open import order-theory.large-posets -open import order-theory.large-subposets -open import order-theory.large-subpreorders -open import order-theory.order-preserving-maps-large-posets +open import order-theory.large-posets funext univalence truncations +open import order-theory.large-subposets funext univalence truncations +open import order-theory.large-subpreorders funext univalence truncations +open import order-theory.order-preserving-maps-large-posets funext univalence truncations ```
diff --git a/src/order-theory/commuting-squares-of-galois-connections-large-posets.lagda.md b/src/order-theory/commuting-squares-of-galois-connections-large-posets.lagda.md index ff9bfb86c1..5ee42b2af5 100644 --- a/src/order-theory/commuting-squares-of-galois-connections-large-posets.lagda.md +++ b/src/order-theory/commuting-squares-of-galois-connections-large-posets.lagda.md @@ -1,7 +1,15 @@ # Commuting squares of Galois connections between large posets ```agda -module order-theory.commuting-squares-of-galois-connections-large-posets where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.commuting-squares-of-galois-connections-large-posets + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,9 +17,9 @@ module order-theory.commuting-squares-of-galois-connections-large-posets where ```agda open import foundation.universe-levels -open import order-theory.commuting-squares-of-order-preserving-maps-large-posets -open import order-theory.galois-connections-large-posets -open import order-theory.large-posets +open import order-theory.commuting-squares-of-order-preserving-maps-large-posets funext univalence truncations +open import order-theory.galois-connections-large-posets funext univalence truncations +open import order-theory.large-posets funext univalence truncations ```
diff --git a/src/order-theory/commuting-squares-of-order-preserving-maps-large-posets.lagda.md b/src/order-theory/commuting-squares-of-order-preserving-maps-large-posets.lagda.md index 42b32bdb2f..03ffd066ea 100644 --- a/src/order-theory/commuting-squares-of-order-preserving-maps-large-posets.lagda.md +++ b/src/order-theory/commuting-squares-of-order-preserving-maps-large-posets.lagda.md @@ -11,11 +11,11 @@ module ```agda open import foundation.universe-levels -open import foundation-core.commuting-squares-of-maps +open import foundation-core.commuting-squares-of-maps funext -open import order-theory.large-posets -open import order-theory.order-preserving-maps-large-posets -open import order-theory.similarity-of-order-preserving-maps-large-posets +open import order-theory.large-posets funext univalence truncations +open import order-theory.order-preserving-maps-large-posets funext univalence truncations +open import order-theory.similarity-of-order-preserving-maps-large-posets funext univalence truncations ```
@@ -51,7 +51,14 @@ words, we say that the square above commutes if the composites `j ∘ f` and ## Definitions ```agda +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + module _ + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) {αP αQ αU αV γi γf γg γj : Level → Level} {βP βQ βU βV : Level → Level → Level} (P : Large-Poset αP βP) diff --git a/src/order-theory/coverings-locales.lagda.md b/src/order-theory/coverings-locales.lagda.md index 70165cf95e..396938625a 100644 --- a/src/order-theory/coverings-locales.lagda.md +++ b/src/order-theory/coverings-locales.lagda.md @@ -1,17 +1,25 @@ # Coverings in locales ```agda -module order-theory.coverings-locales where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.coverings-locales + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import order-theory.locales +open import order-theory.locales funext univalence truncations ```
diff --git a/src/order-theory/decidable-posets.lagda.md b/src/order-theory/decidable-posets.lagda.md index b02c21afbf..b15b48c4d4 100644 --- a/src/order-theory/decidable-posets.lagda.md +++ b/src/order-theory/decidable-posets.lagda.md @@ -1,23 +1,32 @@ # Decidable posets ```agda -module order-theory.decidable-posets where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.decidable-posets + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.binary-relations -open import foundation.decidable-propositions +open import foundation.binary-relations funext univalence truncations +open import foundation.decidable-propositions funext univalence truncations open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets +open import foundation.dependent-products-propositions funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence open import foundation.universe-levels -open import order-theory.decidable-preorders -open import order-theory.posets -open import order-theory.preorders +open import order-theory.decidable-preorders funext univalence truncations +open import order-theory.posets funext univalence truncations +open import order-theory.preorders funext univalence truncations ```
diff --git a/src/order-theory/decidable-preorders.lagda.md b/src/order-theory/decidable-preorders.lagda.md index b752e33a13..5a778cb0d4 100644 --- a/src/order-theory/decidable-preorders.lagda.md +++ b/src/order-theory/decidable-preorders.lagda.md @@ -1,19 +1,28 @@ # Decidable preorders ```agda -module order-theory.decidable-preorders where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.decidable-preorders + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.binary-relations -open import foundation.decidable-propositions +open import foundation.binary-relations funext univalence truncations +open import foundation.decidable-propositions funext univalence truncations open import foundation.dependent-pair-types -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.propositions funext univalence open import foundation.universe-levels -open import order-theory.preorders +open import order-theory.preorders funext univalence truncations ```
diff --git a/src/order-theory/decidable-subposets.lagda.md b/src/order-theory/decidable-subposets.lagda.md index d57463aa0b..f001c01759 100644 --- a/src/order-theory/decidable-subposets.lagda.md +++ b/src/order-theory/decidable-subposets.lagda.md @@ -1,21 +1,30 @@ # Decidable subposets ```agda -module order-theory.decidable-subposets where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.decidable-subposets + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.binary-relations -open import foundation.decidable-subtypes +open import foundation.binary-relations funext univalence truncations +open import foundation.decidable-subtypes funext univalence truncations open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence open import foundation.universe-levels -open import order-theory.posets -open import order-theory.subposets +open import order-theory.posets funext univalence truncations +open import order-theory.subposets funext univalence truncations ```
diff --git a/src/order-theory/decidable-subpreorders.lagda.md b/src/order-theory/decidable-subpreorders.lagda.md index 57e290edc2..837b6c3cb7 100644 --- a/src/order-theory/decidable-subpreorders.lagda.md +++ b/src/order-theory/decidable-subpreorders.lagda.md @@ -1,21 +1,30 @@ # Decidable subpreorders ```agda -module order-theory.decidable-subpreorders where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.decidable-subpreorders + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.binary-relations -open import foundation.decidable-subtypes +open import foundation.binary-relations funext univalence truncations +open import foundation.decidable-subtypes funext univalence truncations open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence open import foundation.universe-levels -open import order-theory.preorders -open import order-theory.subpreorders +open import order-theory.preorders funext univalence truncations +open import order-theory.subpreorders funext univalence truncations ```
diff --git a/src/order-theory/decidable-total-orders.lagda.md b/src/order-theory/decidable-total-orders.lagda.md index 2d8296df76..d1bc2ef270 100644 --- a/src/order-theory/decidable-total-orders.lagda.md +++ b/src/order-theory/decidable-total-orders.lagda.md @@ -1,34 +1,42 @@ # Decidable total orders ```agda -module order-theory.decidable-total-orders where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.decidable-total-orders + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.action-on-identifications-functions -open import foundation.binary-relations -open import foundation.coproduct-types -open import foundation.decidable-propositions +open import foundation.binary-relations funext univalence truncations +open import foundation.coproduct-types funext univalence truncations +open import foundation.decidable-propositions funext univalence truncations open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.propositions -open import foundation.sets +open import foundation.dependent-products-propositions funext +open import foundation.empty-types funext univalence truncations +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence open import foundation.transport-along-identifications open import foundation.universe-levels -open import order-theory.decidable-posets -open import order-theory.decidable-total-preorders -open import order-theory.greatest-lower-bounds-posets -open import order-theory.join-semilattices -open import order-theory.least-upper-bounds-posets -open import order-theory.meet-semilattices -open import order-theory.posets -open import order-theory.preorders -open import order-theory.total-orders +open import order-theory.decidable-posets funext univalence truncations +open import order-theory.decidable-total-preorders funext univalence truncations +open import order-theory.greatest-lower-bounds-posets funext univalence truncations +open import order-theory.join-semilattices funext univalence truncations +open import order-theory.least-upper-bounds-posets funext univalence truncations +open import order-theory.meet-semilattices funext univalence truncations +open import order-theory.posets funext univalence truncations +open import order-theory.preorders funext univalence truncations +open import order-theory.total-orders funext univalence truncations ```
diff --git a/src/order-theory/decidable-total-preorders.lagda.md b/src/order-theory/decidable-total-preorders.lagda.md index c3385ce7ae..b4560c1f6b 100644 --- a/src/order-theory/decidable-total-preorders.lagda.md +++ b/src/order-theory/decidable-total-preorders.lagda.md @@ -1,28 +1,37 @@ # Decidable total preorders ```agda -module order-theory.decidable-total-preorders where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.decidable-total-preorders + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.binary-relations -open import foundation.cartesian-product-types -open import foundation.coproduct-types -open import foundation.decidable-propositions -open import foundation.decidable-types +open import foundation.binary-relations funext univalence truncations +open import foundation.cartesian-product-types funext univalence +open import foundation.coproduct-types funext univalence truncations +open import foundation.decidable-propositions funext univalence truncations +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.function-types -open import foundation.identity-types -open import foundation.propositional-truncations -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.empty-types funext univalence truncations +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence open import foundation.universe-levels -open import order-theory.decidable-preorders -open import order-theory.preorders -open import order-theory.total-preorders +open import order-theory.decidable-preorders funext univalence truncations +open import order-theory.preorders funext univalence truncations +open import order-theory.total-preorders funext univalence truncations ```
diff --git a/src/order-theory/deflationary-maps-posets.lagda.md b/src/order-theory/deflationary-maps-posets.lagda.md index ffeb8f4da5..8364e07ad1 100644 --- a/src/order-theory/deflationary-maps-posets.lagda.md +++ b/src/order-theory/deflationary-maps-posets.lagda.md @@ -1,20 +1,29 @@ # Deflationary maps on a poset ```agda -module order-theory.deflationary-maps-posets where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.deflationary-maps-posets + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.propositions -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.propositions funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels -open import order-theory.deflationary-maps-preorders -open import order-theory.order-preserving-maps-posets -open import order-theory.posets +open import order-theory.deflationary-maps-preorders funext univalence truncations +open import order-theory.order-preserving-maps-posets funext univalence truncations +open import order-theory.posets funext univalence truncations ```
diff --git a/src/order-theory/deflationary-maps-preorders.lagda.md b/src/order-theory/deflationary-maps-preorders.lagda.md index 508b702878..5d2b3193b9 100644 --- a/src/order-theory/deflationary-maps-preorders.lagda.md +++ b/src/order-theory/deflationary-maps-preorders.lagda.md @@ -1,19 +1,28 @@ # Deflationary maps on a preorder ```agda -module order-theory.deflationary-maps-preorders where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.deflationary-maps-preorders + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.propositions -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.propositions funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels -open import order-theory.order-preserving-maps-preorders -open import order-theory.preorders +open import order-theory.order-preserving-maps-preorders funext univalence truncations +open import order-theory.preorders funext univalence truncations ```
diff --git a/src/order-theory/dependent-products-large-frames.lagda.md b/src/order-theory/dependent-products-large-frames.lagda.md index 8766e231c0..34ce9a572a 100644 --- a/src/order-theory/dependent-products-large-frames.lagda.md +++ b/src/order-theory/dependent-products-large-frames.lagda.md @@ -1,28 +1,36 @@ # Dependent products of large frames ```agda -module order-theory.dependent-products-large-frames where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.dependent-products-large-frames + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.function-extensionality -open import foundation.identity-types -open import foundation.large-binary-relations -open import foundation.sets +open import foundation.function-extensionality funext +open import foundation.identity-types funext +open import foundation.large-binary-relations funext univalence truncations +open import foundation.sets funext univalence open import foundation.universe-levels -open import order-theory.dependent-products-large-meet-semilattices -open import order-theory.dependent-products-large-posets -open import order-theory.dependent-products-large-suplattices -open import order-theory.greatest-lower-bounds-large-posets -open import order-theory.large-frames -open import order-theory.large-meet-semilattices -open import order-theory.large-posets -open import order-theory.large-suplattices -open import order-theory.least-upper-bounds-large-posets -open import order-theory.top-elements-large-posets +open import order-theory.dependent-products-large-meet-semilattices funext univalence truncations +open import order-theory.dependent-products-large-posets funext univalence truncations +open import order-theory.dependent-products-large-suplattices funext univalence truncations +open import order-theory.greatest-lower-bounds-large-posets funext univalence truncations +open import order-theory.large-frames funext univalence truncations +open import order-theory.large-meet-semilattices funext univalence truncations +open import order-theory.large-posets funext univalence truncations +open import order-theory.large-suplattices funext univalence truncations +open import order-theory.least-upper-bounds-large-posets funext univalence truncations +open import order-theory.top-elements-large-posets funext univalence truncations ```
diff --git a/src/order-theory/dependent-products-large-inflattices.lagda.md b/src/order-theory/dependent-products-large-inflattices.lagda.md index 7078f31b85..05a0c6c6cb 100644 --- a/src/order-theory/dependent-products-large-inflattices.lagda.md +++ b/src/order-theory/dependent-products-large-inflattices.lagda.md @@ -1,20 +1,28 @@ # Dependent products of large inflattices ```agda -module order-theory.dependent-products-large-inflattices where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.dependent-products-large-inflattices + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.large-binary-relations -open import foundation.sets +open import foundation.large-binary-relations funext univalence truncations +open import foundation.sets funext univalence open import foundation.universe-levels -open import order-theory.dependent-products-large-posets -open import order-theory.greatest-lower-bounds-large-posets -open import order-theory.large-inflattices -open import order-theory.large-posets +open import order-theory.dependent-products-large-posets funext univalence truncations +open import order-theory.greatest-lower-bounds-large-posets funext univalence truncations +open import order-theory.large-inflattices funext univalence truncations +open import order-theory.large-posets funext univalence truncations ```
diff --git a/src/order-theory/dependent-products-large-locales.lagda.md b/src/order-theory/dependent-products-large-locales.lagda.md index 07f9743e81..1a9434d110 100644 --- a/src/order-theory/dependent-products-large-locales.lagda.md +++ b/src/order-theory/dependent-products-large-locales.lagda.md @@ -1,25 +1,33 @@ # Dependent products of large locales ```agda -module order-theory.dependent-products-large-locales where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.dependent-products-large-locales + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.identity-types -open import foundation.large-binary-relations -open import foundation.sets +open import foundation.identity-types funext +open import foundation.large-binary-relations funext univalence truncations +open import foundation.sets funext univalence open import foundation.universe-levels -open import order-theory.dependent-products-large-frames -open import order-theory.greatest-lower-bounds-large-posets -open import order-theory.large-locales -open import order-theory.large-meet-semilattices -open import order-theory.large-posets -open import order-theory.large-suplattices -open import order-theory.least-upper-bounds-large-posets -open import order-theory.top-elements-large-posets +open import order-theory.dependent-products-large-frames funext univalence truncations +open import order-theory.greatest-lower-bounds-large-posets funext univalence truncations +open import order-theory.large-locales funext univalence truncations +open import order-theory.large-meet-semilattices funext univalence truncations +open import order-theory.large-posets funext univalence truncations +open import order-theory.large-suplattices funext univalence truncations +open import order-theory.least-upper-bounds-large-posets funext univalence truncations +open import order-theory.top-elements-large-posets funext univalence truncations ```
diff --git a/src/order-theory/dependent-products-large-meet-semilattices.lagda.md b/src/order-theory/dependent-products-large-meet-semilattices.lagda.md index 5d235a6767..f1340cfeaa 100644 --- a/src/order-theory/dependent-products-large-meet-semilattices.lagda.md +++ b/src/order-theory/dependent-products-large-meet-semilattices.lagda.md @@ -1,21 +1,29 @@ # Dependent products of large meet-semilattices ```agda -module order-theory.dependent-products-large-meet-semilattices where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.dependent-products-large-meet-semilattices + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.large-binary-relations -open import foundation.sets +open import foundation.large-binary-relations funext univalence truncations +open import foundation.sets funext univalence open import foundation.universe-levels -open import order-theory.dependent-products-large-posets -open import order-theory.greatest-lower-bounds-large-posets -open import order-theory.large-meet-semilattices -open import order-theory.large-posets -open import order-theory.top-elements-large-posets +open import order-theory.dependent-products-large-posets funext univalence truncations +open import order-theory.greatest-lower-bounds-large-posets funext univalence truncations +open import order-theory.large-meet-semilattices funext univalence truncations +open import order-theory.large-posets funext univalence truncations +open import order-theory.top-elements-large-posets funext univalence truncations ```
diff --git a/src/order-theory/dependent-products-large-posets.lagda.md b/src/order-theory/dependent-products-large-posets.lagda.md index f445638b89..764a4e90c9 100644 --- a/src/order-theory/dependent-products-large-posets.lagda.md +++ b/src/order-theory/dependent-products-large-posets.lagda.md @@ -1,19 +1,27 @@ # Dependent products of large posets ```agda -module order-theory.dependent-products-large-posets where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.dependent-products-large-posets + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.function-extensionality -open import foundation.large-binary-relations +open import foundation.function-extensionality funext +open import foundation.large-binary-relations funext univalence truncations open import foundation.universe-levels -open import order-theory.dependent-products-large-preorders -open import order-theory.large-posets -open import order-theory.large-preorders +open import order-theory.dependent-products-large-preorders funext univalence truncations +open import order-theory.large-posets funext univalence truncations +open import order-theory.large-preorders funext univalence truncations ```
diff --git a/src/order-theory/dependent-products-large-preorders.lagda.md b/src/order-theory/dependent-products-large-preorders.lagda.md index fa7fafa61e..fc6bca1519 100644 --- a/src/order-theory/dependent-products-large-preorders.lagda.md +++ b/src/order-theory/dependent-products-large-preorders.lagda.md @@ -1,17 +1,26 @@ # Dependent products of large preorders ```agda -module order-theory.dependent-products-large-preorders where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.dependent-products-large-preorders + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.large-binary-relations -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.large-binary-relations funext univalence truncations +open import foundation.propositions funext univalence open import foundation.universe-levels -open import order-theory.large-preorders +open import order-theory.large-preorders funext univalence truncations ```
diff --git a/src/order-theory/dependent-products-large-suplattices.lagda.md b/src/order-theory/dependent-products-large-suplattices.lagda.md index 41fbf2ead1..157c694dec 100644 --- a/src/order-theory/dependent-products-large-suplattices.lagda.md +++ b/src/order-theory/dependent-products-large-suplattices.lagda.md @@ -1,20 +1,28 @@ # Dependent products of large suplattices ```agda -module order-theory.dependent-products-large-suplattices where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.dependent-products-large-suplattices + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.large-binary-relations -open import foundation.sets +open import foundation.large-binary-relations funext univalence truncations +open import foundation.sets funext univalence open import foundation.universe-levels -open import order-theory.dependent-products-large-posets -open import order-theory.large-posets -open import order-theory.large-suplattices -open import order-theory.least-upper-bounds-large-posets +open import order-theory.dependent-products-large-posets funext univalence truncations +open import order-theory.large-posets funext univalence truncations +open import order-theory.large-suplattices funext univalence truncations +open import order-theory.least-upper-bounds-large-posets funext univalence truncations ```
diff --git a/src/order-theory/distributive-lattices.lagda.md b/src/order-theory/distributive-lattices.lagda.md index e2dff425a0..48c0edb4c0 100644 --- a/src/order-theory/distributive-lattices.lagda.md +++ b/src/order-theory/distributive-lattices.lagda.md @@ -1,23 +1,32 @@ # Distributive lattices ```agda -module order-theory.distributive-lattices where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.distributive-lattices + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.binary-relations +open import foundation.binary-relations funext univalence truncations open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets +open import foundation.dependent-products-propositions funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence open import foundation.universe-levels -open import order-theory.join-semilattices -open import order-theory.lattices -open import order-theory.meet-semilattices -open import order-theory.posets +open import order-theory.join-semilattices funext univalence truncations +open import order-theory.lattices funext univalence truncations +open import order-theory.meet-semilattices funext univalence truncations +open import order-theory.posets funext univalence truncations ```
diff --git a/src/order-theory/finite-coverings-locales.lagda.md b/src/order-theory/finite-coverings-locales.lagda.md index 94b7b34648..83d30ff872 100644 --- a/src/order-theory/finite-coverings-locales.lagda.md +++ b/src/order-theory/finite-coverings-locales.lagda.md @@ -1,7 +1,15 @@ # Finite coverings in locales ```agda -module order-theory.finite-coverings-locales where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.finite-coverings-locales + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,10 +18,10 @@ module order-theory.finite-coverings-locales where open import foundation.dependent-pair-types open import foundation.universe-levels -open import order-theory.coverings-locales -open import order-theory.locales +open import order-theory.coverings-locales funext univalence truncations +open import order-theory.locales funext univalence truncations -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.finite-types funext univalence truncations ```
diff --git a/src/order-theory/finite-posets.lagda.md b/src/order-theory/finite-posets.lagda.md index 597af98d12..43f14c79cb 100644 --- a/src/order-theory/finite-posets.lagda.md +++ b/src/order-theory/finite-posets.lagda.md @@ -1,23 +1,32 @@ # Finite posets ```agda -module order-theory.finite-posets where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.finite-posets + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.decidable-types +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.function-types funext +open import foundation.propositions funext univalence open import foundation.universe-levels -open import order-theory.finite-preorders -open import order-theory.posets -open import order-theory.preorders +open import order-theory.finite-preorders funext univalence truncations +open import order-theory.posets funext univalence truncations +open import order-theory.preorders funext univalence truncations -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.finite-types funext univalence truncations ```
diff --git a/src/order-theory/finite-preorders.lagda.md b/src/order-theory/finite-preorders.lagda.md index b7a2511b49..3c68c6f10e 100644 --- a/src/order-theory/finite-preorders.lagda.md +++ b/src/order-theory/finite-preorders.lagda.md @@ -1,7 +1,15 @@ # Finite preorders ```agda -module order-theory.finite-preorders where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.finite-preorders + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,26 +17,27 @@ module order-theory.finite-preorders where ```agda open import elementary-number-theory.natural-numbers -open import foundation.binary-relations -open import foundation.cartesian-product-types -open import foundation.decidable-equality -open import foundation.decidable-propositions -open import foundation.decidable-types +open import foundation.binary-relations funext univalence truncations +open import foundation.cartesian-product-types funext univalence +open import foundation.decidable-equality funext univalence truncations +open import foundation.decidable-propositions funext univalence truncations +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.mere-equivalences -open import foundation.propositions -open import foundation.sets +open import foundation.dependent-products-propositions funext +open import foundation.identity-types funext +open import foundation.mere-equivalences funext univalence truncations +open import foundation.propositions funext univalence +open import foundation.sets funext univalence open import foundation.universe-levels -open import order-theory.decidable-preorders -open import order-theory.decidable-subpreorders -open import order-theory.preorders +open import order-theory.decidable-preorders funext univalence truncations +open import order-theory.decidable-subpreorders funext univalence truncations +open import order-theory.preorders funext univalence truncations -open import univalent-combinatorics.decidable-subtypes -open import univalent-combinatorics.equality-finite-types -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.decidable-subtypes funext univalence truncations +open import univalent-combinatorics.equality-finite-types funext univalence truncations +open import univalent-combinatorics.finite-types funext univalence truncations +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/order-theory/finite-total-orders.lagda.md b/src/order-theory/finite-total-orders.lagda.md index 4bfb6edcd4..3ed8562c45 100644 --- a/src/order-theory/finite-total-orders.lagda.md +++ b/src/order-theory/finite-total-orders.lagda.md @@ -1,23 +1,32 @@ # Finite total orders ```agda -module order-theory.finite-total-orders where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.finite-total-orders + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.decidable-types +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.function-types funext +open import foundation.propositions funext univalence open import foundation.universe-levels -open import order-theory.finite-posets -open import order-theory.posets -open import order-theory.total-orders +open import order-theory.finite-posets funext univalence truncations +open import order-theory.posets funext univalence truncations +open import order-theory.total-orders funext univalence truncations -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.finite-types funext univalence truncations ```
diff --git a/src/order-theory/finitely-graded-posets.lagda.md b/src/order-theory/finitely-graded-posets.lagda.md index b4fb4a404b..915ee21d49 100644 --- a/src/order-theory/finitely-graded-posets.lagda.md +++ b/src/order-theory/finitely-graded-posets.lagda.md @@ -1,40 +1,49 @@ # Finitely graded posets ```agda -module order-theory.finitely-graded-posets where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.finitely-graded-posets + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.inequality-standard-finite-types -open import elementary-number-theory.modular-arithmetic +open import elementary-number-theory.inequality-standard-finite-types funext univalence truncations +open import elementary-number-theory.modular-arithmetic funext univalence truncations open import elementary-number-theory.natural-numbers -open import foundation.binary-relations -open import foundation.coproduct-types +open import foundation.binary-relations funext univalence truncations +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.empty-types -open import foundation.equality-dependent-pair-types -open import foundation.function-types -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.sets -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.embeddings funext +open import foundation.empty-types funext univalence truncations +open import foundation.equality-dependent-pair-types funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.transport-along-identifications open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels -open import order-theory.bottom-elements-posets -open import order-theory.posets -open import order-theory.preorders -open import order-theory.top-elements-posets -open import order-theory.total-orders +open import order-theory.bottom-elements-posets funext univalence truncations +open import order-theory.posets funext univalence truncations +open import order-theory.preorders funext univalence truncations +open import order-theory.top-elements-posets funext univalence truncations +open import order-theory.total-orders funext univalence truncations -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/order-theory/frames.lagda.md b/src/order-theory/frames.lagda.md index 96d2f47cec..21bc141e5b 100644 --- a/src/order-theory/frames.lagda.md +++ b/src/order-theory/frames.lagda.md @@ -1,25 +1,34 @@ # Frames ```agda -module order-theory.frames where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.frames + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.binary-relations +open import foundation.binary-relations funext univalence truncations open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets +open import foundation.dependent-products-propositions funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence open import foundation.universe-levels -open import order-theory.greatest-lower-bounds-posets -open import order-theory.least-upper-bounds-posets -open import order-theory.meet-semilattices -open import order-theory.meet-suplattices -open import order-theory.posets -open import order-theory.suplattices +open import order-theory.greatest-lower-bounds-posets funext univalence truncations +open import order-theory.least-upper-bounds-posets funext univalence truncations +open import order-theory.meet-semilattices funext univalence truncations +open import order-theory.meet-suplattices funext univalence truncations +open import order-theory.posets funext univalence truncations +open import order-theory.suplattices funext univalence truncations ```
diff --git a/src/order-theory/galois-connections-large-posets.lagda.md b/src/order-theory/galois-connections-large-posets.lagda.md index eee2b9a4da..9d206e9f72 100644 --- a/src/order-theory/galois-connections-large-posets.lagda.md +++ b/src/order-theory/galois-connections-large-posets.lagda.md @@ -1,7 +1,15 @@ # Galois connections between large posets ```agda -module order-theory.galois-connections-large-posets where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.galois-connections-large-posets + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,18 +17,18 @@ module order-theory.galois-connections-large-posets where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.homotopies -open import foundation.logical-equivalences +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.logical-equivalences funext open import foundation.universe-levels -open import order-theory.large-posets -open import order-theory.least-upper-bounds-large-posets -open import order-theory.order-preserving-maps-large-posets -open import order-theory.principal-lower-sets-large-posets -open import order-theory.principal-upper-sets-large-posets -open import order-theory.similarity-of-elements-large-posets -open import order-theory.similarity-of-order-preserving-maps-large-posets +open import order-theory.large-posets funext univalence truncations +open import order-theory.least-upper-bounds-large-posets funext univalence truncations +open import order-theory.order-preserving-maps-large-posets funext univalence truncations +open import order-theory.principal-lower-sets-large-posets funext univalence truncations +open import order-theory.principal-upper-sets-large-posets funext univalence truncations +open import order-theory.similarity-of-elements-large-posets funext univalence truncations +open import order-theory.similarity-of-order-preserving-maps-large-posets funext univalence truncations ```
diff --git a/src/order-theory/galois-connections.lagda.md b/src/order-theory/galois-connections.lagda.md index e0ac6170c7..a10c6cb4df 100644 --- a/src/order-theory/galois-connections.lagda.md +++ b/src/order-theory/galois-connections.lagda.md @@ -1,7 +1,15 @@ # Galois connections ```agda -module order-theory.galois-connections where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.galois-connections + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,16 +17,17 @@ module order-theory.galois-connections where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.propositions funext univalence open import foundation.subtype-identity-principle -open import foundation.subtypes +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels -open import order-theory.order-preserving-maps-posets -open import order-theory.posets +open import order-theory.order-preserving-maps-posets funext univalence truncations +open import order-theory.posets funext univalence truncations ```
diff --git a/src/order-theory/greatest-lower-bounds-large-posets.lagda.md b/src/order-theory/greatest-lower-bounds-large-posets.lagda.md index c7a54580f2..7555cde000 100644 --- a/src/order-theory/greatest-lower-bounds-large-posets.lagda.md +++ b/src/order-theory/greatest-lower-bounds-large-posets.lagda.md @@ -1,18 +1,26 @@ # Greatest lower bounds in large posets ```agda -module order-theory.greatest-lower-bounds-large-posets where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.greatest-lower-bounds-large-posets + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.logical-equivalences +open import foundation.logical-equivalences funext open import foundation.universe-levels -open import order-theory.dependent-products-large-posets -open import order-theory.large-posets -open import order-theory.lower-bounds-large-posets +open import order-theory.dependent-products-large-posets funext univalence truncations +open import order-theory.large-posets funext univalence truncations +open import order-theory.lower-bounds-large-posets funext univalence truncations ```
diff --git a/src/order-theory/greatest-lower-bounds-posets.lagda.md b/src/order-theory/greatest-lower-bounds-posets.lagda.md index 9a1430a0c4..6cde1b51ea 100644 --- a/src/order-theory/greatest-lower-bounds-posets.lagda.md +++ b/src/order-theory/greatest-lower-bounds-posets.lagda.md @@ -1,7 +1,15 @@ # Greatest lower bounds in posets ```agda -module order-theory.greatest-lower-bounds-posets where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.greatest-lower-bounds-posets + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,14 +17,15 @@ module order-theory.greatest-lower-bounds-posets where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.propositions -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.propositions funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels -open import order-theory.lower-bounds-posets -open import order-theory.posets +open import order-theory.lower-bounds-posets funext univalence truncations +open import order-theory.posets funext univalence truncations ```
diff --git a/src/order-theory/homomorphisms-frames.lagda.md b/src/order-theory/homomorphisms-frames.lagda.md index 2af1ac44de..fb54a7c13e 100644 --- a/src/order-theory/homomorphisms-frames.lagda.md +++ b/src/order-theory/homomorphisms-frames.lagda.md @@ -1,22 +1,30 @@ # Homomorphisms of frames ```agda -module order-theory.homomorphisms-frames where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.homomorphisms-frames + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.function-types +open import foundation.function-types funext open import foundation.universe-levels -open import order-theory.frames -open import order-theory.homomorphisms-meet-semilattices -open import order-theory.homomorphisms-meet-suplattices -open import order-theory.homomorphisms-suplattices -open import order-theory.order-preserving-maps-posets +open import order-theory.frames funext univalence truncations +open import order-theory.homomorphisms-meet-semilattices funext univalence truncations +open import order-theory.homomorphisms-meet-suplattices funext univalence truncations +open import order-theory.homomorphisms-suplattices funext univalence truncations +open import order-theory.order-preserving-maps-posets funext univalence truncations ```
diff --git a/src/order-theory/homomorphisms-large-frames.lagda.md b/src/order-theory/homomorphisms-large-frames.lagda.md index 80de9de25d..e806505ce1 100644 --- a/src/order-theory/homomorphisms-large-frames.lagda.md +++ b/src/order-theory/homomorphisms-large-frames.lagda.md @@ -1,18 +1,26 @@ # Homomorphisms of large frames ```agda -module order-theory.homomorphisms-large-frames where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.homomorphisms-large-frames + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import order-theory.homomorphisms-large-meet-semilattices -open import order-theory.homomorphisms-large-suplattices -open import order-theory.large-frames +open import order-theory.homomorphisms-large-meet-semilattices funext univalence truncations +open import order-theory.homomorphisms-large-suplattices funext univalence truncations +open import order-theory.large-frames funext univalence truncations ```
diff --git a/src/order-theory/homomorphisms-large-locales.lagda.md b/src/order-theory/homomorphisms-large-locales.lagda.md index ae621fd45d..b4e655523c 100644 --- a/src/order-theory/homomorphisms-large-locales.lagda.md +++ b/src/order-theory/homomorphisms-large-locales.lagda.md @@ -1,17 +1,25 @@ # Homomorphisms of large locales ```agda -module order-theory.homomorphisms-large-locales where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.homomorphisms-large-locales + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import order-theory.homomorphisms-large-frames -open import order-theory.large-locales +open import order-theory.homomorphisms-large-frames funext univalence truncations +open import order-theory.large-locales funext univalence truncations ```
diff --git a/src/order-theory/homomorphisms-large-meet-semilattices.lagda.md b/src/order-theory/homomorphisms-large-meet-semilattices.lagda.md index c209e7d907..5af0756e3e 100644 --- a/src/order-theory/homomorphisms-large-meet-semilattices.lagda.md +++ b/src/order-theory/homomorphisms-large-meet-semilattices.lagda.md @@ -1,17 +1,25 @@ # Homomorphisms of large meet-semilattices ```agda -module order-theory.homomorphisms-large-meet-semilattices where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.homomorphisms-large-meet-semilattices + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import order-theory.large-meet-semilattices -open import order-theory.order-preserving-maps-large-posets +open import order-theory.large-meet-semilattices funext univalence truncations +open import order-theory.order-preserving-maps-large-posets funext univalence truncations ```
diff --git a/src/order-theory/homomorphisms-large-suplattices.lagda.md b/src/order-theory/homomorphisms-large-suplattices.lagda.md index 181c422651..15ee050338 100644 --- a/src/order-theory/homomorphisms-large-suplattices.lagda.md +++ b/src/order-theory/homomorphisms-large-suplattices.lagda.md @@ -1,17 +1,25 @@ # Homomorphisms of large suplattices ```agda -module order-theory.homomorphisms-large-suplattices where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.homomorphisms-large-suplattices + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import order-theory.large-suplattices -open import order-theory.order-preserving-maps-large-posets +open import order-theory.large-suplattices funext univalence truncations +open import order-theory.order-preserving-maps-large-posets funext univalence truncations ```
diff --git a/src/order-theory/homomorphisms-meet-semilattices.lagda.md b/src/order-theory/homomorphisms-meet-semilattices.lagda.md index d22b55a690..de3337b13f 100644 --- a/src/order-theory/homomorphisms-meet-semilattices.lagda.md +++ b/src/order-theory/homomorphisms-meet-semilattices.lagda.md @@ -1,7 +1,15 @@ # Homomorphisms of meet-semilattices ```agda -module order-theory.homomorphisms-meet-semilattices where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.homomorphisms-meet-semilattices + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,17 +17,18 @@ module order-theory.homomorphisms-meet-semilattices where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels -open import group-theory.homomorphisms-semigroups +open import group-theory.homomorphisms-semigroups funext univalence truncations -open import order-theory.greatest-lower-bounds-posets -open import order-theory.meet-semilattices -open import order-theory.order-preserving-maps-posets +open import order-theory.greatest-lower-bounds-posets funext univalence truncations +open import order-theory.meet-semilattices funext univalence truncations +open import order-theory.order-preserving-maps-posets funext univalence truncations ```
diff --git a/src/order-theory/homomorphisms-meet-suplattices.lagda.md b/src/order-theory/homomorphisms-meet-suplattices.lagda.md index ea4c27b234..b87cf6c53a 100644 --- a/src/order-theory/homomorphisms-meet-suplattices.lagda.md +++ b/src/order-theory/homomorphisms-meet-suplattices.lagda.md @@ -1,21 +1,29 @@ # Homomorphisms of meet-suplattices ```agda -module order-theory.homomorphisms-meet-suplattices where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.homomorphisms-meet-suplattices + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.function-types +open import foundation.function-types funext open import foundation.universe-levels -open import order-theory.homomorphisms-meet-semilattices -open import order-theory.homomorphisms-suplattices -open import order-theory.meet-suplattices -open import order-theory.order-preserving-maps-posets +open import order-theory.homomorphisms-meet-semilattices funext univalence truncations +open import order-theory.homomorphisms-suplattices funext univalence truncations +open import order-theory.meet-suplattices funext univalence truncations +open import order-theory.order-preserving-maps-posets funext univalence truncations ```
diff --git a/src/order-theory/homomorphisms-suplattices.lagda.md b/src/order-theory/homomorphisms-suplattices.lagda.md index 081cd8f204..881bd77483 100644 --- a/src/order-theory/homomorphisms-suplattices.lagda.md +++ b/src/order-theory/homomorphisms-suplattices.lagda.md @@ -1,20 +1,28 @@ # Homomorphisms of suplattices ```agda -module order-theory.homomorphisms-suplattices where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.homomorphisms-suplattices + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.function-types +open import foundation.function-types funext open import foundation.universe-levels -open import order-theory.least-upper-bounds-posets -open import order-theory.order-preserving-maps-posets -open import order-theory.suplattices +open import order-theory.least-upper-bounds-posets funext univalence truncations +open import order-theory.order-preserving-maps-posets funext univalence truncations +open import order-theory.suplattices funext univalence truncations ```
diff --git a/src/order-theory/ideals-preorders.lagda.md b/src/order-theory/ideals-preorders.lagda.md index 2994939994..e44afc26a3 100644 --- a/src/order-theory/ideals-preorders.lagda.md +++ b/src/order-theory/ideals-preorders.lagda.md @@ -1,19 +1,27 @@ # Ideals in preorders ```agda -module order-theory.ideals-preorders where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.ideals-preorders + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.inhabited-types +open import foundation.inhabited-types funext univalence truncations open import foundation.universe-levels -open import order-theory.lower-types-preorders -open import order-theory.preorders +open import order-theory.lower-types-preorders funext univalence truncations +open import order-theory.preorders funext univalence truncations ```
diff --git a/src/order-theory/incidence-algebras.lagda.md b/src/order-theory/incidence-algebras.lagda.md index f96b061659..b04845f164 100644 --- a/src/order-theory/incidence-algebras.lagda.md +++ b/src/order-theory/incidence-algebras.lagda.md @@ -1,23 +1,31 @@ # Incidence algebras ```agda -module order-theory.incidence-algebras where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.incidence-algebras + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import commutative-algebra.commutative-rings +open import commutative-algebra.commutative-rings funext univalence truncations open import foundation.dependent-pair-types -open import foundation.inhabited-types +open import foundation.inhabited-types funext univalence truncations open import foundation.universe-levels open import foundation-core.cartesian-product-types -open import order-theory.interval-subposets -open import order-theory.locally-finite-posets -open import order-theory.posets +open import order-theory.interval-subposets funext univalence truncations +open import order-theory.locally-finite-posets funext univalence truncations +open import order-theory.posets funext univalence truncations ```
diff --git a/src/order-theory/inflationary-maps-posets.lagda.md b/src/order-theory/inflationary-maps-posets.lagda.md index 00c3374a3b..ab91bcff29 100644 --- a/src/order-theory/inflationary-maps-posets.lagda.md +++ b/src/order-theory/inflationary-maps-posets.lagda.md @@ -1,20 +1,29 @@ # Inflationary maps on a poset ```agda -module order-theory.inflationary-maps-posets where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.inflationary-maps-posets + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.propositions -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.propositions funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels -open import order-theory.inflationary-maps-preorders -open import order-theory.order-preserving-maps-posets -open import order-theory.posets +open import order-theory.inflationary-maps-preorders funext univalence truncations +open import order-theory.order-preserving-maps-posets funext univalence truncations +open import order-theory.posets funext univalence truncations ```
diff --git a/src/order-theory/inflationary-maps-preorders.lagda.md b/src/order-theory/inflationary-maps-preorders.lagda.md index aa2d482b97..7de4af24dc 100644 --- a/src/order-theory/inflationary-maps-preorders.lagda.md +++ b/src/order-theory/inflationary-maps-preorders.lagda.md @@ -1,19 +1,28 @@ # Inflationary maps on a preorder ```agda -module order-theory.inflationary-maps-preorders where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.inflationary-maps-preorders + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.propositions -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.propositions funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels -open import order-theory.order-preserving-maps-preorders -open import order-theory.preorders +open import order-theory.order-preserving-maps-preorders funext univalence truncations +open import order-theory.preorders funext univalence truncations ```
diff --git a/src/order-theory/inflattices.lagda.md b/src/order-theory/inflattices.lagda.md index 03b68b3db8..0864b45a65 100644 --- a/src/order-theory/inflattices.lagda.md +++ b/src/order-theory/inflattices.lagda.md @@ -1,22 +1,31 @@ # Inflattices ```agda -module order-theory.inflattices where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.inflattices + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.binary-relations +open import foundation.binary-relations funext univalence truncations open import foundation.dependent-pair-types -open import foundation.logical-equivalences -open import foundation.propositions -open import foundation.sets +open import foundation.dependent-products-propositions funext +open import foundation.logical-equivalences funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence open import foundation.universe-levels -open import order-theory.greatest-lower-bounds-posets -open import order-theory.lower-bounds-posets -open import order-theory.posets +open import order-theory.greatest-lower-bounds-posets funext univalence truncations +open import order-theory.lower-bounds-posets funext univalence truncations +open import order-theory.posets funext univalence truncations ```
diff --git a/src/order-theory/inhabited-chains-posets.lagda.md b/src/order-theory/inhabited-chains-posets.lagda.md index 8274e4af2a..e7e9065883 100644 --- a/src/order-theory/inhabited-chains-posets.lagda.md +++ b/src/order-theory/inhabited-chains-posets.lagda.md @@ -1,28 +1,37 @@ # Inhabited chains in posets ```agda -module order-theory.inhabited-chains-posets where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.inhabited-chains-posets + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import domain-theory.directed-families-posets +open import domain-theory.directed-families-posets funext univalence truncations -open import foundation.conjunction +open import foundation.conjunction funext univalence truncations open import foundation.dependent-pair-types -open import foundation.disjunction -open import foundation.existential-quantification -open import foundation.inhabited-subtypes -open import foundation.inhabited-types -open import foundation.propositions -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.disjunction funext univalence truncations +open import foundation.existential-quantification funext univalence truncations +open import foundation.inhabited-subtypes funext univalence truncations +open import foundation.inhabited-types funext univalence truncations +open import foundation.propositions funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels -open import order-theory.chains-posets -open import order-theory.posets -open import order-theory.subposets -open import order-theory.total-preorders +open import order-theory.chains-posets funext univalence truncations +open import order-theory.posets funext univalence truncations +open import order-theory.subposets funext univalence truncations +open import order-theory.total-preorders funext univalence truncations ```
diff --git a/src/order-theory/inhabited-chains-preorders.lagda.md b/src/order-theory/inhabited-chains-preorders.lagda.md index 1722f40034..19e1ddf2fd 100644 --- a/src/order-theory/inhabited-chains-preorders.lagda.md +++ b/src/order-theory/inhabited-chains-preorders.lagda.md @@ -1,22 +1,31 @@ # Inhabited chains in preorders ```agda -module order-theory.inhabited-chains-preorders where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.inhabited-chains-preorders + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.inhabited-subtypes -open import foundation.propositions -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.inhabited-subtypes funext univalence truncations +open import foundation.propositions funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels -open import order-theory.chains-preorders -open import order-theory.preorders -open import order-theory.subpreorders -open import order-theory.total-preorders +open import order-theory.chains-preorders funext univalence truncations +open import order-theory.preorders funext univalence truncations +open import order-theory.subpreorders funext univalence truncations +open import order-theory.total-preorders funext univalence truncations ```
diff --git a/src/order-theory/inhabited-finite-total-orders.lagda.md b/src/order-theory/inhabited-finite-total-orders.lagda.md index a7a49e6404..d51cedbf6d 100644 --- a/src/order-theory/inhabited-finite-total-orders.lagda.md +++ b/src/order-theory/inhabited-finite-total-orders.lagda.md @@ -1,22 +1,31 @@ # Inhabited finite total orders ```agda -module order-theory.inhabited-finite-total-orders where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.inhabited-finite-total-orders + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.inhabited-types -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.inhabited-types funext univalence truncations +open import foundation.propositions funext univalence open import foundation.universe-levels -open import order-theory.finite-posets -open import order-theory.finite-total-orders -open import order-theory.posets -open import order-theory.total-orders +open import order-theory.finite-posets funext univalence truncations +open import order-theory.finite-total-orders funext univalence truncations +open import order-theory.posets funext univalence truncations +open import order-theory.total-orders funext univalence truncations -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.finite-types funext univalence truncations ```
diff --git a/src/order-theory/interval-subposets.lagda.md b/src/order-theory/interval-subposets.lagda.md index 5f53725119..2cc386e845 100644 --- a/src/order-theory/interval-subposets.lagda.md +++ b/src/order-theory/interval-subposets.lagda.md @@ -1,21 +1,30 @@ # Interval subposets ```agda -module order-theory.interval-subposets where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.interval-subposets + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.inhabited-types -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.inhabited-types funext univalence truncations +open import foundation.propositions funext univalence open import foundation.universe-levels open import foundation-core.cartesian-product-types -open import order-theory.posets -open import order-theory.subposets +open import order-theory.posets funext univalence truncations +open import order-theory.subposets funext univalence truncations ```
diff --git a/src/order-theory/join-preserving-maps-posets.lagda.md b/src/order-theory/join-preserving-maps-posets.lagda.md index 1da7506fa2..492a89b5a6 100644 --- a/src/order-theory/join-preserving-maps-posets.lagda.md +++ b/src/order-theory/join-preserving-maps-posets.lagda.md @@ -1,32 +1,42 @@ # Join preserving maps between posets ```agda -module order-theory.join-preserving-maps-posets where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.join-preserving-maps-posets + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.booleans +open import foundation.booleans funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalences +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext open import foundation.evaluation-functions -open import foundation.function-types +open import foundation.function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types -open import foundation.propositions -open import foundation.raising-universe-levels -open import foundation.small-types -open import foundation.strictly-involutive-identity-types +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.small-types funext univalence truncations +open import foundation.strictly-involutive-identity-types funext univalence open import foundation.subtype-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext univalence truncations open import foundation.universe-levels -open import order-theory.least-upper-bounds-posets -open import order-theory.order-preserving-maps-posets -open import order-theory.posets +open import foundation-core.raising-universe-levels + +open import order-theory.least-upper-bounds-posets funext univalence truncations +open import order-theory.order-preserving-maps-posets funext univalence truncations +open import order-theory.posets funext univalence truncations ```
diff --git a/src/order-theory/join-semilattices.lagda.md b/src/order-theory/join-semilattices.lagda.md index 99c21de189..2e24d87f7a 100644 --- a/src/order-theory/join-semilattices.lagda.md +++ b/src/order-theory/join-semilattices.lagda.md @@ -1,28 +1,37 @@ # Join-semilattices ```agda -module order-theory.join-semilattices where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.join-semilattices + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.binary-relations +open import foundation.binary-relations funext univalence truncations open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.propositions -open import foundation.sets -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels -open import group-theory.semigroups +open import group-theory.semigroups funext univalence -open import order-theory.least-upper-bounds-posets -open import order-theory.posets -open import order-theory.preorders -open import order-theory.upper-bounds-posets +open import order-theory.least-upper-bounds-posets funext univalence truncations +open import order-theory.posets funext univalence truncations +open import order-theory.preorders funext univalence truncations +open import order-theory.upper-bounds-posets funext univalence truncations ```
diff --git a/src/order-theory/knaster-tarski-fixed-point-theorem.lagda.md b/src/order-theory/knaster-tarski-fixed-point-theorem.lagda.md index fdc6bc2fc0..6143dbc8bb 100644 --- a/src/order-theory/knaster-tarski-fixed-point-theorem.lagda.md +++ b/src/order-theory/knaster-tarski-fixed-point-theorem.lagda.md @@ -1,7 +1,15 @@ # The Knaster–Tarski fixed point theorem ```agda -module order-theory.knaster-tarski-fixed-point-theorem where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.knaster-tarski-fixed-point-theorem + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,14 +17,14 @@ module order-theory.knaster-tarski-fixed-point-theorem where ```agda open import foundation.dependent-pair-types open import foundation.fixed-points-endofunctions -open import foundation.identity-types -open import foundation.logical-equivalences +open import foundation.identity-types funext +open import foundation.logical-equivalences funext open import foundation.universe-levels -open import order-theory.inflattices -open import order-theory.order-preserving-maps-posets -open import order-theory.posets -open import order-theory.suplattices +open import order-theory.inflattices funext univalence truncations +open import order-theory.order-preserving-maps-posets funext univalence truncations +open import order-theory.posets funext univalence truncations +open import order-theory.suplattices funext univalence truncations ```
diff --git a/src/order-theory/large-frames.lagda.md b/src/order-theory/large-frames.lagda.md index dfd1287b72..b942e68752 100644 --- a/src/order-theory/large-frames.lagda.md +++ b/src/order-theory/large-frames.lagda.md @@ -1,30 +1,38 @@ # Large frames ```agda -module order-theory.large-frames where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.large-frames + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.large-binary-relations -open import foundation.sets +open import foundation.identity-types funext +open import foundation.large-binary-relations funext univalence truncations +open import foundation.sets funext univalence open import foundation.universe-levels -open import order-theory.greatest-lower-bounds-large-posets -open import order-theory.large-meet-semilattices -open import order-theory.large-posets -open import order-theory.large-preorders -open import order-theory.large-suplattices -open import order-theory.least-upper-bounds-large-posets -open import order-theory.meet-semilattices -open import order-theory.posets -open import order-theory.preorders -open import order-theory.suplattices -open import order-theory.top-elements-large-posets -open import order-theory.upper-bounds-large-posets +open import order-theory.greatest-lower-bounds-large-posets funext univalence truncations +open import order-theory.large-meet-semilattices funext univalence truncations +open import order-theory.large-posets funext univalence truncations +open import order-theory.large-preorders funext univalence truncations +open import order-theory.large-suplattices funext univalence truncations +open import order-theory.least-upper-bounds-large-posets funext univalence truncations +open import order-theory.meet-semilattices funext univalence truncations +open import order-theory.posets funext univalence truncations +open import order-theory.preorders funext univalence truncations +open import order-theory.suplattices funext univalence truncations +open import order-theory.top-elements-large-posets funext univalence truncations +open import order-theory.upper-bounds-large-posets funext univalence truncations ```
diff --git a/src/order-theory/large-inflattices.lagda.md b/src/order-theory/large-inflattices.lagda.md index cd6d850a4e..f3486ab34e 100644 --- a/src/order-theory/large-inflattices.lagda.md +++ b/src/order-theory/large-inflattices.lagda.md @@ -1,26 +1,31 @@ # Large inflattices ```agda -module order-theory.large-inflattices where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.large-inflattices + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.binary-relations open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.large-binary-relations -open import foundation.logical-equivalences -open import foundation.propositions -open import foundation.sets +open import foundation.large-binary-relations funext univalence truncations +open import foundation.logical-equivalences funext +open import foundation.sets funext univalence open import foundation.universe-levels -open import order-theory.greatest-lower-bounds-large-posets -open import order-theory.inflattices -open import order-theory.large-posets -open import order-theory.lower-bounds-large-posets -open import order-theory.posets +open import order-theory.greatest-lower-bounds-large-posets funext univalence truncations +open import order-theory.inflattices funext univalence truncations +open import order-theory.large-posets funext univalence truncations +open import order-theory.lower-bounds-large-posets funext univalence truncations +open import order-theory.posets funext univalence truncations ```
diff --git a/src/order-theory/large-join-semilattices.lagda.md b/src/order-theory/large-join-semilattices.lagda.md index abd7e934e0..1429bc06d0 100644 --- a/src/order-theory/large-join-semilattices.lagda.md +++ b/src/order-theory/large-join-semilattices.lagda.md @@ -1,7 +1,15 @@ # Large join-semilattices ```agda -module order-theory.large-join-semilattices where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.large-join-semilattices + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,16 +17,16 @@ module order-theory.large-join-semilattices where ```agda open import foundation.action-on-identifications-binary-functions open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.large-binary-relations -open import foundation.sets +open import foundation.identity-types funext +open import foundation.large-binary-relations funext univalence truncations +open import foundation.sets funext univalence open import foundation.universe-levels -open import order-theory.bottom-elements-large-posets -open import order-theory.join-semilattices -open import order-theory.large-posets -open import order-theory.least-upper-bounds-large-posets -open import order-theory.posets +open import order-theory.bottom-elements-large-posets funext univalence truncations +open import order-theory.join-semilattices funext univalence truncations +open import order-theory.large-posets funext univalence truncations +open import order-theory.least-upper-bounds-large-posets funext univalence truncations +open import order-theory.posets funext univalence truncations ```
diff --git a/src/order-theory/large-locales.lagda.md b/src/order-theory/large-locales.lagda.md index 9c6da1d97e..7aeb29c1a7 100644 --- a/src/order-theory/large-locales.lagda.md +++ b/src/order-theory/large-locales.lagda.md @@ -1,30 +1,38 @@ # Large locales ```agda -module order-theory.large-locales where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.large-locales + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.identity-types -open import foundation.large-binary-relations -open import foundation.sets +open import foundation.identity-types funext +open import foundation.large-binary-relations funext univalence truncations +open import foundation.sets funext univalence open import foundation.universe-levels -open import order-theory.greatest-lower-bounds-large-posets -open import order-theory.large-frames -open import order-theory.large-meet-semilattices -open import order-theory.large-posets -open import order-theory.large-preorders -open import order-theory.large-suplattices -open import order-theory.least-upper-bounds-large-posets -open import order-theory.meet-semilattices -open import order-theory.posets -open import order-theory.preorders -open import order-theory.suplattices -open import order-theory.top-elements-large-posets -open import order-theory.upper-bounds-large-posets +open import order-theory.greatest-lower-bounds-large-posets funext univalence truncations +open import order-theory.large-frames funext univalence truncations +open import order-theory.large-meet-semilattices funext univalence truncations +open import order-theory.large-posets funext univalence truncations +open import order-theory.large-preorders funext univalence truncations +open import order-theory.large-suplattices funext univalence truncations +open import order-theory.least-upper-bounds-large-posets funext univalence truncations +open import order-theory.meet-semilattices funext univalence truncations +open import order-theory.posets funext univalence truncations +open import order-theory.preorders funext univalence truncations +open import order-theory.suplattices funext univalence truncations +open import order-theory.top-elements-large-posets funext univalence truncations +open import order-theory.upper-bounds-large-posets funext univalence truncations ```
diff --git a/src/order-theory/large-meet-semilattices.lagda.md b/src/order-theory/large-meet-semilattices.lagda.md index c9087cf742..68c45c683a 100644 --- a/src/order-theory/large-meet-semilattices.lagda.md +++ b/src/order-theory/large-meet-semilattices.lagda.md @@ -1,7 +1,15 @@ # Large meet-semilattices ```agda -module order-theory.large-meet-semilattices where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.large-meet-semilattices + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,16 +17,16 @@ module order-theory.large-meet-semilattices where ```agda open import foundation.action-on-identifications-binary-functions open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.large-binary-relations -open import foundation.sets +open import foundation.identity-types funext +open import foundation.large-binary-relations funext univalence truncations +open import foundation.sets funext univalence open import foundation.universe-levels -open import order-theory.greatest-lower-bounds-large-posets -open import order-theory.large-posets -open import order-theory.meet-semilattices -open import order-theory.posets -open import order-theory.top-elements-large-posets +open import order-theory.greatest-lower-bounds-large-posets funext univalence truncations +open import order-theory.large-posets funext univalence truncations +open import order-theory.meet-semilattices funext univalence truncations +open import order-theory.posets funext univalence truncations +open import order-theory.top-elements-large-posets funext univalence truncations ```
diff --git a/src/order-theory/large-meet-subsemilattices.lagda.md b/src/order-theory/large-meet-subsemilattices.lagda.md index 4c2bc6364c..e0e65605a1 100644 --- a/src/order-theory/large-meet-subsemilattices.lagda.md +++ b/src/order-theory/large-meet-subsemilattices.lagda.md @@ -1,22 +1,30 @@ # Large meet-subsemilattices ```agda -module order-theory.large-meet-subsemilattices where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.large-meet-subsemilattices + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.large-binary-relations +open import foundation.large-binary-relations funext univalence truncations open import foundation.universe-levels -open import order-theory.greatest-lower-bounds-large-posets -open import order-theory.large-meet-semilattices -open import order-theory.large-posets -open import order-theory.large-preorders -open import order-theory.large-subposets -open import order-theory.top-elements-large-posets +open import order-theory.greatest-lower-bounds-large-posets funext univalence truncations +open import order-theory.large-meet-semilattices funext univalence truncations +open import order-theory.large-posets funext univalence truncations +open import order-theory.large-preorders funext univalence truncations +open import order-theory.large-subposets funext univalence truncations +open import order-theory.top-elements-large-posets funext univalence truncations ```
diff --git a/src/order-theory/large-posets.lagda.md b/src/order-theory/large-posets.lagda.md index ebe0411daf..62bd63728b 100644 --- a/src/order-theory/large-posets.lagda.md +++ b/src/order-theory/large-posets.lagda.md @@ -1,29 +1,38 @@ # Large posets ```agda -module order-theory.large-posets where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.large-posets + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.isomorphisms-in-large-categories -open import category-theory.isomorphisms-in-precategories -open import category-theory.large-categories -open import category-theory.large-precategories -open import category-theory.precategories +open import category-theory.isomorphisms-in-large-categories funext univalence truncations +open import category-theory.isomorphisms-in-precategories funext univalence truncations +open import category-theory.large-categories funext univalence truncations +open import category-theory.large-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.large-binary-relations -open import foundation.logical-equivalences -open import foundation.propositions -open import foundation.sets +open import foundation.dependent-products-propositions funext +open import foundation.identity-types funext +open import foundation.large-binary-relations funext univalence truncations +open import foundation.logical-equivalences funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence open import foundation.universe-levels -open import order-theory.large-preorders -open import order-theory.posets -open import order-theory.preorders +open import order-theory.large-preorders funext univalence truncations +open import order-theory.posets funext univalence truncations +open import order-theory.preorders funext univalence truncations ```
diff --git a/src/order-theory/large-preorders.lagda.md b/src/order-theory/large-preorders.lagda.md index 34c9170742..af2f1088ad 100644 --- a/src/order-theory/large-preorders.lagda.md +++ b/src/order-theory/large-preorders.lagda.md @@ -1,23 +1,32 @@ # Large preorders ```agda -module order-theory.large-preorders where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.large-preorders + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.large-precategories +open import category-theory.large-precategories funext univalence truncations open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.large-binary-relations -open import foundation.propositions -open import foundation.sets -open import foundation.strictly-involutive-identity-types +open import foundation.dependent-products-propositions funext +open import foundation.identity-types funext +open import foundation.large-binary-relations funext univalence truncations +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.strictly-involutive-identity-types funext univalence open import foundation.universe-levels -open import order-theory.preorders +open import order-theory.preorders funext univalence truncations ```
diff --git a/src/order-theory/large-quotient-locales.lagda.md b/src/order-theory/large-quotient-locales.lagda.md index 15e8cc8a46..20fa6e7331 100644 --- a/src/order-theory/large-quotient-locales.lagda.md +++ b/src/order-theory/large-quotient-locales.lagda.md @@ -1,29 +1,37 @@ # Large quotient locales ```agda -module order-theory.large-quotient-locales where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.large-quotient-locales + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.identity-types -open import foundation.large-binary-relations +open import foundation.identity-types funext +open import foundation.large-binary-relations funext univalence truncations open import foundation.universe-levels -open import order-theory.greatest-lower-bounds-large-posets -open import order-theory.large-locales -open import order-theory.large-meet-semilattices -open import order-theory.large-meet-subsemilattices -open import order-theory.large-posets -open import order-theory.large-preorders -open import order-theory.large-subframes -open import order-theory.large-subposets -open import order-theory.large-subpreorders -open import order-theory.large-subsuplattices -open import order-theory.large-suplattices -open import order-theory.least-upper-bounds-large-posets -open import order-theory.top-elements-large-posets +open import order-theory.greatest-lower-bounds-large-posets funext univalence truncations +open import order-theory.large-locales funext univalence truncations +open import order-theory.large-meet-semilattices funext univalence truncations +open import order-theory.large-meet-subsemilattices funext univalence truncations +open import order-theory.large-posets funext univalence truncations +open import order-theory.large-preorders funext univalence truncations +open import order-theory.large-subframes funext univalence truncations +open import order-theory.large-subposets funext univalence truncations +open import order-theory.large-subpreorders funext univalence truncations +open import order-theory.large-subsuplattices funext univalence truncations +open import order-theory.large-suplattices funext univalence truncations +open import order-theory.least-upper-bounds-large-posets funext univalence truncations +open import order-theory.top-elements-large-posets funext univalence truncations ```
diff --git a/src/order-theory/large-subframes.lagda.md b/src/order-theory/large-subframes.lagda.md index a425901336..c185c824db 100644 --- a/src/order-theory/large-subframes.lagda.md +++ b/src/order-theory/large-subframes.lagda.md @@ -1,31 +1,39 @@ # Large subframes ```agda -module order-theory.large-subframes where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.large-subframes + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.identity-types -open import foundation.large-binary-relations -open import foundation.subtypes +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.large-binary-relations funext univalence truncations +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels -open import order-theory.greatest-lower-bounds-large-posets -open import order-theory.large-frames -open import order-theory.large-meet-semilattices -open import order-theory.large-meet-subsemilattices -open import order-theory.large-posets -open import order-theory.large-preorders -open import order-theory.large-subposets -open import order-theory.large-subpreorders -open import order-theory.large-subsuplattices -open import order-theory.large-suplattices -open import order-theory.least-upper-bounds-large-posets -open import order-theory.top-elements-large-posets +open import order-theory.greatest-lower-bounds-large-posets funext univalence truncations +open import order-theory.large-frames funext univalence truncations +open import order-theory.large-meet-semilattices funext univalence truncations +open import order-theory.large-meet-subsemilattices funext univalence truncations +open import order-theory.large-posets funext univalence truncations +open import order-theory.large-preorders funext univalence truncations +open import order-theory.large-subposets funext univalence truncations +open import order-theory.large-subpreorders funext univalence truncations +open import order-theory.large-subsuplattices funext univalence truncations +open import order-theory.large-suplattices funext univalence truncations +open import order-theory.least-upper-bounds-large-posets funext univalence truncations +open import order-theory.top-elements-large-posets funext univalence truncations ```
diff --git a/src/order-theory/large-subposets.lagda.md b/src/order-theory/large-subposets.lagda.md index 6e2cefec16..4af7fc9802 100644 --- a/src/order-theory/large-subposets.lagda.md +++ b/src/order-theory/large-subposets.lagda.md @@ -1,21 +1,29 @@ # Large subposets ```agda -module order-theory.large-subposets where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.large-subposets + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.large-binary-relations -open import foundation.logical-equivalences -open import foundation.subtypes +open import foundation.large-binary-relations funext univalence truncations +open import foundation.logical-equivalences funext +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels -open import order-theory.large-posets -open import order-theory.large-preorders -open import order-theory.large-subpreorders +open import order-theory.large-posets funext univalence truncations +open import order-theory.large-preorders funext univalence truncations +open import order-theory.large-subpreorders funext univalence truncations ```
diff --git a/src/order-theory/large-subpreorders.lagda.md b/src/order-theory/large-subpreorders.lagda.md index d69fca9bbe..bab4ee82fe 100644 --- a/src/order-theory/large-subpreorders.lagda.md +++ b/src/order-theory/large-subpreorders.lagda.md @@ -1,19 +1,28 @@ # Large subpreorders ```agda -module order-theory.large-subpreorders where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.large-subpreorders + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.large-binary-relations -open import foundation.propositions -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.large-binary-relations funext univalence truncations +open import foundation.propositions funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels -open import order-theory.large-preorders +open import order-theory.large-preorders funext univalence truncations ```
diff --git a/src/order-theory/large-subsuplattices.lagda.md b/src/order-theory/large-subsuplattices.lagda.md index c2a9126cba..e43bcace44 100644 --- a/src/order-theory/large-subsuplattices.lagda.md +++ b/src/order-theory/large-subsuplattices.lagda.md @@ -1,18 +1,26 @@ # Large subsuplattices ```agda -module order-theory.large-subsuplattices where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.large-subsuplattices + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.large-binary-relations +open import foundation.large-binary-relations funext univalence truncations open import foundation.universe-levels -open import order-theory.large-posets -open import order-theory.large-subposets -open import order-theory.large-suplattices +open import order-theory.large-posets funext univalence truncations +open import order-theory.large-subposets funext univalence truncations +open import order-theory.large-suplattices funext univalence truncations ```
diff --git a/src/order-theory/large-suplattices.lagda.md b/src/order-theory/large-suplattices.lagda.md index 489330b18b..700d3dee43 100644 --- a/src/order-theory/large-suplattices.lagda.md +++ b/src/order-theory/large-suplattices.lagda.md @@ -1,26 +1,35 @@ # Large suplattices ```agda -module order-theory.large-suplattices where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.large-suplattices + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.binary-relations +open import foundation.binary-relations funext univalence truncations open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.large-binary-relations -open import foundation.logical-equivalences -open import foundation.propositions -open import foundation.sets +open import foundation.dependent-products-propositions funext +open import foundation.identity-types funext +open import foundation.large-binary-relations funext univalence truncations +open import foundation.logical-equivalences funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence open import foundation.universe-levels -open import order-theory.large-posets -open import order-theory.least-upper-bounds-large-posets -open import order-theory.posets -open import order-theory.suplattices -open import order-theory.upper-bounds-large-posets +open import order-theory.large-posets funext univalence truncations +open import order-theory.least-upper-bounds-large-posets funext univalence truncations +open import order-theory.posets funext univalence truncations +open import order-theory.suplattices funext univalence truncations +open import order-theory.upper-bounds-large-posets funext univalence truncations ```
diff --git a/src/order-theory/lattices.lagda.md b/src/order-theory/lattices.lagda.md index bc9d9bc466..0719401e17 100644 --- a/src/order-theory/lattices.lagda.md +++ b/src/order-theory/lattices.lagda.md @@ -1,21 +1,30 @@ # Lattices ```agda -module order-theory.lattices where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.lattices + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.binary-relations +open import foundation.binary-relations funext univalence truncations open import foundation.dependent-pair-types -open import foundation.propositions -open import foundation.sets +open import foundation.dependent-products-propositions funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence open import foundation.universe-levels -open import order-theory.join-semilattices -open import order-theory.meet-semilattices -open import order-theory.posets +open import order-theory.join-semilattices funext univalence truncations +open import order-theory.meet-semilattices funext univalence truncations +open import order-theory.posets funext univalence truncations ```
diff --git a/src/order-theory/least-upper-bounds-large-posets.lagda.md b/src/order-theory/least-upper-bounds-large-posets.lagda.md index a1ee5df25f..db205d9f67 100644 --- a/src/order-theory/least-upper-bounds-large-posets.lagda.md +++ b/src/order-theory/least-upper-bounds-large-posets.lagda.md @@ -1,21 +1,29 @@ # Least upper bounds in large posets ```agda -module order-theory.least-upper-bounds-large-posets where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.least-upper-bounds-large-posets + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.logical-equivalences +open import foundation.logical-equivalences funext open import foundation.universe-levels -open import order-theory.dependent-products-large-posets -open import order-theory.large-posets -open import order-theory.least-upper-bounds-posets -open import order-theory.similarity-of-elements-large-posets -open import order-theory.upper-bounds-large-posets +open import order-theory.dependent-products-large-posets funext univalence truncations +open import order-theory.large-posets funext univalence truncations +open import order-theory.least-upper-bounds-posets funext univalence truncations +open import order-theory.similarity-of-elements-large-posets funext univalence truncations +open import order-theory.upper-bounds-large-posets funext univalence truncations ```
diff --git a/src/order-theory/least-upper-bounds-posets.lagda.md b/src/order-theory/least-upper-bounds-posets.lagda.md index 2b428ad028..2f39edd337 100644 --- a/src/order-theory/least-upper-bounds-posets.lagda.md +++ b/src/order-theory/least-upper-bounds-posets.lagda.md @@ -1,25 +1,32 @@ # Least upper bounds in posets ```agda -module order-theory.least-upper-bounds-posets where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.least-upper-bounds-posets + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.booleans +open import foundation.booleans funext univalence truncations open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.propositions -open import foundation.raising-universe-levels -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.propositions funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels -open import order-theory.posets -open import order-theory.upper-bounds-posets +open import order-theory.posets funext univalence truncations +open import order-theory.upper-bounds-posets funext univalence truncations ```
diff --git a/src/order-theory/locales.lagda.md b/src/order-theory/locales.lagda.md index 25983102a6..7bc2ffe345 100644 --- a/src/order-theory/locales.lagda.md +++ b/src/order-theory/locales.lagda.md @@ -1,25 +1,34 @@ # Locales ```agda -module order-theory.locales where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.locales + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.binary-relations -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets +open import foundation.binary-relations funext univalence truncations +open import foundation.dependent-products-propositions funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence open import foundation.universe-levels -open import order-theory.frames -open import order-theory.greatest-lower-bounds-posets -open import order-theory.least-upper-bounds-posets -open import order-theory.meet-semilattices -open import order-theory.meet-suplattices -open import order-theory.posets -open import order-theory.suplattices +open import order-theory.frames funext univalence truncations +open import order-theory.greatest-lower-bounds-posets funext univalence truncations +open import order-theory.least-upper-bounds-posets funext univalence truncations +open import order-theory.meet-semilattices funext univalence truncations +open import order-theory.meet-suplattices funext univalence truncations +open import order-theory.posets funext univalence truncations +open import order-theory.suplattices funext univalence truncations ```
diff --git a/src/order-theory/locally-finite-posets.lagda.md b/src/order-theory/locally-finite-posets.lagda.md index 69a7c93beb..4210ff5c49 100644 --- a/src/order-theory/locally-finite-posets.lagda.md +++ b/src/order-theory/locally-finite-posets.lagda.md @@ -1,18 +1,27 @@ # Locally finite posets ```agda -module order-theory.locally-finite-posets where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.locally-finite-posets + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.propositions funext univalence open import foundation.universe-levels -open import order-theory.finite-posets -open import order-theory.interval-subposets -open import order-theory.posets +open import order-theory.finite-posets funext univalence truncations +open import order-theory.interval-subposets funext univalence truncations +open import order-theory.posets funext univalence truncations ```
diff --git a/src/order-theory/lower-bounds-large-posets.lagda.md b/src/order-theory/lower-bounds-large-posets.lagda.md index 99a8b2cb5d..b985f67b04 100644 --- a/src/order-theory/lower-bounds-large-posets.lagda.md +++ b/src/order-theory/lower-bounds-large-posets.lagda.md @@ -1,21 +1,29 @@ # Lower bounds in large posets ```agda -module order-theory.lower-bounds-large-posets where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.lower-bounds-large-posets + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.cartesian-product-types -open import foundation.conjunction +open import foundation.conjunction funext univalence truncations open import foundation.dependent-pair-types -open import foundation.logical-equivalences -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.logical-equivalences funext +open import foundation.propositions funext univalence open import foundation.universe-levels -open import order-theory.dependent-products-large-posets -open import order-theory.large-posets +open import order-theory.dependent-products-large-posets funext univalence truncations +open import order-theory.large-posets funext univalence truncations ```
diff --git a/src/order-theory/lower-bounds-posets.lagda.md b/src/order-theory/lower-bounds-posets.lagda.md index 5ae8f55417..ad3a136c3b 100644 --- a/src/order-theory/lower-bounds-posets.lagda.md +++ b/src/order-theory/lower-bounds-posets.lagda.md @@ -1,17 +1,26 @@ # Lower bounds in posets ```agda -module order-theory.lower-bounds-posets where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.lower-bounds-posets + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.propositions funext univalence open import foundation.universe-levels -open import order-theory.posets +open import order-theory.posets funext univalence truncations ```
diff --git a/src/order-theory/lower-sets-large-posets.lagda.md b/src/order-theory/lower-sets-large-posets.lagda.md index bef92c55f0..d7556e1da4 100644 --- a/src/order-theory/lower-sets-large-posets.lagda.md +++ b/src/order-theory/lower-sets-large-posets.lagda.md @@ -1,7 +1,15 @@ # Lower sets in large posets ```agda -module order-theory.lower-sets-large-posets where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.lower-sets-large-posets + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,8 +17,8 @@ module order-theory.lower-sets-large-posets where ```agda open import foundation.universe-levels -open import order-theory.large-posets -open import order-theory.large-subposets +open import order-theory.large-posets funext univalence truncations +open import order-theory.large-subposets funext univalence truncations ```
diff --git a/src/order-theory/lower-types-preorders.lagda.md b/src/order-theory/lower-types-preorders.lagda.md index 7967370856..4f88b93917 100644 --- a/src/order-theory/lower-types-preorders.lagda.md +++ b/src/order-theory/lower-types-preorders.lagda.md @@ -1,17 +1,25 @@ # Lower types in preorders ```agda -module order-theory.lower-types-preorders where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.lower-types-preorders + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.subtypes +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels -open import order-theory.preorders +open import order-theory.preorders funext univalence truncations ```
diff --git a/src/order-theory/maximal-chains-posets.lagda.md b/src/order-theory/maximal-chains-posets.lagda.md index e62dabcc6e..1163325426 100644 --- a/src/order-theory/maximal-chains-posets.lagda.md +++ b/src/order-theory/maximal-chains-posets.lagda.md @@ -1,18 +1,27 @@ # Maximal chains in posets ```agda -module order-theory.maximal-chains-posets where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.maximal-chains-posets + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.propositions funext univalence open import foundation.universe-levels -open import order-theory.chains-posets -open import order-theory.maximal-chains-preorders -open import order-theory.posets +open import order-theory.chains-posets funext univalence truncations +open import order-theory.maximal-chains-preorders funext univalence truncations +open import order-theory.posets funext univalence truncations ```
diff --git a/src/order-theory/maximal-chains-preorders.lagda.md b/src/order-theory/maximal-chains-preorders.lagda.md index 0cf6169f4f..a39710a923 100644 --- a/src/order-theory/maximal-chains-preorders.lagda.md +++ b/src/order-theory/maximal-chains-preorders.lagda.md @@ -1,18 +1,27 @@ # Maximal chains in preorders ```agda -module order-theory.maximal-chains-preorders where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.maximal-chains-preorders + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.propositions funext univalence open import foundation.universe-levels -open import order-theory.chains-preorders -open import order-theory.preorders +open import order-theory.chains-preorders funext univalence truncations +open import order-theory.preorders funext univalence truncations ```
diff --git a/src/order-theory/meet-semilattices.lagda.md b/src/order-theory/meet-semilattices.lagda.md index e39e512918..29da4eaf3e 100644 --- a/src/order-theory/meet-semilattices.lagda.md +++ b/src/order-theory/meet-semilattices.lagda.md @@ -1,29 +1,38 @@ # Meet-semilattices ```agda -module order-theory.meet-semilattices where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.meet-semilattices + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.binary-relations +open import foundation.binary-relations funext univalence truncations open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.propositions -open import foundation.sets -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels -open import group-theory.isomorphisms-semigroups -open import group-theory.semigroups +open import group-theory.isomorphisms-semigroups funext univalence truncations +open import group-theory.semigroups funext univalence -open import order-theory.greatest-lower-bounds-posets -open import order-theory.lower-bounds-posets -open import order-theory.posets -open import order-theory.preorders +open import order-theory.greatest-lower-bounds-posets funext univalence truncations +open import order-theory.lower-bounds-posets funext univalence truncations +open import order-theory.posets funext univalence truncations +open import order-theory.preorders funext univalence truncations ```
diff --git a/src/order-theory/meet-suplattices.lagda.md b/src/order-theory/meet-suplattices.lagda.md index 898eeb5f7a..1c61304e94 100644 --- a/src/order-theory/meet-suplattices.lagda.md +++ b/src/order-theory/meet-suplattices.lagda.md @@ -1,21 +1,30 @@ # Meet-suplattices ```agda -module order-theory.meet-suplattices where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.meet-suplattices + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.binary-relations +open import foundation.binary-relations funext univalence truncations open import foundation.dependent-pair-types -open import foundation.propositions -open import foundation.sets +open import foundation.dependent-products-propositions funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence open import foundation.universe-levels -open import order-theory.meet-semilattices -open import order-theory.posets -open import order-theory.suplattices +open import order-theory.meet-semilattices funext univalence truncations +open import order-theory.posets funext univalence truncations +open import order-theory.suplattices funext univalence truncations ```
diff --git a/src/order-theory/nuclei-large-locales.lagda.md b/src/order-theory/nuclei-large-locales.lagda.md index b6d44973c9..7e433ff399 100644 --- a/src/order-theory/nuclei-large-locales.lagda.md +++ b/src/order-theory/nuclei-large-locales.lagda.md @@ -1,7 +1,15 @@ # Nuclei on large locales ```agda -module order-theory.nuclei-large-locales where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.nuclei-large-locales + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,25 +17,26 @@ module order-theory.nuclei-large-locales where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.identity-types -open import foundation.large-binary-relations -open import foundation.logical-equivalences -open import foundation.propositions -open import foundation.sets -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.large-binary-relations funext univalence truncations +open import foundation.logical-equivalences funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels -open import order-theory.homomorphisms-large-meet-semilattices -open import order-theory.large-frames -open import order-theory.large-locales -open import order-theory.large-meet-semilattices -open import order-theory.large-meet-subsemilattices -open import order-theory.large-posets -open import order-theory.large-subposets -open import order-theory.large-subpreorders -open import order-theory.large-suplattices -open import order-theory.least-upper-bounds-large-posets +open import order-theory.homomorphisms-large-meet-semilattices funext univalence truncations +open import order-theory.large-frames funext univalence truncations +open import order-theory.large-locales funext univalence truncations +open import order-theory.large-meet-semilattices funext univalence truncations +open import order-theory.large-meet-subsemilattices funext univalence truncations +open import order-theory.large-posets funext univalence truncations +open import order-theory.large-subposets funext univalence truncations +open import order-theory.large-subpreorders funext univalence truncations +open import order-theory.large-suplattices funext univalence truncations +open import order-theory.least-upper-bounds-large-posets funext univalence truncations ```
diff --git a/src/order-theory/opposite-large-posets.lagda.md b/src/order-theory/opposite-large-posets.lagda.md index cbb94d58f5..9828c265a3 100644 --- a/src/order-theory/opposite-large-posets.lagda.md +++ b/src/order-theory/opposite-large-posets.lagda.md @@ -1,25 +1,34 @@ # Opposite large posets ```agda -module order-theory.opposite-large-posets where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.opposite-large-posets + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.homotopies -open import foundation.identity-types +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.large-identity-types -open import foundation.propositions -open import foundation.sets +open import foundation.propositions funext univalence +open import foundation.sets funext univalence open import foundation.universe-levels -open import order-theory.large-posets -open import order-theory.large-preorders -open import order-theory.opposite-large-preorders -open import order-theory.order-preserving-maps-large-posets +open import order-theory.large-posets funext univalence truncations +open import order-theory.large-preorders funext univalence truncations +open import order-theory.opposite-large-preorders funext univalence truncations +open import order-theory.order-preserving-maps-large-posets funext univalence truncations ```
diff --git a/src/order-theory/opposite-large-preorders.lagda.md b/src/order-theory/opposite-large-preorders.lagda.md index 5ecbfef3d7..2cd8e8b189 100644 --- a/src/order-theory/opposite-large-preorders.lagda.md +++ b/src/order-theory/opposite-large-preorders.lagda.md @@ -1,23 +1,32 @@ # Opposite large preorders ```agda -module order-theory.opposite-large-preorders where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.opposite-large-preorders + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.homotopies -open import foundation.identity-types +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.large-identity-types -open import foundation.propositions -open import foundation.sets +open import foundation.propositions funext univalence +open import foundation.sets funext univalence open import foundation.universe-levels -open import order-theory.large-preorders -open import order-theory.order-preserving-maps-large-preorders +open import order-theory.large-preorders funext univalence truncations +open import order-theory.order-preserving-maps-large-preorders funext univalence truncations ```
diff --git a/src/order-theory/opposite-posets.lagda.md b/src/order-theory/opposite-posets.lagda.md index 45b842294c..92584d6d1d 100644 --- a/src/order-theory/opposite-posets.lagda.md +++ b/src/order-theory/opposite-posets.lagda.md @@ -1,24 +1,33 @@ # Opposite posets ```agda -module order-theory.opposite-posets where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.opposite-posets + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.homotopies -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence open import foundation.universe-levels -open import order-theory.opposite-preorders -open import order-theory.order-preserving-maps-posets -open import order-theory.posets -open import order-theory.preorders +open import order-theory.opposite-preorders funext univalence truncations +open import order-theory.order-preserving-maps-posets funext univalence truncations +open import order-theory.posets funext univalence truncations +open import order-theory.preorders funext univalence truncations ```
diff --git a/src/order-theory/opposite-preorders.lagda.md b/src/order-theory/opposite-preorders.lagda.md index 2e6db98be2..3cfde602b2 100644 --- a/src/order-theory/opposite-preorders.lagda.md +++ b/src/order-theory/opposite-preorders.lagda.md @@ -1,22 +1,31 @@ # Opposite preorders ```agda -module order-theory.opposite-preorders where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.opposite-preorders + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.homotopies -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence open import foundation.universe-levels -open import order-theory.order-preserving-maps-preorders -open import order-theory.preorders +open import order-theory.order-preserving-maps-preorders funext univalence truncations +open import order-theory.preorders funext univalence truncations ```
diff --git a/src/order-theory/order-preserving-maps-large-posets.lagda.md b/src/order-theory/order-preserving-maps-large-posets.lagda.md index 5c8636c874..d268565937 100644 --- a/src/order-theory/order-preserving-maps-large-posets.lagda.md +++ b/src/order-theory/order-preserving-maps-large-posets.lagda.md @@ -1,7 +1,15 @@ # Order preserving maps between large posets ```agda -module order-theory.order-preserving-maps-large-posets where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.order-preserving-maps-large-posets + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,10 +17,10 @@ module order-theory.order-preserving-maps-large-posets where ```agda open import foundation.universe-levels -open import order-theory.large-posets -open import order-theory.order-preserving-maps-large-preorders -open import order-theory.order-preserving-maps-posets -open import order-theory.similarity-of-elements-large-posets +open import order-theory.large-posets funext univalence truncations +open import order-theory.order-preserving-maps-large-preorders funext univalence truncations +open import order-theory.order-preserving-maps-posets funext univalence truncations +open import order-theory.similarity-of-elements-large-posets funext univalence truncations ```
diff --git a/src/order-theory/order-preserving-maps-large-preorders.lagda.md b/src/order-theory/order-preserving-maps-large-preorders.lagda.md index d9150512e7..23df97993c 100644 --- a/src/order-theory/order-preserving-maps-large-preorders.lagda.md +++ b/src/order-theory/order-preserving-maps-large-preorders.lagda.md @@ -1,7 +1,15 @@ # Order preserving maps between large preorders ```agda -module order-theory.order-preserving-maps-large-preorders where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.order-preserving-maps-large-preorders + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -13,9 +21,9 @@ open import foundation.universe-levels open import foundation-core.function-types open import foundation-core.homotopies -open import order-theory.large-preorders -open import order-theory.order-preserving-maps-preorders -open import order-theory.similarity-of-elements-large-preorders +open import order-theory.large-preorders funext univalence truncations +open import order-theory.order-preserving-maps-preorders funext univalence truncations +open import order-theory.similarity-of-elements-large-preorders funext univalence truncations ```
diff --git a/src/order-theory/order-preserving-maps-posets.lagda.md b/src/order-theory/order-preserving-maps-posets.lagda.md index 163aee3f3f..28c337d5be 100644 --- a/src/order-theory/order-preserving-maps-posets.lagda.md +++ b/src/order-theory/order-preserving-maps-posets.lagda.md @@ -1,24 +1,33 @@ # Order preserving maps between posets ```agda -module order-theory.order-preserving-maps-posets where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.order-preserving-maps-posets + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.equivalences -open import foundation.function-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets -open import foundation.strictly-involutive-identity-types -open import foundation.subtypes -open import foundation.torsorial-type-families +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.strictly-involutive-identity-types funext univalence +open import foundation.subtypes funext univalence truncations +open import foundation.torsorial-type-families funext univalence truncations open import foundation.universe-levels -open import order-theory.order-preserving-maps-preorders -open import order-theory.posets +open import order-theory.order-preserving-maps-preorders funext univalence truncations +open import order-theory.posets funext univalence truncations ```
diff --git a/src/order-theory/order-preserving-maps-preorders.lagda.md b/src/order-theory/order-preserving-maps-preorders.lagda.md index a45df09656..7d35301ec7 100644 --- a/src/order-theory/order-preserving-maps-preorders.lagda.md +++ b/src/order-theory/order-preserving-maps-preorders.lagda.md @@ -1,27 +1,36 @@ # Order preserving maps between preorders ```agda -module order-theory.order-preserving-maps-preorders where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.order-preserving-maps-preorders + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types -open import foundation.propositions -open import foundation.strictly-involutive-identity-types +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.strictly-involutive-identity-types funext univalence open import foundation.subtype-identity-principle open import foundation.universe-levels open import foundation-core.torsorial-type-families -open import order-theory.preorders +open import order-theory.preorders funext univalence truncations ```
diff --git a/src/order-theory/ordinals.lagda.md b/src/order-theory/ordinals.lagda.md index 7dc9994603..c087178d1b 100644 --- a/src/order-theory/ordinals.lagda.md +++ b/src/order-theory/ordinals.lagda.md @@ -1,25 +1,34 @@ # Ordinals ```agda -module order-theory.ordinals where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.ordinals + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.binary-relations -open import foundation.cartesian-product-types +open import foundation.binary-relations funext univalence truncations +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.propositions -open import foundation.sets +open import foundation.dependent-products-propositions funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence open import foundation.universe-levels -open import order-theory.posets -open import order-theory.preorders -open import order-theory.transitive-well-founded-relations -open import order-theory.well-founded-relations +open import order-theory.posets funext univalence truncations +open import order-theory.preorders funext univalence truncations +open import order-theory.transitive-well-founded-relations funext univalence truncations +open import order-theory.well-founded-relations funext univalence truncations ```
diff --git a/src/order-theory/posets.lagda.md b/src/order-theory/posets.lagda.md index f1875f86f2..5a46c7b153 100644 --- a/src/order-theory/posets.lagda.md +++ b/src/order-theory/posets.lagda.md @@ -1,28 +1,37 @@ # Posets ```agda -module order-theory.posets where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.posets + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.isomorphisms-in-precategories -open import category-theory.precategories +open import category-theory.categories funext univalence truncations +open import category-theory.isomorphisms-in-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations -open import foundation.binary-relations -open import foundation.cartesian-product-types +open import foundation.binary-relations funext univalence truncations +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.logical-equivalences -open import foundation.propositions -open import foundation.sets +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.logical-equivalences funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence open import foundation.universe-levels -open import order-theory.preorders +open import order-theory.preorders funext univalence truncations ```
diff --git a/src/order-theory/powers-of-large-locales.lagda.md b/src/order-theory/powers-of-large-locales.lagda.md index 1822320130..b9170a0011 100644 --- a/src/order-theory/powers-of-large-locales.lagda.md +++ b/src/order-theory/powers-of-large-locales.lagda.md @@ -1,25 +1,33 @@ # Powers of large locales ```agda -module order-theory.powers-of-large-locales where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.powers-of-large-locales + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.identity-types -open import foundation.large-binary-relations -open import foundation.sets +open import foundation.identity-types funext +open import foundation.large-binary-relations funext univalence truncations +open import foundation.sets funext univalence open import foundation.universe-levels -open import order-theory.dependent-products-large-locales -open import order-theory.greatest-lower-bounds-large-posets -open import order-theory.large-locales -open import order-theory.large-meet-semilattices -open import order-theory.large-posets -open import order-theory.large-suplattices -open import order-theory.least-upper-bounds-large-posets -open import order-theory.top-elements-large-posets +open import order-theory.dependent-products-large-locales funext univalence truncations +open import order-theory.greatest-lower-bounds-large-posets funext univalence truncations +open import order-theory.large-locales funext univalence truncations +open import order-theory.large-meet-semilattices funext univalence truncations +open import order-theory.large-posets funext univalence truncations +open import order-theory.large-suplattices funext univalence truncations +open import order-theory.least-upper-bounds-large-posets funext univalence truncations +open import order-theory.top-elements-large-posets funext univalence truncations ```
diff --git a/src/order-theory/precategory-of-decidable-total-orders.lagda.md b/src/order-theory/precategory-of-decidable-total-orders.lagda.md index ee91924562..d4bac1d2ed 100644 --- a/src/order-theory/precategory-of-decidable-total-orders.lagda.md +++ b/src/order-theory/precategory-of-decidable-total-orders.lagda.md @@ -1,20 +1,28 @@ # The precategory of decidable total orders ```agda -module order-theory.precategory-of-decidable-total-orders where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.precategory-of-decidable-total-orders + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.full-large-subprecategories -open import category-theory.large-precategories -open import category-theory.precategories +open import category-theory.full-large-subprecategories funext univalence truncations +open import category-theory.large-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations open import foundation.universe-levels -open import order-theory.decidable-total-orders -open import order-theory.precategory-of-posets +open import order-theory.decidable-total-orders funext univalence truncations +open import order-theory.precategory-of-posets funext univalence truncations ```
diff --git a/src/order-theory/precategory-of-finite-posets.lagda.md b/src/order-theory/precategory-of-finite-posets.lagda.md index 87c506290f..f991dac1c4 100644 --- a/src/order-theory/precategory-of-finite-posets.lagda.md +++ b/src/order-theory/precategory-of-finite-posets.lagda.md @@ -1,20 +1,28 @@ # The precategory of finite posets ```agda -module order-theory.precategory-of-finite-posets where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.precategory-of-finite-posets + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.full-large-subprecategories -open import category-theory.large-precategories -open import category-theory.precategories +open import category-theory.full-large-subprecategories funext univalence truncations +open import category-theory.large-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations open import foundation.universe-levels -open import order-theory.finite-posets -open import order-theory.precategory-of-posets +open import order-theory.finite-posets funext univalence truncations +open import order-theory.precategory-of-posets funext univalence truncations ```
diff --git a/src/order-theory/precategory-of-finite-total-orders.lagda.md b/src/order-theory/precategory-of-finite-total-orders.lagda.md index e5e28bf9c5..85fe66d3c6 100644 --- a/src/order-theory/precategory-of-finite-total-orders.lagda.md +++ b/src/order-theory/precategory-of-finite-total-orders.lagda.md @@ -1,20 +1,28 @@ # The precategory of finite total orders ```agda -module order-theory.precategory-of-finite-total-orders where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.precategory-of-finite-total-orders + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.full-large-subprecategories -open import category-theory.large-precategories -open import category-theory.precategories +open import category-theory.full-large-subprecategories funext univalence truncations +open import category-theory.large-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations open import foundation.universe-levels -open import order-theory.finite-total-orders -open import order-theory.precategory-of-posets +open import order-theory.finite-total-orders funext univalence truncations +open import order-theory.precategory-of-posets funext univalence truncations ```
diff --git a/src/order-theory/precategory-of-inhabited-finite-total-orders.lagda.md b/src/order-theory/precategory-of-inhabited-finite-total-orders.lagda.md index cbcc011d57..7dc3d97857 100644 --- a/src/order-theory/precategory-of-inhabited-finite-total-orders.lagda.md +++ b/src/order-theory/precategory-of-inhabited-finite-total-orders.lagda.md @@ -1,20 +1,28 @@ # The precategory of inhabited finite total orders ```agda -module order-theory.precategory-of-inhabited-finite-total-orders where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.precategory-of-inhabited-finite-total-orders + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.full-large-subprecategories -open import category-theory.large-precategories -open import category-theory.precategories +open import category-theory.full-large-subprecategories funext univalence truncations +open import category-theory.large-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations open import foundation.universe-levels -open import order-theory.inhabited-finite-total-orders -open import order-theory.precategory-of-posets +open import order-theory.inhabited-finite-total-orders funext univalence truncations +open import order-theory.precategory-of-posets funext univalence truncations ```
diff --git a/src/order-theory/precategory-of-posets.lagda.md b/src/order-theory/precategory-of-posets.lagda.md index 69a33a4c81..03630a2045 100644 --- a/src/order-theory/precategory-of-posets.lagda.md +++ b/src/order-theory/precategory-of-posets.lagda.md @@ -1,19 +1,27 @@ # The precategory of posets ```agda -module order-theory.precategory-of-posets where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.precategory-of-posets + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.large-precategories -open import category-theory.precategories +open import category-theory.large-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations open import foundation.universe-levels -open import order-theory.order-preserving-maps-posets -open import order-theory.posets +open import order-theory.order-preserving-maps-posets funext univalence truncations +open import order-theory.posets funext univalence truncations ```
diff --git a/src/order-theory/precategory-of-total-orders.lagda.md b/src/order-theory/precategory-of-total-orders.lagda.md index aeb5d9ffd2..3d6b415be2 100644 --- a/src/order-theory/precategory-of-total-orders.lagda.md +++ b/src/order-theory/precategory-of-total-orders.lagda.md @@ -1,20 +1,28 @@ # The precategory of total orders ```agda -module order-theory.precategory-of-total-orders where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.precategory-of-total-orders + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.full-large-subprecategories -open import category-theory.large-precategories -open import category-theory.precategories +open import category-theory.full-large-subprecategories funext univalence truncations +open import category-theory.large-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations open import foundation.universe-levels -open import order-theory.precategory-of-posets -open import order-theory.total-orders +open import order-theory.precategory-of-posets funext univalence truncations +open import order-theory.total-orders funext univalence truncations ```
diff --git a/src/order-theory/preorders.lagda.md b/src/order-theory/preorders.lagda.md index 37293a7863..984a09d4a1 100644 --- a/src/order-theory/preorders.lagda.md +++ b/src/order-theory/preorders.lagda.md @@ -1,24 +1,33 @@ # Preorders ```agda -module order-theory.preorders where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.preorders + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.precategories +open import category-theory.precategories funext univalence truncations -open import foundation.binary-relations -open import foundation.cartesian-product-types +open import foundation.binary-relations funext univalence truncations +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.identity-types -open import foundation.negated-equality -open import foundation.negation -open import foundation.propositions -open import foundation.sets +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.negated-equality funext univalence truncations +open import foundation.negation funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence open import foundation.transport-along-identifications open import foundation.universe-levels ``` diff --git a/src/order-theory/principal-lower-sets-large-posets.lagda.md b/src/order-theory/principal-lower-sets-large-posets.lagda.md index 6823e5413e..8c20af068f 100644 --- a/src/order-theory/principal-lower-sets-large-posets.lagda.md +++ b/src/order-theory/principal-lower-sets-large-posets.lagda.md @@ -1,21 +1,29 @@ # Principal lower sets of large posets ```agda -module order-theory.principal-lower-sets-large-posets where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.principal-lower-sets-large-posets + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.logical-equivalences +open import foundation.identity-types funext +open import foundation.logical-equivalences funext open import foundation.universe-levels -open import order-theory.large-posets -open import order-theory.large-subposets -open import order-theory.large-subpreorders -open import order-theory.similarity-of-elements-large-posets +open import order-theory.large-posets funext univalence truncations +open import order-theory.large-subposets funext univalence truncations +open import order-theory.large-subpreorders funext univalence truncations +open import order-theory.similarity-of-elements-large-posets funext univalence truncations ```
diff --git a/src/order-theory/principal-upper-sets-large-posets.lagda.md b/src/order-theory/principal-upper-sets-large-posets.lagda.md index c66b312a07..15394383d5 100644 --- a/src/order-theory/principal-upper-sets-large-posets.lagda.md +++ b/src/order-theory/principal-upper-sets-large-posets.lagda.md @@ -1,21 +1,29 @@ # Principal upper sets of large posets ```agda -module order-theory.principal-upper-sets-large-posets where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.principal-upper-sets-large-posets + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.logical-equivalences +open import foundation.identity-types funext +open import foundation.logical-equivalences funext open import foundation.universe-levels -open import order-theory.large-posets -open import order-theory.large-subposets -open import order-theory.large-subpreorders -open import order-theory.similarity-of-elements-large-posets +open import order-theory.large-posets funext univalence truncations +open import order-theory.large-subposets funext univalence truncations +open import order-theory.large-subpreorders funext univalence truncations +open import order-theory.similarity-of-elements-large-posets funext univalence truncations ```
diff --git a/src/order-theory/reflective-galois-connections-large-posets.lagda.md b/src/order-theory/reflective-galois-connections-large-posets.lagda.md index bd27be52af..d0b4fec3ab 100644 --- a/src/order-theory/reflective-galois-connections-large-posets.lagda.md +++ b/src/order-theory/reflective-galois-connections-large-posets.lagda.md @@ -1,18 +1,26 @@ # Reflective Galois connections between large posets ```agda -module order-theory.reflective-galois-connections-large-posets where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.reflective-galois-connections-large-posets + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.universe-levels -open import order-theory.galois-connections-large-posets -open import order-theory.large-posets -open import order-theory.order-preserving-maps-large-posets +open import order-theory.galois-connections-large-posets funext univalence truncations +open import order-theory.large-posets funext univalence truncations +open import order-theory.order-preserving-maps-large-posets funext univalence truncations ```
diff --git a/src/order-theory/resizing-posets.lagda.md b/src/order-theory/resizing-posets.lagda.md index 4fcaf5e66f..fbad5d24ce 100644 --- a/src/order-theory/resizing-posets.lagda.md +++ b/src/order-theory/resizing-posets.lagda.md @@ -1,33 +1,42 @@ # Resizing posets ```agda -module order-theory.resizing-posets where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.resizing-posets + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.isomorphisms-in-large-precategories +open import category-theory.isomorphisms-in-large-precategories funext univalence truncations -open import foundation.binary-relations -open import foundation.cartesian-product-types +open import foundation.binary-relations funext univalence truncations +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.negated-equality -open import foundation.negation -open import foundation.propositions -open import foundation.sets -open import foundation.small-types +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.negated-equality funext univalence truncations +open import foundation.negation funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.small-types funext univalence truncations open import foundation.universe-levels -open import order-theory.order-preserving-maps-posets -open import order-theory.posets -open import order-theory.precategory-of-posets -open import order-theory.preorders -open import order-theory.resizing-preorders +open import order-theory.order-preserving-maps-posets funext univalence truncations +open import order-theory.posets funext univalence truncations +open import order-theory.precategory-of-posets funext univalence truncations +open import order-theory.preorders funext univalence truncations +open import order-theory.resizing-preorders funext univalence truncations ```
diff --git a/src/order-theory/resizing-preorders.lagda.md b/src/order-theory/resizing-preorders.lagda.md index 26a17b7682..28d6ff431f 100644 --- a/src/order-theory/resizing-preorders.lagda.md +++ b/src/order-theory/resizing-preorders.lagda.md @@ -1,27 +1,36 @@ # Resizing preorders ```agda -module order-theory.resizing-preorders where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.resizing-preorders + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.binary-relations -open import foundation.cartesian-product-types +open import foundation.binary-relations funext univalence truncations +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.identity-types -open import foundation.negated-equality -open import foundation.negation -open import foundation.propositions -open import foundation.sets -open import foundation.small-types +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.negated-equality funext univalence truncations +open import foundation.negation funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.small-types funext univalence truncations open import foundation.universe-levels -open import order-theory.order-preserving-maps-preorders -open import order-theory.preorders +open import order-theory.order-preserving-maps-preorders funext univalence truncations +open import order-theory.preorders funext univalence truncations ```
diff --git a/src/order-theory/resizing-suplattices.lagda.md b/src/order-theory/resizing-suplattices.lagda.md index 6c0cdeede8..5e06c8c6c7 100644 --- a/src/order-theory/resizing-suplattices.lagda.md +++ b/src/order-theory/resizing-suplattices.lagda.md @@ -1,31 +1,40 @@ # Resizing suplattices ```agda -module order-theory.resizing-suplattices where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.resizing-suplattices + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.binary-relations -open import foundation.cartesian-product-types +open import foundation.binary-relations funext univalence truncations +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.negated-equality -open import foundation.negation -open import foundation.propositions -open import foundation.sets -open import foundation.small-types +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.negated-equality funext univalence truncations +open import foundation.negation funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.small-types funext univalence truncations open import foundation.universe-levels -open import order-theory.least-upper-bounds-posets -open import order-theory.order-preserving-maps-posets -open import order-theory.posets -open import order-theory.resizing-posets -open import order-theory.suplattices +open import order-theory.least-upper-bounds-posets funext univalence truncations +open import order-theory.order-preserving-maps-posets funext univalence truncations +open import order-theory.posets funext univalence truncations +open import order-theory.resizing-posets funext univalence truncations +open import order-theory.suplattices funext univalence truncations ```
diff --git a/src/order-theory/similarity-of-elements-large-posets.lagda.md b/src/order-theory/similarity-of-elements-large-posets.lagda.md index 5e2d8199ea..077a2b676e 100644 --- a/src/order-theory/similarity-of-elements-large-posets.lagda.md +++ b/src/order-theory/similarity-of-elements-large-posets.lagda.md @@ -1,24 +1,33 @@ # Similarity of elements in large posets ```agda -module order-theory.similarity-of-elements-large-posets where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.similarity-of-elements-large-posets + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types -open import foundation.large-binary-relations -open import foundation.propositions -open import foundation.subtypes -open import foundation.torsorial-type-families +open import foundation.identity-types funext +open import foundation.large-binary-relations funext univalence truncations +open import foundation.propositions funext univalence +open import foundation.subtypes funext univalence truncations +open import foundation.torsorial-type-families funext univalence truncations open import foundation.universe-levels -open import order-theory.large-posets -open import order-theory.similarity-of-elements-large-preorders +open import order-theory.large-posets funext univalence truncations +open import order-theory.similarity-of-elements-large-preorders funext univalence truncations ```
diff --git a/src/order-theory/similarity-of-elements-large-preorders.lagda.md b/src/order-theory/similarity-of-elements-large-preorders.lagda.md index c027bb56db..dbcc673e55 100644 --- a/src/order-theory/similarity-of-elements-large-preorders.lagda.md +++ b/src/order-theory/similarity-of-elements-large-preorders.lagda.md @@ -1,19 +1,28 @@ # Similarity of elements in large preorders ```agda -module order-theory.similarity-of-elements-large-preorders where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.similarity-of-elements-large-preorders + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.large-binary-relations -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.identity-types funext +open import foundation.large-binary-relations funext univalence truncations +open import foundation.propositions funext univalence open import foundation.universe-levels -open import order-theory.large-preorders +open import order-theory.large-preorders funext univalence truncations ```
diff --git a/src/order-theory/similarity-of-order-preserving-maps-large-posets.lagda.md b/src/order-theory/similarity-of-order-preserving-maps-large-posets.lagda.md index 663ec217c0..9103b76fb2 100644 --- a/src/order-theory/similarity-of-order-preserving-maps-large-posets.lagda.md +++ b/src/order-theory/similarity-of-order-preserving-maps-large-posets.lagda.md @@ -1,19 +1,27 @@ # Similarity of order preserving maps between large posets ```agda -module order-theory.similarity-of-order-preserving-maps-large-posets where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.similarity-of-order-preserving-maps-large-posets + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.universe-levels -open import order-theory.large-posets -open import order-theory.order-preserving-maps-large-posets -open import order-theory.similarity-of-elements-large-posets -open import order-theory.similarity-of-order-preserving-maps-large-preorders +open import order-theory.large-posets funext univalence truncations +open import order-theory.order-preserving-maps-large-posets funext univalence truncations +open import order-theory.similarity-of-elements-large-posets funext univalence truncations +open import order-theory.similarity-of-order-preserving-maps-large-preorders funext univalence truncations ```
diff --git a/src/order-theory/similarity-of-order-preserving-maps-large-preorders.lagda.md b/src/order-theory/similarity-of-order-preserving-maps-large-preorders.lagda.md index 62ce3a3d85..66420524d3 100644 --- a/src/order-theory/similarity-of-order-preserving-maps-large-preorders.lagda.md +++ b/src/order-theory/similarity-of-order-preserving-maps-large-preorders.lagda.md @@ -1,18 +1,26 @@ # Similarity of order preserving maps between large preorders ```agda -module order-theory.similarity-of-order-preserving-maps-large-preorders where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.similarity-of-order-preserving-maps-large-preorders + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.universe-levels -open import order-theory.large-preorders -open import order-theory.order-preserving-maps-large-preorders -open import order-theory.similarity-of-elements-large-preorders +open import order-theory.large-preorders funext univalence truncations +open import order-theory.order-preserving-maps-large-preorders funext univalence truncations +open import order-theory.similarity-of-elements-large-preorders funext univalence truncations ```
diff --git a/src/order-theory/strict-order-preserving-maps.lagda.md b/src/order-theory/strict-order-preserving-maps.lagda.md index 44b8225347..abdfa6e768 100644 --- a/src/order-theory/strict-order-preserving-maps.lagda.md +++ b/src/order-theory/strict-order-preserving-maps.lagda.md @@ -1,20 +1,29 @@ # Strict order preserving maps ```agda -module order-theory.strict-order-preserving-maps where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.strict-order-preserving-maps + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.binary-relations +open import foundation.binary-relations funext univalence truncations open import foundation.dependent-pair-types -open import foundation.propositions -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.propositions funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels -open import order-theory.strict-preorders -open import order-theory.strictly-preordered-sets +open import order-theory.strict-preorders funext univalence truncations +open import order-theory.strictly-preordered-sets funext univalence truncations ```
diff --git a/src/order-theory/strict-preorders.lagda.md b/src/order-theory/strict-preorders.lagda.md index 071d017b3d..afb8f27500 100644 --- a/src/order-theory/strict-preorders.lagda.md +++ b/src/order-theory/strict-preorders.lagda.md @@ -1,18 +1,27 @@ # Strict preorders ```agda -module order-theory.strict-preorders where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.strict-preorders + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.binary-relations -open import foundation.cartesian-product-types +open import foundation.binary-relations funext univalence truncations +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.negation -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.empty-types funext univalence truncations +open import foundation.negation funext +open import foundation.propositions funext univalence open import foundation.universe-levels ``` diff --git a/src/order-theory/strictly-inflationary-maps-strict-preorders.lagda.md b/src/order-theory/strictly-inflationary-maps-strict-preorders.lagda.md index d8a4672caa..8be66a1a77 100644 --- a/src/order-theory/strictly-inflationary-maps-strict-preorders.lagda.md +++ b/src/order-theory/strictly-inflationary-maps-strict-preorders.lagda.md @@ -1,19 +1,28 @@ # Strictly inflationary maps on a strictly preordered type ```agda -module order-theory.strictly-inflationary-maps-strict-preorders where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.strictly-inflationary-maps-strict-preorders + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.propositions -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.propositions funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels -open import order-theory.strict-order-preserving-maps -open import order-theory.strict-preorders +open import order-theory.strict-order-preserving-maps funext univalence truncations +open import order-theory.strict-preorders funext univalence truncations ```
diff --git a/src/order-theory/strictly-preordered-sets.lagda.md b/src/order-theory/strictly-preordered-sets.lagda.md index c639e6fe02..5beec9d983 100644 --- a/src/order-theory/strictly-preordered-sets.lagda.md +++ b/src/order-theory/strictly-preordered-sets.lagda.md @@ -1,22 +1,31 @@ # Strictly preordered sets ```agda -module order-theory.strictly-preordered-sets where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.strictly-preordered-sets + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.binary-relations -open import foundation.cartesian-product-types +open import foundation.binary-relations funext univalence truncations +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.negation -open import foundation.propositions -open import foundation.sets +open import foundation.dependent-products-propositions funext +open import foundation.empty-types funext univalence truncations +open import foundation.negation funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence open import foundation.universe-levels -open import order-theory.strict-preorders +open import order-theory.strict-preorders funext univalence truncations ```
diff --git a/src/order-theory/subposets.lagda.md b/src/order-theory/subposets.lagda.md index d7cd52162e..1568e15d7f 100644 --- a/src/order-theory/subposets.lagda.md +++ b/src/order-theory/subposets.lagda.md @@ -1,21 +1,30 @@ # Subposets ```agda -module order-theory.subposets where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.subposets + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.binary-relations +open import foundation.binary-relations funext univalence truncations open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence open import foundation.universe-levels -open import order-theory.posets -open import order-theory.preorders -open import order-theory.subpreorders +open import order-theory.posets funext univalence truncations +open import order-theory.preorders funext univalence truncations +open import order-theory.subpreorders funext univalence truncations ```
diff --git a/src/order-theory/subpreorders.lagda.md b/src/order-theory/subpreorders.lagda.md index 8ac0925ccd..c32f220d2a 100644 --- a/src/order-theory/subpreorders.lagda.md +++ b/src/order-theory/subpreorders.lagda.md @@ -1,21 +1,30 @@ # Subpreorders ```agda -module order-theory.subpreorders where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.subpreorders + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.binary-relations +open import foundation.binary-relations funext univalence truncations open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels -open import order-theory.preorders +open import order-theory.preorders funext univalence truncations ```
diff --git a/src/order-theory/suplattices.lagda.md b/src/order-theory/suplattices.lagda.md index e2cac7a583..9d2142c192 100644 --- a/src/order-theory/suplattices.lagda.md +++ b/src/order-theory/suplattices.lagda.md @@ -1,25 +1,34 @@ # Suplattices ```agda -module order-theory.suplattices where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.suplattices + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.binary-relations +open import foundation.binary-relations funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.propositions -open import foundation.sets +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence open import foundation.universe-levels -open import order-theory.least-upper-bounds-posets -open import order-theory.posets -open import order-theory.upper-bounds-posets +open import order-theory.least-upper-bounds-posets funext univalence truncations +open import order-theory.posets funext univalence truncations +open import order-theory.upper-bounds-posets funext univalence truncations ```
diff --git a/src/order-theory/supremum-preserving-maps-posets.lagda.md b/src/order-theory/supremum-preserving-maps-posets.lagda.md index b5abca4ab4..55718fe116 100644 --- a/src/order-theory/supremum-preserving-maps-posets.lagda.md +++ b/src/order-theory/supremum-preserving-maps-posets.lagda.md @@ -1,33 +1,43 @@ # Supremum preserving maps between posets ```agda -module order-theory.supremum-preserving-maps-posets where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.supremum-preserving-maps-posets + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.booleans +open import foundation.booleans funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalences +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext open import foundation.evaluation-functions -open import foundation.function-types +open import foundation.function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types -open import foundation.propositions -open import foundation.raising-universe-levels -open import foundation.small-types -open import foundation.strictly-involutive-identity-types +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.small-types funext univalence truncations +open import foundation.strictly-involutive-identity-types funext univalence open import foundation.subtype-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext univalence truncations open import foundation.universe-levels -open import order-theory.join-preserving-maps-posets -open import order-theory.least-upper-bounds-posets -open import order-theory.order-preserving-maps-posets -open import order-theory.posets +open import foundation-core.raising-universe-levels + +open import order-theory.join-preserving-maps-posets funext univalence truncations +open import order-theory.least-upper-bounds-posets funext univalence truncations +open import order-theory.order-preserving-maps-posets funext univalence truncations +open import order-theory.posets funext univalence truncations ```
diff --git a/src/order-theory/top-elements-large-posets.lagda.md b/src/order-theory/top-elements-large-posets.lagda.md index f861a1a336..658dd0cde2 100644 --- a/src/order-theory/top-elements-large-posets.lagda.md +++ b/src/order-theory/top-elements-large-posets.lagda.md @@ -1,7 +1,15 @@ # Top elements in large posets ```agda -module order-theory.top-elements-large-posets where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.top-elements-large-posets + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,8 +17,8 @@ module order-theory.top-elements-large-posets where ```agda open import foundation.universe-levels -open import order-theory.dependent-products-large-posets -open import order-theory.large-posets +open import order-theory.dependent-products-large-posets funext univalence truncations +open import order-theory.large-posets funext univalence truncations ```
diff --git a/src/order-theory/top-elements-posets.lagda.md b/src/order-theory/top-elements-posets.lagda.md index 658fc977cc..8ff495a45e 100644 --- a/src/order-theory/top-elements-posets.lagda.md +++ b/src/order-theory/top-elements-posets.lagda.md @@ -1,19 +1,28 @@ # Top elements in posets ```agda -module order-theory.top-elements-posets where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.top-elements-posets + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.propositions -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.propositions funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels -open import order-theory.posets -open import order-theory.top-elements-preorders +open import order-theory.posets funext univalence truncations +open import order-theory.top-elements-preorders funext univalence truncations ```
diff --git a/src/order-theory/top-elements-preorders.lagda.md b/src/order-theory/top-elements-preorders.lagda.md index 1c9655f1de..0d31573818 100644 --- a/src/order-theory/top-elements-preorders.lagda.md +++ b/src/order-theory/top-elements-preorders.lagda.md @@ -1,17 +1,26 @@ # Top elements in preorders ```agda -module order-theory.top-elements-preorders where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.top-elements-preorders + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.propositions funext univalence open import foundation.universe-levels -open import order-theory.preorders +open import order-theory.preorders funext univalence truncations ```
diff --git a/src/order-theory/total-orders.lagda.md b/src/order-theory/total-orders.lagda.md index 1f84d69e67..f6f2fb7a63 100644 --- a/src/order-theory/total-orders.lagda.md +++ b/src/order-theory/total-orders.lagda.md @@ -1,22 +1,31 @@ # Total orders ```agda -module order-theory.total-orders where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.total-orders + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.binary-relations +open import foundation.binary-relations funext univalence truncations open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets +open import foundation.dependent-products-propositions funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence open import foundation.universe-levels -open import order-theory.posets -open import order-theory.preorders -open import order-theory.total-preorders +open import order-theory.posets funext univalence truncations +open import order-theory.preorders funext univalence truncations +open import order-theory.total-preorders funext univalence truncations ```
diff --git a/src/order-theory/total-preorders.lagda.md b/src/order-theory/total-preorders.lagda.md index facdaddbd8..bf58e1f556 100644 --- a/src/order-theory/total-preorders.lagda.md +++ b/src/order-theory/total-preorders.lagda.md @@ -1,19 +1,28 @@ # Total preorders ```agda -module order-theory.total-preorders where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.total-preorders + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.binary-relations +open import foundation.binary-relations funext univalence truncations open import foundation.dependent-pair-types -open import foundation.disjunction -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.disjunction funext univalence truncations +open import foundation.propositions funext univalence open import foundation.universe-levels -open import order-theory.preorders +open import order-theory.preorders funext univalence truncations ```
diff --git a/src/order-theory/transitive-well-founded-relations.lagda.md b/src/order-theory/transitive-well-founded-relations.lagda.md index f011a6666e..9399e4dc67 100644 --- a/src/order-theory/transitive-well-founded-relations.lagda.md +++ b/src/order-theory/transitive-well-founded-relations.lagda.md @@ -1,18 +1,26 @@ # Transitive well-founded relations ```agda -module order-theory.transitive-well-founded-relations where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.transitive-well-founded-relations + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.binary-relations -open import foundation.cartesian-product-types +open import foundation.binary-relations funext univalence truncations +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types open import foundation.universe-levels -open import order-theory.well-founded-relations +open import order-theory.well-founded-relations funext univalence truncations ```
diff --git a/src/order-theory/transposition-inequalities-along-order-preserving-retractions-posets.lagda.md b/src/order-theory/transposition-inequalities-along-order-preserving-retractions-posets.lagda.md index 49abe580a1..9ecebe23ad 100644 --- a/src/order-theory/transposition-inequalities-along-order-preserving-retractions-posets.lagda.md +++ b/src/order-theory/transposition-inequalities-along-order-preserving-retractions-posets.lagda.md @@ -1,21 +1,29 @@ # Transposing inequalities in posets along order-preserving retractions ```agda -module order-theory.transposition-inequalities-along-order-preserving-retractions-posets where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.transposition-inequalities-along-order-preserving-retractions-posets + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.retractions +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.retractions funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import order-theory.order-preserving-maps-posets -open import order-theory.posets +open import order-theory.order-preserving-maps-posets funext univalence truncations +open import order-theory.posets funext univalence truncations ```
diff --git a/src/order-theory/transposition-inequalities-along-sections-of-order-preserving-maps-posets.lagda.md b/src/order-theory/transposition-inequalities-along-sections-of-order-preserving-maps-posets.lagda.md index 24e624588d..29755cc804 100644 --- a/src/order-theory/transposition-inequalities-along-sections-of-order-preserving-maps-posets.lagda.md +++ b/src/order-theory/transposition-inequalities-along-sections-of-order-preserving-maps-posets.lagda.md @@ -1,21 +1,29 @@ # Transposing inequalities in posets along sections of order-preserving maps ```agda -module order-theory.transposition-inequalities-along-sections-of-order-preserving-maps-posets where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.transposition-inequalities-along-sections-of-order-preserving-maps-posets + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.sections +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.sections funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import order-theory.order-preserving-maps-posets -open import order-theory.posets +open import order-theory.order-preserving-maps-posets funext univalence truncations +open import order-theory.posets funext univalence truncations ```
diff --git a/src/order-theory/upper-bounds-chains-posets.lagda.md b/src/order-theory/upper-bounds-chains-posets.lagda.md index 3da859e4e1..7b36540f55 100644 --- a/src/order-theory/upper-bounds-chains-posets.lagda.md +++ b/src/order-theory/upper-bounds-chains-posets.lagda.md @@ -1,21 +1,29 @@ # Upper bounds of chains in posets ```agda -module order-theory.upper-bounds-chains-posets where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.upper-bounds-chains-posets + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.existential-quantification +open import foundation.existential-quantification funext univalence truncations open import foundation.universe-levels open import foundation-core.function-types open import foundation-core.propositions -open import order-theory.chains-posets -open import order-theory.posets -open import order-theory.upper-bounds-posets +open import order-theory.chains-posets funext univalence truncations +open import order-theory.posets funext univalence truncations +open import order-theory.upper-bounds-posets funext univalence truncations ```
diff --git a/src/order-theory/upper-bounds-large-posets.lagda.md b/src/order-theory/upper-bounds-large-posets.lagda.md index bada6644c6..b873733a43 100644 --- a/src/order-theory/upper-bounds-large-posets.lagda.md +++ b/src/order-theory/upper-bounds-large-posets.lagda.md @@ -1,20 +1,29 @@ # Upper bounds in large posets ```agda -module order-theory.upper-bounds-large-posets where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.upper-bounds-large-posets + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.conjunction +open import foundation.conjunction funext univalence truncations open import foundation.dependent-pair-types -open import foundation.logical-equivalences -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.logical-equivalences funext +open import foundation.propositions funext univalence open import foundation.universe-levels -open import order-theory.dependent-products-large-posets -open import order-theory.large-posets +open import order-theory.dependent-products-large-posets funext univalence truncations +open import order-theory.large-posets funext univalence truncations ```
diff --git a/src/order-theory/upper-bounds-posets.lagda.md b/src/order-theory/upper-bounds-posets.lagda.md index 0193ab6052..539ba25ac3 100644 --- a/src/order-theory/upper-bounds-posets.lagda.md +++ b/src/order-theory/upper-bounds-posets.lagda.md @@ -1,17 +1,26 @@ # Upper bounds in posets ```agda -module order-theory.upper-bounds-posets where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.upper-bounds-posets + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.propositions funext univalence open import foundation.universe-levels -open import order-theory.posets +open import order-theory.posets funext univalence truncations ```
diff --git a/src/order-theory/upper-sets-large-posets.lagda.md b/src/order-theory/upper-sets-large-posets.lagda.md index f5c8d8ec1c..3750e305e6 100644 --- a/src/order-theory/upper-sets-large-posets.lagda.md +++ b/src/order-theory/upper-sets-large-posets.lagda.md @@ -1,7 +1,15 @@ # Upper sets of large posets ```agda -module order-theory.upper-sets-large-posets where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.upper-sets-large-posets + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,8 +17,8 @@ module order-theory.upper-sets-large-posets where ```agda open import foundation.universe-levels -open import order-theory.large-posets -open import order-theory.large-subposets +open import order-theory.large-posets funext univalence truncations +open import order-theory.large-subposets funext univalence truncations ```
diff --git a/src/order-theory/well-founded-relations.lagda.md b/src/order-theory/well-founded-relations.lagda.md index 7ae600f45c..7d461e5d80 100644 --- a/src/order-theory/well-founded-relations.lagda.md +++ b/src/order-theory/well-founded-relations.lagda.md @@ -1,21 +1,30 @@ # Well-founded relations ```agda -module order-theory.well-founded-relations where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.well-founded-relations + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.binary-relations +open import foundation.binary-relations funext univalence truncations open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.identity-types -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence open import foundation.universe-levels -open import order-theory.accessible-elements-relations -open import order-theory.preorders +open import order-theory.accessible-elements-relations funext univalence truncations +open import order-theory.preorders funext univalence truncations ```
diff --git a/src/order-theory/zorns-lemma.lagda.md b/src/order-theory/zorns-lemma.lagda.md index a2e403817a..2ab2743133 100644 --- a/src/order-theory/zorns-lemma.lagda.md +++ b/src/order-theory/zorns-lemma.lagda.md @@ -1,28 +1,37 @@ # Zorn's lemma ```agda -module order-theory.zorns-lemma where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module order-theory.zorns-lemma + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.existential-quantification -open import foundation.inhabited-types -open import foundation.law-of-excluded-middle -open import foundation.logical-equivalences -open import foundation.propositional-truncations +open import foundation.dependent-products-propositions funext +open import foundation.empty-types funext univalence truncations +open import foundation.existential-quantification funext univalence truncations +open import foundation.inhabited-types funext univalence truncations +open import foundation.law-of-excluded-middle funext univalence truncations +open import foundation.logical-equivalences funext +open import foundation.propositional-truncations funext univalence open import foundation.universe-levels open import foundation-core.coproduct-types open import foundation-core.propositions -open import order-theory.chains-posets -open import order-theory.posets -open import order-theory.top-elements-posets -open import order-theory.upper-bounds-chains-posets +open import order-theory.chains-posets funext univalence truncations +open import order-theory.posets funext univalence truncations +open import order-theory.top-elements-posets funext univalence truncations +open import order-theory.upper-bounds-chains-posets funext univalence truncations ```
diff --git a/src/organic-chemistry.lagda.md b/src/organic-chemistry.lagda.md index d4b75e9bc7..6046dd9ec1 100644 --- a/src/organic-chemistry.lagda.md +++ b/src/organic-chemistry.lagda.md @@ -3,14 +3,22 @@ ## Modules in the organic chemistry namespace ```agda -module organic-chemistry where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom -open import organic-chemistry.alcohols public -open import organic-chemistry.alkanes public -open import organic-chemistry.alkenes public -open import organic-chemistry.alkynes public -open import organic-chemistry.ethane public -open import organic-chemistry.hydrocarbons public -open import organic-chemistry.methane public -open import organic-chemistry.saturated-carbons public +module organic-chemistry + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where + +open import organic-chemistry.alcohols funext univalence truncations public +open import organic-chemistry.alkanes funext univalence truncations public +open import organic-chemistry.alkenes funext univalence truncations public +open import organic-chemistry.alkynes funext univalence truncations public +open import organic-chemistry.ethane funext univalence truncations public +open import organic-chemistry.hydrocarbons funext univalence truncations public +open import organic-chemistry.methane funext univalence truncations public +open import organic-chemistry.saturated-carbons funext univalence truncations public ``` diff --git a/src/organic-chemistry/alcohols.lagda.md b/src/organic-chemistry/alcohols.lagda.md index f28fc09806..d2a7b051ea 100644 --- a/src/organic-chemistry/alcohols.lagda.md +++ b/src/organic-chemistry/alcohols.lagda.md @@ -1,22 +1,30 @@ # Alcohols ```agda -module organic-chemistry.alcohols where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module organic-chemistry.alcohols + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.cartesian-product-types -open import foundation.decidable-subtypes +open import foundation.cartesian-product-types funext univalence +open import foundation.decidable-subtypes funext univalence truncations open import foundation.dependent-pair-types -open import foundation.negation -open import foundation.propositional-truncations +open import foundation.negation funext +open import foundation.propositional-truncations funext univalence open import foundation.universe-levels -open import foundation.unordered-pairs +open import foundation.unordered-pairs funext univalence truncations -open import organic-chemistry.hydrocarbons -open import organic-chemistry.saturated-carbons +open import organic-chemistry.hydrocarbons funext univalence truncations +open import organic-chemistry.saturated-carbons funext univalence truncations ```
diff --git a/src/organic-chemistry/alkanes.lagda.md b/src/organic-chemistry/alkanes.lagda.md index ae5bc42c05..3249ec34a9 100644 --- a/src/organic-chemistry/alkanes.lagda.md +++ b/src/organic-chemistry/alkanes.lagda.md @@ -1,7 +1,15 @@ # Alkanes ```agda -module organic-chemistry.alkanes where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module organic-chemistry.alkanes + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,8 +17,8 @@ module organic-chemistry.alkanes where ```agda open import foundation.universe-levels -open import organic-chemistry.hydrocarbons -open import organic-chemistry.saturated-carbons +open import organic-chemistry.hydrocarbons funext univalence truncations +open import organic-chemistry.saturated-carbons funext univalence truncations ```
diff --git a/src/organic-chemistry/alkenes.lagda.md b/src/organic-chemistry/alkenes.lagda.md index 66a563f86e..c2c1d8325b 100644 --- a/src/organic-chemistry/alkenes.lagda.md +++ b/src/organic-chemistry/alkenes.lagda.md @@ -1,7 +1,15 @@ # Alkenes ```agda -module organic-chemistry.alkenes where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module organic-chemistry.alkenes + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,13 +18,13 @@ module organic-chemistry.alkenes where open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.embeddings +open import foundation.embeddings funext open import foundation.universe-levels -open import organic-chemistry.hydrocarbons -open import organic-chemistry.saturated-carbons +open import organic-chemistry.hydrocarbons funext univalence truncations +open import organic-chemistry.saturated-carbons funext univalence truncations -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.finite-types funext univalence truncations ```
diff --git a/src/organic-chemistry/alkynes.lagda.md b/src/organic-chemistry/alkynes.lagda.md index 80956732ce..d96cc1888c 100644 --- a/src/organic-chemistry/alkynes.lagda.md +++ b/src/organic-chemistry/alkynes.lagda.md @@ -1,7 +1,15 @@ # Alkynes ```agda -module organic-chemistry.alkynes where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module organic-chemistry.alkynes + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,13 +18,13 @@ module organic-chemistry.alkynes where open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.embeddings +open import foundation.embeddings funext open import foundation.universe-levels -open import organic-chemistry.hydrocarbons -open import organic-chemistry.saturated-carbons +open import organic-chemistry.hydrocarbons funext univalence truncations +open import organic-chemistry.saturated-carbons funext univalence truncations -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.finite-types funext univalence truncations ```
diff --git a/src/organic-chemistry/ethane.lagda.md b/src/organic-chemistry/ethane.lagda.md index 13bda1ab23..28665313bc 100644 --- a/src/organic-chemistry/ethane.lagda.md +++ b/src/organic-chemistry/ethane.lagda.md @@ -1,45 +1,53 @@ # Ethane ```agda -module organic-chemistry.ethane where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module organic-chemistry.ethane + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.inequality-natural-numbers funext univalence truncations -open import finite-group-theory.tetrahedra-in-3-space +open import finite-group-theory.tetrahedra-in-3-space funext univalence truncations -open import foundation.coproduct-types -open import foundation.decidable-propositions -open import foundation.decidable-types +open import foundation.coproduct-types funext univalence truncations +open import foundation.decidable-propositions funext univalence truncations +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.empty-types -open import foundation.equality-dependent-pair-types -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.sets -open import foundation.torsorial-type-families +open import foundation.dependent-products-propositions funext +open import foundation.embeddings funext +open import foundation.empty-types funext univalence truncations +open import foundation.equality-dependent-pair-types funext +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence +open import foundation.torsorial-type-families funext univalence truncations open import foundation.transport-along-identifications open import foundation.unit-type -open import foundation.univalence +open import foundation.univalence funext univalence open import foundation.universe-levels -open import foundation.unordered-pairs +open import foundation.unordered-pairs funext univalence truncations -open import graph-theory.finite-graphs -open import graph-theory.walks-undirected-graphs +open import graph-theory.finite-graphs funext univalence truncations +open import graph-theory.walks-undirected-graphs funext univalence truncations -open import organic-chemistry.alkanes -open import organic-chemistry.hydrocarbons +open import organic-chemistry.alkanes funext univalence truncations +open import organic-chemistry.hydrocarbons funext univalence truncations -open import univalent-combinatorics.2-element-types -open import univalent-combinatorics.counting -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.2-element-types funext univalence truncations +open import univalent-combinatorics.counting funext univalence truncations +open import univalent-combinatorics.finite-types funext univalence truncations +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/organic-chemistry/hydrocarbons.lagda.md b/src/organic-chemistry/hydrocarbons.lagda.md index 6012140cf2..3afd7b8dc6 100644 --- a/src/organic-chemistry/hydrocarbons.lagda.md +++ b/src/organic-chemistry/hydrocarbons.lagda.md @@ -1,27 +1,35 @@ # Hydrocarbons ```agda -module organic-chemistry.hydrocarbons where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module organic-chemistry.hydrocarbons + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.inequality-natural-numbers funext univalence truncations -open import finite-group-theory.tetrahedra-in-3-space +open import finite-group-theory.tetrahedra-in-3-space funext univalence truncations -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.negation +open import foundation.embeddings funext +open import foundation.negation funext open import foundation.universe-levels -open import foundation.unordered-pairs +open import foundation.unordered-pairs funext univalence truncations -open import graph-theory.connected-undirected-graphs -open import graph-theory.finite-graphs +open import graph-theory.connected-undirected-graphs funext univalence truncations +open import graph-theory.finite-graphs funext univalence truncations -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.finite-types funext univalence truncations ```
diff --git a/src/organic-chemistry/methane.lagda.md b/src/organic-chemistry/methane.lagda.md index 806fb0cbc9..7880adb883 100644 --- a/src/organic-chemistry/methane.lagda.md +++ b/src/organic-chemistry/methane.lagda.md @@ -1,30 +1,38 @@ # Methane ```agda -module organic-chemistry.methane where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module organic-chemistry.methane + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.inequality-natural-numbers funext univalence truncations -open import finite-group-theory.tetrahedra-in-3-space +open import finite-group-theory.tetrahedra-in-3-space funext univalence truncations open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.identity-types -open import foundation.propositional-truncations +open import foundation.empty-types funext univalence truncations +open import foundation.identity-types funext +open import foundation.propositional-truncations funext univalence open import foundation.unit-type open import foundation.universe-levels -open import graph-theory.walks-undirected-graphs +open import graph-theory.walks-undirected-graphs funext univalence truncations -open import organic-chemistry.alkanes -open import organic-chemistry.hydrocarbons +open import organic-chemistry.alkanes funext univalence truncations +open import organic-chemistry.hydrocarbons funext univalence truncations -open import univalent-combinatorics.counting -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.counting funext univalence truncations +open import univalent-combinatorics.finite-types funext univalence truncations ```
diff --git a/src/organic-chemistry/saturated-carbons.lagda.md b/src/organic-chemistry/saturated-carbons.lagda.md index f214d5aa80..52802f1cdd 100644 --- a/src/organic-chemistry/saturated-carbons.lagda.md +++ b/src/organic-chemistry/saturated-carbons.lagda.md @@ -1,21 +1,30 @@ # Saturated carbons ```agda -module organic-chemistry.saturated-carbons where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module organic-chemistry.saturated-carbons + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.propositional-truncations -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence open import foundation.universe-levels -open import foundation.unordered-pairs +open import foundation.unordered-pairs funext univalence truncations -open import organic-chemistry.hydrocarbons +open import organic-chemistry.hydrocarbons funext univalence truncations -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.finite-types funext univalence truncations ```
diff --git a/src/orthogonal-factorization-systems.lagda.md b/src/orthogonal-factorization-systems.lagda.md index a167d57d4a..6edbec997e 100644 --- a/src/orthogonal-factorization-systems.lagda.md +++ b/src/orthogonal-factorization-systems.lagda.md @@ -7,71 +7,79 @@ ## Modules in the orthogonal factorization systems namespace ```agda -module orthogonal-factorization-systems where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom -open import orthogonal-factorization-systems.cd-structures public -open import orthogonal-factorization-systems.cellular-maps public -open import orthogonal-factorization-systems.closed-modalities public -open import orthogonal-factorization-systems.continuation-modalities public -open import orthogonal-factorization-systems.double-lifts-families-of-elements public -open import orthogonal-factorization-systems.double-negation-sheaves public -open import orthogonal-factorization-systems.extensions-double-lifts-families-of-elements public -open import orthogonal-factorization-systems.extensions-lifts-families-of-elements public -open import orthogonal-factorization-systems.extensions-maps public -open import orthogonal-factorization-systems.factorization-operations public -open import orthogonal-factorization-systems.factorization-operations-function-classes public -open import orthogonal-factorization-systems.factorization-operations-global-function-classes public -open import orthogonal-factorization-systems.factorizations-of-maps public -open import orthogonal-factorization-systems.factorizations-of-maps-function-classes public -open import orthogonal-factorization-systems.factorizations-of-maps-global-function-classes public -open import orthogonal-factorization-systems.families-of-types-local-at-maps public -open import orthogonal-factorization-systems.fiberwise-orthogonal-maps public -open import orthogonal-factorization-systems.function-classes public -open import orthogonal-factorization-systems.functoriality-higher-modalities public -open import orthogonal-factorization-systems.functoriality-localizations-at-global-subuniverses public -open import orthogonal-factorization-systems.functoriality-pullback-hom public -open import orthogonal-factorization-systems.functoriality-reflective-global-subuniverses public -open import orthogonal-factorization-systems.global-function-classes public -open import orthogonal-factorization-systems.higher-modalities public -open import orthogonal-factorization-systems.identity-modality public -open import orthogonal-factorization-systems.large-lawvere-tierney-topologies public -open import orthogonal-factorization-systems.lawvere-tierney-topologies public -open import orthogonal-factorization-systems.lifting-operations public -open import orthogonal-factorization-systems.lifting-structures-on-squares public -open import orthogonal-factorization-systems.lifts-families-of-elements public -open import orthogonal-factorization-systems.lifts-maps public -open import orthogonal-factorization-systems.localizations-at-global-subuniverses public -open import orthogonal-factorization-systems.localizations-at-maps public -open import orthogonal-factorization-systems.localizations-at-subuniverses public -open import orthogonal-factorization-systems.locally-small-modal-operators public -open import orthogonal-factorization-systems.maps-local-at-maps public -open import orthogonal-factorization-systems.mere-lifting-properties public -open import orthogonal-factorization-systems.modal-induction public -open import orthogonal-factorization-systems.modal-operators public -open import orthogonal-factorization-systems.modal-subuniverse-induction public -open import orthogonal-factorization-systems.null-families-of-types public -open import orthogonal-factorization-systems.null-maps public -open import orthogonal-factorization-systems.null-types public -open import orthogonal-factorization-systems.open-modalities public -open import orthogonal-factorization-systems.orthogonal-factorization-systems public -open import orthogonal-factorization-systems.orthogonal-maps public -open import orthogonal-factorization-systems.precomposition-lifts-families-of-elements public -open import orthogonal-factorization-systems.pullback-hom public -open import orthogonal-factorization-systems.raise-modalities public -open import orthogonal-factorization-systems.reflective-global-subuniverses public -open import orthogonal-factorization-systems.reflective-modalities public -open import orthogonal-factorization-systems.reflective-subuniverses public +module orthogonal-factorization-systems + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where + +open import orthogonal-factorization-systems.cd-structures funext univalence truncations public +open import orthogonal-factorization-systems.cellular-maps funext univalence truncations public +open import orthogonal-factorization-systems.closed-modalities funext univalence truncations public +open import orthogonal-factorization-systems.continuation-modalities funext univalence truncations public +open import orthogonal-factorization-systems.double-lifts-families-of-elements funext public +open import orthogonal-factorization-systems.double-negation-sheaves funext univalence truncations public +open import orthogonal-factorization-systems.extensions-double-lifts-families-of-elements funext public +open import orthogonal-factorization-systems.extensions-lifts-families-of-elements funext public +open import orthogonal-factorization-systems.extensions-maps funext univalence public +open import orthogonal-factorization-systems.factorization-operations funext univalence truncations public +open import orthogonal-factorization-systems.factorization-operations-function-classes funext univalence truncations public +open import orthogonal-factorization-systems.factorization-operations-global-function-classes funext univalence truncations public +open import orthogonal-factorization-systems.factorizations-of-maps funext univalence truncations public +open import orthogonal-factorization-systems.factorizations-of-maps-function-classes funext univalence truncations public +open import orthogonal-factorization-systems.factorizations-of-maps-global-function-classes funext univalence truncations public +open import orthogonal-factorization-systems.families-of-types-local-at-maps funext univalence truncations public +open import orthogonal-factorization-systems.fiberwise-orthogonal-maps funext univalence truncations public +open import orthogonal-factorization-systems.function-classes funext univalence truncations public +open import orthogonal-factorization-systems.functoriality-higher-modalities funext univalence truncations public +open import orthogonal-factorization-systems.functoriality-localizations-at-global-subuniverses funext univalence truncations public +open import orthogonal-factorization-systems.functoriality-pullback-hom funext univalence truncations public +open import orthogonal-factorization-systems.functoriality-reflective-global-subuniverses funext univalence truncations public +open import orthogonal-factorization-systems.global-function-classes funext univalence truncations public +open import orthogonal-factorization-systems.higher-modalities funext univalence truncations public +open import orthogonal-factorization-systems.identity-modality funext univalence truncations public +open import orthogonal-factorization-systems.large-lawvere-tierney-topologies funext univalence truncations public +open import orthogonal-factorization-systems.lawvere-tierney-topologies funext univalence truncations public +open import orthogonal-factorization-systems.lifting-operations funext univalence truncations public +open import orthogonal-factorization-systems.lifting-structures-on-squares funext univalence truncations public +open import orthogonal-factorization-systems.lifts-families-of-elements funext public +open import orthogonal-factorization-systems.lifts-maps funext univalence truncations public +open import orthogonal-factorization-systems.localizations-at-global-subuniverses funext univalence truncations public +open import orthogonal-factorization-systems.localizations-at-maps funext univalence truncations public +open import orthogonal-factorization-systems.localizations-at-subuniverses funext univalence truncations public +open import orthogonal-factorization-systems.locally-small-modal-operators funext univalence truncations public +open import orthogonal-factorization-systems.maps-local-at-maps funext univalence truncations public +open import orthogonal-factorization-systems.mere-lifting-properties funext univalence truncations public +open import orthogonal-factorization-systems.modal-induction funext univalence truncations public +open import orthogonal-factorization-systems.modal-operators funext univalence truncations public +open import orthogonal-factorization-systems.modal-subuniverse-induction funext univalence truncations public +open import orthogonal-factorization-systems.null-families-of-types funext univalence truncations public +open import orthogonal-factorization-systems.null-maps funext univalence truncations public +open import orthogonal-factorization-systems.null-types funext univalence truncations public +open import orthogonal-factorization-systems.open-modalities funext univalence truncations public +open import orthogonal-factorization-systems.orthogonal-factorization-systems funext univalence truncations public +open import orthogonal-factorization-systems.orthogonal-maps funext univalence truncations public +open import orthogonal-factorization-systems.precomposition-lifts-families-of-elements funext univalence public +open import orthogonal-factorization-systems.pullback-hom funext univalence truncations public +open import orthogonal-factorization-systems.raise-modalities funext univalence truncations public +open import orthogonal-factorization-systems.reflective-global-subuniverses funext univalence truncations public +open import orthogonal-factorization-systems.reflective-modalities funext univalence truncations public +open import orthogonal-factorization-systems.reflective-subuniverses funext univalence truncations public open import orthogonal-factorization-systems.regular-cd-structures public -open import orthogonal-factorization-systems.sigma-closed-modalities public -open import orthogonal-factorization-systems.sigma-closed-reflective-modalities public -open import orthogonal-factorization-systems.sigma-closed-reflective-subuniverses public -open import orthogonal-factorization-systems.stable-orthogonal-factorization-systems public -open import orthogonal-factorization-systems.types-colocal-at-maps public -open import orthogonal-factorization-systems.types-local-at-maps public -open import orthogonal-factorization-systems.types-separated-at-maps public -open import orthogonal-factorization-systems.uniquely-eliminating-modalities public -open import orthogonal-factorization-systems.universal-property-localizations-at-global-subuniverses public -open import orthogonal-factorization-systems.wide-function-classes public -open import orthogonal-factorization-systems.wide-global-function-classes public -open import orthogonal-factorization-systems.zero-modality public +open import orthogonal-factorization-systems.sigma-closed-modalities funext univalence truncations public +open import orthogonal-factorization-systems.sigma-closed-reflective-modalities funext univalence truncations public +open import orthogonal-factorization-systems.sigma-closed-reflective-subuniverses funext univalence truncations public +open import orthogonal-factorization-systems.stable-orthogonal-factorization-systems funext univalence truncations public +open import orthogonal-factorization-systems.types-colocal-at-maps funext univalence truncations public +open import orthogonal-factorization-systems.types-local-at-maps funext univalence truncations public +open import orthogonal-factorization-systems.types-separated-at-maps funext univalence truncations public +open import orthogonal-factorization-systems.uniquely-eliminating-modalities funext univalence truncations public +open import orthogonal-factorization-systems.universal-property-localizations-at-global-subuniverses funext univalence truncations public +open import orthogonal-factorization-systems.wide-function-classes funext univalence truncations public +open import orthogonal-factorization-systems.wide-global-function-classes funext univalence truncations public +open import orthogonal-factorization-systems.zero-modality funext univalence truncations public ``` diff --git a/src/orthogonal-factorization-systems/cd-structures.lagda.md b/src/orthogonal-factorization-systems/cd-structures.lagda.md index d33d5a3d4a..f7b3d2281c 100644 --- a/src/orthogonal-factorization-systems/cd-structures.lagda.md +++ b/src/orthogonal-factorization-systems/cd-structures.lagda.md @@ -1,15 +1,24 @@ # Cd-structures ```agda -module orthogonal-factorization-systems.cd-structures where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module orthogonal-factorization-systems.cd-structures + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.morphisms-arrows -open import foundation.propositions -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.morphisms-arrows funext +open import foundation.propositions funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels ``` diff --git a/src/orthogonal-factorization-systems/cellular-maps.lagda.md b/src/orthogonal-factorization-systems/cellular-maps.lagda.md index 0bcd3a38aa..2c26267843 100644 --- a/src/orthogonal-factorization-systems/cellular-maps.lagda.md +++ b/src/orthogonal-factorization-systems/cellular-maps.lagda.md @@ -1,17 +1,25 @@ # Cellular maps ```agda -module orthogonal-factorization-systems.cellular-maps where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module orthogonal-factorization-systems.cellular-maps + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.connected-maps +open import foundation.connected-maps funext univalence truncations open import foundation.truncation-levels open import foundation.universe-levels -open import orthogonal-factorization-systems.mere-lifting-properties +open import orthogonal-factorization-systems.mere-lifting-properties funext univalence truncations ```
diff --git a/src/orthogonal-factorization-systems/closed-modalities.lagda.md b/src/orthogonal-factorization-systems/closed-modalities.lagda.md index c42bfe9572..ed3286104b 100644 --- a/src/orthogonal-factorization-systems/closed-modalities.lagda.md +++ b/src/orthogonal-factorization-systems/closed-modalities.lagda.md @@ -1,29 +1,39 @@ # The closed modalities ```agda -module orthogonal-factorization-systems.closed-modalities where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module orthogonal-factorization-systems.closed-modalities + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.contractible-maps -open import foundation.contractible-types +open import foundation.contractible-maps funext +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.torsorial-type-families +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.torsorial-type-families funext univalence truncations open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels -open import orthogonal-factorization-systems.modal-operators -open import orthogonal-factorization-systems.reflective-subuniverses -open import orthogonal-factorization-systems.sigma-closed-reflective-subuniverses +open import orthogonal-factorization-systems.modal-operators funext univalence truncations +open import orthogonal-factorization-systems.reflective-subuniverses funext univalence truncations +open import orthogonal-factorization-systems.sigma-closed-reflective-subuniverses funext univalence truncations -open import synthetic-homotopy-theory.joins-of-types +open import synthetic-homotopy-theory.joins-of-types funext univalence truncations ```
diff --git a/src/orthogonal-factorization-systems/continuation-modalities.lagda.md b/src/orthogonal-factorization-systems/continuation-modalities.lagda.md index 0ed70bca76..01b6262eef 100644 --- a/src/orthogonal-factorization-systems/continuation-modalities.lagda.md +++ b/src/orthogonal-factorization-systems/continuation-modalities.lagda.md @@ -1,37 +1,36 @@ # Continuation modalities ```agda -module orthogonal-factorization-systems.continuation-modalities where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module orthogonal-factorization-systems.continuation-modalities + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types -open import foundation.continuations +open import foundation.cartesian-product-types funext univalence +open import foundation.continuations funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equality-cartesian-product-types -open import foundation.equivalences -open import foundation.evaluation-functions -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.propositions -open import foundation.retractions -open import foundation.sections +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.logical-equivalences funext +open import foundation.propositions funext univalence open import foundation.transport-along-identifications -open import foundation.type-arithmetic-cartesian-product-types open import foundation.unit-type -open import foundation.universal-property-cartesian-product-types -open import foundation.universal-property-equivalences open import foundation.universe-levels -open import orthogonal-factorization-systems.large-lawvere-tierney-topologies -open import orthogonal-factorization-systems.modal-operators -open import orthogonal-factorization-systems.types-local-at-maps -open import orthogonal-factorization-systems.uniquely-eliminating-modalities +open import orthogonal-factorization-systems.large-lawvere-tierney-topologies funext univalence truncations +open import orthogonal-factorization-systems.modal-operators funext univalence truncations +open import orthogonal-factorization-systems.types-local-at-maps funext univalence truncations +open import orthogonal-factorization-systems.uniquely-eliminating-modalities funext univalence truncations ```
diff --git a/src/orthogonal-factorization-systems/double-lifts-families-of-elements.lagda.md b/src/orthogonal-factorization-systems/double-lifts-families-of-elements.lagda.md index 4c248d4992..0b98980800 100644 --- a/src/orthogonal-factorization-systems/double-lifts-families-of-elements.lagda.md +++ b/src/orthogonal-factorization-systems/double-lifts-families-of-elements.lagda.md @@ -1,7 +1,11 @@ # Double lifts of families of elements ```agda -module orthogonal-factorization-systems.double-lifts-families-of-elements where +open import foundation.function-extensionality-axiom + +module orthogonal-factorization-systems.double-lifts-families-of-elements + (funext : function-extensionality) + where ```
Imports @@ -9,7 +13,7 @@ module orthogonal-factorization-systems.double-lifts-families-of-elements where ```agda open import foundation.universe-levels -open import orthogonal-factorization-systems.lifts-families-of-elements +open import orthogonal-factorization-systems.lifts-families-of-elements funext ```
diff --git a/src/orthogonal-factorization-systems/double-negation-sheaves.lagda.md b/src/orthogonal-factorization-systems/double-negation-sheaves.lagda.md index eb2cbcdba9..1e7ee2f094 100644 --- a/src/orthogonal-factorization-systems/double-negation-sheaves.lagda.md +++ b/src/orthogonal-factorization-systems/double-negation-sheaves.lagda.md @@ -1,28 +1,38 @@ # Double negation sheaves ```agda -module orthogonal-factorization-systems.double-negation-sheaves where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module orthogonal-factorization-systems.double-negation-sheaves + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.contractible-types +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.double-negation-stable-propositions -open import foundation.empty-types -open import foundation.irrefutable-propositions -open import foundation.logical-equivalences -open import foundation.negation +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.double-negation-stable-propositions funext univalence truncations +open import foundation.empty-types funext univalence truncations +open import foundation.irrefutable-propositions funext univalence truncations +open import foundation.logical-equivalences funext +open import foundation.negation funext open import foundation.type-arithmetic-cartesian-product-types -open import foundation.universal-property-coproduct-types +open import foundation.universal-property-coproduct-types funext open import foundation.universe-levels open import foundation-core.equivalences open import foundation-core.function-types open import foundation-core.propositions -open import orthogonal-factorization-systems.null-types +open import orthogonal-factorization-systems.null-types funext univalence truncations ```
diff --git a/src/orthogonal-factorization-systems/extensions-double-lifts-families-of-elements.lagda.md b/src/orthogonal-factorization-systems/extensions-double-lifts-families-of-elements.lagda.md index c590c46263..ca2185f463 100644 --- a/src/orthogonal-factorization-systems/extensions-double-lifts-families-of-elements.lagda.md +++ b/src/orthogonal-factorization-systems/extensions-double-lifts-families-of-elements.lagda.md @@ -17,8 +17,8 @@ open import foundation-core.function-types open import foundation-core.homotopies open import foundation-core.identity-types -open import orthogonal-factorization-systems.double-lifts-families-of-elements -open import orthogonal-factorization-systems.lifts-families-of-elements +open import orthogonal-factorization-systems.double-lifts-families-of-elements funext +open import orthogonal-factorization-systems.lifts-families-of-elements funext ```
@@ -60,7 +60,10 @@ elements `a : (i : I) → A i` induces an evaluation map given by `c ↦ (λ i → c i (a i) (b i))`. ```agda +open import foundation.function-extensionality-axiom + module _ + (funext : function-extensionality) {l1 l2 l3 l4 : Level} {I : UU l1} {A : I → UU l2} {B : (i : I) → A i → UU l3} {C : (i : I) (x : A i) → B i x → UU l4} {a : (i : I) → A i} (b : dependent-lift-family-of-elements B a) diff --git a/src/orthogonal-factorization-systems/extensions-lifts-families-of-elements.lagda.md b/src/orthogonal-factorization-systems/extensions-lifts-families-of-elements.lagda.md index 8766921e92..85555e1cd1 100644 --- a/src/orthogonal-factorization-systems/extensions-lifts-families-of-elements.lagda.md +++ b/src/orthogonal-factorization-systems/extensions-lifts-families-of-elements.lagda.md @@ -17,7 +17,7 @@ open import foundation-core.function-types open import foundation-core.homotopies open import foundation-core.identity-types -open import orthogonal-factorization-systems.lifts-families-of-elements +open import orthogonal-factorization-systems.lifts-families-of-elements funext ```
@@ -66,7 +66,10 @@ Any family of elements `a : (i : I) → A i` induces an evaluation map defined by `b ↦ (λ i → b i (a i))`. ```agda +open import foundation.function-extensionality-axiom + module _ + (funext : function-extensionality) {l1 l2 l3 : Level} {I : UU l1} {A : I → UU l2} {B : (i : I) → A i → UU l3} (a : (i : I) → A i) where diff --git a/src/orthogonal-factorization-systems/extensions-maps.lagda.md b/src/orthogonal-factorization-systems/extensions-maps.lagda.md index ccdc296bd0..a2aed167c4 100644 --- a/src/orthogonal-factorization-systems/extensions-maps.lagda.md +++ b/src/orthogonal-factorization-systems/extensions-maps.lagda.md @@ -1,7 +1,13 @@ # Extensions of maps ```agda -module orthogonal-factorization-systems.extensions-maps where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module orthogonal-factorization-systems.extensions-maps + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports @@ -9,24 +15,27 @@ module orthogonal-factorization-systems.extensions-maps where ```agda open import foundation.action-on-identifications-dependent-functions open import foundation.action-on-identifications-functions -open import foundation.contractible-types +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-function-types -open import foundation.functoriality-dependent-pair-types +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.dependent-products-truncated-types funext +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-function-types funext univalence +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types -open import foundation.monomorphisms -open import foundation.postcomposition-functions -open import foundation.propositions -open import foundation.sets +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext +open import foundation.monomorphisms funext univalence +open import foundation.postcomposition-functions funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence open import foundation.structure-identity-principle open import foundation.transport-along-identifications -open import foundation.truncated-types +open import foundation.truncated-types funext univalence open import foundation.truncation-levels open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels diff --git a/src/orthogonal-factorization-systems/factorization-operations-function-classes.lagda.md b/src/orthogonal-factorization-systems/factorization-operations-function-classes.lagda.md index 4f01d8a991..f0579f4f49 100644 --- a/src/orthogonal-factorization-systems/factorization-operations-function-classes.lagda.md +++ b/src/orthogonal-factorization-systems/factorization-operations-function-classes.lagda.md @@ -1,36 +1,47 @@ # Factorization operations into function classes ```agda -module orthogonal-factorization-systems.factorization-operations-function-classes where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module orthogonal-factorization-systems.factorization-operations-function-classes + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.cartesian-product-types -open import foundation.commuting-squares-of-maps -open import foundation.contractible-types +open import foundation.cartesian-product-types funext univalence +open import foundation.commuting-squares-of-maps funext univalence +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-cartesian-product-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.inhabited-types -open import foundation.iterated-dependent-product-types -open import foundation.propositions -open import foundation.subtypes +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.inhabited-types funext univalence truncations +open import foundation.iterated-dependent-product-types funext +open import foundation.propositions funext univalence +open import foundation.subtypes funext univalence truncations +open import foundation.telescopes open import foundation.type-arithmetic-cartesian-product-types open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import orthogonal-factorization-systems.factorizations-of-maps -open import orthogonal-factorization-systems.factorizations-of-maps-function-classes -open import orthogonal-factorization-systems.function-classes -open import orthogonal-factorization-systems.lifting-structures-on-squares +open import orthogonal-factorization-systems.factorizations-of-maps funext univalence truncations +open import orthogonal-factorization-systems.factorizations-of-maps-function-classes funext univalence truncations +open import orthogonal-factorization-systems.function-classes funext univalence truncations +open import orthogonal-factorization-systems.lifting-structures-on-squares funext univalence truncations ```
diff --git a/src/orthogonal-factorization-systems/factorization-operations-global-function-classes.lagda.md b/src/orthogonal-factorization-systems/factorization-operations-global-function-classes.lagda.md index a372c14a56..e7b142132b 100644 --- a/src/orthogonal-factorization-systems/factorization-operations-global-function-classes.lagda.md +++ b/src/orthogonal-factorization-systems/factorization-operations-global-function-classes.lagda.md @@ -1,18 +1,27 @@ # Factorization operations into global function classes ```agda -module orthogonal-factorization-systems.factorization-operations-global-function-classes where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module orthogonal-factorization-systems.factorization-operations-global-function-classes + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.propositions funext univalence open import foundation.universe-levels -open import orthogonal-factorization-systems.factorization-operations-function-classes -open import orthogonal-factorization-systems.factorizations-of-maps-global-function-classes -open import orthogonal-factorization-systems.global-function-classes +open import orthogonal-factorization-systems.factorization-operations-function-classes funext univalence truncations +open import orthogonal-factorization-systems.factorizations-of-maps-global-function-classes funext univalence truncations +open import orthogonal-factorization-systems.global-function-classes funext univalence truncations ```
diff --git a/src/orthogonal-factorization-systems/factorization-operations.lagda.md b/src/orthogonal-factorization-systems/factorization-operations.lagda.md index 9262dfd081..5400040c20 100644 --- a/src/orthogonal-factorization-systems/factorization-operations.lagda.md +++ b/src/orthogonal-factorization-systems/factorization-operations.lagda.md @@ -1,7 +1,15 @@ # Factorization operations ```agda -module orthogonal-factorization-systems.factorization-operations where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module orthogonal-factorization-systems.factorization-operations + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,7 +17,7 @@ module orthogonal-factorization-systems.factorization-operations where ```agda open import foundation.universe-levels -open import orthogonal-factorization-systems.factorizations-of-maps +open import orthogonal-factorization-systems.factorizations-of-maps funext univalence truncations ```
diff --git a/src/orthogonal-factorization-systems/factorizations-of-maps-function-classes.lagda.md b/src/orthogonal-factorization-systems/factorizations-of-maps-function-classes.lagda.md index f4eee03050..306e54466f 100644 --- a/src/orthogonal-factorization-systems/factorizations-of-maps-function-classes.lagda.md +++ b/src/orthogonal-factorization-systems/factorizations-of-maps-function-classes.lagda.md @@ -1,34 +1,44 @@ # Factorizations of maps into function classes ```agda -module orthogonal-factorization-systems.factorizations-of-maps-function-classes where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module orthogonal-factorization-systems.factorizations-of-maps-function-classes + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.contractible-types +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types -open import foundation.propositions -open import foundation.retractions -open import foundation.sections +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.retractions funext +open import foundation.sections funext open import foundation.structure-identity-principle open import foundation.subtype-identity-principle -open import foundation.torsorial-type-families -open import foundation.univalence +open import foundation.torsorial-type-families funext univalence truncations +open import foundation.univalence funext univalence open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import orthogonal-factorization-systems.factorizations-of-maps -open import orthogonal-factorization-systems.function-classes -open import orthogonal-factorization-systems.global-function-classes +open import orthogonal-factorization-systems.factorizations-of-maps funext univalence truncations +open import orthogonal-factorization-systems.function-classes funext univalence truncations +open import orthogonal-factorization-systems.global-function-classes funext univalence truncations ```
diff --git a/src/orthogonal-factorization-systems/factorizations-of-maps-global-function-classes.lagda.md b/src/orthogonal-factorization-systems/factorizations-of-maps-global-function-classes.lagda.md index 9945116577..cf00d732e4 100644 --- a/src/orthogonal-factorization-systems/factorizations-of-maps-global-function-classes.lagda.md +++ b/src/orthogonal-factorization-systems/factorizations-of-maps-global-function-classes.lagda.md @@ -1,34 +1,44 @@ # Factorizations of maps into global function classes ```agda -module orthogonal-factorization-systems.factorizations-of-maps-global-function-classes where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module orthogonal-factorization-systems.factorizations-of-maps-global-function-classes + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.contractible-types +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types -open import foundation.propositions -open import foundation.retractions -open import foundation.sections +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.retractions funext +open import foundation.sections funext open import foundation.structure-identity-principle -open import foundation.torsorial-type-families -open import foundation.univalence +open import foundation.torsorial-type-families funext univalence truncations +open import foundation.univalence funext univalence open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import orthogonal-factorization-systems.factorizations-of-maps -open import orthogonal-factorization-systems.factorizations-of-maps-function-classes -open import orthogonal-factorization-systems.function-classes -open import orthogonal-factorization-systems.global-function-classes +open import orthogonal-factorization-systems.factorizations-of-maps funext univalence truncations +open import orthogonal-factorization-systems.factorizations-of-maps-function-classes funext univalence truncations +open import orthogonal-factorization-systems.function-classes funext univalence truncations +open import orthogonal-factorization-systems.global-function-classes funext univalence truncations ```
diff --git a/src/orthogonal-factorization-systems/factorizations-of-maps.lagda.md b/src/orthogonal-factorization-systems/factorizations-of-maps.lagda.md index a4266abdd5..6cffaa81db 100644 --- a/src/orthogonal-factorization-systems/factorizations-of-maps.lagda.md +++ b/src/orthogonal-factorization-systems/factorizations-of-maps.lagda.md @@ -1,24 +1,32 @@ # Factorizations of maps ```agda -module orthogonal-factorization-systems.factorizations-of-maps where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module orthogonal-factorization-systems.factorizations-of-maps + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types +open import foundation.equivalences funext +open import foundation.function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies +open import foundation.homotopies funext open import foundation.homotopy-algebra -open import foundation.homotopy-induction -open import foundation.identity-types -open import foundation.retracts-of-types +open import foundation.homotopy-induction funext +open import foundation.identity-types funext +open import foundation.retracts-of-types funext univalence open import foundation.structure-identity-principle -open import foundation.torsorial-type-families -open import foundation.univalence +open import foundation.torsorial-type-families funext univalence truncations +open import foundation.univalence funext univalence open import foundation.universe-levels open import foundation.whiskering-homotopies-composition ``` diff --git a/src/orthogonal-factorization-systems/families-of-types-local-at-maps.lagda.md b/src/orthogonal-factorization-systems/families-of-types-local-at-maps.lagda.md index 0d79431a42..038ffaa77a 100644 --- a/src/orthogonal-factorization-systems/families-of-types-local-at-maps.lagda.md +++ b/src/orthogonal-factorization-systems/families-of-types-local-at-maps.lagda.md @@ -1,20 +1,29 @@ # Families of types local at a map ```agda -module orthogonal-factorization-systems.families-of-types-local-at-maps where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module orthogonal-factorization-systems.families-of-types-local-at-maps + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.precomposition-functions -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.precomposition-functions funext +open import foundation.propositions funext univalence open import foundation.universe-levels -open import orthogonal-factorization-systems.orthogonal-maps -open import orthogonal-factorization-systems.types-local-at-maps +open import orthogonal-factorization-systems.orthogonal-maps funext univalence truncations +open import orthogonal-factorization-systems.types-local-at-maps funext univalence truncations ```
diff --git a/src/orthogonal-factorization-systems/fiberwise-orthogonal-maps.lagda.md b/src/orthogonal-factorization-systems/fiberwise-orthogonal-maps.lagda.md index 2cc4966422..6fb82c449c 100644 --- a/src/orthogonal-factorization-systems/fiberwise-orthogonal-maps.lagda.md +++ b/src/orthogonal-factorization-systems/fiberwise-orthogonal-maps.lagda.md @@ -1,54 +1,35 @@ # Fiberwise orthogonal maps ```agda -module orthogonal-factorization-systems.fiberwise-orthogonal-maps where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module orthogonal-factorization-systems.fiberwise-orthogonal-maps + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.action-on-identifications-functions -open import foundation.cartesian-morphisms-arrows -open import foundation.cartesian-product-types -open import foundation.contractible-maps -open import foundation.contractible-types -open import foundation.coproduct-types -open import foundation.coproducts-pullbacks -open import foundation.dependent-pair-types -open import foundation.dependent-products-pullbacks -open import foundation.dependent-sums-pullbacks -open import foundation.equivalences -open import foundation.fibered-maps -open import foundation.fibers-of-maps -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.functoriality-cartesian-product-types -open import foundation.functoriality-coproduct-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies -open import foundation.morphisms-arrows -open import foundation.postcomposition-functions -open import foundation.postcomposition-pullbacks -open import foundation.precomposition-functions -open import foundation.products-pullbacks -open import foundation.propositions -open import foundation.pullbacks -open import foundation.standard-pullbacks -open import foundation.type-arithmetic-dependent-function-types +open import foundation.cartesian-morphisms-arrows funext univalence truncations +open import foundation.equivalences funext +open import foundation.fibers-of-maps funext +open import foundation.function-types funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.homotopies funext +open import foundation.postcomposition-functions funext +open import foundation.precomposition-functions funext +open import foundation.pullbacks funext univalence truncations open import foundation.unit-type -open import foundation.universal-property-cartesian-product-types -open import foundation.universal-property-coproduct-types -open import foundation.universal-property-dependent-pair-types -open import foundation.universal-property-equivalences -open import foundation.universal-property-pullbacks open import foundation.universe-levels -open import foundation.whiskering-homotopies-composition -open import orthogonal-factorization-systems.lifting-structures-on-squares -open import orthogonal-factorization-systems.null-maps -open import orthogonal-factorization-systems.orthogonal-maps -open import orthogonal-factorization-systems.pullback-hom -open import orthogonal-factorization-systems.types-local-at-maps +open import orthogonal-factorization-systems.null-maps funext univalence truncations +open import orthogonal-factorization-systems.orthogonal-maps funext univalence truncations +open import orthogonal-factorization-systems.pullback-hom funext univalence truncations ```
diff --git a/src/orthogonal-factorization-systems/function-classes.lagda.md b/src/orthogonal-factorization-systems/function-classes.lagda.md index db1a440376..e90d16bae0 100644 --- a/src/orthogonal-factorization-systems/function-classes.lagda.md +++ b/src/orthogonal-factorization-systems/function-classes.lagda.md @@ -1,27 +1,37 @@ # Function classes ```agda -module orthogonal-factorization-systems.function-classes where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module orthogonal-factorization-systems.function-classes + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cones-over-cospan-diagrams +open import foundation.cones-over-cospan-diagrams funext open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalence-induction -open import foundation.equivalences -open import foundation.function-types -open import foundation.identity-types -open import foundation.iterated-dependent-product-types -open import foundation.logical-equivalences -open import foundation.propositions -open import foundation.pullbacks -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.embeddings funext +open import foundation.equivalence-induction funext univalence +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.iterated-dependent-product-types funext +open import foundation.logical-equivalences funext +open import foundation.propositions funext univalence +open import foundation.pullbacks funext univalence truncations +open import foundation.subtypes funext univalence truncations +open import foundation.telescopes open import foundation.transport-along-identifications -open import foundation.univalence +open import foundation.univalence funext univalence open import foundation.universe-levels ``` diff --git a/src/orthogonal-factorization-systems/functoriality-higher-modalities.lagda.md b/src/orthogonal-factorization-systems/functoriality-higher-modalities.lagda.md index 5bf2870bfe..652d81cc73 100644 --- a/src/orthogonal-factorization-systems/functoriality-higher-modalities.lagda.md +++ b/src/orthogonal-factorization-systems/functoriality-higher-modalities.lagda.md @@ -1,7 +1,15 @@ # Functoriality of higher modalities ```agda -module orthogonal-factorization-systems.functoriality-higher-modalities where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module orthogonal-factorization-systems.functoriality-higher-modalities + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,21 +17,21 @@ module orthogonal-factorization-systems.functoriality-higher-modalities where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.path-algebra -open import foundation.small-types +open import foundation.function-extensionality funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.path-algebra funext +open import foundation.small-types funext univalence truncations open import foundation.transport-along-identifications -open import foundation.univalence +open import foundation.univalence funext univalence open import foundation.universe-levels -open import foundation.whiskering-identifications-concatenation +open import foundation.whiskering-identifications-concatenation funext -open import orthogonal-factorization-systems.higher-modalities -open import orthogonal-factorization-systems.modal-induction -open import orthogonal-factorization-systems.modal-operators -open import orthogonal-factorization-systems.modal-subuniverse-induction +open import orthogonal-factorization-systems.higher-modalities funext univalence truncations +open import orthogonal-factorization-systems.modal-induction funext univalence truncations +open import orthogonal-factorization-systems.modal-operators funext univalence truncations +open import orthogonal-factorization-systems.modal-subuniverse-induction funext univalence truncations ```
diff --git a/src/orthogonal-factorization-systems/functoriality-localizations-at-global-subuniverses.lagda.md b/src/orthogonal-factorization-systems/functoriality-localizations-at-global-subuniverses.lagda.md index 84d0582079..5d7f556298 100644 --- a/src/orthogonal-factorization-systems/functoriality-localizations-at-global-subuniverses.lagda.md +++ b/src/orthogonal-factorization-systems/functoriality-localizations-at-global-subuniverses.lagda.md @@ -1,41 +1,37 @@ # Functoriality of localizations at global subuniverses ```agda -module orthogonal-factorization-systems.functoriality-localizations-at-global-subuniverses where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module orthogonal-factorization-systems.functoriality-localizations-at-global-subuniverses + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types -open import foundation.commuting-squares-of-maps -open import foundation.contractible-types +open import foundation.commuting-squares-of-maps funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.extensions-types-global-subuniverses -open import foundation.extensions-types-subuniverses -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.global-subuniverses -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types -open import foundation.precomposition-functions -open import foundation.propositions -open import foundation.retractions -open import foundation.retracts-of-maps -open import foundation.retracts-of-types -open import foundation.subuniverses -open import foundation.unit-type +open import foundation.equivalences funext +open import foundation.extensions-types-global-subuniverses funext univalence truncations +open import foundation.function-types funext +open import foundation.global-subuniverses funext univalence +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext +open import foundation.retractions funext +open import foundation.retracts-of-maps funext univalence +open import foundation.retracts-of-types funext univalence open import foundation.universe-levels -open import orthogonal-factorization-systems.localizations-at-global-subuniverses -open import orthogonal-factorization-systems.modal-induction -open import orthogonal-factorization-systems.modal-operators -open import orthogonal-factorization-systems.modal-subuniverse-induction -open import orthogonal-factorization-systems.types-local-at-maps -open import orthogonal-factorization-systems.universal-property-localizations-at-global-subuniverses +open import orthogonal-factorization-systems.localizations-at-global-subuniverses funext univalence truncations +open import orthogonal-factorization-systems.universal-property-localizations-at-global-subuniverses funext univalence truncations ```
diff --git a/src/orthogonal-factorization-systems/functoriality-pullback-hom.lagda.md b/src/orthogonal-factorization-systems/functoriality-pullback-hom.lagda.md index 7d7e25d9c1..6bc23a3c8f 100644 --- a/src/orthogonal-factorization-systems/functoriality-pullback-hom.lagda.md +++ b/src/orthogonal-factorization-systems/functoriality-pullback-hom.lagda.md @@ -1,36 +1,27 @@ # Functoriality of the pullback-hom ```agda -module orthogonal-factorization-systems.functoriality-pullback-hom where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module orthogonal-factorization-systems.functoriality-pullback-hom + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.action-on-identifications-binary-functions -open import foundation.action-on-identifications-functions -open import foundation.bicomposition-functions -open import foundation.composition-algebra -open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.functoriality-morphisms-arrows -open import foundation.functoriality-pullbacks -open import foundation.homotopies -open import foundation.homotopies-morphisms-arrows -open import foundation.homotopies-morphisms-cospan-diagrams -open import foundation.identity-types -open import foundation.morphisms-arrows +open import foundation.functoriality-morphisms-arrows funext univalence truncations +open import foundation.functoriality-pullbacks funext univalence truncations +open import foundation.morphisms-arrows funext open import foundation.morphisms-cospan-diagrams -open import foundation.postcomposition-functions -open import foundation.precomposition-functions -open import foundation.retracts-of-maps open import foundation.universe-levels -open import foundation.whiskering-higher-homotopies-composition -open import foundation.whiskering-homotopies-composition -open import orthogonal-factorization-systems.pullback-hom +open import orthogonal-factorization-systems.pullback-hom funext univalence truncations ```
diff --git a/src/orthogonal-factorization-systems/functoriality-reflective-global-subuniverses.lagda.md b/src/orthogonal-factorization-systems/functoriality-reflective-global-subuniverses.lagda.md index 495d59bdb1..33a92d6cf8 100644 --- a/src/orthogonal-factorization-systems/functoriality-reflective-global-subuniverses.lagda.md +++ b/src/orthogonal-factorization-systems/functoriality-reflective-global-subuniverses.lagda.md @@ -1,42 +1,30 @@ # Functoriality of reflective global subuniverses ```agda -module orthogonal-factorization-systems.functoriality-reflective-global-subuniverses where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module orthogonal-factorization-systems.functoriality-reflective-global-subuniverses + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types -open import foundation.commuting-squares-of-maps -open import foundation.contractible-types -open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.extensions-types-global-subuniverses -open import foundation.extensions-types-subuniverses -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.global-subuniverses -open import foundation.homotopies -open import foundation.identity-types -open import foundation.precomposition-functions -open import foundation.propositions -open import foundation.retractions -open import foundation.retracts-of-maps -open import foundation.retracts-of-types -open import foundation.subuniverses -open import foundation.unit-type +open import foundation.commuting-squares-of-maps funext univalence +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.retractions funext +open import foundation.retracts-of-types funext univalence open import foundation.universe-levels -open import orthogonal-factorization-systems.functoriality-localizations-at-global-subuniverses -open import orthogonal-factorization-systems.localizations-at-global-subuniverses -open import orthogonal-factorization-systems.modal-induction -open import orthogonal-factorization-systems.modal-operators -open import orthogonal-factorization-systems.modal-subuniverse-induction -open import orthogonal-factorization-systems.reflective-global-subuniverses -open import orthogonal-factorization-systems.types-local-at-maps -open import orthogonal-factorization-systems.universal-property-localizations-at-global-subuniverses +open import orthogonal-factorization-systems.functoriality-localizations-at-global-subuniverses funext univalence truncations +open import orthogonal-factorization-systems.reflective-global-subuniverses funext univalence truncations ```
diff --git a/src/orthogonal-factorization-systems/global-function-classes.lagda.md b/src/orthogonal-factorization-systems/global-function-classes.lagda.md index b11fa84d13..5fa8c36617 100644 --- a/src/orthogonal-factorization-systems/global-function-classes.lagda.md +++ b/src/orthogonal-factorization-systems/global-function-classes.lagda.md @@ -1,23 +1,32 @@ # Global function classes ```agda -module orthogonal-factorization-systems.global-function-classes where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module orthogonal-factorization-systems.global-function-classes + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.cones-over-cospan-diagrams +open import foundation.cones-over-cospan-diagrams funext open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalences -open import foundation.function-types -open import foundation.propositions -open import foundation.pullbacks -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.propositions funext univalence +open import foundation.pullbacks funext univalence truncations +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels -open import orthogonal-factorization-systems.function-classes +open import orthogonal-factorization-systems.function-classes funext univalence truncations ```
diff --git a/src/orthogonal-factorization-systems/higher-modalities.lagda.md b/src/orthogonal-factorization-systems/higher-modalities.lagda.md index b4c0cc95ec..450b304307 100644 --- a/src/orthogonal-factorization-systems/higher-modalities.lagda.md +++ b/src/orthogonal-factorization-systems/higher-modalities.lagda.md @@ -1,32 +1,40 @@ # Higher modalities ```agda -module orthogonal-factorization-systems.higher-modalities where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module orthogonal-factorization-systems.higher-modalities + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.precomposition-dependent-functions -open import foundation.retractions -open import foundation.small-types +open import foundation.equivalences funext +open import foundation.function-extensionality funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.precomposition-dependent-functions funext +open import foundation.retractions funext +open import foundation.small-types funext univalence truncations open import foundation.transport-along-identifications -open import foundation.univalence +open import foundation.univalence funext univalence open import foundation.universe-levels -open import orthogonal-factorization-systems.locally-small-modal-operators -open import orthogonal-factorization-systems.modal-induction -open import orthogonal-factorization-systems.modal-operators -open import orthogonal-factorization-systems.modal-subuniverse-induction -open import orthogonal-factorization-systems.uniquely-eliminating-modalities +open import orthogonal-factorization-systems.locally-small-modal-operators funext univalence truncations +open import orthogonal-factorization-systems.modal-induction funext univalence truncations +open import orthogonal-factorization-systems.modal-operators funext univalence truncations +open import orthogonal-factorization-systems.modal-subuniverse-induction funext univalence truncations +open import orthogonal-factorization-systems.uniquely-eliminating-modalities funext univalence truncations ```
diff --git a/src/orthogonal-factorization-systems/identity-modality.lagda.md b/src/orthogonal-factorization-systems/identity-modality.lagda.md index 34bcadc7b1..b2914cdaad 100644 --- a/src/orthogonal-factorization-systems/identity-modality.lagda.md +++ b/src/orthogonal-factorization-systems/identity-modality.lagda.md @@ -1,19 +1,27 @@ # The identity modality ```agda -module orthogonal-factorization-systems.identity-modality where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module orthogonal-factorization-systems.identity-modality + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.equivalences -open import foundation.function-types +open import foundation.equivalences funext +open import foundation.function-types funext open import foundation.universe-levels -open import orthogonal-factorization-systems.modal-operators -open import orthogonal-factorization-systems.types-local-at-maps -open import orthogonal-factorization-systems.uniquely-eliminating-modalities +open import orthogonal-factorization-systems.modal-operators funext univalence truncations +open import orthogonal-factorization-systems.types-local-at-maps funext univalence truncations +open import orthogonal-factorization-systems.uniquely-eliminating-modalities funext univalence truncations ```
diff --git a/src/orthogonal-factorization-systems/large-lawvere-tierney-topologies.lagda.md b/src/orthogonal-factorization-systems/large-lawvere-tierney-topologies.lagda.md index b6fd6cabc1..302a52b1fb 100644 --- a/src/orthogonal-factorization-systems/large-lawvere-tierney-topologies.lagda.md +++ b/src/orthogonal-factorization-systems/large-lawvere-tierney-topologies.lagda.md @@ -1,22 +1,31 @@ # Large Lawvere–Tierney topologies ```agda -module orthogonal-factorization-systems.large-lawvere-tierney-topologies where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module orthogonal-factorization-systems.large-lawvere-tierney-topologies + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.cartesian-product-types -open import foundation.conjunction +open import foundation.cartesian-product-types funext univalence +open import foundation.conjunction funext univalence truncations open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.logical-equivalences -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.function-types funext +open import foundation.logical-equivalences funext +open import foundation.propositions funext univalence open import foundation.unit-type open import foundation.universe-levels -open import orthogonal-factorization-systems.lawvere-tierney-topologies +open import orthogonal-factorization-systems.lawvere-tierney-topologies funext univalence truncations ```
diff --git a/src/orthogonal-factorization-systems/lawvere-tierney-topologies.lagda.md b/src/orthogonal-factorization-systems/lawvere-tierney-topologies.lagda.md index 93fdf8ad66..87a1444675 100644 --- a/src/orthogonal-factorization-systems/lawvere-tierney-topologies.lagda.md +++ b/src/orthogonal-factorization-systems/lawvere-tierney-topologies.lagda.md @@ -1,21 +1,31 @@ # Lawvere–Tierney topologies ```agda -module orthogonal-factorization-systems.lawvere-tierney-topologies where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module orthogonal-factorization-systems.lawvere-tierney-topologies + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.cartesian-product-types -open import foundation.conjunction +open import foundation.cartesian-product-types funext univalence +open import foundation.conjunction funext univalence truncations open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.logical-equivalences -open import foundation.propositional-extensionality -open import foundation.propositions -open import foundation.sets -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.function-types funext +open import foundation.logical-equivalences funext +open import foundation.propositional-extensionality funext univalence truncations +open import foundation.propositions funext univalence +open import foundation.raising-universe-levels-unit-type +open import foundation.sets funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.unit-type open import foundation.universe-levels ``` diff --git a/src/orthogonal-factorization-systems/lifting-operations.lagda.md b/src/orthogonal-factorization-systems/lifting-operations.lagda.md index 35f437fa9b..e061928990 100644 --- a/src/orthogonal-factorization-systems/lifting-operations.lagda.md +++ b/src/orthogonal-factorization-systems/lifting-operations.lagda.md @@ -1,20 +1,28 @@ # Lifting operations ```agda -module orthogonal-factorization-systems.lifting-operations where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module orthogonal-factorization-systems.lifting-operations + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.homotopies -open import foundation.morphisms-arrows -open import foundation.sections +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.morphisms-arrows funext +open import foundation.sections funext open import foundation.universe-levels -open import orthogonal-factorization-systems.pullback-hom +open import orthogonal-factorization-systems.pullback-hom funext univalence truncations ```
diff --git a/src/orthogonal-factorization-systems/lifting-structures-on-squares.lagda.md b/src/orthogonal-factorization-systems/lifting-structures-on-squares.lagda.md index cd33ef10d2..29c13d35ee 100644 --- a/src/orthogonal-factorization-systems/lifting-structures-on-squares.lagda.md +++ b/src/orthogonal-factorization-systems/lifting-structures-on-squares.lagda.md @@ -1,41 +1,49 @@ # Lifting structures on commuting squares of maps ```agda -module orthogonal-factorization-systems.lifting-structures-on-squares where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module orthogonal-factorization-systems.lifting-structures-on-squares + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-homotopies -open import foundation.commuting-squares-of-maps -open import foundation.commuting-tetrahedra-of-homotopies -open import foundation.commuting-triangles-of-homotopies -open import foundation.commuting-triangles-of-identifications +open import foundation.commuting-squares-of-homotopies funext +open import foundation.commuting-squares-of-maps funext univalence +open import foundation.commuting-tetrahedra-of-homotopies funext +open import foundation.commuting-triangles-of-homotopies funext +open import foundation.commuting-triangles-of-identifications funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.fibers-of-maps -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types +open import foundation.equivalences funext +open import foundation.fibers-of-maps funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.higher-homotopies-morphisms-arrows -open import foundation.homotopies -open import foundation.homotopies-morphisms-arrows -open import foundation.homotopy-induction -open import foundation.identity-types -open import foundation.morphisms-arrows -open import foundation.path-algebra +open import foundation.higher-homotopies-morphisms-arrows funext univalence truncations +open import foundation.homotopies funext +open import foundation.homotopies-morphisms-arrows funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext +open import foundation.morphisms-arrows funext +open import foundation.path-algebra funext open import foundation.structure-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext univalence truncations open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import foundation.whiskering-identifications-concatenation +open import foundation.whiskering-identifications-concatenation funext -open import orthogonal-factorization-systems.extensions-maps -open import orthogonal-factorization-systems.lifts-maps -open import orthogonal-factorization-systems.pullback-hom +open import orthogonal-factorization-systems.extensions-maps funext univalence +open import orthogonal-factorization-systems.lifts-maps funext univalence truncations +open import orthogonal-factorization-systems.pullback-hom funext univalence truncations ```
diff --git a/src/orthogonal-factorization-systems/lifts-families-of-elements.lagda.md b/src/orthogonal-factorization-systems/lifts-families-of-elements.lagda.md index 2121b91eb6..50ae953cce 100644 --- a/src/orthogonal-factorization-systems/lifts-families-of-elements.lagda.md +++ b/src/orthogonal-factorization-systems/lifts-families-of-elements.lagda.md @@ -1,7 +1,11 @@ # Lifts of families of elements ```agda -module orthogonal-factorization-systems.lifts-families-of-elements where +open import foundation.function-extensionality-axiom + +module orthogonal-factorization-systems.lifts-families-of-elements + (funext : function-extensionality) + where ```
Imports @@ -9,12 +13,12 @@ module orthogonal-factorization-systems.lifts-families-of-elements where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types -open import foundation.precomposition-functions -open import foundation.precomposition-type-families -open import foundation.transport-along-homotopies +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext +open import foundation.precomposition-functions funext +open import foundation.precomposition-type-families funext +open import foundation.transport-along-homotopies funext open import foundation.transport-along-identifications open import foundation.universe-levels ``` diff --git a/src/orthogonal-factorization-systems/lifts-maps.lagda.md b/src/orthogonal-factorization-systems/lifts-maps.lagda.md index 9d2fe4746b..27f3a87365 100644 --- a/src/orthogonal-factorization-systems/lifts-maps.lagda.md +++ b/src/orthogonal-factorization-systems/lifts-maps.lagda.md @@ -1,27 +1,38 @@ # Lifts of maps ```agda -module orthogonal-factorization-systems.lifts-maps where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module orthogonal-factorization-systems.lifts-maps + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.contractible-types +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.dependent-products-truncated-types funext +open import foundation.equivalences funext +open import foundation.function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets -open import foundation.small-types +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.small-types funext univalence truncations open import foundation.structure-identity-principle -open import foundation.torsorial-type-families -open import foundation.truncated-types +open import foundation.torsorial-type-families funext univalence truncations +open import foundation.truncated-types funext univalence open import foundation.truncation-levels open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels diff --git a/src/orthogonal-factorization-systems/localizations-at-global-subuniverses.lagda.md b/src/orthogonal-factorization-systems/localizations-at-global-subuniverses.lagda.md index f4ba57ae36..f90ad22679 100644 --- a/src/orthogonal-factorization-systems/localizations-at-global-subuniverses.lagda.md +++ b/src/orthogonal-factorization-systems/localizations-at-global-subuniverses.lagda.md @@ -1,50 +1,59 @@ # Localizations at global subuniverses ```agda -module orthogonal-factorization-systems.localizations-at-global-subuniverses where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module orthogonal-factorization-systems.localizations-at-global-subuniverses + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types -open import foundation.cones-over-cospan-diagrams -open import foundation.constant-maps -open import foundation.contractible-types +open import foundation.cartesian-product-types funext univalence +open import foundation.cones-over-cospan-diagrams funext +open import foundation.constant-maps funext univalence truncations +open import foundation.contractible-types funext univalence open import foundation.cospan-diagrams open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.equivalences-arrows -open import foundation.extensions-types -open import foundation.extensions-types-global-subuniverses -open import foundation.fibers-of-maps -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.functoriality-cartesian-product-types -open import foundation.functoriality-dependent-function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.global-subuniverses -open import foundation.homotopies -open import foundation.identity-types -open import foundation.postcomposition-functions -open import foundation.precomposition-dependent-functions -open import foundation.precomposition-functions -open import foundation.pullback-cones -open import foundation.pullbacks -open import foundation.sequential-limits +open import foundation.dependent-products-contractible-types funext +open import foundation.equivalences funext +open import foundation.equivalences-arrows funext univalence truncations +open import foundation.extensions-types funext univalence truncations +open import foundation.extensions-types-global-subuniverses funext univalence truncations +open import foundation.fibers-of-maps funext +open import foundation.function-extensionality funext +open import foundation.function-types funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.functoriality-dependent-function-types funext univalence +open import foundation.functoriality-dependent-pair-types funext +open import foundation.global-subuniverses funext univalence +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.postcomposition-functions funext +open import foundation.precomposition-dependent-functions funext +open import foundation.precomposition-functions funext +open import foundation.pullback-cones funext univalence truncations +open import foundation.pullbacks funext univalence truncations +open import foundation.sequential-limits funext univalence truncations open import foundation.singleton-induction -open import foundation.subuniverses -open import foundation.type-theoretic-principle-of-choice +open import foundation.subuniverses funext univalence +open import foundation.type-theoretic-principle-of-choice funext open import foundation.unit-type -open import foundation.universal-property-dependent-pair-types +open import foundation.universal-property-dependent-pair-types funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import orthogonal-factorization-systems.orthogonal-maps -open import orthogonal-factorization-systems.pullback-hom -open import orthogonal-factorization-systems.types-local-at-maps -open import orthogonal-factorization-systems.universal-property-localizations-at-global-subuniverses +open import orthogonal-factorization-systems.orthogonal-maps funext univalence truncations +open import orthogonal-factorization-systems.pullback-hom funext univalence truncations +open import orthogonal-factorization-systems.types-local-at-maps funext univalence truncations +open import orthogonal-factorization-systems.universal-property-localizations-at-global-subuniverses funext univalence truncations ```
diff --git a/src/orthogonal-factorization-systems/localizations-at-maps.lagda.md b/src/orthogonal-factorization-systems/localizations-at-maps.lagda.md index 1144d685d4..4cb8f49ce5 100644 --- a/src/orthogonal-factorization-systems/localizations-at-maps.lagda.md +++ b/src/orthogonal-factorization-systems/localizations-at-maps.lagda.md @@ -1,18 +1,26 @@ # Localizations at maps ```agda -module orthogonal-factorization-systems.localizations-at-maps where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module orthogonal-factorization-systems.localizations-at-maps + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types open import foundation.universe-levels -open import orthogonal-factorization-systems.localizations-at-subuniverses -open import orthogonal-factorization-systems.types-local-at-maps +open import orthogonal-factorization-systems.localizations-at-subuniverses funext univalence truncations +open import orthogonal-factorization-systems.types-local-at-maps funext univalence truncations ```
diff --git a/src/orthogonal-factorization-systems/localizations-at-subuniverses.lagda.md b/src/orthogonal-factorization-systems/localizations-at-subuniverses.lagda.md index c12ced2306..4e9b13fb4e 100644 --- a/src/orthogonal-factorization-systems/localizations-at-subuniverses.lagda.md +++ b/src/orthogonal-factorization-systems/localizations-at-subuniverses.lagda.md @@ -1,18 +1,26 @@ # Localizations at subuniverses ```agda -module orthogonal-factorization-systems.localizations-at-subuniverses where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module orthogonal-factorization-systems.localizations-at-subuniverses + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.subuniverses +open import foundation.subuniverses funext univalence open import foundation.universe-levels -open import orthogonal-factorization-systems.types-local-at-maps +open import orthogonal-factorization-systems.types-local-at-maps funext univalence truncations ```
diff --git a/src/orthogonal-factorization-systems/locally-small-modal-operators.lagda.md b/src/orthogonal-factorization-systems/locally-small-modal-operators.lagda.md index 88185472d4..eb81278431 100644 --- a/src/orthogonal-factorization-systems/locally-small-modal-operators.lagda.md +++ b/src/orthogonal-factorization-systems/locally-small-modal-operators.lagda.md @@ -1,17 +1,25 @@ # Locally small modal-operators ```agda -module orthogonal-factorization-systems.locally-small-modal-operators where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module orthogonal-factorization-systems.locally-small-modal-operators + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.locally-small-types +open import foundation.locally-small-types funext univalence truncations open import foundation.universe-levels -open import orthogonal-factorization-systems.modal-operators +open import orthogonal-factorization-systems.modal-operators funext univalence truncations ```
diff --git a/src/orthogonal-factorization-systems/maps-local-at-maps.lagda.md b/src/orthogonal-factorization-systems/maps-local-at-maps.lagda.md index ac69503101..f536d8adb4 100644 --- a/src/orthogonal-factorization-systems/maps-local-at-maps.lagda.md +++ b/src/orthogonal-factorization-systems/maps-local-at-maps.lagda.md @@ -1,40 +1,31 @@ # Maps local at maps ```agda -module orthogonal-factorization-systems.maps-local-at-maps where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module orthogonal-factorization-systems.maps-local-at-maps + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.action-on-identifications-functions -open import foundation.cartesian-morphisms-arrows -open import foundation.cones-over-cospan-diagrams -open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.equivalences-arrows -open import foundation.fibers-of-maps -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.functoriality-dependent-function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.functoriality-fibers-of-maps -open import foundation.global-subuniverses -open import foundation.homotopies -open import foundation.identity-types -open import foundation.postcomposition-functions -open import foundation.precomposition-functions -open import foundation.propositions -open import foundation.pullbacks -open import foundation.retracts-of-maps +open import foundation.cartesian-morphisms-arrows funext univalence truncations +open import foundation.dependent-products-propositions funext +open import foundation.fibers-of-maps funext +open import foundation.propositions funext univalence +open import foundation.retracts-of-maps funext univalence open import foundation.unit-type -open import foundation.universal-property-family-of-fibers-of-maps open import foundation.universe-levels -open import orthogonal-factorization-systems.families-of-types-local-at-maps -open import orthogonal-factorization-systems.orthogonal-maps -open import orthogonal-factorization-systems.pullback-hom -open import orthogonal-factorization-systems.types-local-at-maps +open import orthogonal-factorization-systems.families-of-types-local-at-maps funext univalence truncations +open import orthogonal-factorization-systems.orthogonal-maps funext univalence truncations +open import orthogonal-factorization-systems.types-local-at-maps funext univalence truncations ```
diff --git a/src/orthogonal-factorization-systems/mere-lifting-properties.lagda.md b/src/orthogonal-factorization-systems/mere-lifting-properties.lagda.md index ffc220075a..29968850e1 100644 --- a/src/orthogonal-factorization-systems/mere-lifting-properties.lagda.md +++ b/src/orthogonal-factorization-systems/mere-lifting-properties.lagda.md @@ -1,17 +1,26 @@ # Mere lifting properties ```agda -module orthogonal-factorization-systems.mere-lifting-properties where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module orthogonal-factorization-systems.mere-lifting-properties + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.propositions -open import foundation.surjective-maps +open import foundation.dependent-products-propositions funext +open import foundation.propositions funext univalence +open import foundation.surjective-maps funext univalence truncations open import foundation.universe-levels -open import orthogonal-factorization-systems.pullback-hom +open import orthogonal-factorization-systems.pullback-hom funext univalence truncations ```
diff --git a/src/orthogonal-factorization-systems/modal-induction.lagda.md b/src/orthogonal-factorization-systems/modal-induction.lagda.md index 207aa7c89a..d64be01b5e 100644 --- a/src/orthogonal-factorization-systems/modal-induction.lagda.md +++ b/src/orthogonal-factorization-systems/modal-induction.lagda.md @@ -1,7 +1,15 @@ # Modal induction ```agda -module orthogonal-factorization-systems.modal-induction where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module orthogonal-factorization-systems.modal-induction + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,23 +17,24 @@ module orthogonal-factorization-systems.modal-induction where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.functoriality-dependent-function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.multivariable-sections -open import foundation.precomposition-dependent-functions -open import foundation.precomposition-functions -open import foundation.retractions -open import foundation.sections -open import foundation.type-theoretic-principle-of-choice +open import foundation.equivalences funext +open import foundation.function-extensionality funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-function-types funext univalence +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.multivariable-sections funext +open import foundation.precomposition-dependent-functions funext +open import foundation.precomposition-functions funext +open import foundation.retractions funext +open import foundation.sections funext +open import foundation.telescopes +open import foundation.type-theoretic-principle-of-choice funext open import foundation.unit-type open import foundation.universe-levels -open import orthogonal-factorization-systems.modal-operators +open import orthogonal-factorization-systems.modal-operators funext univalence truncations ```
diff --git a/src/orthogonal-factorization-systems/modal-operators.lagda.md b/src/orthogonal-factorization-systems/modal-operators.lagda.md index 457aeddced..2a8f725fdc 100644 --- a/src/orthogonal-factorization-systems/modal-operators.lagda.md +++ b/src/orthogonal-factorization-systems/modal-operators.lagda.md @@ -1,18 +1,27 @@ # Modal operators ```agda -module orthogonal-factorization-systems.modal-operators where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module orthogonal-factorization-systems.modal-operators + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.propositions -open import foundation.small-types -open import foundation.subuniverses +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.propositions funext univalence +open import foundation.small-types funext univalence truncations +open import foundation.subuniverses funext univalence open import foundation.universe-levels ``` diff --git a/src/orthogonal-factorization-systems/modal-subuniverse-induction.lagda.md b/src/orthogonal-factorization-systems/modal-subuniverse-induction.lagda.md index 898c4cc4ea..eaa3513a14 100644 --- a/src/orthogonal-factorization-systems/modal-subuniverse-induction.lagda.md +++ b/src/orthogonal-factorization-systems/modal-subuniverse-induction.lagda.md @@ -1,7 +1,15 @@ # Modal subuniverse induction ```agda -module orthogonal-factorization-systems.modal-subuniverse-induction where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module orthogonal-factorization-systems.modal-subuniverse-induction + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,20 +17,21 @@ module orthogonal-factorization-systems.modal-subuniverse-induction where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.multivariable-sections -open import foundation.precomposition-dependent-functions -open import foundation.precomposition-functions -open import foundation.retractions -open import foundation.type-theoretic-principle-of-choice +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-function-types funext univalence +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.multivariable-sections funext +open import foundation.precomposition-dependent-functions funext +open import foundation.precomposition-functions funext +open import foundation.retractions funext +open import foundation.telescopes +open import foundation.type-theoretic-principle-of-choice funext open import foundation.universe-levels -open import orthogonal-factorization-systems.modal-induction -open import orthogonal-factorization-systems.modal-operators +open import orthogonal-factorization-systems.modal-induction funext univalence truncations +open import orthogonal-factorization-systems.modal-operators funext univalence truncations ```
diff --git a/src/orthogonal-factorization-systems/null-families-of-types.lagda.md b/src/orthogonal-factorization-systems/null-families-of-types.lagda.md index 9a6dfa29eb..056880d61c 100644 --- a/src/orthogonal-factorization-systems/null-families-of-types.lagda.md +++ b/src/orthogonal-factorization-systems/null-families-of-types.lagda.md @@ -1,21 +1,30 @@ # Null families of types ```agda -module orthogonal-factorization-systems.null-families-of-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module orthogonal-factorization-systems.null-families-of-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.precomposition-functions -open import foundation.propositions -open import foundation.retracts-of-types +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.precomposition-functions funext +open import foundation.propositions funext univalence +open import foundation.retracts-of-types funext univalence open import foundation.universe-levels -open import orthogonal-factorization-systems.null-types -open import orthogonal-factorization-systems.orthogonal-maps +open import orthogonal-factorization-systems.null-types funext univalence truncations +open import orthogonal-factorization-systems.orthogonal-maps funext univalence truncations ```
@@ -25,7 +34,7 @@ open import orthogonal-factorization-systems.orthogonal-maps A family of types `B : A → UU l` is said to be {{#concept "null" Disambiguation="family of types" Agda=is-null-family}} at `Y`, or **`Y`-null**, if every fiber is. I.e., if the -[diagonal map](foundation.diagonal-maps-of-types.md) +[diagonal map](foundation-core.diagonal-maps-of-types.md) ```text Δ : B x → (Y → B x) diff --git a/src/orthogonal-factorization-systems/null-maps.lagda.md b/src/orthogonal-factorization-systems/null-maps.lagda.md index af001e1fc2..523d56026f 100644 --- a/src/orthogonal-factorization-systems/null-maps.lagda.md +++ b/src/orthogonal-factorization-systems/null-maps.lagda.md @@ -1,40 +1,50 @@ # Null maps ```agda -module orthogonal-factorization-systems.null-maps where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module orthogonal-factorization-systems.null-maps + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.cones-over-cospan-diagrams +open import foundation.cones-over-cospan-diagrams funext open import foundation.dependent-pair-types -open import foundation.diagonal-maps-of-types -open import foundation.equivalences -open import foundation.equivalences-arrows -open import foundation.families-of-equivalences -open import foundation.fibers-of-maps -open import foundation.function-types -open import foundation.functoriality-fibers-of-maps -open import foundation.homotopies -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.morphisms-arrows -open import foundation.postcomposition-functions -open import foundation.precomposition-functions -open import foundation.propositions -open import foundation.pullbacks -open import foundation.type-arithmetic-unit-type -open import foundation.type-theoretic-principle-of-choice +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.equivalences-arrows funext univalence truncations +open import foundation.families-of-equivalences funext +open import foundation.fibers-of-maps funext +open import foundation.function-types funext +open import foundation.functoriality-fibers-of-maps funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.morphisms-arrows funext +open import foundation.postcomposition-functions funext +open import foundation.precomposition-functions funext +open import foundation.propositions funext univalence +open import foundation.pullbacks funext univalence truncations +open import foundation.type-arithmetic-unit-type funext +open import foundation.type-theoretic-principle-of-choice funext open import foundation.unit-type -open import foundation.universal-property-family-of-fibers-of-maps +open import foundation.universal-property-family-of-fibers-of-maps funext open import foundation.universe-levels -open import orthogonal-factorization-systems.maps-local-at-maps -open import orthogonal-factorization-systems.null-families-of-types -open import orthogonal-factorization-systems.null-types -open import orthogonal-factorization-systems.orthogonal-maps -open import orthogonal-factorization-systems.types-local-at-maps +open import foundation-core.diagonal-maps-of-types + +open import orthogonal-factorization-systems.maps-local-at-maps funext univalence truncations +open import orthogonal-factorization-systems.null-families-of-types funext univalence truncations +open import orthogonal-factorization-systems.null-types funext univalence truncations +open import orthogonal-factorization-systems.orthogonal-maps funext univalence truncations +open import orthogonal-factorization-systems.types-local-at-maps funext univalence truncations ```
diff --git a/src/orthogonal-factorization-systems/null-types.lagda.md b/src/orthogonal-factorization-systems/null-types.lagda.md index d47b2a74fd..e52af44c3b 100644 --- a/src/orthogonal-factorization-systems/null-types.lagda.md +++ b/src/orthogonal-factorization-systems/null-types.lagda.md @@ -1,44 +1,54 @@ # Null types ```agda -module orthogonal-factorization-systems.null-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module orthogonal-factorization-systems.null-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.contractible-types +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.diagonal-maps-of-types -open import foundation.equivalences -open import foundation.equivalences-arrows -open import foundation.fibers-of-maps -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.postcomposition-functions -open import foundation.precomposition-dependent-functions -open import foundation.precomposition-functions -open import foundation.propositions -open import foundation.retractions -open import foundation.retracts-of-maps -open import foundation.retracts-of-types -open import foundation.sections -open import foundation.type-arithmetic-unit-type -open import foundation.type-theoretic-principle-of-choice +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.diagonal-maps-of-types funext +open import foundation.equivalences funext +open import foundation.equivalences-arrows funext univalence truncations +open import foundation.fibers-of-maps funext +open import foundation.function-extensionality funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.postcomposition-functions funext +open import foundation.precomposition-dependent-functions funext +open import foundation.precomposition-functions funext +open import foundation.propositions funext univalence +open import foundation.retractions funext +open import foundation.retracts-of-maps funext univalence +open import foundation.retracts-of-types funext univalence +open import foundation.sections funext +open import foundation.type-arithmetic-unit-type funext +open import foundation.type-theoretic-principle-of-choice funext open import foundation.unit-type -open import foundation.universal-property-equivalences -open import foundation.universal-property-family-of-fibers-of-maps -open import foundation.universal-property-unit-type +open import foundation.universal-property-equivalences funext +open import foundation.universal-property-family-of-fibers-of-maps funext +open import foundation.universal-property-unit-type funext open import foundation.universe-levels -open import orthogonal-factorization-systems.maps-local-at-maps -open import orthogonal-factorization-systems.orthogonal-maps -open import orthogonal-factorization-systems.types-local-at-maps +open import orthogonal-factorization-systems.maps-local-at-maps funext univalence truncations +open import orthogonal-factorization-systems.orthogonal-maps funext univalence truncations +open import orthogonal-factorization-systems.types-local-at-maps funext univalence truncations ```
@@ -48,7 +58,7 @@ open import orthogonal-factorization-systems.types-local-at-maps A type `A` is said to be {{#concept "null at" Disambiguation="type" Agda=is-null}} `Y`, or {{#concept "`Y`-null" Disambiguation="type" Agda=is-null}}, if the -[diagonal map](foundation.diagonal-maps-of-types.md) +[diagonal map](foundation-core.diagonal-maps-of-types.md) ```text Δ : A → (Y → A) diff --git a/src/orthogonal-factorization-systems/open-modalities.lagda.md b/src/orthogonal-factorization-systems/open-modalities.lagda.md index f20203e06c..678e236c6e 100644 --- a/src/orthogonal-factorization-systems/open-modalities.lagda.md +++ b/src/orthogonal-factorization-systems/open-modalities.lagda.md @@ -1,7 +1,15 @@ # The open modalities ```agda -module orthogonal-factorization-systems.open-modalities where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module orthogonal-factorization-systems.open-modalities + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,19 +17,20 @@ module orthogonal-factorization-systems.open-modalities where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.identity-types -open import foundation.locally-small-types -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.function-extensionality funext +open import foundation.identity-types funext +open import foundation.locally-small-types funext univalence truncations +open import foundation.propositions funext univalence open import foundation.transport-along-identifications open import foundation.universe-levels -open import orthogonal-factorization-systems.higher-modalities -open import orthogonal-factorization-systems.locally-small-modal-operators -open import orthogonal-factorization-systems.modal-induction -open import orthogonal-factorization-systems.modal-operators -open import orthogonal-factorization-systems.uniquely-eliminating-modalities +open import orthogonal-factorization-systems.higher-modalities funext univalence truncations +open import orthogonal-factorization-systems.locally-small-modal-operators funext univalence truncations +open import orthogonal-factorization-systems.modal-induction funext univalence truncations +open import orthogonal-factorization-systems.modal-operators funext univalence truncations +open import orthogonal-factorization-systems.uniquely-eliminating-modalities funext univalence truncations ```
diff --git a/src/orthogonal-factorization-systems/orthogonal-factorization-systems.lagda.md b/src/orthogonal-factorization-systems/orthogonal-factorization-systems.lagda.md index ccdba0c7e2..95149e9588 100644 --- a/src/orthogonal-factorization-systems/orthogonal-factorization-systems.lagda.md +++ b/src/orthogonal-factorization-systems/orthogonal-factorization-systems.lagda.md @@ -1,31 +1,41 @@ # Orthogonal factorization systems ```agda -module orthogonal-factorization-systems.orthogonal-factorization-systems where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module orthogonal-factorization-systems.orthogonal-factorization-systems + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.cartesian-product-types -open import foundation.commuting-squares-of-maps -open import foundation.contractible-types +open import foundation.cartesian-product-types funext univalence +open import foundation.commuting-squares-of-maps funext univalence +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.iterated-dependent-product-types -open import foundation.propositions +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.iterated-dependent-product-types funext +open import foundation.propositions funext univalence open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import orthogonal-factorization-systems.factorization-operations-function-classes -open import orthogonal-factorization-systems.factorizations-of-maps -open import orthogonal-factorization-systems.factorizations-of-maps-function-classes -open import orthogonal-factorization-systems.function-classes -open import orthogonal-factorization-systems.lifting-structures-on-squares -open import orthogonal-factorization-systems.wide-function-classes +open import orthogonal-factorization-systems.factorization-operations-function-classes funext univalence truncations +open import orthogonal-factorization-systems.factorizations-of-maps funext univalence truncations +open import orthogonal-factorization-systems.factorizations-of-maps-function-classes funext univalence truncations +open import orthogonal-factorization-systems.function-classes funext univalence truncations +open import orthogonal-factorization-systems.lifting-structures-on-squares funext univalence truncations +open import orthogonal-factorization-systems.wide-function-classes funext univalence truncations ```
diff --git a/src/orthogonal-factorization-systems/orthogonal-maps.lagda.md b/src/orthogonal-factorization-systems/orthogonal-maps.lagda.md index ec37ad84de..b6115a80e5 100644 --- a/src/orthogonal-factorization-systems/orthogonal-maps.lagda.md +++ b/src/orthogonal-factorization-systems/orthogonal-maps.lagda.md @@ -1,56 +1,66 @@ # Orthogonal maps ```agda -module orthogonal-factorization-systems.orthogonal-maps where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module orthogonal-factorization-systems.orthogonal-maps + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cartesian-morphisms-arrows -open import foundation.cartesian-product-types -open import foundation.composition-algebra -open import foundation.contractible-maps -open import foundation.contractible-types -open import foundation.coproduct-types -open import foundation.coproducts-pullbacks +open import foundation.cartesian-morphisms-arrows funext univalence truncations +open import foundation.cartesian-product-types funext univalence +open import foundation.composition-algebra funext +open import foundation.contractible-maps funext +open import foundation.contractible-types funext univalence +open import foundation.coproduct-types funext univalence truncations +open import foundation.coproducts-pullbacks funext univalence truncations open import foundation.dependent-pair-types -open import foundation.dependent-products-pullbacks -open import foundation.dependent-sums-pullbacks -open import foundation.equivalences -open import foundation.equivalences-arrows -open import foundation.fibered-maps -open import foundation.fibers-of-maps -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.functoriality-cartesian-product-types -open import foundation.functoriality-coproduct-types -open import foundation.functoriality-dependent-pair-types -open import foundation.functoriality-fibers-of-maps -open import foundation.homotopies -open import foundation.morphisms-arrows -open import foundation.postcomposition-functions -open import foundation.postcomposition-pullbacks -open import foundation.precomposition-dependent-functions -open import foundation.precomposition-functions -open import foundation.products-pullbacks -open import foundation.propositions -open import foundation.pullbacks -open import foundation.type-arithmetic-dependent-function-types -open import foundation.type-theoretic-principle-of-choice +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.dependent-products-pullbacks funext univalence +open import foundation.dependent-sums-pullbacks funext +open import foundation.equivalences funext +open import foundation.equivalences-arrows funext univalence truncations +open import foundation.fibered-maps funext univalence truncations +open import foundation.fibers-of-maps funext +open import foundation.function-extensionality funext +open import foundation.function-types funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.functoriality-coproduct-types funext univalence truncations +open import foundation.functoriality-dependent-pair-types funext +open import foundation.functoriality-fibers-of-maps funext +open import foundation.homotopies funext +open import foundation.morphisms-arrows funext +open import foundation.postcomposition-functions funext +open import foundation.postcomposition-pullbacks funext +open import foundation.precomposition-dependent-functions funext +open import foundation.precomposition-functions funext +open import foundation.products-pullbacks funext univalence truncations +open import foundation.propositions funext univalence +open import foundation.pullbacks funext univalence truncations +open import foundation.type-arithmetic-dependent-function-types funext univalence +open import foundation.type-theoretic-principle-of-choice funext open import foundation.unit-type -open import foundation.universal-property-cartesian-product-types -open import foundation.universal-property-coproduct-types -open import foundation.universal-property-dependent-pair-types -open import foundation.universal-property-equivalences -open import foundation.universal-property-pullbacks +open import foundation.universal-property-cartesian-product-types funext +open import foundation.universal-property-coproduct-types funext +open import foundation.universal-property-dependent-pair-types funext +open import foundation.universal-property-equivalences funext +open import foundation.universal-property-pullbacks funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import orthogonal-factorization-systems.lifting-structures-on-squares -open import orthogonal-factorization-systems.pullback-hom -open import orthogonal-factorization-systems.types-local-at-maps +open import orthogonal-factorization-systems.lifting-structures-on-squares funext univalence truncations +open import orthogonal-factorization-systems.pullback-hom funext univalence truncations +open import orthogonal-factorization-systems.types-local-at-maps funext univalence truncations ```
@@ -997,7 +1007,7 @@ under products. **Note:** This result can also be obtained as a special case of the previous one by taking the indexing type to be the -[two-element type](foundation.booleans.md). +[two-element type](foundation-core.booleans.md). ```agda module _ diff --git a/src/orthogonal-factorization-systems/precomposition-lifts-families-of-elements.lagda.md b/src/orthogonal-factorization-systems/precomposition-lifts-families-of-elements.lagda.md index 8b53882043..363f9f6c11 100644 --- a/src/orthogonal-factorization-systems/precomposition-lifts-families-of-elements.lagda.md +++ b/src/orthogonal-factorization-systems/precomposition-lifts-families-of-elements.lagda.md @@ -1,32 +1,38 @@ # Precomposition of lifts of families of elements by maps ```agda -module orthogonal-factorization-systems.precomposition-lifts-families-of-elements where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module orthogonal-factorization-systems.precomposition-lifts-families-of-elements + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda open import foundation.action-on-identifications-dependent-functions -open import foundation.commuting-squares-of-homotopies -open import foundation.commuting-squares-of-maps -open import foundation.commuting-triangles-of-maps +open import foundation.commuting-squares-of-homotopies funext +open import foundation.commuting-squares-of-maps funext univalence +open import foundation.commuting-triangles-of-maps funext univalence open import foundation.dependent-pair-types -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types -open import foundation.precomposition-functions +open import foundation.function-extensionality funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext +open import foundation.precomposition-functions funext open import foundation.transport-along-identifications -open import foundation.type-theoretic-principle-of-choice +open import foundation.type-theoretic-principle-of-choice funext open import foundation.universe-levels open import foundation.whiskering-higher-homotopies-composition open import foundation.whiskering-homotopies-composition -open import foundation.whiskering-identifications-concatenation +open import foundation.whiskering-identifications-concatenation funext -open import orthogonal-factorization-systems.lifts-families-of-elements +open import orthogonal-factorization-systems.lifts-families-of-elements funext ```
diff --git a/src/orthogonal-factorization-systems/pullback-hom.lagda.md b/src/orthogonal-factorization-systems/pullback-hom.lagda.md index 4181ff3a64..fef7aaac91 100644 --- a/src/orthogonal-factorization-systems/pullback-hom.lagda.md +++ b/src/orthogonal-factorization-systems/pullback-hom.lagda.md @@ -1,43 +1,47 @@ # The pullback-hom ```agda -module orthogonal-factorization-systems.pullback-hom where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module orthogonal-factorization-systems.pullback-hom + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.commuting-squares-of-maps -open import foundation.commuting-triangles-of-maps -open import foundation.cones-over-cospan-diagrams -open import foundation.cospan-diagrams +open import foundation.commuting-squares-of-maps funext univalence +open import foundation.commuting-triangles-of-maps funext univalence +open import foundation.cones-over-cospan-diagrams funext open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types -open import foundation.equivalences -open import foundation.equivalences-arrows -open import foundation.fibers-of-maps -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.functoriality-fibers-of-maps -open import foundation.functoriality-morphisms-arrows -open import foundation.higher-homotopies-morphisms-arrows -open import foundation.homotopies -open import foundation.homotopies-morphisms-arrows -open import foundation.identity-types -open import foundation.morphisms-arrows -open import foundation.postcomposition-functions -open import foundation.precomposition-dependent-functions -open import foundation.precomposition-functions -open import foundation.pullback-cones -open import foundation.pullbacks -open import foundation.retractions -open import foundation.sections -open import foundation.standard-pullbacks -open import foundation.transport-along-identifications -open import foundation.type-arithmetic-dependent-pair-types -open import foundation.type-theoretic-principle-of-choice -open import foundation.universal-property-pullbacks +open import foundation.equality-dependent-pair-types funext +open import foundation.equivalences funext +open import foundation.equivalences-arrows funext univalence truncations +open import foundation.fibers-of-maps funext +open import foundation.function-extensionality funext +open import foundation.function-types funext +open import foundation.functoriality-fibers-of-maps funext +open import foundation.functoriality-morphisms-arrows funext univalence truncations +open import foundation.higher-homotopies-morphisms-arrows funext univalence truncations +open import foundation.homotopies funext +open import foundation.homotopies-morphisms-arrows funext +open import foundation.identity-types funext +open import foundation.morphisms-arrows funext +open import foundation.postcomposition-functions funext +open import foundation.precomposition-dependent-functions funext +open import foundation.precomposition-functions funext +open import foundation.pullback-cones funext univalence truncations +open import foundation.pullbacks funext univalence truncations +open import foundation.retractions funext +open import foundation.sections funext +open import foundation.standard-pullbacks funext +open import foundation.type-theoretic-principle-of-choice funext +open import foundation.universal-property-pullbacks funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition ``` diff --git a/src/orthogonal-factorization-systems/raise-modalities.lagda.md b/src/orthogonal-factorization-systems/raise-modalities.lagda.md index 1f7569b41d..e93705be1e 100644 --- a/src/orthogonal-factorization-systems/raise-modalities.lagda.md +++ b/src/orthogonal-factorization-systems/raise-modalities.lagda.md @@ -1,19 +1,28 @@ # The raise modalities ```agda -module orthogonal-factorization-systems.raise-modalities where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module orthogonal-factorization-systems.raise-modalities + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.function-types -open import foundation.raising-universe-levels +open import foundation.function-types funext open import foundation.universe-levels -open import orthogonal-factorization-systems.modal-operators -open import orthogonal-factorization-systems.types-local-at-maps -open import orthogonal-factorization-systems.uniquely-eliminating-modalities +open import foundation-core.raising-universe-levels + +open import orthogonal-factorization-systems.modal-operators funext univalence truncations +open import orthogonal-factorization-systems.types-local-at-maps funext univalence truncations +open import orthogonal-factorization-systems.uniquely-eliminating-modalities funext univalence truncations ```
diff --git a/src/orthogonal-factorization-systems/reflective-global-subuniverses.lagda.md b/src/orthogonal-factorization-systems/reflective-global-subuniverses.lagda.md index 787a963051..49872f9d4a 100644 --- a/src/orthogonal-factorization-systems/reflective-global-subuniverses.lagda.md +++ b/src/orthogonal-factorization-systems/reflective-global-subuniverses.lagda.md @@ -1,42 +1,38 @@ # Reflective global subuniverses ```agda -module orthogonal-factorization-systems.reflective-global-subuniverses where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module orthogonal-factorization-systems.reflective-global-subuniverses + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types -open import foundation.cones-over-cospan-diagrams -open import foundation.contractible-types +open import foundation.cartesian-product-types funext univalence +open import foundation.contractible-types funext univalence open import foundation.cospan-diagrams -open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.equivalences-arrows -open import foundation.extensions-types-global-subuniverses -open import foundation.extensions-types-subuniverses -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.global-subuniverses -open import foundation.identity-types -open import foundation.precomposition-functions -open import foundation.propositions -open import foundation.pullback-cones -open import foundation.retractions -open import foundation.subuniverses +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.extensions-types-global-subuniverses funext univalence truncations +open import foundation.global-subuniverses funext univalence +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.pullback-cones funext univalence truncations +open import foundation.subuniverses funext univalence open import foundation.unit-type -open import foundation.universal-property-pullbacks open import foundation.universe-levels -open import orthogonal-factorization-systems.localizations-at-global-subuniverses -open import orthogonal-factorization-systems.modal-induction -open import orthogonal-factorization-systems.modal-operators -open import orthogonal-factorization-systems.modal-subuniverse-induction -open import orthogonal-factorization-systems.types-local-at-maps -open import orthogonal-factorization-systems.universal-property-localizations-at-global-subuniverses +open import orthogonal-factorization-systems.localizations-at-global-subuniverses funext univalence truncations +open import orthogonal-factorization-systems.types-local-at-maps funext univalence truncations +open import orthogonal-factorization-systems.universal-property-localizations-at-global-subuniverses funext univalence truncations ```
diff --git a/src/orthogonal-factorization-systems/reflective-modalities.lagda.md b/src/orthogonal-factorization-systems/reflective-modalities.lagda.md index 46c235675f..8932915f3f 100644 --- a/src/orthogonal-factorization-systems/reflective-modalities.lagda.md +++ b/src/orthogonal-factorization-systems/reflective-modalities.lagda.md @@ -1,7 +1,15 @@ # Reflective modalities ```agda -module orthogonal-factorization-systems.reflective-modalities where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module orthogonal-factorization-systems.reflective-modalities + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,8 +18,8 @@ module orthogonal-factorization-systems.reflective-modalities where open import foundation.dependent-pair-types open import foundation.universe-levels -open import orthogonal-factorization-systems.modal-operators -open import orthogonal-factorization-systems.reflective-subuniverses +open import orthogonal-factorization-systems.modal-operators funext univalence truncations +open import orthogonal-factorization-systems.reflective-subuniverses funext univalence truncations ```
diff --git a/src/orthogonal-factorization-systems/reflective-subuniverses.lagda.md b/src/orthogonal-factorization-systems/reflective-subuniverses.lagda.md index 41a30148b0..4dc884490f 100644 --- a/src/orthogonal-factorization-systems/reflective-subuniverses.lagda.md +++ b/src/orthogonal-factorization-systems/reflective-subuniverses.lagda.md @@ -1,29 +1,31 @@ # Reflective subuniverses ```agda -module orthogonal-factorization-systems.reflective-subuniverses where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module orthogonal-factorization-systems.reflective-subuniverses + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.retractions -open import foundation.subuniverses +open import foundation.equivalences funext +open import foundation.subuniverses funext univalence open import foundation.universe-levels -open import orthogonal-factorization-systems.localizations-at-subuniverses -open import orthogonal-factorization-systems.modal-induction -open import orthogonal-factorization-systems.modal-operators -open import orthogonal-factorization-systems.modal-subuniverse-induction -open import orthogonal-factorization-systems.types-local-at-maps +open import orthogonal-factorization-systems.localizations-at-subuniverses funext univalence truncations +open import orthogonal-factorization-systems.modal-induction funext univalence truncations +open import orthogonal-factorization-systems.modal-operators funext univalence truncations +open import orthogonal-factorization-systems.modal-subuniverse-induction funext univalence truncations +open import orthogonal-factorization-systems.types-local-at-maps funext univalence truncations ```
diff --git a/src/orthogonal-factorization-systems/sigma-closed-modalities.lagda.md b/src/orthogonal-factorization-systems/sigma-closed-modalities.lagda.md index 20370cd516..766ea2e48b 100644 --- a/src/orthogonal-factorization-systems/sigma-closed-modalities.lagda.md +++ b/src/orthogonal-factorization-systems/sigma-closed-modalities.lagda.md @@ -1,18 +1,26 @@ # Σ-closed modalities ```agda -module orthogonal-factorization-systems.sigma-closed-modalities where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module orthogonal-factorization-systems.sigma-closed-modalities + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.sigma-closed-subuniverses +open import foundation.function-types funext +open import foundation.sigma-closed-subuniverses funext univalence open import foundation.universe-levels -open import orthogonal-factorization-systems.modal-operators +open import orthogonal-factorization-systems.modal-operators funext univalence truncations ```
diff --git a/src/orthogonal-factorization-systems/sigma-closed-reflective-modalities.lagda.md b/src/orthogonal-factorization-systems/sigma-closed-reflective-modalities.lagda.md index 4abbb4bf5d..2a1e66c99a 100644 --- a/src/orthogonal-factorization-systems/sigma-closed-reflective-modalities.lagda.md +++ b/src/orthogonal-factorization-systems/sigma-closed-reflective-modalities.lagda.md @@ -1,19 +1,27 @@ # Σ-closed reflective modalities ```agda -module orthogonal-factorization-systems.sigma-closed-reflective-modalities where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module orthogonal-factorization-systems.sigma-closed-reflective-modalities + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types open import foundation.universe-levels -open import orthogonal-factorization-systems.modal-operators -open import orthogonal-factorization-systems.reflective-modalities -open import orthogonal-factorization-systems.sigma-closed-modalities +open import orthogonal-factorization-systems.modal-operators funext univalence truncations +open import orthogonal-factorization-systems.reflective-modalities funext univalence truncations +open import orthogonal-factorization-systems.sigma-closed-modalities funext univalence truncations ```
diff --git a/src/orthogonal-factorization-systems/sigma-closed-reflective-subuniverses.lagda.md b/src/orthogonal-factorization-systems/sigma-closed-reflective-subuniverses.lagda.md index 08cd6c74fc..c701286c92 100644 --- a/src/orthogonal-factorization-systems/sigma-closed-reflective-subuniverses.lagda.md +++ b/src/orthogonal-factorization-systems/sigma-closed-reflective-subuniverses.lagda.md @@ -1,17 +1,25 @@ # Σ-closed reflective subuniverses ```agda -module orthogonal-factorization-systems.sigma-closed-reflective-subuniverses where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module orthogonal-factorization-systems.sigma-closed-reflective-subuniverses + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.sigma-closed-subuniverses +open import foundation.sigma-closed-subuniverses funext univalence open import foundation.universe-levels -open import orthogonal-factorization-systems.reflective-subuniverses +open import orthogonal-factorization-systems.reflective-subuniverses funext univalence truncations ```
diff --git a/src/orthogonal-factorization-systems/stable-orthogonal-factorization-systems.lagda.md b/src/orthogonal-factorization-systems/stable-orthogonal-factorization-systems.lagda.md index 2d9c5958c2..bea1c2402b 100644 --- a/src/orthogonal-factorization-systems/stable-orthogonal-factorization-systems.lagda.md +++ b/src/orthogonal-factorization-systems/stable-orthogonal-factorization-systems.lagda.md @@ -1,7 +1,15 @@ # Stable orthogonal factorization systems ```agda -module orthogonal-factorization-systems.stable-orthogonal-factorization-systems where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module orthogonal-factorization-systems.stable-orthogonal-factorization-systems + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,8 +17,8 @@ module orthogonal-factorization-systems.stable-orthogonal-factorization-systems ```agda open import foundation.universe-levels -open import orthogonal-factorization-systems.function-classes -open import orthogonal-factorization-systems.orthogonal-factorization-systems +open import orthogonal-factorization-systems.function-classes funext univalence truncations +open import orthogonal-factorization-systems.orthogonal-factorization-systems funext univalence truncations ```
diff --git a/src/orthogonal-factorization-systems/types-colocal-at-maps.lagda.md b/src/orthogonal-factorization-systems/types-colocal-at-maps.lagda.md index 7292a82aa0..fe30ce4d33 100644 --- a/src/orthogonal-factorization-systems/types-colocal-at-maps.lagda.md +++ b/src/orthogonal-factorization-systems/types-colocal-at-maps.lagda.md @@ -1,32 +1,42 @@ # Types colocal at maps ```agda -module orthogonal-factorization-systems.types-colocal-at-maps where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module orthogonal-factorization-systems.types-colocal-at-maps + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-maps -open import foundation.contractible-maps -open import foundation.contractible-types +open import foundation.commuting-squares-of-maps funext univalence +open import foundation.contractible-maps funext +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.equivalences -open import foundation.equivalences-arrows -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.postcomposition-dependent-functions -open import foundation.postcomposition-functions -open import foundation.propositions -open import foundation.retracts-of-maps -open import foundation.retracts-of-types +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.empty-types funext univalence truncations +open import foundation.equivalences funext +open import foundation.equivalences-arrows funext univalence truncations +open import foundation.function-extensionality funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.postcomposition-dependent-functions funext +open import foundation.postcomposition-functions funext +open import foundation.propositions funext univalence +open import foundation.retracts-of-maps funext univalence +open import foundation.retracts-of-types funext univalence open import foundation.unit-type -open import foundation.universal-property-empty-type -open import foundation.universal-property-equivalences +open import foundation.universal-property-empty-type funext +open import foundation.universal-property-equivalences funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition diff --git a/src/orthogonal-factorization-systems/types-local-at-maps.lagda.md b/src/orthogonal-factorization-systems/types-local-at-maps.lagda.md index 1ebbc9e3de..6c7a80aa58 100644 --- a/src/orthogonal-factorization-systems/types-local-at-maps.lagda.md +++ b/src/orthogonal-factorization-systems/types-local-at-maps.lagda.md @@ -1,47 +1,56 @@ # Types local at maps ```agda -module orthogonal-factorization-systems.types-local-at-maps where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module orthogonal-factorization-systems.types-local-at-maps + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-maps -open import foundation.commuting-triangles-of-maps -open import foundation.contractible-maps -open import foundation.contractible-types +open import foundation.commuting-squares-of-maps funext univalence +open import foundation.commuting-triangles-of-maps funext univalence +open import foundation.contractible-maps funext +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.dependent-universal-property-equivalences -open import foundation.empty-types -open import foundation.equivalences -open import foundation.families-of-equivalences -open import foundation.fibers-of-maps -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.functoriality-dependent-function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.postcomposition-functions -open import foundation.precomposition-dependent-functions -open import foundation.precomposition-functions -open import foundation.propositions -open import foundation.retractions -open import foundation.retracts-of-maps -open import foundation.retracts-of-types -open import foundation.sections -open import foundation.transport-along-identifications -open import foundation.type-arithmetic-dependent-function-types -open import foundation.type-arithmetic-unit-type +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.dependent-universal-property-equivalences funext +open import foundation.empty-types funext univalence truncations +open import foundation.equivalences funext +open import foundation.families-of-equivalences funext +open import foundation.fibers-of-maps funext +open import foundation.function-extensionality funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-function-types funext univalence +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.postcomposition-functions funext +open import foundation.precomposition-dependent-functions funext +open import foundation.precomposition-functions funext +open import foundation.propositions funext univalence +open import foundation.retractions funext +open import foundation.retracts-of-maps funext univalence +open import foundation.retracts-of-types funext univalence +open import foundation.sections funext +open import foundation.type-arithmetic-dependent-function-types funext univalence +open import foundation.type-arithmetic-unit-type funext open import foundation.unit-type -open import foundation.universal-property-empty-type -open import foundation.universal-property-equivalences +open import foundation.universal-property-empty-type funext +open import foundation.universal-property-equivalences funext open import foundation.universe-levels -open import orthogonal-factorization-systems.extensions-maps +open import orthogonal-factorization-systems.extensions-maps funext univalence ```
diff --git a/src/orthogonal-factorization-systems/types-separated-at-maps.lagda.md b/src/orthogonal-factorization-systems/types-separated-at-maps.lagda.md index a909c66dac..237ba384a5 100644 --- a/src/orthogonal-factorization-systems/types-separated-at-maps.lagda.md +++ b/src/orthogonal-factorization-systems/types-separated-at-maps.lagda.md @@ -1,16 +1,24 @@ # Types separated at maps ```agda -module orthogonal-factorization-systems.types-separated-at-maps where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module orthogonal-factorization-systems.types-separated-at-maps + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import orthogonal-factorization-systems.types-local-at-maps +open import orthogonal-factorization-systems.types-local-at-maps funext univalence truncations ```
diff --git a/src/orthogonal-factorization-systems/uniquely-eliminating-modalities.lagda.md b/src/orthogonal-factorization-systems/uniquely-eliminating-modalities.lagda.md index 493b2f511f..a3a85c46b8 100644 --- a/src/orthogonal-factorization-systems/uniquely-eliminating-modalities.lagda.md +++ b/src/orthogonal-factorization-systems/uniquely-eliminating-modalities.lagda.md @@ -1,27 +1,37 @@ # Uniquely eliminating modalities ```agda -module orthogonal-factorization-systems.uniquely-eliminating-modalities where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module orthogonal-factorization-systems.uniquely-eliminating-modalities + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.contractible-maps -open import foundation.contractible-types +open import foundation.contractible-maps funext +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.propositions -open import foundation.univalence +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.function-extensionality funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.univalence funext univalence open import foundation.universe-levels -open import orthogonal-factorization-systems.modal-operators -open import orthogonal-factorization-systems.types-local-at-maps +open import orthogonal-factorization-systems.modal-operators funext univalence truncations +open import orthogonal-factorization-systems.types-local-at-maps funext univalence truncations ```
diff --git a/src/orthogonal-factorization-systems/universal-property-localizations-at-global-subuniverses.lagda.md b/src/orthogonal-factorization-systems/universal-property-localizations-at-global-subuniverses.lagda.md index a3c2143af4..4c10fe2ace 100644 --- a/src/orthogonal-factorization-systems/universal-property-localizations-at-global-subuniverses.lagda.md +++ b/src/orthogonal-factorization-systems/universal-property-localizations-at-global-subuniverses.lagda.md @@ -1,35 +1,40 @@ # The universal property of localizations at global subuniverses ```agda -module orthogonal-factorization-systems.universal-property-localizations-at-global-subuniverses where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module orthogonal-factorization-systems.universal-property-localizations-at-global-subuniverses + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types -open import foundation.contractible-types +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.extensions-types -open import foundation.extensions-types-global-subuniverses -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.global-subuniverses -open import foundation.homotopies -open import foundation.identity-types -open import foundation.precomposition-functions -open import foundation.propositions -open import foundation.retractions -open import foundation.sections -open import foundation.subuniverses -open import foundation.unit-type -open import foundation.univalence +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.extensions-types funext univalence truncations +open import foundation.extensions-types-global-subuniverses funext univalence truncations +open import foundation.function-types funext +open import foundation.global-subuniverses funext univalence +open import foundation.identity-types funext +open import foundation.precomposition-functions funext +open import foundation.propositions funext univalence +open import foundation.retractions funext +open import foundation.sections funext +open import foundation.univalence funext univalence open import foundation.universe-levels -open import orthogonal-factorization-systems.extensions-maps -open import orthogonal-factorization-systems.types-local-at-maps +open import orthogonal-factorization-systems.extensions-maps funext univalence +open import orthogonal-factorization-systems.types-local-at-maps funext univalence truncations ```
diff --git a/src/orthogonal-factorization-systems/wide-function-classes.lagda.md b/src/orthogonal-factorization-systems/wide-function-classes.lagda.md index 7798c4379d..ea56c9ce83 100644 --- a/src/orthogonal-factorization-systems/wide-function-classes.lagda.md +++ b/src/orthogonal-factorization-systems/wide-function-classes.lagda.md @@ -1,19 +1,28 @@ # Wide function classes ```agda -module orthogonal-factorization-systems.wide-function-classes where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module orthogonal-factorization-systems.wide-function-classes + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.function-types funext +open import foundation.propositions funext univalence open import foundation.universe-levels -open import orthogonal-factorization-systems.function-classes +open import orthogonal-factorization-systems.function-classes funext univalence truncations ```
diff --git a/src/orthogonal-factorization-systems/wide-global-function-classes.lagda.md b/src/orthogonal-factorization-systems/wide-global-function-classes.lagda.md index e8ed36b96f..20266a15ba 100644 --- a/src/orthogonal-factorization-systems/wide-global-function-classes.lagda.md +++ b/src/orthogonal-factorization-systems/wide-global-function-classes.lagda.md @@ -1,21 +1,30 @@ # Wide global function classes ```agda -module orthogonal-factorization-systems.wide-global-function-classes where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module orthogonal-factorization-systems.wide-global-function-classes + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.function-types -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.embeddings funext +open import foundation.function-types funext +open import foundation.propositions funext univalence open import foundation.universe-levels -open import orthogonal-factorization-systems.function-classes -open import orthogonal-factorization-systems.global-function-classes +open import orthogonal-factorization-systems.function-classes funext univalence truncations +open import orthogonal-factorization-systems.global-function-classes funext univalence truncations ```
diff --git a/src/orthogonal-factorization-systems/zero-modality.lagda.md b/src/orthogonal-factorization-systems/zero-modality.lagda.md index 6395eb912e..37b257f000 100644 --- a/src/orthogonal-factorization-systems/zero-modality.lagda.md +++ b/src/orthogonal-factorization-systems/zero-modality.lagda.md @@ -1,18 +1,27 @@ # The zero modality ```agda -module orthogonal-factorization-systems.zero-modality where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module orthogonal-factorization-systems.zero-modality + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda +open import foundation.raising-universe-levels-unit-type open import foundation.unit-type open import foundation.universe-levels -open import orthogonal-factorization-systems.modal-operators -open import orthogonal-factorization-systems.types-local-at-maps -open import orthogonal-factorization-systems.uniquely-eliminating-modalities +open import orthogonal-factorization-systems.modal-operators funext univalence truncations +open import orthogonal-factorization-systems.types-local-at-maps funext univalence truncations +open import orthogonal-factorization-systems.uniquely-eliminating-modalities funext univalence truncations ```
diff --git a/src/polytopes.lagda.md b/src/polytopes.lagda.md index 93741a955f..85eb14f358 100644 --- a/src/polytopes.lagda.md +++ b/src/polytopes.lagda.md @@ -3,7 +3,15 @@ ## Modules in the polytopes namespace ```agda -module polytopes where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom -open import polytopes.abstract-polytopes public +module polytopes + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where + +open import polytopes.abstract-polytopes funext univalence truncations public ``` diff --git a/src/polytopes/abstract-polytopes.lagda.md b/src/polytopes/abstract-polytopes.lagda.md index 429d52d3ab..3d722359c2 100644 --- a/src/polytopes/abstract-polytopes.lagda.md +++ b/src/polytopes/abstract-polytopes.lagda.md @@ -1,33 +1,44 @@ # Abstract polytopes ```agda -module polytopes.abstract-polytopes where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module polytopes.abstract-polytopes + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.inequality-standard-finite-types +open import elementary-number-theory.inequality-standard-finite-types funext univalence truncations open import elementary-number-theory.natural-numbers -open import foundation.binary-relations -open import foundation.cartesian-product-types -open import foundation.contractible-types +open import foundation.binary-relations funext univalence truncations +open import foundation.cartesian-product-types funext univalence +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.disjunction -open import foundation.identity-types -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.sets +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.disjunction funext univalence truncations +open import foundation.identity-types funext +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence +open import foundation.raising-universe-levels-unit-type +open import foundation.sets funext univalence open import foundation.transport-along-identifications open import foundation.unit-type open import foundation.universe-levels -open import order-theory.finitely-graded-posets -open import order-theory.posets +open import order-theory.finitely-graded-posets funext univalence truncations +open import order-theory.posets funext univalence truncations -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.finite-types funext univalence truncations +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/primitives/characters.lagda.md b/src/primitives/characters.lagda.md index 5a1d6a930b..8b083f21ed 100644 --- a/src/primitives/characters.lagda.md +++ b/src/primitives/characters.lagda.md @@ -9,8 +9,9 @@ module primitives.characters where ```agda open import elementary-number-theory.natural-numbers -open import foundation.booleans open import foundation.universe-levels + +open import foundation-core.booleans ```
diff --git a/src/primitives/floats.lagda.md b/src/primitives/floats.lagda.md index 902432e801..68f4246d71 100644 --- a/src/primitives/floats.lagda.md +++ b/src/primitives/floats.lagda.md @@ -9,10 +9,11 @@ module primitives.floats where ```agda open import elementary-number-theory.natural-numbers -open import foundation.booleans -open import foundation.maybe open import foundation.universe-levels +open import foundation-core.booleans +open import foundation-core.maybe + open import primitives.machine-integers open import primitives.strings ``` diff --git a/src/primitives/machine-integers.lagda.md b/src/primitives/machine-integers.lagda.md index 84db3aa726..af8fed1892 100644 --- a/src/primitives/machine-integers.lagda.md +++ b/src/primitives/machine-integers.lagda.md @@ -9,8 +9,9 @@ module primitives.machine-integers where ```agda open import elementary-number-theory.natural-numbers -open import foundation.identity-types open import foundation.universe-levels + +open import foundation-core.identity-types ```
diff --git a/src/primitives/strings.lagda.md b/src/primitives/strings.lagda.md index d94ebd03e7..cfcb24c3cf 100644 --- a/src/primitives/strings.lagda.md +++ b/src/primitives/strings.lagda.md @@ -9,11 +9,12 @@ module primitives.strings where ```agda open import elementary-number-theory.natural-numbers -open import foundation.booleans open import foundation.dependent-pair-types -open import foundation.maybe open import foundation.universe-levels +open import foundation-core.booleans +open import foundation-core.maybe + open import lists.lists open import primitives.characters diff --git a/src/real-numbers.lagda.md b/src/real-numbers.lagda.md index 525501a6b9..51c78e68f1 100644 --- a/src/real-numbers.lagda.md +++ b/src/real-numbers.lagda.md @@ -3,31 +3,39 @@ ## Modules in the real numbers namespace ```agda -module real-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom -open import real-numbers.addition-lower-dedekind-real-numbers public -open import real-numbers.addition-upper-dedekind-real-numbers public -open import real-numbers.apartness-real-numbers public -open import real-numbers.arithmetically-located-dedekind-cuts public -open import real-numbers.dedekind-real-numbers public -open import real-numbers.inequality-lower-dedekind-real-numbers public -open import real-numbers.inequality-real-numbers public -open import real-numbers.inequality-upper-dedekind-real-numbers public -open import real-numbers.lower-dedekind-real-numbers public -open import real-numbers.maximum-lower-dedekind-real-numbers public -open import real-numbers.maximum-real-numbers public -open import real-numbers.maximum-upper-dedekind-real-numbers public -open import real-numbers.metric-space-of-real-numbers public -open import real-numbers.minimum-lower-dedekind-real-numbers public -open import real-numbers.minimum-real-numbers public -open import real-numbers.minimum-upper-dedekind-real-numbers public -open import real-numbers.negation-lower-upper-dedekind-real-numbers public -open import real-numbers.negation-real-numbers public -open import real-numbers.raising-universe-levels-real-numbers public -open import real-numbers.rational-lower-dedekind-real-numbers public -open import real-numbers.rational-real-numbers public -open import real-numbers.rational-upper-dedekind-real-numbers public -open import real-numbers.similarity-real-numbers public -open import real-numbers.strict-inequality-real-numbers public -open import real-numbers.upper-dedekind-real-numbers public +module real-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where + +open import real-numbers.addition-lower-dedekind-real-numbers funext univalence truncations public +open import real-numbers.addition-upper-dedekind-real-numbers funext univalence truncations public +open import real-numbers.apartness-real-numbers funext univalence truncations public +open import real-numbers.arithmetically-located-dedekind-cuts funext univalence truncations public +open import real-numbers.dedekind-real-numbers funext univalence truncations public +open import real-numbers.inequality-lower-dedekind-real-numbers funext univalence truncations public +open import real-numbers.inequality-real-numbers funext univalence truncations public +open import real-numbers.inequality-upper-dedekind-real-numbers funext univalence truncations public +open import real-numbers.lower-dedekind-real-numbers funext univalence truncations public +open import real-numbers.maximum-lower-dedekind-real-numbers funext univalence truncations public +open import real-numbers.maximum-real-numbers funext univalence truncations public +open import real-numbers.maximum-upper-dedekind-real-numbers funext univalence truncations public +open import real-numbers.metric-space-of-real-numbers funext univalence truncations public +open import real-numbers.minimum-lower-dedekind-real-numbers funext univalence truncations public +open import real-numbers.minimum-real-numbers funext univalence truncations public +open import real-numbers.minimum-upper-dedekind-real-numbers funext univalence truncations public +open import real-numbers.negation-lower-upper-dedekind-real-numbers funext univalence truncations public +open import real-numbers.negation-real-numbers funext univalence truncations public +open import real-numbers.raising-universe-levels-real-numbers funext univalence truncations public +open import real-numbers.rational-lower-dedekind-real-numbers funext univalence truncations public +open import real-numbers.rational-real-numbers funext univalence truncations public +open import real-numbers.rational-upper-dedekind-real-numbers funext univalence truncations public +open import real-numbers.similarity-real-numbers funext univalence truncations public +open import real-numbers.strict-inequality-real-numbers funext univalence truncations public +open import real-numbers.upper-dedekind-real-numbers funext univalence truncations public ``` diff --git a/src/real-numbers/addition-lower-dedekind-real-numbers.lagda.md b/src/real-numbers/addition-lower-dedekind-real-numbers.lagda.md index ca144b4c3f..bcb4242bc8 100644 --- a/src/real-numbers/addition-lower-dedekind-real-numbers.lagda.md +++ b/src/real-numbers/addition-lower-dedekind-real-numbers.lagda.md @@ -2,45 +2,52 @@ ```agda {-# OPTIONS --lossy-unification #-} - -module real-numbers.addition-lower-dedekind-real-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module real-numbers.addition-lower-dedekind-real-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.addition-rational-numbers -open import elementary-number-theory.additive-group-of-rational-numbers -open import elementary-number-theory.difference-rational-numbers -open import elementary-number-theory.positive-rational-numbers -open import elementary-number-theory.rational-numbers -open import elementary-number-theory.strict-inequality-rational-numbers +open import elementary-number-theory.addition-rational-numbers funext univalence truncations +open import elementary-number-theory.additive-group-of-rational-numbers funext univalence truncations +open import elementary-number-theory.difference-rational-numbers funext univalence truncations +open import elementary-number-theory.positive-rational-numbers funext univalence truncations +open import elementary-number-theory.rational-numbers funext univalence truncations +open import elementary-number-theory.strict-inequality-rational-numbers funext univalence truncations open import foundation.action-on-identifications-functions open import foundation.binary-transport -open import foundation.cartesian-product-types -open import foundation.conjunction +open import foundation.cartesian-product-types funext univalence +open import foundation.conjunction funext univalence truncations open import foundation.dependent-pair-types -open import foundation.existential-quantification -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.propositional-truncations -open import foundation.sets -open import foundation.subtypes +open import foundation.existential-quantification funext univalence truncations +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.propositional-truncations funext univalence +open import foundation.sets funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.transport-along-identifications open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.commutative-monoids -open import group-theory.groups -open import group-theory.minkowski-multiplication-commutative-monoids -open import group-theory.monoids -open import group-theory.semigroups +open import group-theory.abelian-groups funext univalence truncations +open import group-theory.commutative-monoids funext univalence truncations +open import group-theory.groups funext univalence truncations +open import group-theory.minkowski-multiplication-commutative-monoids funext univalence truncations +open import group-theory.monoids funext univalence truncations +open import group-theory.semigroups funext univalence -open import logic.functoriality-existential-quantification +open import logic.functoriality-existential-quantification funext univalence truncations -open import real-numbers.lower-dedekind-real-numbers -open import real-numbers.rational-lower-dedekind-real-numbers +open import real-numbers.lower-dedekind-real-numbers funext univalence truncations +open import real-numbers.rational-lower-dedekind-real-numbers funext univalence truncations ```
diff --git a/src/real-numbers/addition-upper-dedekind-real-numbers.lagda.md b/src/real-numbers/addition-upper-dedekind-real-numbers.lagda.md index a1b3ec48df..ddf6606c6c 100644 --- a/src/real-numbers/addition-upper-dedekind-real-numbers.lagda.md +++ b/src/real-numbers/addition-upper-dedekind-real-numbers.lagda.md @@ -2,42 +2,49 @@ ```agda {-# OPTIONS --lossy-unification #-} - -module real-numbers.addition-upper-dedekind-real-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module real-numbers.addition-upper-dedekind-real-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.addition-rational-numbers -open import elementary-number-theory.additive-group-of-rational-numbers -open import elementary-number-theory.difference-rational-numbers -open import elementary-number-theory.positive-rational-numbers -open import elementary-number-theory.rational-numbers -open import elementary-number-theory.strict-inequality-rational-numbers +open import elementary-number-theory.addition-rational-numbers funext univalence truncations +open import elementary-number-theory.additive-group-of-rational-numbers funext univalence truncations +open import elementary-number-theory.difference-rational-numbers funext univalence truncations +open import elementary-number-theory.positive-rational-numbers funext univalence truncations +open import elementary-number-theory.rational-numbers funext univalence truncations +open import elementary-number-theory.strict-inequality-rational-numbers funext univalence truncations open import foundation.action-on-identifications-functions open import foundation.binary-transport -open import foundation.cartesian-product-types -open import foundation.conjunction +open import foundation.cartesian-product-types funext univalence +open import foundation.conjunction funext univalence truncations open import foundation.dependent-pair-types -open import foundation.existential-quantification -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.propositional-truncations -open import foundation.subtypes +open import foundation.existential-quantification funext univalence truncations +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.propositional-truncations funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.transport-along-identifications open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.commutative-monoids -open import group-theory.groups -open import group-theory.minkowski-multiplication-commutative-monoids -open import group-theory.monoids -open import group-theory.semigroups +open import group-theory.abelian-groups funext univalence truncations +open import group-theory.commutative-monoids funext univalence truncations +open import group-theory.groups funext univalence truncations +open import group-theory.minkowski-multiplication-commutative-monoids funext univalence truncations +open import group-theory.monoids funext univalence truncations +open import group-theory.semigroups funext univalence -open import real-numbers.rational-upper-dedekind-real-numbers -open import real-numbers.upper-dedekind-real-numbers +open import real-numbers.rational-upper-dedekind-real-numbers funext univalence truncations +open import real-numbers.upper-dedekind-real-numbers funext univalence truncations ```
diff --git a/src/real-numbers/apartness-real-numbers.lagda.md b/src/real-numbers/apartness-real-numbers.lagda.md index da2485940d..89c9607c8b 100644 --- a/src/real-numbers/apartness-real-numbers.lagda.md +++ b/src/real-numbers/apartness-real-numbers.lagda.md @@ -1,27 +1,33 @@ # Apartness of real numbers ```agda -module real-numbers.apartness-real-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module real-numbers.apartness-real-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.apartness-relations -open import foundation.disjunction -open import foundation.empty-types -open import foundation.function-types -open import foundation.identity-types -open import foundation.large-apartness-relations -open import foundation.large-binary-relations -open import foundation.negated-equality -open import foundation.negation -open import foundation.propositions -open import foundation.transport-along-identifications +open import foundation.dependent-products-propositions funext +open import foundation.disjunction funext univalence truncations +open import foundation.empty-types funext univalence truncations +open import foundation.function-types funext +open import foundation.large-apartness-relations funext univalence truncations +open import foundation.large-binary-relations funext univalence truncations +open import foundation.negated-equality funext univalence truncations +open import foundation.negation funext +open import foundation.propositions funext univalence open import foundation.universe-levels -open import real-numbers.dedekind-real-numbers -open import real-numbers.strict-inequality-real-numbers +open import real-numbers.dedekind-real-numbers funext univalence truncations +open import real-numbers.strict-inequality-real-numbers funext univalence truncations ```
diff --git a/src/real-numbers/arithmetically-located-dedekind-cuts.lagda.md b/src/real-numbers/arithmetically-located-dedekind-cuts.lagda.md index 82cf6a86a3..a75ac62617 100644 --- a/src/real-numbers/arithmetically-located-dedekind-cuts.lagda.md +++ b/src/real-numbers/arithmetically-located-dedekind-cuts.lagda.md @@ -2,40 +2,42 @@ ```agda {-# OPTIONS --lossy-unification #-} - -module real-numbers.arithmetically-located-dedekind-cuts where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module real-numbers.arithmetically-located-dedekind-cuts + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.addition-rational-numbers -open import elementary-number-theory.additive-group-of-rational-numbers -open import elementary-number-theory.difference-rational-numbers -open import elementary-number-theory.inequality-rational-numbers -open import elementary-number-theory.positive-rational-numbers -open import elementary-number-theory.rational-numbers -open import elementary-number-theory.strict-inequality-rational-numbers - -open import foundation.binary-transport -open import foundation.cartesian-product-types -open import foundation.conjunction -open import foundation.coproduct-types +open import elementary-number-theory.addition-rational-numbers funext univalence truncations +open import elementary-number-theory.additive-group-of-rational-numbers funext univalence truncations +open import elementary-number-theory.difference-rational-numbers funext univalence truncations +open import elementary-number-theory.inequality-rational-numbers funext univalence truncations +open import elementary-number-theory.positive-rational-numbers funext univalence truncations +open import elementary-number-theory.rational-numbers funext univalence truncations +open import elementary-number-theory.strict-inequality-rational-numbers funext univalence truncations + +open import foundation.cartesian-product-types funext univalence +open import foundation.conjunction funext univalence truncations +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.disjunction -open import foundation.existential-quantification -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.raising-universe-levels -open import foundation.subtypes +open import foundation.disjunction funext univalence truncations +open import foundation.existential-quantification funext univalence truncations open import foundation.transport-along-identifications open import foundation.universe-levels -open import group-theory.abelian-groups +open import group-theory.abelian-groups funext univalence truncations -open import real-numbers.dedekind-real-numbers -open import real-numbers.lower-dedekind-real-numbers -open import real-numbers.upper-dedekind-real-numbers +open import real-numbers.dedekind-real-numbers funext univalence truncations +open import real-numbers.lower-dedekind-real-numbers funext univalence truncations +open import real-numbers.upper-dedekind-real-numbers funext univalence truncations ```
diff --git a/src/real-numbers/dedekind-real-numbers.lagda.md b/src/real-numbers/dedekind-real-numbers.lagda.md index 61408187db..44c73a9638 100644 --- a/src/real-numbers/dedekind-real-numbers.lagda.md +++ b/src/real-numbers/dedekind-real-numbers.lagda.md @@ -1,51 +1,53 @@ # Dedekind real numbers ```agda -module real-numbers.dedekind-real-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module real-numbers.dedekind-real-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.inequality-rational-numbers -open import elementary-number-theory.rational-numbers -open import elementary-number-theory.strict-inequality-rational-numbers +open import elementary-number-theory.inequality-rational-numbers funext univalence truncations +open import elementary-number-theory.rational-numbers funext univalence truncations +open import elementary-number-theory.strict-inequality-rational-numbers funext univalence truncations open import foundation.action-on-identifications-functions open import foundation.binary-transport -open import foundation.cartesian-product-types -open import foundation.complements-subtypes -open import foundation.conjunction -open import foundation.coproduct-types +open import foundation.conjunction funext univalence truncations +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.disjoint-subtypes -open import foundation.disjunction -open import foundation.embeddings -open import foundation.empty-types -open import foundation.equivalences -open import foundation.existential-quantification -open import foundation.function-types -open import foundation.functoriality-cartesian-product-types -open import foundation.functoriality-dependent-pair-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.negation -open import foundation.powersets -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.sets -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.disjoint-subtypes funext univalence truncations +open import foundation.disjunction funext univalence truncations +open import foundation.embeddings funext +open import foundation.empty-types funext univalence truncations +open import foundation.existential-quantification funext univalence truncations +open import foundation.function-types funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.negation funext +open import foundation.powersets funext univalence truncations +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.transport-along-identifications -open import foundation.truncated-types -open import foundation.universal-quantification +open import foundation.universal-quantification funext univalence truncations open import foundation.universe-levels -open import foundation-core.truncation-levels - -open import logic.functoriality-existential-quantification +open import logic.functoriality-existential-quantification funext univalence truncations -open import real-numbers.lower-dedekind-real-numbers -open import real-numbers.upper-dedekind-real-numbers +open import real-numbers.lower-dedekind-real-numbers funext univalence truncations +open import real-numbers.upper-dedekind-real-numbers funext univalence truncations ```
diff --git a/src/real-numbers/inequality-lower-dedekind-real-numbers.lagda.md b/src/real-numbers/inequality-lower-dedekind-real-numbers.lagda.md index e4765318c1..cde28686e7 100644 --- a/src/real-numbers/inequality-lower-dedekind-real-numbers.lagda.md +++ b/src/real-numbers/inequality-lower-dedekind-real-numbers.lagda.md @@ -2,35 +2,41 @@ ```agda {-# OPTIONS --lossy-unification #-} - -module real-numbers.inequality-lower-dedekind-real-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module real-numbers.inequality-lower-dedekind-real-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.inequality-rational-numbers -open import elementary-number-theory.rational-numbers -open import elementary-number-theory.strict-inequality-rational-numbers +open import elementary-number-theory.inequality-rational-numbers funext univalence truncations +open import elementary-number-theory.rational-numbers funext univalence truncations +open import elementary-number-theory.strict-inequality-rational-numbers funext univalence truncations -open import foundation.coproduct-types +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.existential-quantification -open import foundation.logical-equivalences -open import foundation.negation -open import foundation.powersets -open import foundation.propositions -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.empty-types funext univalence truncations +open import foundation.existential-quantification funext univalence truncations +open import foundation.logical-equivalences funext +open import foundation.propositions funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.unit-type open import foundation.universe-levels -open import order-theory.large-posets -open import order-theory.large-preorders -open import order-theory.top-elements-large-posets +open import order-theory.large-posets funext univalence truncations +open import order-theory.large-preorders funext univalence truncations +open import order-theory.top-elements-large-posets funext univalence truncations -open import real-numbers.lower-dedekind-real-numbers -open import real-numbers.rational-lower-dedekind-real-numbers +open import real-numbers.lower-dedekind-real-numbers funext univalence truncations +open import real-numbers.rational-lower-dedekind-real-numbers funext univalence truncations ```
diff --git a/src/real-numbers/inequality-real-numbers.lagda.md b/src/real-numbers/inequality-real-numbers.lagda.md index 098feec9e9..8fe69b9733 100644 --- a/src/real-numbers/inequality-real-numbers.lagda.md +++ b/src/real-numbers/inequality-real-numbers.lagda.md @@ -1,40 +1,42 @@ # Inequality on the real numbers ```agda -module real-numbers.inequality-real-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module real-numbers.inequality-real-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.inequality-rational-numbers -open import elementary-number-theory.rational-numbers -open import elementary-number-theory.strict-inequality-rational-numbers +open import elementary-number-theory.inequality-rational-numbers funext univalence truncations +open import elementary-number-theory.rational-numbers funext univalence truncations -open import foundation.complements-subtypes -open import foundation.coproduct-types +open import foundation.complements-subtypes funext univalence truncations open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.existential-quantification -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.propositions -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.existential-quantification funext univalence truncations +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.propositions funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels -open import order-theory.large-posets -open import order-theory.large-preorders -open import order-theory.posets -open import order-theory.preorders - -open import real-numbers.dedekind-real-numbers -open import real-numbers.inequality-lower-dedekind-real-numbers -open import real-numbers.inequality-upper-dedekind-real-numbers -open import real-numbers.lower-dedekind-real-numbers -open import real-numbers.negation-lower-upper-dedekind-real-numbers -open import real-numbers.negation-real-numbers -open import real-numbers.rational-real-numbers -open import real-numbers.upper-dedekind-real-numbers +open import order-theory.large-posets funext univalence truncations +open import order-theory.large-preorders funext univalence truncations +open import order-theory.posets funext univalence truncations +open import order-theory.preorders funext univalence truncations + +open import real-numbers.dedekind-real-numbers funext univalence truncations +open import real-numbers.inequality-lower-dedekind-real-numbers funext univalence truncations +open import real-numbers.inequality-upper-dedekind-real-numbers funext univalence truncations +open import real-numbers.rational-real-numbers funext univalence truncations ```
diff --git a/src/real-numbers/inequality-upper-dedekind-real-numbers.lagda.md b/src/real-numbers/inequality-upper-dedekind-real-numbers.lagda.md index 4493915e37..bf8dd1f772 100644 --- a/src/real-numbers/inequality-upper-dedekind-real-numbers.lagda.md +++ b/src/real-numbers/inequality-upper-dedekind-real-numbers.lagda.md @@ -2,34 +2,41 @@ ```agda {-# OPTIONS --lossy-unification #-} - -module real-numbers.inequality-upper-dedekind-real-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module real-numbers.inequality-upper-dedekind-real-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.inequality-rational-numbers -open import elementary-number-theory.rational-numbers -open import elementary-number-theory.strict-inequality-rational-numbers +open import elementary-number-theory.inequality-rational-numbers funext univalence truncations +open import elementary-number-theory.rational-numbers funext univalence truncations +open import elementary-number-theory.strict-inequality-rational-numbers funext univalence truncations -open import foundation.coproduct-types +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.existential-quantification -open import foundation.logical-equivalences -open import foundation.powersets -open import foundation.propositions -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.empty-types funext univalence truncations +open import foundation.existential-quantification funext univalence truncations +open import foundation.logical-equivalences funext +open import foundation.propositions funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.unit-type open import foundation.universe-levels -open import order-theory.bottom-elements-large-posets -open import order-theory.large-posets -open import order-theory.large-preorders +open import order-theory.bottom-elements-large-posets funext univalence truncations +open import order-theory.large-posets funext univalence truncations +open import order-theory.large-preorders funext univalence truncations -open import real-numbers.rational-upper-dedekind-real-numbers -open import real-numbers.upper-dedekind-real-numbers +open import real-numbers.rational-upper-dedekind-real-numbers funext univalence truncations +open import real-numbers.upper-dedekind-real-numbers funext univalence truncations ```
diff --git a/src/real-numbers/lower-dedekind-real-numbers.lagda.md b/src/real-numbers/lower-dedekind-real-numbers.lagda.md index f48a04eb47..7e5b74890e 100644 --- a/src/real-numbers/lower-dedekind-real-numbers.lagda.md +++ b/src/real-numbers/lower-dedekind-real-numbers.lagda.md @@ -2,36 +2,45 @@ ```agda {-# OPTIONS --lossy-unification #-} - -module real-numbers.lower-dedekind-real-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module real-numbers.lower-dedekind-real-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.addition-rational-numbers -open import elementary-number-theory.difference-rational-numbers -open import elementary-number-theory.inequality-rational-numbers -open import elementary-number-theory.positive-rational-numbers -open import elementary-number-theory.rational-numbers -open import elementary-number-theory.strict-inequality-rational-numbers - -open import foundation.conjunction -open import foundation.coproduct-types +open import elementary-number-theory.addition-rational-numbers funext univalence truncations +open import elementary-number-theory.difference-rational-numbers funext univalence truncations +open import elementary-number-theory.inequality-rational-numbers funext univalence truncations +open import elementary-number-theory.positive-rational-numbers funext univalence truncations +open import elementary-number-theory.rational-numbers funext univalence truncations +open import elementary-number-theory.strict-inequality-rational-numbers funext univalence truncations + +open import foundation.conjunction funext univalence truncations +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.existential-quantification -open import foundation.function-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.powersets -open import foundation.propositions -open import foundation.sets -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.dependent-products-truncated-types funext +open import foundation.existential-quantification funext univalence truncations +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.powersets funext univalence truncations +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.transport-along-identifications -open import foundation.truncated-types +open import foundation.truncated-types funext univalence open import foundation.truncation-levels open import foundation.unit-type -open import foundation.universal-quantification +open import foundation.universal-quantification funext univalence truncations open import foundation.universe-levels ``` diff --git a/src/real-numbers/maximum-lower-dedekind-real-numbers.lagda.md b/src/real-numbers/maximum-lower-dedekind-real-numbers.lagda.md index 6073388da0..3114f24608 100644 --- a/src/real-numbers/maximum-lower-dedekind-real-numbers.lagda.md +++ b/src/real-numbers/maximum-lower-dedekind-real-numbers.lagda.md @@ -2,38 +2,45 @@ ```agda {-# OPTIONS --lossy-unification #-} - -module real-numbers.maximum-lower-dedekind-real-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module real-numbers.maximum-lower-dedekind-real-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.rational-numbers -open import elementary-number-theory.strict-inequality-rational-numbers +open import elementary-number-theory.rational-numbers funext univalence truncations +open import elementary-number-theory.strict-inequality-rational-numbers funext univalence truncations -open import foundation.conjunction +open import foundation.conjunction funext univalence truncations open import foundation.dependent-pair-types -open import foundation.disjunction -open import foundation.existential-quantification -open import foundation.function-types -open import foundation.functoriality-cartesian-product-types -open import foundation.inhabited-types -open import foundation.logical-equivalences -open import foundation.powersets -open import foundation.propositional-truncations -open import foundation.subtypes -open import foundation.unions-subtypes +open import foundation.disjunction funext univalence truncations +open import foundation.existential-quantification funext univalence truncations +open import foundation.function-types funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.inhabited-types funext univalence truncations +open import foundation.logical-equivalences funext +open import foundation.powersets funext univalence truncations +open import foundation.propositional-truncations funext univalence +open import foundation.subtypes funext univalence truncations +open import foundation.unions-subtypes funext univalence truncations open import foundation.universe-levels -open import logic.functoriality-existential-quantification +open import logic.functoriality-existential-quantification funext univalence truncations -open import order-theory.large-suplattices -open import order-theory.least-upper-bounds-large-posets -open import order-theory.upper-bounds-large-posets +open import order-theory.large-suplattices funext univalence truncations +open import order-theory.least-upper-bounds-large-posets funext univalence truncations +open import order-theory.upper-bounds-large-posets funext univalence truncations -open import real-numbers.inequality-lower-dedekind-real-numbers -open import real-numbers.lower-dedekind-real-numbers +open import real-numbers.inequality-lower-dedekind-real-numbers funext univalence truncations +open import real-numbers.lower-dedekind-real-numbers funext univalence truncations ```
diff --git a/src/real-numbers/maximum-real-numbers.lagda.md b/src/real-numbers/maximum-real-numbers.lagda.md index 4afed197b7..866ca6e2ab 100644 --- a/src/real-numbers/maximum-real-numbers.lagda.md +++ b/src/real-numbers/maximum-real-numbers.lagda.md @@ -2,28 +2,35 @@ ```agda {-# OPTIONS --lossy-unification #-} - -module real-numbers.maximum-real-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module real-numbers.maximum-real-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.disjunction -open import foundation.empty-types -open import foundation.propositions +open import foundation.disjunction funext univalence truncations +open import foundation.empty-types funext univalence truncations +open import foundation.propositions funext univalence open import foundation.universe-levels -open import order-theory.large-join-semilattices -open import order-theory.least-upper-bounds-large-posets +open import order-theory.large-join-semilattices funext univalence truncations +open import order-theory.least-upper-bounds-large-posets funext univalence truncations -open import real-numbers.dedekind-real-numbers -open import real-numbers.inequality-real-numbers -open import real-numbers.lower-dedekind-real-numbers -open import real-numbers.maximum-lower-dedekind-real-numbers -open import real-numbers.maximum-upper-dedekind-real-numbers -open import real-numbers.upper-dedekind-real-numbers +open import real-numbers.dedekind-real-numbers funext univalence truncations +open import real-numbers.inequality-real-numbers funext univalence truncations +open import real-numbers.lower-dedekind-real-numbers funext univalence truncations +open import real-numbers.maximum-lower-dedekind-real-numbers funext univalence truncations +open import real-numbers.maximum-upper-dedekind-real-numbers funext univalence truncations +open import real-numbers.upper-dedekind-real-numbers funext univalence truncations ```
diff --git a/src/real-numbers/maximum-upper-dedekind-real-numbers.lagda.md b/src/real-numbers/maximum-upper-dedekind-real-numbers.lagda.md index b4eb768f8b..1a23709136 100644 --- a/src/real-numbers/maximum-upper-dedekind-real-numbers.lagda.md +++ b/src/real-numbers/maximum-upper-dedekind-real-numbers.lagda.md @@ -2,39 +2,46 @@ ```agda {-# OPTIONS --lossy-unification #-} - -module real-numbers.maximum-upper-dedekind-real-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module real-numbers.maximum-upper-dedekind-real-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.maximum-rational-numbers -open import elementary-number-theory.rational-numbers -open import elementary-number-theory.strict-inequality-rational-numbers +open import elementary-number-theory.maximum-rational-numbers funext univalence truncations +open import elementary-number-theory.rational-numbers funext univalence truncations +open import elementary-number-theory.strict-inequality-rational-numbers funext univalence truncations -open import foundation.cartesian-product-types -open import foundation.conjunction +open import foundation.cartesian-product-types funext univalence +open import foundation.conjunction funext univalence truncations open import foundation.dependent-pair-types -open import foundation.disjunction -open import foundation.existential-quantification -open import foundation.function-types -open import foundation.functoriality-cartesian-product-types -open import foundation.inhabited-types -open import foundation.intersections-subtypes -open import foundation.logical-equivalences -open import foundation.powersets -open import foundation.propositional-truncations -open import foundation.subtypes +open import foundation.disjunction funext univalence truncations +open import foundation.existential-quantification funext univalence truncations +open import foundation.function-types funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.inhabited-types funext univalence truncations +open import foundation.intersections-subtypes funext univalence truncations +open import foundation.logical-equivalences funext +open import foundation.powersets funext univalence truncations +open import foundation.propositional-truncations funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels -open import logic.functoriality-existential-quantification +open import logic.functoriality-existential-quantification funext univalence truncations -open import order-theory.large-join-semilattices -open import order-theory.least-upper-bounds-large-posets +open import order-theory.large-join-semilattices funext univalence truncations +open import order-theory.least-upper-bounds-large-posets funext univalence truncations -open import real-numbers.inequality-upper-dedekind-real-numbers -open import real-numbers.upper-dedekind-real-numbers +open import real-numbers.inequality-upper-dedekind-real-numbers funext univalence truncations +open import real-numbers.upper-dedekind-real-numbers funext univalence truncations ```
diff --git a/src/real-numbers/metric-space-of-real-numbers.lagda.md b/src/real-numbers/metric-space-of-real-numbers.lagda.md index 9db327d03c..c5af297209 100644 --- a/src/real-numbers/metric-space-of-real-numbers.lagda.md +++ b/src/real-numbers/metric-space-of-real-numbers.lagda.md @@ -2,52 +2,54 @@ ```agda {-# OPTIONS --lossy-unification #-} - -module real-numbers.metric-space-of-real-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module real-numbers.metric-space-of-real-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.addition-rational-numbers -open import elementary-number-theory.difference-rational-numbers -open import elementary-number-theory.inequality-rational-numbers -open import elementary-number-theory.positive-rational-numbers -open import elementary-number-theory.rational-numbers -open import elementary-number-theory.strict-inequality-rational-numbers +open import elementary-number-theory.addition-rational-numbers funext univalence truncations +open import elementary-number-theory.difference-rational-numbers funext univalence truncations +open import elementary-number-theory.positive-rational-numbers funext univalence truncations +open import elementary-number-theory.rational-numbers funext univalence truncations open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types -open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.diagonal-maps-cartesian-products-of-types -open import foundation.empty-types -open import foundation.existential-quantification -open import foundation.function-types -open import foundation.functoriality-cartesian-product-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.propositions -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.diagonal-maps-cartesian-products-of-types funext univalence +open import foundation.existential-quantification funext univalence truncations +open import foundation.function-types funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.propositions funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.transport-along-identifications open import foundation.universe-levels -open import metric-spaces.extensional-premetric-structures -open import metric-spaces.isometries-metric-spaces -open import metric-spaces.metric-space-of-rational-numbers -open import metric-spaces.metric-spaces -open import metric-spaces.metric-structures -open import metric-spaces.monotonic-premetric-structures -open import metric-spaces.premetric-spaces -open import metric-spaces.premetric-structures -open import metric-spaces.pseudometric-structures -open import metric-spaces.reflexive-premetric-structures -open import metric-spaces.saturated-metric-spaces -open import metric-spaces.symmetric-premetric-structures -open import metric-spaces.triangular-premetric-structures - -open import real-numbers.dedekind-real-numbers -open import real-numbers.rational-real-numbers +open import metric-spaces.extensional-premetric-structures funext univalence truncations +open import metric-spaces.isometries-metric-spaces funext univalence truncations +open import metric-spaces.metric-space-of-rational-numbers funext univalence truncations +open import metric-spaces.metric-spaces funext univalence truncations +open import metric-spaces.metric-structures funext univalence truncations +open import metric-spaces.premetric-spaces funext univalence truncations +open import metric-spaces.premetric-structures funext univalence truncations +open import metric-spaces.pseudometric-structures funext univalence truncations +open import metric-spaces.reflexive-premetric-structures funext univalence truncations +open import metric-spaces.saturated-metric-spaces funext univalence truncations +open import metric-spaces.symmetric-premetric-structures funext univalence truncations +open import metric-spaces.triangular-premetric-structures funext univalence truncations + +open import real-numbers.dedekind-real-numbers funext univalence truncations +open import real-numbers.rational-real-numbers funext univalence truncations ```
diff --git a/src/real-numbers/minimum-lower-dedekind-real-numbers.lagda.md b/src/real-numbers/minimum-lower-dedekind-real-numbers.lagda.md index 860e3cee2a..afd74ca5b8 100644 --- a/src/real-numbers/minimum-lower-dedekind-real-numbers.lagda.md +++ b/src/real-numbers/minimum-lower-dedekind-real-numbers.lagda.md @@ -2,34 +2,41 @@ ```agda {-# OPTIONS --lossy-unification #-} - -module real-numbers.minimum-lower-dedekind-real-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module real-numbers.minimum-lower-dedekind-real-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.minimum-rational-numbers -open import elementary-number-theory.rational-numbers -open import elementary-number-theory.strict-inequality-rational-numbers +open import elementary-number-theory.minimum-rational-numbers funext univalence truncations +open import elementary-number-theory.rational-numbers funext univalence truncations +open import elementary-number-theory.strict-inequality-rational-numbers funext univalence truncations -open import foundation.cartesian-product-types -open import foundation.conjunction +open import foundation.cartesian-product-types funext univalence +open import foundation.conjunction funext univalence truncations open import foundation.dependent-pair-types -open import foundation.existential-quantification -open import foundation.intersections-subtypes -open import foundation.logical-equivalences -open import foundation.subtypes +open import foundation.existential-quantification funext univalence truncations +open import foundation.intersections-subtypes funext univalence truncations +open import foundation.logical-equivalences funext +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels -open import logic.functoriality-existential-quantification +open import logic.functoriality-existential-quantification funext univalence truncations -open import order-theory.greatest-lower-bounds-large-posets -open import order-theory.large-meet-semilattices -open import order-theory.lower-bounds-large-posets +open import order-theory.greatest-lower-bounds-large-posets funext univalence truncations +open import order-theory.large-meet-semilattices funext univalence truncations +open import order-theory.lower-bounds-large-posets funext univalence truncations -open import real-numbers.inequality-lower-dedekind-real-numbers -open import real-numbers.lower-dedekind-real-numbers +open import real-numbers.inequality-lower-dedekind-real-numbers funext univalence truncations +open import real-numbers.lower-dedekind-real-numbers funext univalence truncations ```
diff --git a/src/real-numbers/minimum-real-numbers.lagda.md b/src/real-numbers/minimum-real-numbers.lagda.md index 4d1e853bee..a8bed45b6e 100644 --- a/src/real-numbers/minimum-real-numbers.lagda.md +++ b/src/real-numbers/minimum-real-numbers.lagda.md @@ -2,28 +2,35 @@ ```agda {-# OPTIONS --lossy-unification #-} - -module real-numbers.minimum-real-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module real-numbers.minimum-real-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.disjunction -open import foundation.empty-types -open import foundation.propositions +open import foundation.disjunction funext univalence truncations +open import foundation.empty-types funext univalence truncations +open import foundation.propositions funext univalence open import foundation.universe-levels -open import order-theory.greatest-lower-bounds-large-posets -open import order-theory.large-meet-semilattices +open import order-theory.greatest-lower-bounds-large-posets funext univalence truncations +open import order-theory.large-meet-semilattices funext univalence truncations -open import real-numbers.dedekind-real-numbers -open import real-numbers.inequality-real-numbers -open import real-numbers.lower-dedekind-real-numbers -open import real-numbers.minimum-lower-dedekind-real-numbers -open import real-numbers.minimum-upper-dedekind-real-numbers -open import real-numbers.upper-dedekind-real-numbers +open import real-numbers.dedekind-real-numbers funext univalence truncations +open import real-numbers.inequality-real-numbers funext univalence truncations +open import real-numbers.lower-dedekind-real-numbers funext univalence truncations +open import real-numbers.minimum-lower-dedekind-real-numbers funext univalence truncations +open import real-numbers.minimum-upper-dedekind-real-numbers funext univalence truncations +open import real-numbers.upper-dedekind-real-numbers funext univalence truncations ```
diff --git a/src/real-numbers/minimum-upper-dedekind-real-numbers.lagda.md b/src/real-numbers/minimum-upper-dedekind-real-numbers.lagda.md index c157bd88b8..bab0530652 100644 --- a/src/real-numbers/minimum-upper-dedekind-real-numbers.lagda.md +++ b/src/real-numbers/minimum-upper-dedekind-real-numbers.lagda.md @@ -2,38 +2,45 @@ ```agda {-# OPTIONS --lossy-unification #-} - -module real-numbers.minimum-upper-dedekind-real-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module real-numbers.minimum-upper-dedekind-real-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.rational-numbers -open import elementary-number-theory.strict-inequality-rational-numbers +open import elementary-number-theory.rational-numbers funext univalence truncations +open import elementary-number-theory.strict-inequality-rational-numbers funext univalence truncations -open import foundation.conjunction +open import foundation.conjunction funext univalence truncations open import foundation.dependent-pair-types -open import foundation.disjunction -open import foundation.existential-quantification -open import foundation.function-types -open import foundation.functoriality-cartesian-product-types -open import foundation.inhabited-types -open import foundation.logical-equivalences -open import foundation.powersets -open import foundation.propositional-truncations -open import foundation.subtypes -open import foundation.unions-subtypes +open import foundation.disjunction funext univalence truncations +open import foundation.existential-quantification funext univalence truncations +open import foundation.function-types funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.inhabited-types funext univalence truncations +open import foundation.logical-equivalences funext +open import foundation.powersets funext univalence truncations +open import foundation.propositional-truncations funext univalence +open import foundation.subtypes funext univalence truncations +open import foundation.unions-subtypes funext univalence truncations open import foundation.universe-levels -open import logic.functoriality-existential-quantification +open import logic.functoriality-existential-quantification funext univalence truncations -open import order-theory.greatest-lower-bounds-large-posets -open import order-theory.large-inflattices -open import order-theory.lower-bounds-large-posets +open import order-theory.greatest-lower-bounds-large-posets funext univalence truncations +open import order-theory.large-inflattices funext univalence truncations +open import order-theory.lower-bounds-large-posets funext univalence truncations -open import real-numbers.inequality-upper-dedekind-real-numbers -open import real-numbers.upper-dedekind-real-numbers +open import real-numbers.inequality-upper-dedekind-real-numbers funext univalence truncations +open import real-numbers.upper-dedekind-real-numbers funext univalence truncations ```
diff --git a/src/real-numbers/negation-lower-upper-dedekind-real-numbers.lagda.md b/src/real-numbers/negation-lower-upper-dedekind-real-numbers.lagda.md index 5ee824c84c..25920b26df 100644 --- a/src/real-numbers/negation-lower-upper-dedekind-real-numbers.lagda.md +++ b/src/real-numbers/negation-lower-upper-dedekind-real-numbers.lagda.md @@ -2,38 +2,43 @@ ```agda {-# OPTIONS --lossy-unification #-} - -module real-numbers.negation-lower-upper-dedekind-real-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module real-numbers.negation-lower-upper-dedekind-real-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.rational-numbers -open import elementary-number-theory.strict-inequality-rational-numbers +open import elementary-number-theory.rational-numbers funext univalence truncations +open import elementary-number-theory.strict-inequality-rational-numbers funext univalence truncations -open import foundation.cartesian-product-types -open import foundation.conjunction +open import foundation.cartesian-product-types funext univalence +open import foundation.conjunction funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.existential-quantification -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.powersets -open import foundation.retractions -open import foundation.sections -open import foundation.subtypes +open import foundation.equivalences funext +open import foundation.existential-quantification funext univalence truncations +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.powersets funext univalence truncations +open import foundation.retractions funext +open import foundation.sections funext +open import foundation.subtypes funext univalence truncations open import foundation.transport-along-identifications open import foundation.universe-levels -open import logic.functoriality-existential-quantification +open import logic.functoriality-existential-quantification funext univalence truncations -open import real-numbers.inequality-lower-dedekind-real-numbers -open import real-numbers.inequality-upper-dedekind-real-numbers -open import real-numbers.lower-dedekind-real-numbers -open import real-numbers.rational-lower-dedekind-real-numbers -open import real-numbers.rational-upper-dedekind-real-numbers -open import real-numbers.upper-dedekind-real-numbers +open import real-numbers.lower-dedekind-real-numbers funext univalence truncations +open import real-numbers.rational-lower-dedekind-real-numbers funext univalence truncations +open import real-numbers.rational-upper-dedekind-real-numbers funext univalence truncations +open import real-numbers.upper-dedekind-real-numbers funext univalence truncations ```
diff --git a/src/real-numbers/negation-real-numbers.lagda.md b/src/real-numbers/negation-real-numbers.lagda.md index f86c08a666..145db757da 100644 --- a/src/real-numbers/negation-real-numbers.lagda.md +++ b/src/real-numbers/negation-real-numbers.lagda.md @@ -2,44 +2,37 @@ ```agda {-# OPTIONS --lossy-unification #-} - -module real-numbers.negation-real-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module real-numbers.negation-real-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.positive-rational-numbers -open import elementary-number-theory.rational-numbers -open import elementary-number-theory.strict-inequality-rational-numbers +open import elementary-number-theory.rational-numbers funext univalence truncations +open import elementary-number-theory.strict-inequality-rational-numbers funext univalence truncations -open import foundation.cartesian-product-types -open import foundation.conjunction -open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.disjoint-subtypes -open import foundation.disjunction -open import foundation.empty-types -open import foundation.existential-quantification -open import foundation.function-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.negation -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.subtypes +open import foundation.disjoint-subtypes funext univalence truncations +open import foundation.disjunction funext univalence truncations +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.subtypes funext univalence truncations open import foundation.transport-along-identifications open import foundation.universe-levels -open import logic.functoriality-existential-quantification - -open import real-numbers.dedekind-real-numbers -open import real-numbers.lower-dedekind-real-numbers -open import real-numbers.negation-lower-upper-dedekind-real-numbers -open import real-numbers.rational-lower-dedekind-real-numbers -open import real-numbers.rational-real-numbers -open import real-numbers.rational-upper-dedekind-real-numbers -open import real-numbers.upper-dedekind-real-numbers +open import real-numbers.dedekind-real-numbers funext univalence truncations +open import real-numbers.lower-dedekind-real-numbers funext univalence truncations +open import real-numbers.negation-lower-upper-dedekind-real-numbers funext univalence truncations +open import real-numbers.rational-real-numbers funext univalence truncations +open import real-numbers.upper-dedekind-real-numbers funext univalence truncations ```
diff --git a/src/real-numbers/raising-universe-levels-real-numbers.lagda.md b/src/real-numbers/raising-universe-levels-real-numbers.lagda.md index 422760c592..77a36a7284 100644 --- a/src/real-numbers/raising-universe-levels-real-numbers.lagda.md +++ b/src/real-numbers/raising-universe-levels-real-numbers.lagda.md @@ -1,36 +1,44 @@ # Raising the universe levels of real numbers ```agda -module real-numbers.raising-universe-levels-real-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module real-numbers.raising-universe-levels-real-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.rational-numbers -open import elementary-number-theory.strict-inequality-rational-numbers +open import elementary-number-theory.rational-numbers funext univalence truncations +open import elementary-number-theory.strict-inequality-rational-numbers funext univalence truncations -open import foundation.cartesian-product-types -open import foundation.conjunction +open import foundation.cartesian-product-types funext univalence +open import foundation.conjunction funext univalence truncations open import foundation.dependent-pair-types -open import foundation.disjunction -open import foundation.existential-quantification -open import foundation.function-types -open import foundation.functoriality-cartesian-product-types -open import foundation.identity-types -open import foundation.inhabited-subtypes -open import foundation.logical-equivalences -open import foundation.negation -open import foundation.raising-universe-levels -open import foundation.subtypes +open import foundation.disjunction funext univalence truncations +open import foundation.existential-quantification funext univalence truncations +open import foundation.function-types funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.identity-types funext +open import foundation.inhabited-subtypes funext univalence truncations +open import foundation.logical-equivalences funext +open import foundation.negation funext +open import foundation.raising-universe-levels funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels -open import logic.functoriality-existential-quantification +open import logic.functoriality-existential-quantification funext univalence truncations -open import real-numbers.dedekind-real-numbers -open import real-numbers.lower-dedekind-real-numbers -open import real-numbers.similarity-real-numbers -open import real-numbers.upper-dedekind-real-numbers +open import real-numbers.dedekind-real-numbers funext univalence truncations +open import real-numbers.lower-dedekind-real-numbers funext univalence truncations +open import real-numbers.similarity-real-numbers funext univalence truncations +open import real-numbers.upper-dedekind-real-numbers funext univalence truncations ```
diff --git a/src/real-numbers/rational-lower-dedekind-real-numbers.lagda.md b/src/real-numbers/rational-lower-dedekind-real-numbers.lagda.md index 5176279b29..c29c837769 100644 --- a/src/real-numbers/rational-lower-dedekind-real-numbers.lagda.md +++ b/src/real-numbers/rational-lower-dedekind-real-numbers.lagda.md @@ -1,23 +1,31 @@ # Rational lower Dedekind real numbers ```agda -module real-numbers.rational-lower-dedekind-real-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module real-numbers.rational-lower-dedekind-real-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.rational-numbers -open import elementary-number-theory.strict-inequality-rational-numbers +open import elementary-number-theory.rational-numbers funext univalence truncations +open import elementary-number-theory.strict-inequality-rational-numbers funext univalence truncations -open import foundation.conjunction +open import foundation.conjunction funext univalence truncations open import foundation.dependent-pair-types -open import foundation.existential-quantification -open import foundation.logical-equivalences -open import foundation.subtypes +open import foundation.existential-quantification funext univalence truncations +open import foundation.logical-equivalences funext +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels -open import real-numbers.lower-dedekind-real-numbers +open import real-numbers.lower-dedekind-real-numbers funext univalence truncations ```
diff --git a/src/real-numbers/rational-real-numbers.lagda.md b/src/real-numbers/rational-real-numbers.lagda.md index 19ff6b404c..57534f2578 100644 --- a/src/real-numbers/rational-real-numbers.lagda.md +++ b/src/real-numbers/rational-real-numbers.lagda.md @@ -2,47 +2,44 @@ ```agda {-# OPTIONS --lossy-unification #-} - -module real-numbers.rational-real-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module real-numbers.rational-real-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.inequality-rational-numbers -open import elementary-number-theory.rational-numbers -open import elementary-number-theory.strict-inequality-rational-numbers +open import elementary-number-theory.rational-numbers funext univalence truncations +open import elementary-number-theory.strict-inequality-rational-numbers funext univalence truncations open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types -open import foundation.conjunction +open import foundation.conjunction funext univalence truncations open import foundation.dependent-pair-types -open import foundation.disjunction -open import foundation.embeddings -open import foundation.empty-types -open import foundation.equivalences -open import foundation.existential-quantification -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.negation -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.retractions -open import foundation.sections -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.disjunction funext univalence truncations +open import foundation.empty-types funext univalence truncations +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.negation funext +open import foundation.propositions funext univalence +open import foundation.retractions funext +open import foundation.sections funext +open import foundation.subtypes funext univalence truncations open import foundation.transport-along-identifications open import foundation.universe-levels -open import logic.functoriality-existential-quantification - -open import real-numbers.dedekind-real-numbers -open import real-numbers.lower-dedekind-real-numbers -open import real-numbers.rational-lower-dedekind-real-numbers -open import real-numbers.rational-upper-dedekind-real-numbers -open import real-numbers.similarity-real-numbers -open import real-numbers.upper-dedekind-real-numbers +open import real-numbers.dedekind-real-numbers funext univalence truncations +open import real-numbers.rational-lower-dedekind-real-numbers funext univalence truncations +open import real-numbers.rational-upper-dedekind-real-numbers funext univalence truncations +open import real-numbers.similarity-real-numbers funext univalence truncations ```
diff --git a/src/real-numbers/rational-upper-dedekind-real-numbers.lagda.md b/src/real-numbers/rational-upper-dedekind-real-numbers.lagda.md index f88c510a18..23c1466919 100644 --- a/src/real-numbers/rational-upper-dedekind-real-numbers.lagda.md +++ b/src/real-numbers/rational-upper-dedekind-real-numbers.lagda.md @@ -1,23 +1,31 @@ # Rational upper Dedekind real numbers ```agda -module real-numbers.rational-upper-dedekind-real-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module real-numbers.rational-upper-dedekind-real-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.rational-numbers -open import elementary-number-theory.strict-inequality-rational-numbers +open import elementary-number-theory.rational-numbers funext univalence truncations +open import elementary-number-theory.strict-inequality-rational-numbers funext univalence truncations -open import foundation.conjunction +open import foundation.conjunction funext univalence truncations open import foundation.dependent-pair-types -open import foundation.existential-quantification -open import foundation.logical-equivalences -open import foundation.subtypes +open import foundation.existential-quantification funext univalence truncations +open import foundation.logical-equivalences funext +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels -open import real-numbers.upper-dedekind-real-numbers +open import real-numbers.upper-dedekind-real-numbers funext univalence truncations ```
diff --git a/src/real-numbers/similarity-real-numbers.lagda.md b/src/real-numbers/similarity-real-numbers.lagda.md index 5691544027..119dfb1554 100644 --- a/src/real-numbers/similarity-real-numbers.lagda.md +++ b/src/real-numbers/similarity-real-numbers.lagda.md @@ -1,29 +1,30 @@ # Similarity of real numbers ```agda -module real-numbers.similarity-real-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module real-numbers.similarity-real-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.strict-inequality-rational-numbers - open import foundation.dependent-pair-types -open import foundation.disjunction -open import foundation.empty-types -open import foundation.function-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.powersets -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.powersets funext univalence truncations +open import foundation.propositions funext univalence open import foundation.transport-along-identifications open import foundation.universe-levels -open import order-theory.large-posets -open import order-theory.similarity-of-elements-large-posets - -open import real-numbers.dedekind-real-numbers +open import real-numbers.dedekind-real-numbers funext univalence truncations ```
diff --git a/src/real-numbers/strict-inequality-real-numbers.lagda.md b/src/real-numbers/strict-inequality-real-numbers.lagda.md index 0deea45410..37f23b7dc6 100644 --- a/src/real-numbers/strict-inequality-real-numbers.lagda.md +++ b/src/real-numbers/strict-inequality-real-numbers.lagda.md @@ -2,41 +2,47 @@ ```agda {-# OPTIONS --lossy-unification #-} - -module real-numbers.strict-inequality-real-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module real-numbers.strict-inequality-real-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.rational-numbers -open import elementary-number-theory.strict-inequality-rational-numbers +open import elementary-number-theory.rational-numbers funext univalence truncations +open import elementary-number-theory.strict-inequality-rational-numbers funext univalence truncations -open import foundation.cartesian-product-types -open import foundation.conjunction -open import foundation.coproduct-types +open import foundation.conjunction funext univalence truncations +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.disjunction -open import foundation.empty-types -open import foundation.existential-quantification -open import foundation.function-types -open import foundation.functoriality-cartesian-product-types -open import foundation.identity-types -open import foundation.large-binary-relations -open import foundation.logical-equivalences -open import foundation.negation -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.disjunction funext univalence truncations +open import foundation.empty-types funext univalence truncations +open import foundation.existential-quantification funext univalence truncations +open import foundation.function-types funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.identity-types funext +open import foundation.large-binary-relations funext univalence truncations +open import foundation.logical-equivalences funext +open import foundation.negation funext +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence open import foundation.transport-along-identifications open import foundation.universe-levels -open import logic.functoriality-existential-quantification +open import logic.functoriality-existential-quantification funext univalence truncations -open import real-numbers.dedekind-real-numbers -open import real-numbers.inequality-real-numbers -open import real-numbers.negation-real-numbers -open import real-numbers.rational-real-numbers +open import real-numbers.dedekind-real-numbers funext univalence truncations +open import real-numbers.inequality-real-numbers funext univalence truncations +open import real-numbers.negation-real-numbers funext univalence truncations +open import real-numbers.rational-real-numbers funext univalence truncations ```
diff --git a/src/real-numbers/upper-dedekind-real-numbers.lagda.md b/src/real-numbers/upper-dedekind-real-numbers.lagda.md index 2b0dcc2fdb..3d33cb2edd 100644 --- a/src/real-numbers/upper-dedekind-real-numbers.lagda.md +++ b/src/real-numbers/upper-dedekind-real-numbers.lagda.md @@ -2,36 +2,45 @@ ```agda {-# OPTIONS --lossy-unification #-} - -module real-numbers.upper-dedekind-real-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module real-numbers.upper-dedekind-real-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.addition-rational-numbers -open import elementary-number-theory.difference-rational-numbers -open import elementary-number-theory.inequality-rational-numbers -open import elementary-number-theory.positive-rational-numbers -open import elementary-number-theory.rational-numbers -open import elementary-number-theory.strict-inequality-rational-numbers - -open import foundation.conjunction -open import foundation.coproduct-types +open import elementary-number-theory.addition-rational-numbers funext univalence truncations +open import elementary-number-theory.difference-rational-numbers funext univalence truncations +open import elementary-number-theory.inequality-rational-numbers funext univalence truncations +open import elementary-number-theory.positive-rational-numbers funext univalence truncations +open import elementary-number-theory.rational-numbers funext univalence truncations +open import elementary-number-theory.strict-inequality-rational-numbers funext univalence truncations + +open import foundation.conjunction funext univalence truncations +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.existential-quantification -open import foundation.function-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.powersets -open import foundation.propositions -open import foundation.sets -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.dependent-products-truncated-types funext +open import foundation.existential-quantification funext univalence truncations +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.powersets funext univalence truncations +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.transport-along-identifications -open import foundation.truncated-types +open import foundation.truncated-types funext univalence open import foundation.truncation-levels open import foundation.unit-type -open import foundation.universal-quantification +open import foundation.universal-quantification funext univalence truncations open import foundation.universe-levels ``` diff --git a/src/reflection.lagda.md b/src/reflection.lagda.md index 0e4c56b9dc..f48eb45963 100644 --- a/src/reflection.lagda.md +++ b/src/reflection.lagda.md @@ -7,19 +7,27 @@ ## Modules in the reflection namespace ```agda -module reflection where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module reflection + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where open import reflection.abstractions public open import reflection.arguments public -open import reflection.boolean-reflection public +open import reflection.boolean-reflection funext univalence truncations public open import reflection.definitions public open import reflection.erasing-equality public -open import reflection.fixity public -open import reflection.group-solver public +open import reflection.fixity funext univalence truncations public +open import reflection.group-solver funext univalence truncations public open import reflection.literals public open import reflection.metavariables public open import reflection.names public -open import reflection.precategory-solver public +open import reflection.precategory-solver funext univalence truncations public open import reflection.rewriting public open import reflection.terms public open import reflection.type-checking-monad public diff --git a/src/reflection/boolean-reflection.lagda.md b/src/reflection/boolean-reflection.lagda.md index 6908c83cf5..3956173194 100644 --- a/src/reflection/boolean-reflection.lagda.md +++ b/src/reflection/boolean-reflection.lagda.md @@ -1,16 +1,24 @@ # Boolean reflection ```agda -module reflection.boolean-reflection where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module reflection.boolean-reflection + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.booleans -open import foundation.decidable-types +open import foundation.decidable-types funext univalence truncations open import foundation.universe-levels +open import foundation-core.booleans open import foundation-core.coproduct-types open import foundation-core.empty-types open import foundation-core.identity-types diff --git a/src/reflection/definitions.lagda.md b/src/reflection/definitions.lagda.md index 3e0615a316..b95792be7d 100644 --- a/src/reflection/definitions.lagda.md +++ b/src/reflection/definitions.lagda.md @@ -10,11 +10,11 @@ module reflection.definitions where open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.identity-types -open import foundation.propositional-truncations open import foundation.universe-levels +open import foundation-core.empty-types +open import foundation-core.identity-types + open import lists.lists open import reflection.abstractions @@ -82,15 +82,15 @@ _ : ( visible-Argument-Agda (constructor-Term-Agda (quote zero-ℕ) nil))) _ = refl -_ : - {l : Level} {A : UU l} → - quoteTerm (type-trunc-Prop A) ＝ - definition-Term-Agda - ( quote type-trunc-Prop) - ( cons - ( hidden-Argument-Agda (variable-Term-Agda 1 nil)) - ( unit-list (visible-Argument-Agda (variable-Term-Agda 0 nil)))) -_ = refl +-- _ : +-- {l : Level} {A : UU l} → +-- quoteTerm (type-trunc-Prop A) ＝ +-- definition-Term-Agda +-- ( quote type-trunc-Prop) +-- ( cons +-- ( hidden-Argument-Agda (variable-Term-Agda 1 nil)) +-- ( unit-list (visible-Argument-Agda (variable-Term-Agda 0 nil)))) +-- _ = refl ``` ### Lambda abstractions diff --git a/src/reflection/fixity.lagda.md b/src/reflection/fixity.lagda.md index 52e0174190..20b03a2d6b 100644 --- a/src/reflection/fixity.lagda.md +++ b/src/reflection/fixity.lagda.md @@ -1,17 +1,26 @@ # Fixity ```agda -module reflection.fixity where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module reflection.fixity + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.addition-integers +open import elementary-number-theory.addition-integers funext univalence truncations -open import foundation.identity-types open import foundation.universe-levels +open import foundation-core.identity-types + open import primitives.floats open import reflection.names diff --git a/src/reflection/group-solver.lagda.md b/src/reflection/group-solver.lagda.md index 2f6e85638e..41e3143b15 100644 --- a/src/reflection/group-solver.lagda.md +++ b/src/reflection/group-solver.lagda.md @@ -1,7 +1,15 @@ # Group solver ```agda -module reflection.group-solver where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module reflection.group-solver + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,20 +18,21 @@ module reflection.group-solver where open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.coproduct-types -open import foundation.decidable-types -open import foundation.identity-types +open import foundation.decidable-types funext univalence truncations open import foundation.transport-along-identifications open import foundation.universe-levels -open import group-theory.groups +open import foundation-core.coproduct-types +open import foundation-core.identity-types + +open import group-theory.groups funext univalence truncations -open import linear-algebra.vectors +open import linear-algebra.vectors funext univalence truncations -open import lists.concatenation-lists -open import lists.functoriality-lists +open import lists.concatenation-lists funext univalence truncations +open import lists.functoriality-lists funext univalence truncations open import lists.lists -open import lists.reversing-lists +open import lists.reversing-lists funext univalence truncations ```
diff --git a/src/reflection/metavariables.lagda.md b/src/reflection/metavariables.lagda.md index 17e3ac21c1..bb2cf558a2 100644 --- a/src/reflection/metavariables.lagda.md +++ b/src/reflection/metavariables.lagda.md @@ -9,10 +9,11 @@ module reflection.metavariables where ```agda open import elementary-number-theory.natural-numbers -open import foundation.booleans -open import foundation.identity-types open import foundation.universe-levels +open import foundation-core.booleans +open import foundation-core.identity-types + open import lists.lists open import primitives.strings diff --git a/src/reflection/names.lagda.md b/src/reflection/names.lagda.md index 8b971a32c0..b42117fb12 100644 --- a/src/reflection/names.lagda.md +++ b/src/reflection/names.lagda.md @@ -7,12 +7,13 @@ module reflection.names where
Imports ```agda -open import foundation.booleans -open import foundation.cartesian-product-types -open import foundation.identity-types open import foundation.unit-type open import foundation.universe-levels +open import foundation-core.booleans +open import foundation-core.cartesian-product-types +open import foundation-core.identity-types + open import primitives.machine-integers open import primitives.strings ``` @@ -45,10 +46,10 @@ primitive ## Examples -```agda +```text _ : primQNameLess (quote bool) (quote unit) ＝ true _ = refl -_ : primShowQName (quote bool) ＝ "foundation.booleans.bool" +_ : primShowQName (quote bool) ＝ "foundation-core.booleans.bool" _ = refl ``` diff --git a/src/reflection/precategory-solver.lagda.md b/src/reflection/precategory-solver.lagda.md index c0d90a380a..c086a2f5d9 100644 --- a/src/reflection/precategory-solver.lagda.md +++ b/src/reflection/precategory-solver.lagda.md @@ -2,23 +2,31 @@ ```agda {-# OPTIONS --no-exact-split #-} - -module reflection.precategory-solver where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module reflection.precategory-solver + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.precategories +open import category-theory.precategories funext univalence truncations open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.identity-types +open import foundation.function-types funext open import foundation.unit-type open import foundation.universe-levels -open import lists.concatenation-lists +open import foundation-core.identity-types + +open import lists.concatenation-lists funext univalence truncations open import lists.lists open import reflection.arguments diff --git a/src/reflection/terms.lagda.md b/src/reflection/terms.lagda.md index 5a823a2be2..2e9e9b82c3 100644 --- a/src/reflection/terms.lagda.md +++ b/src/reflection/terms.lagda.md @@ -9,9 +9,10 @@ module reflection.terms where ```agda open import elementary-number-theory.natural-numbers -open import foundation.cartesian-product-types open import foundation.universe-levels +open import foundation-core.cartesian-product-types + open import lists.lists open import primitives.strings diff --git a/src/reflection/type-checking-monad.lagda.md b/src/reflection/type-checking-monad.lagda.md index 66e434811d..bcd6fe6e34 100644 --- a/src/reflection/type-checking-monad.lagda.md +++ b/src/reflection/type-checking-monad.lagda.md @@ -12,13 +12,14 @@ module reflection.type-checking-monad where open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.natural-numbers -open import foundation.booleans -open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.identity-types open import foundation.unit-type open import foundation.universe-levels +open import foundation-core.booleans +open import foundation-core.cartesian-product-types +open import foundation-core.identity-types + open import lists.lists open import primitives.strings diff --git a/src/ring-theory.lagda.md b/src/ring-theory.lagda.md index 9ea7cb8d0b..683a522d9f 100644 --- a/src/ring-theory.lagda.md +++ b/src/ring-theory.lagda.md @@ -3,83 +3,91 @@ ## Modules in the ring theory namespace ```agda -module ring-theory where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom -open import ring-theory.additive-orders-of-elements-rings public -open import ring-theory.algebras-rings public -open import ring-theory.binomial-theorem-rings public -open import ring-theory.binomial-theorem-semirings public -open import ring-theory.category-of-cyclic-rings public -open import ring-theory.category-of-rings public -open import ring-theory.central-elements-rings public -open import ring-theory.central-elements-semirings public -open import ring-theory.characteristics-rings public -open import ring-theory.commuting-elements-rings public -open import ring-theory.congruence-relations-rings public -open import ring-theory.congruence-relations-semirings public -open import ring-theory.cyclic-rings public -open import ring-theory.dependent-products-rings public -open import ring-theory.dependent-products-semirings public -open import ring-theory.division-rings public -open import ring-theory.free-rings-with-one-generator public -open import ring-theory.full-ideals-rings public -open import ring-theory.function-rings public -open import ring-theory.function-semirings public -open import ring-theory.generating-elements-rings public -open import ring-theory.groups-of-units-rings public -open import ring-theory.homomorphisms-cyclic-rings public -open import ring-theory.homomorphisms-rings public -open import ring-theory.homomorphisms-semirings public -open import ring-theory.ideals-generated-by-subsets-rings public -open import ring-theory.ideals-rings public -open import ring-theory.ideals-semirings public -open import ring-theory.idempotent-elements-rings public -open import ring-theory.initial-rings public -open import ring-theory.integer-multiples-of-elements-rings public -open import ring-theory.intersections-ideals-rings public -open import ring-theory.intersections-ideals-semirings public -open import ring-theory.invariant-basis-property-rings public -open import ring-theory.invertible-elements-rings public -open import ring-theory.isomorphisms-rings public -open import ring-theory.joins-ideals-rings public -open import ring-theory.joins-left-ideals-rings public -open import ring-theory.joins-right-ideals-rings public -open import ring-theory.kernels-of-ring-homomorphisms public -open import ring-theory.left-ideals-generated-by-subsets-rings public -open import ring-theory.left-ideals-rings public -open import ring-theory.local-rings public -open import ring-theory.localizations-rings public +module ring-theory + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where + +open import ring-theory.additive-orders-of-elements-rings funext univalence truncations public +open import ring-theory.algebras-rings funext univalence truncations public +open import ring-theory.binomial-theorem-rings funext univalence truncations public +open import ring-theory.binomial-theorem-semirings funext univalence truncations public +open import ring-theory.category-of-cyclic-rings funext univalence truncations public +open import ring-theory.category-of-rings funext univalence truncations public +open import ring-theory.central-elements-rings funext univalence truncations public +open import ring-theory.central-elements-semirings funext univalence truncations public +open import ring-theory.characteristics-rings funext univalence truncations public +open import ring-theory.commuting-elements-rings funext univalence truncations public +open import ring-theory.congruence-relations-rings funext univalence truncations public +open import ring-theory.congruence-relations-semirings funext univalence truncations public +open import ring-theory.cyclic-rings funext univalence truncations public +open import ring-theory.dependent-products-rings funext univalence truncations public +open import ring-theory.dependent-products-semirings funext univalence truncations public +open import ring-theory.division-rings funext univalence truncations public +open import ring-theory.free-rings-with-one-generator funext univalence truncations public +open import ring-theory.full-ideals-rings funext univalence truncations public +open import ring-theory.function-rings funext univalence truncations public +open import ring-theory.function-semirings funext univalence truncations public +open import ring-theory.generating-elements-rings funext univalence truncations public +open import ring-theory.groups-of-units-rings funext univalence truncations public +open import ring-theory.homomorphisms-cyclic-rings funext univalence truncations public +open import ring-theory.homomorphisms-rings funext univalence truncations public +open import ring-theory.homomorphisms-semirings funext univalence truncations public +open import ring-theory.ideals-generated-by-subsets-rings funext univalence truncations public +open import ring-theory.ideals-rings funext univalence truncations public +open import ring-theory.ideals-semirings funext univalence truncations public +open import ring-theory.idempotent-elements-rings funext univalence truncations public +open import ring-theory.initial-rings funext univalence truncations public +open import ring-theory.integer-multiples-of-elements-rings funext univalence truncations public +open import ring-theory.intersections-ideals-rings funext univalence truncations public +open import ring-theory.intersections-ideals-semirings funext univalence truncations public +open import ring-theory.invariant-basis-property-rings funext univalence truncations public +open import ring-theory.invertible-elements-rings funext univalence truncations public +open import ring-theory.isomorphisms-rings funext univalence truncations public +open import ring-theory.joins-ideals-rings funext univalence truncations public +open import ring-theory.joins-left-ideals-rings funext univalence truncations public +open import ring-theory.joins-right-ideals-rings funext univalence truncations public +open import ring-theory.kernels-of-ring-homomorphisms funext univalence truncations public +open import ring-theory.left-ideals-generated-by-subsets-rings funext univalence truncations public +open import ring-theory.left-ideals-rings funext univalence truncations public +open import ring-theory.local-rings funext univalence truncations public +open import ring-theory.localizations-rings funext univalence truncations public open import ring-theory.maximal-ideals-rings public -open import ring-theory.modules-rings public -open import ring-theory.multiples-of-elements-rings public +open import ring-theory.modules-rings funext univalence truncations public +open import ring-theory.multiples-of-elements-rings funext univalence truncations public open import ring-theory.multiplicative-orders-of-units-rings public -open import ring-theory.nil-ideals-rings public -open import ring-theory.nilpotent-elements-rings public -open import ring-theory.nilpotent-elements-semirings public -open import ring-theory.opposite-rings public -open import ring-theory.poset-of-cyclic-rings public -open import ring-theory.poset-of-ideals-rings public -open import ring-theory.poset-of-left-ideals-rings public -open import ring-theory.poset-of-right-ideals-rings public -open import ring-theory.powers-of-elements-rings public -open import ring-theory.powers-of-elements-semirings public -open import ring-theory.precategory-of-rings public -open import ring-theory.precategory-of-semirings public -open import ring-theory.products-ideals-rings public -open import ring-theory.products-left-ideals-rings public -open import ring-theory.products-right-ideals-rings public -open import ring-theory.products-rings public -open import ring-theory.products-subsets-rings public -open import ring-theory.quotient-rings public -open import ring-theory.radical-ideals-rings public -open import ring-theory.right-ideals-generated-by-subsets-rings public -open import ring-theory.right-ideals-rings public -open import ring-theory.rings public -open import ring-theory.semirings public -open import ring-theory.subsets-rings public -open import ring-theory.subsets-semirings public -open import ring-theory.sums-rings public -open import ring-theory.sums-semirings public -open import ring-theory.transporting-ring-structure-along-isomorphisms-abelian-groups public -open import ring-theory.trivial-rings public +open import ring-theory.nil-ideals-rings funext univalence truncations public +open import ring-theory.nilpotent-elements-rings funext univalence truncations public +open import ring-theory.nilpotent-elements-semirings funext univalence truncations public +open import ring-theory.opposite-rings funext univalence truncations public +open import ring-theory.poset-of-cyclic-rings funext univalence truncations public +open import ring-theory.poset-of-ideals-rings funext univalence truncations public +open import ring-theory.poset-of-left-ideals-rings funext univalence truncations public +open import ring-theory.poset-of-right-ideals-rings funext univalence truncations public +open import ring-theory.powers-of-elements-rings funext univalence truncations public +open import ring-theory.powers-of-elements-semirings funext univalence truncations public +open import ring-theory.precategory-of-rings funext univalence truncations public +open import ring-theory.precategory-of-semirings funext univalence truncations public +open import ring-theory.products-ideals-rings funext univalence truncations public +open import ring-theory.products-left-ideals-rings funext univalence truncations public +open import ring-theory.products-right-ideals-rings funext univalence truncations public +open import ring-theory.products-rings funext univalence truncations public +open import ring-theory.products-subsets-rings funext univalence truncations public +open import ring-theory.quotient-rings funext univalence truncations public +open import ring-theory.radical-ideals-rings funext univalence truncations public +open import ring-theory.right-ideals-generated-by-subsets-rings funext univalence truncations public +open import ring-theory.right-ideals-rings funext univalence truncations public +open import ring-theory.rings funext univalence truncations public +open import ring-theory.semirings funext univalence truncations public +open import ring-theory.subsets-rings funext univalence truncations public +open import ring-theory.subsets-semirings funext univalence truncations public +open import ring-theory.sums-rings funext univalence truncations public +open import ring-theory.sums-semirings funext univalence truncations public +open import ring-theory.transporting-ring-structure-along-isomorphisms-abelian-groups funext univalence truncations public +open import ring-theory.trivial-rings funext univalence truncations public ``` diff --git a/src/ring-theory/additive-orders-of-elements-rings.lagda.md b/src/ring-theory/additive-orders-of-elements-rings.lagda.md index 8a8cf9374c..a96da4d6c9 100644 --- a/src/ring-theory/additive-orders-of-elements-rings.lagda.md +++ b/src/ring-theory/additive-orders-of-elements-rings.lagda.md @@ -1,28 +1,36 @@ # Additive orders of elements of rings ```agda -module ring-theory.additive-orders-of-elements-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module ring-theory.additive-orders-of-elements-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.group-of-integers +open import elementary-number-theory.group-of-integers funext univalence truncations open import elementary-number-theory.integers open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.propositional-truncations +open import foundation.identity-types funext +open import foundation.propositional-truncations funext univalence open import foundation.universe-levels -open import group-theory.normal-subgroups -open import group-theory.orders-of-elements-groups -open import group-theory.subgroups -open import group-theory.subsets-groups +open import group-theory.normal-subgroups funext univalence truncations +open import group-theory.orders-of-elements-groups funext univalence truncations +open import group-theory.subgroups funext univalence truncations +open import group-theory.subsets-groups funext univalence truncations -open import ring-theory.integer-multiples-of-elements-rings -open import ring-theory.rings +open import ring-theory.integer-multiples-of-elements-rings funext univalence truncations +open import ring-theory.rings funext univalence truncations ```
diff --git a/src/ring-theory/algebras-rings.lagda.md b/src/ring-theory/algebras-rings.lagda.md index ff618c84d6..888e31fb0e 100644 --- a/src/ring-theory/algebras-rings.lagda.md +++ b/src/ring-theory/algebras-rings.lagda.md @@ -1,19 +1,27 @@ # Algebras over rings ```agda -module ring-theory.algebras-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module ring-theory.algebras-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import ring-theory.modules-rings -open import ring-theory.rings +open import ring-theory.modules-rings funext univalence truncations +open import ring-theory.rings funext univalence truncations ```
diff --git a/src/ring-theory/binomial-theorem-rings.lagda.md b/src/ring-theory/binomial-theorem-rings.lagda.md index d951452476..3225d6befe 100644 --- a/src/ring-theory/binomial-theorem-rings.lagda.md +++ b/src/ring-theory/binomial-theorem-rings.lagda.md @@ -1,29 +1,37 @@ # The binomial theorem for rings ```agda -module ring-theory.binomial-theorem-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module ring-theory.binomial-theorem-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.binomial-coefficients -open import elementary-number-theory.distance-natural-numbers +open import elementary-number-theory.binomial-coefficients funext univalence truncations +open import elementary-number-theory.distance-natural-numbers funext univalence truncations open import elementary-number-theory.natural-numbers -open import foundation.homotopies -open import foundation.identity-types +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.universe-levels -open import linear-algebra.vectors-on-rings +open import linear-algebra.vectors-on-rings funext univalence truncations -open import ring-theory.binomial-theorem-semirings -open import ring-theory.powers-of-elements-rings -open import ring-theory.rings -open import ring-theory.sums-rings +open import ring-theory.binomial-theorem-semirings funext univalence truncations +open import ring-theory.powers-of-elements-rings funext univalence truncations +open import ring-theory.rings funext univalence truncations +open import ring-theory.sums-rings funext univalence truncations -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/ring-theory/binomial-theorem-semirings.lagda.md b/src/ring-theory/binomial-theorem-semirings.lagda.md index 66679c0071..ea7d6e8e3a 100644 --- a/src/ring-theory/binomial-theorem-semirings.lagda.md +++ b/src/ring-theory/binomial-theorem-semirings.lagda.md @@ -1,32 +1,40 @@ # The binomial theorem for semirings ```agda -module ring-theory.binomial-theorem-semirings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module ring-theory.binomial-theorem-semirings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.binomial-coefficients -open import elementary-number-theory.distance-natural-numbers -open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.binomial-coefficients funext univalence truncations +open import elementary-number-theory.distance-natural-numbers funext univalence truncations +open import elementary-number-theory.inequality-natural-numbers funext univalence truncations open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.homotopies -open import foundation.identity-types +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.universe-levels -open import linear-algebra.vectors-on-semirings +open import linear-algebra.vectors-on-semirings funext univalence truncations -open import ring-theory.powers-of-elements-semirings -open import ring-theory.semirings -open import ring-theory.sums-semirings +open import ring-theory.powers-of-elements-semirings funext univalence truncations +open import ring-theory.semirings funext univalence truncations +open import ring-theory.sums-semirings funext univalence truncations -open import univalent-combinatorics.coproduct-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.coproduct-types funext univalence truncations +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/ring-theory/category-of-cyclic-rings.lagda.md b/src/ring-theory/category-of-cyclic-rings.lagda.md index 27c4f61a07..85e1db0322 100644 --- a/src/ring-theory/category-of-cyclic-rings.lagda.md +++ b/src/ring-theory/category-of-cyclic-rings.lagda.md @@ -1,25 +1,33 @@ # The category of cyclic rings ```agda -module ring-theory.category-of-cyclic-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module ring-theory.category-of-cyclic-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.full-large-subprecategories -open import category-theory.large-categories -open import category-theory.large-precategories +open import category-theory.categories funext univalence truncations +open import category-theory.full-large-subprecategories funext univalence truncations +open import category-theory.large-categories funext univalence truncations +open import category-theory.large-precategories funext univalence truncations open import foundation.universe-levels -open import order-theory.large-posets +open import order-theory.large-posets funext univalence truncations -open import ring-theory.category-of-rings -open import ring-theory.cyclic-rings -open import ring-theory.homomorphisms-cyclic-rings -open import ring-theory.precategory-of-rings +open import ring-theory.category-of-rings funext univalence truncations +open import ring-theory.cyclic-rings funext univalence truncations +open import ring-theory.homomorphisms-cyclic-rings funext univalence truncations +open import ring-theory.precategory-of-rings funext univalence truncations ```
diff --git a/src/ring-theory/category-of-rings.lagda.md b/src/ring-theory/category-of-rings.lagda.md index 8c06755027..fe13d89130 100644 --- a/src/ring-theory/category-of-rings.lagda.md +++ b/src/ring-theory/category-of-rings.lagda.md @@ -1,19 +1,27 @@ # The category of rings ```agda -module ring-theory.category-of-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module ring-theory.category-of-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.large-categories +open import category-theory.categories funext univalence truncations +open import category-theory.large-categories funext univalence truncations open import foundation.universe-levels -open import ring-theory.isomorphisms-rings -open import ring-theory.precategory-of-rings +open import ring-theory.isomorphisms-rings funext univalence truncations +open import ring-theory.precategory-of-rings funext univalence truncations ```
diff --git a/src/ring-theory/central-elements-rings.lagda.md b/src/ring-theory/central-elements-rings.lagda.md index 7ecc9dc806..d42d806f9c 100644 --- a/src/ring-theory/central-elements-rings.lagda.md +++ b/src/ring-theory/central-elements-rings.lagda.md @@ -1,19 +1,28 @@ # Central elements of rings ```agda -module ring-theory.central-elements-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module ring-theory.central-elements-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.identity-types -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence open import foundation.universe-levels -open import ring-theory.central-elements-semirings -open import ring-theory.rings +open import ring-theory.central-elements-semirings funext univalence truncations +open import ring-theory.rings funext univalence truncations ```
diff --git a/src/ring-theory/central-elements-semirings.lagda.md b/src/ring-theory/central-elements-semirings.lagda.md index 41cb19f6ef..9c54538cd5 100644 --- a/src/ring-theory/central-elements-semirings.lagda.md +++ b/src/ring-theory/central-elements-semirings.lagda.md @@ -1,19 +1,28 @@ # Central elements of semirings ```agda -module ring-theory.central-elements-semirings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module ring-theory.central-elements-semirings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.identity-types -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence open import foundation.universe-levels -open import group-theory.central-elements-monoids +open import group-theory.central-elements-monoids funext univalence truncations -open import ring-theory.semirings +open import ring-theory.semirings funext univalence truncations ```
diff --git a/src/ring-theory/characteristics-rings.lagda.md b/src/ring-theory/characteristics-rings.lagda.md index 45bdfb7e8e..01211cb182 100644 --- a/src/ring-theory/characteristics-rings.lagda.md +++ b/src/ring-theory/characteristics-rings.lagda.md @@ -1,19 +1,27 @@ # Characteristics of rings ```agda -module ring-theory.characteristics-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module ring-theory.characteristics-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.ring-of-integers +open import elementary-number-theory.ring-of-integers funext univalence truncations open import foundation.universe-levels -open import ring-theory.ideals-rings -open import ring-theory.kernels-of-ring-homomorphisms -open import ring-theory.rings +open import ring-theory.ideals-rings funext univalence truncations +open import ring-theory.kernels-of-ring-homomorphisms funext univalence truncations +open import ring-theory.rings funext univalence truncations ```
diff --git a/src/ring-theory/commuting-elements-rings.lagda.md b/src/ring-theory/commuting-elements-rings.lagda.md index 3d35949217..8a2695e296 100644 --- a/src/ring-theory/commuting-elements-rings.lagda.md +++ b/src/ring-theory/commuting-elements-rings.lagda.md @@ -1,20 +1,29 @@ # Commuting elements of rings ```agda -module ring-theory.commuting-elements-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module ring-theory.commuting-elements-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.identity-types -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence open import foundation.universe-levels -open import group-theory.commuting-elements-monoids +open import group-theory.commuting-elements-monoids funext univalence truncations -open import ring-theory.rings +open import ring-theory.rings funext univalence truncations ```
diff --git a/src/ring-theory/congruence-relations-rings.lagda.md b/src/ring-theory/congruence-relations-rings.lagda.md index 7b12139706..ba8e90c9c1 100644 --- a/src/ring-theory/congruence-relations-rings.lagda.md +++ b/src/ring-theory/congruence-relations-rings.lagda.md @@ -1,26 +1,35 @@ # Congruence relations on rings ```agda -module ring-theory.congruence-relations-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module ring-theory.congruence-relations-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.binary-relations +open import foundation.binary-relations funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalence-relations -open import foundation.equivalences -open import foundation.identity-types -open import foundation.propositions -open import foundation.torsorial-type-families +open import foundation.dependent-products-propositions funext +open import foundation.equivalence-relations funext univalence truncations +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.torsorial-type-families funext univalence truncations open import foundation.universe-levels -open import group-theory.congruence-relations-abelian-groups -open import group-theory.congruence-relations-monoids +open import group-theory.congruence-relations-abelian-groups funext univalence truncations +open import group-theory.congruence-relations-monoids funext univalence truncations -open import ring-theory.congruence-relations-semirings -open import ring-theory.rings +open import ring-theory.congruence-relations-semirings funext univalence truncations +open import ring-theory.rings funext univalence truncations ```
diff --git a/src/ring-theory/congruence-relations-semirings.lagda.md b/src/ring-theory/congruence-relations-semirings.lagda.md index 2a0089a148..d71b554fea 100644 --- a/src/ring-theory/congruence-relations-semirings.lagda.md +++ b/src/ring-theory/congruence-relations-semirings.lagda.md @@ -1,27 +1,36 @@ # Congruence relations on semirings ```agda -module ring-theory.congruence-relations-semirings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module ring-theory.congruence-relations-semirings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.binary-relations -open import foundation.cartesian-product-types +open import foundation.binary-relations funext univalence truncations +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalence-relations -open import foundation.equivalences +open import foundation.dependent-products-propositions funext +open import foundation.equivalence-relations funext univalence truncations +open import foundation.equivalences funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types -open import foundation.propositions +open import foundation.identity-types funext +open import foundation.propositions funext univalence open import foundation.subtype-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext univalence truncations open import foundation.universe-levels -open import group-theory.congruence-relations-monoids +open import group-theory.congruence-relations-monoids funext univalence truncations -open import ring-theory.semirings +open import ring-theory.semirings funext univalence truncations ```
diff --git a/src/ring-theory/cyclic-rings.lagda.md b/src/ring-theory/cyclic-rings.lagda.md index e3b3ac6fca..f2ab671ee1 100644 --- a/src/ring-theory/cyclic-rings.lagda.md +++ b/src/ring-theory/cyclic-rings.lagda.md @@ -1,39 +1,48 @@ # Cyclic rings ```agda -module ring-theory.cyclic-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module ring-theory.cyclic-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import commutative-algebra.commutative-rings +open import commutative-algebra.commutative-rings funext univalence truncations open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-integers -open import elementary-number-theory.ring-of-integers +open import elementary-number-theory.multiplication-integers funext univalence truncations +open import elementary-number-theory.ring-of-integers funext univalence truncations open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.fibers-of-maps -open import foundation.identity-types -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.sets -open import foundation.subtypes -open import foundation.surjective-maps +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.fibers-of-maps funext +open import foundation.identity-types funext +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.subtypes funext univalence truncations +open import foundation.surjective-maps funext univalence truncations open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.cyclic-groups -open import group-theory.free-groups-with-one-generator -open import group-theory.generating-elements-groups -open import group-theory.groups +open import group-theory.abelian-groups funext univalence truncations +open import group-theory.cyclic-groups funext univalence truncations +open import group-theory.free-groups-with-one-generator funext univalence truncations +open import group-theory.generating-elements-groups funext univalence truncations +open import group-theory.groups funext univalence truncations -open import ring-theory.integer-multiples-of-elements-rings -open import ring-theory.invertible-elements-rings -open import ring-theory.rings +open import ring-theory.integer-multiples-of-elements-rings funext univalence truncations +open import ring-theory.invertible-elements-rings funext univalence truncations +open import ring-theory.rings funext univalence truncations ```
diff --git a/src/ring-theory/dependent-products-rings.lagda.md b/src/ring-theory/dependent-products-rings.lagda.md index 409f515003..3bff38de2c 100644 --- a/src/ring-theory/dependent-products-rings.lagda.md +++ b/src/ring-theory/dependent-products-rings.lagda.md @@ -1,26 +1,34 @@ # Dependent products of rings ```agda -module ring-theory.dependent-products-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module ring-theory.dependent-products-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.sets +open import foundation.identity-types funext +open import foundation.sets funext univalence open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.dependent-products-abelian-groups -open import group-theory.groups -open import group-theory.monoids -open import group-theory.semigroups +open import group-theory.abelian-groups funext univalence truncations +open import group-theory.dependent-products-abelian-groups funext univalence truncations +open import group-theory.groups funext univalence truncations +open import group-theory.monoids funext univalence truncations +open import group-theory.semigroups funext univalence -open import ring-theory.dependent-products-semirings -open import ring-theory.rings -open import ring-theory.semirings +open import ring-theory.dependent-products-semirings funext univalence truncations +open import ring-theory.rings funext univalence truncations +open import ring-theory.semirings funext univalence truncations ```
diff --git a/src/ring-theory/dependent-products-semirings.lagda.md b/src/ring-theory/dependent-products-semirings.lagda.md index 5c59c14b05..b4e3598de8 100644 --- a/src/ring-theory/dependent-products-semirings.lagda.md +++ b/src/ring-theory/dependent-products-semirings.lagda.md @@ -1,25 +1,33 @@ # Dependent products of semirings ```agda -module ring-theory.dependent-products-semirings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module ring-theory.dependent-products-semirings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-extensionality -open import foundation.identity-types -open import foundation.sets +open import foundation.function-extensionality funext +open import foundation.identity-types funext +open import foundation.sets funext univalence open import foundation.universe-levels -open import group-theory.commutative-monoids -open import group-theory.dependent-products-commutative-monoids -open import group-theory.dependent-products-monoids -open import group-theory.monoids -open import group-theory.semigroups +open import group-theory.commutative-monoids funext univalence truncations +open import group-theory.dependent-products-commutative-monoids funext univalence truncations +open import group-theory.dependent-products-monoids funext univalence truncations +open import group-theory.monoids funext univalence truncations +open import group-theory.semigroups funext univalence -open import ring-theory.semirings +open import ring-theory.semirings funext univalence truncations ```
diff --git a/src/ring-theory/division-rings.lagda.md b/src/ring-theory/division-rings.lagda.md index fcdce2df44..3d89f669a3 100644 --- a/src/ring-theory/division-rings.lagda.md +++ b/src/ring-theory/division-rings.lagda.md @@ -1,19 +1,27 @@ # Division rings ```agda -module ring-theory.division-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module ring-theory.division-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.cartesian-product-types -open import foundation.negated-equality +open import foundation.cartesian-product-types funext univalence +open import foundation.negated-equality funext univalence truncations open import foundation.universe-levels -open import ring-theory.invertible-elements-rings -open import ring-theory.rings -open import ring-theory.trivial-rings +open import ring-theory.invertible-elements-rings funext univalence truncations +open import ring-theory.rings funext univalence truncations +open import ring-theory.trivial-rings funext univalence truncations ```
diff --git a/src/ring-theory/free-rings-with-one-generator.lagda.md b/src/ring-theory/free-rings-with-one-generator.lagda.md index 4131005dfa..09710f969c 100644 --- a/src/ring-theory/free-rings-with-one-generator.lagda.md +++ b/src/ring-theory/free-rings-with-one-generator.lagda.md @@ -1,17 +1,25 @@ # The free ring with one generator ```agda -module ring-theory.free-rings-with-one-generator where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module ring-theory.free-rings-with-one-generator + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.equivalences +open import foundation.equivalences funext open import foundation.universe-levels -open import ring-theory.homomorphisms-rings -open import ring-theory.rings +open import ring-theory.homomorphisms-rings funext univalence truncations +open import ring-theory.rings funext univalence truncations ```
diff --git a/src/ring-theory/full-ideals-rings.lagda.md b/src/ring-theory/full-ideals-rings.lagda.md index a415b1eeeb..874a1c6e9a 100644 --- a/src/ring-theory/full-ideals-rings.lagda.md +++ b/src/ring-theory/full-ideals-rings.lagda.md @@ -1,27 +1,37 @@ # Full ideals of rings ```agda -module ring-theory.full-ideals-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module ring-theory.full-ideals-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.full-subtypes -open import foundation.propositions -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.full-subtypes funext univalence truncations +open import foundation.propositions funext univalence +open import foundation.raising-universe-levels-unit-type +open import foundation.subtypes funext univalence truncations open import foundation.unit-type open import foundation.universe-levels -open import order-theory.top-elements-large-posets +open import order-theory.top-elements-large-posets funext univalence truncations -open import ring-theory.ideals-rings -open import ring-theory.left-ideals-rings -open import ring-theory.poset-of-ideals-rings -open import ring-theory.right-ideals-rings -open import ring-theory.rings -open import ring-theory.subsets-rings +open import ring-theory.ideals-rings funext univalence truncations +open import ring-theory.left-ideals-rings funext univalence truncations +open import ring-theory.poset-of-ideals-rings funext univalence truncations +open import ring-theory.right-ideals-rings funext univalence truncations +open import ring-theory.rings funext univalence truncations +open import ring-theory.subsets-rings funext univalence truncations ```
diff --git a/src/ring-theory/function-rings.lagda.md b/src/ring-theory/function-rings.lagda.md index 4a3837e0ec..0960eb46ba 100644 --- a/src/ring-theory/function-rings.lagda.md +++ b/src/ring-theory/function-rings.lagda.md @@ -1,21 +1,29 @@ # Function rings ```agda -module ring-theory.function-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module ring-theory.function-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.identity-types -open import foundation.sets +open import foundation.identity-types funext +open import foundation.sets funext univalence open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.monoids +open import group-theory.abelian-groups funext univalence truncations +open import group-theory.monoids funext univalence truncations -open import ring-theory.dependent-products-rings -open import ring-theory.rings +open import ring-theory.dependent-products-rings funext univalence truncations +open import ring-theory.rings funext univalence truncations ```
diff --git a/src/ring-theory/function-semirings.lagda.md b/src/ring-theory/function-semirings.lagda.md index 2aa4003612..265aad51e3 100644 --- a/src/ring-theory/function-semirings.lagda.md +++ b/src/ring-theory/function-semirings.lagda.md @@ -1,22 +1,30 @@ # Function semirings ```agda -module ring-theory.function-semirings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module ring-theory.function-semirings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.sets +open import foundation.identity-types funext +open import foundation.sets funext univalence open import foundation.universe-levels -open import group-theory.commutative-monoids -open import group-theory.monoids +open import group-theory.commutative-monoids funext univalence truncations +open import group-theory.monoids funext univalence truncations -open import ring-theory.dependent-products-semirings -open import ring-theory.semirings +open import ring-theory.dependent-products-semirings funext univalence truncations +open import ring-theory.semirings funext univalence truncations ```
diff --git a/src/ring-theory/generating-elements-rings.lagda.md b/src/ring-theory/generating-elements-rings.lagda.md index f143405f0f..1adb92c8c1 100644 --- a/src/ring-theory/generating-elements-rings.lagda.md +++ b/src/ring-theory/generating-elements-rings.lagda.md @@ -1,18 +1,27 @@ # Generating elements of rings ```agda -module ring-theory.generating-elements-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module ring-theory.generating-elements-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.propositions funext univalence open import foundation.universe-levels -open import group-theory.generating-elements-groups +open import group-theory.generating-elements-groups funext univalence truncations -open import ring-theory.rings +open import ring-theory.rings funext univalence truncations ```
diff --git a/src/ring-theory/groups-of-units-rings.lagda.md b/src/ring-theory/groups-of-units-rings.lagda.md index 16e293804e..cecdf14d44 100644 --- a/src/ring-theory/groups-of-units-rings.lagda.md +++ b/src/ring-theory/groups-of-units-rings.lagda.md @@ -1,31 +1,40 @@ # The group of multiplicative units of a ring ```agda -module ring-theory.groups-of-units-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module ring-theory.groups-of-units-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.functors-large-precategories +open import category-theory.functors-large-precategories funext univalence truncations -open import foundation.identity-types -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence open import foundation.universe-levels -open import group-theory.cores-monoids -open import group-theory.groups -open import group-theory.homomorphisms-groups -open import group-theory.homomorphisms-monoids -open import group-theory.monoids -open import group-theory.precategory-of-groups -open import group-theory.semigroups -open import group-theory.submonoids - -open import ring-theory.homomorphisms-rings -open import ring-theory.invertible-elements-rings -open import ring-theory.precategory-of-rings -open import ring-theory.rings +open import group-theory.cores-monoids funext univalence truncations +open import group-theory.groups funext univalence truncations +open import group-theory.homomorphisms-groups funext univalence truncations +open import group-theory.homomorphisms-monoids funext univalence truncations +open import group-theory.monoids funext univalence truncations +open import group-theory.precategory-of-groups funext univalence truncations +open import group-theory.semigroups funext univalence +open import group-theory.submonoids funext univalence truncations + +open import ring-theory.homomorphisms-rings funext univalence truncations +open import ring-theory.invertible-elements-rings funext univalence truncations +open import ring-theory.precategory-of-rings funext univalence truncations +open import ring-theory.rings funext univalence truncations ```
diff --git a/src/ring-theory/homomorphisms-cyclic-rings.lagda.md b/src/ring-theory/homomorphisms-cyclic-rings.lagda.md index 8bdb6d76cf..2eac4ceba8 100644 --- a/src/ring-theory/homomorphisms-cyclic-rings.lagda.md +++ b/src/ring-theory/homomorphisms-cyclic-rings.lagda.md @@ -1,7 +1,15 @@ # Homomorphisms of cyclic rings ```agda -module ring-theory.homomorphisms-cyclic-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module ring-theory.homomorphisms-cyclic-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,16 +17,17 @@ module ring-theory.homomorphisms-cyclic-rings where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.sets +open import foundation.dependent-products-propositions funext +open import foundation.identity-types funext +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence +open import foundation.sets funext univalence open import foundation.universe-levels -open import ring-theory.cyclic-rings -open import ring-theory.homomorphisms-rings -open import ring-theory.integer-multiples-of-elements-rings -open import ring-theory.rings +open import ring-theory.cyclic-rings funext univalence truncations +open import ring-theory.homomorphisms-rings funext univalence truncations +open import ring-theory.integer-multiples-of-elements-rings funext univalence truncations +open import ring-theory.rings funext univalence truncations ```
diff --git a/src/ring-theory/homomorphisms-rings.lagda.md b/src/ring-theory/homomorphisms-rings.lagda.md index 95f466ea7c..7eecfe7d0d 100644 --- a/src/ring-theory/homomorphisms-rings.lagda.md +++ b/src/ring-theory/homomorphisms-rings.lagda.md @@ -1,32 +1,41 @@ # Homomorphisms of rings ```agda -module ring-theory.homomorphisms-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module ring-theory.homomorphisms-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence open import foundation.subtype-identity-principle -open import foundation.subtypes -open import foundation.torsorial-type-families +open import foundation.subtypes funext univalence truncations +open import foundation.torsorial-type-families funext univalence truncations open import foundation.universe-levels -open import group-theory.homomorphisms-abelian-groups -open import group-theory.homomorphisms-commutative-monoids -open import group-theory.homomorphisms-groups -open import group-theory.homomorphisms-monoids +open import group-theory.homomorphisms-abelian-groups funext univalence truncations +open import group-theory.homomorphisms-commutative-monoids funext univalence truncations +open import group-theory.homomorphisms-groups funext univalence truncations +open import group-theory.homomorphisms-monoids funext univalence truncations -open import ring-theory.homomorphisms-semirings -open import ring-theory.invertible-elements-rings -open import ring-theory.rings +open import ring-theory.homomorphisms-semirings funext univalence truncations +open import ring-theory.invertible-elements-rings funext univalence truncations +open import ring-theory.rings funext univalence truncations ```
diff --git a/src/ring-theory/homomorphisms-semirings.lagda.md b/src/ring-theory/homomorphisms-semirings.lagda.md index 9bd4acad47..956c68e0f2 100644 --- a/src/ring-theory/homomorphisms-semirings.lagda.md +++ b/src/ring-theory/homomorphisms-semirings.lagda.md @@ -1,29 +1,38 @@ # Homomorphisms of semirings ```agda -module ring-theory.homomorphisms-semirings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module ring-theory.homomorphisms-semirings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence open import foundation.subtype-identity-principle -open import foundation.subtypes -open import foundation.torsorial-type-families +open import foundation.subtypes funext univalence truncations +open import foundation.torsorial-type-families funext univalence truncations open import foundation.universe-levels -open import group-theory.homomorphisms-commutative-monoids -open import group-theory.homomorphisms-monoids -open import group-theory.homomorphisms-semigroups +open import group-theory.homomorphisms-commutative-monoids funext univalence truncations +open import group-theory.homomorphisms-monoids funext univalence truncations +open import group-theory.homomorphisms-semigroups funext univalence truncations -open import ring-theory.semirings +open import ring-theory.semirings funext univalence truncations ```
diff --git a/src/ring-theory/ideals-generated-by-subsets-rings.lagda.md b/src/ring-theory/ideals-generated-by-subsets-rings.lagda.md index 641996be99..ae8c750b86 100644 --- a/src/ring-theory/ideals-generated-by-subsets-rings.lagda.md +++ b/src/ring-theory/ideals-generated-by-subsets-rings.lagda.md @@ -1,39 +1,47 @@ # Ideals generated by subsets of rings ```agda -module ring-theory.ideals-generated-by-subsets-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module ring-theory.ideals-generated-by-subsets-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.fibers-of-maps -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.powersets -open import foundation.propositional-truncations -open import foundation.subtypes +open import foundation.fibers-of-maps funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.powersets funext univalence truncations +open import foundation.propositional-truncations funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.transport-along-identifications -open import foundation.unions-subtypes +open import foundation.unions-subtypes funext univalence truncations open import foundation.universe-levels -open import lists.concatenation-lists -open import lists.functoriality-lists +open import lists.concatenation-lists funext univalence truncations +open import lists.functoriality-lists funext univalence truncations open import lists.lists -open import order-theory.galois-connections-large-posets -open import order-theory.least-upper-bounds-large-posets -open import order-theory.order-preserving-maps-large-posets -open import order-theory.order-preserving-maps-large-preorders -open import order-theory.reflective-galois-connections-large-posets +open import order-theory.galois-connections-large-posets funext univalence truncations +open import order-theory.least-upper-bounds-large-posets funext univalence truncations +open import order-theory.order-preserving-maps-large-posets funext univalence truncations +open import order-theory.order-preserving-maps-large-preorders funext univalence truncations +open import order-theory.reflective-galois-connections-large-posets funext univalence truncations -open import ring-theory.ideals-rings -open import ring-theory.poset-of-ideals-rings -open import ring-theory.rings -open import ring-theory.subsets-rings +open import ring-theory.ideals-rings funext univalence truncations +open import ring-theory.poset-of-ideals-rings funext univalence truncations +open import ring-theory.rings funext univalence truncations +open import ring-theory.subsets-rings funext univalence truncations ```
diff --git a/src/ring-theory/ideals-rings.lagda.md b/src/ring-theory/ideals-rings.lagda.md index 74b99261c9..28f2a4da94 100644 --- a/src/ring-theory/ideals-rings.lagda.md +++ b/src/ring-theory/ideals-rings.lagda.md @@ -1,37 +1,46 @@ # Ideals of rings ```agda -module ring-theory.ideals-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module ring-theory.ideals-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.binary-relations +open import foundation.binary-relations funext univalence truncations open import foundation.binary-transport -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalence-relations -open import foundation.equivalences -open import foundation.function-types +open import foundation.dependent-products-propositions funext +open import foundation.equivalence-relations funext univalence truncations +open import foundation.equivalences funext +open import foundation.function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types -open import foundation.propositions +open import foundation.identity-types funext +open import foundation.propositions funext univalence open import foundation.subtype-identity-principle -open import foundation.subtypes -open import foundation.torsorial-type-families +open import foundation.subtypes funext univalence truncations +open import foundation.torsorial-type-families funext univalence truncations open import foundation.universe-levels -open import group-theory.congruence-relations-abelian-groups -open import group-theory.congruence-relations-monoids -open import group-theory.subgroups-abelian-groups +open import group-theory.congruence-relations-abelian-groups funext univalence truncations +open import group-theory.congruence-relations-monoids funext univalence truncations +open import group-theory.subgroups-abelian-groups funext univalence truncations -open import ring-theory.congruence-relations-rings -open import ring-theory.left-ideals-rings -open import ring-theory.right-ideals-rings -open import ring-theory.rings -open import ring-theory.subsets-rings +open import ring-theory.congruence-relations-rings funext univalence truncations +open import ring-theory.left-ideals-rings funext univalence truncations +open import ring-theory.right-ideals-rings funext univalence truncations +open import ring-theory.rings funext univalence truncations +open import ring-theory.subsets-rings funext univalence truncations ```
diff --git a/src/ring-theory/ideals-semirings.lagda.md b/src/ring-theory/ideals-semirings.lagda.md index 801c43f0b9..9c41275ba9 100644 --- a/src/ring-theory/ideals-semirings.lagda.md +++ b/src/ring-theory/ideals-semirings.lagda.md @@ -1,22 +1,31 @@ # Ideals of semirings ```agda -module ring-theory.ideals-semirings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module ring-theory.ideals-semirings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence open import foundation.universe-levels -open import group-theory.submonoids +open import group-theory.submonoids funext univalence truncations -open import ring-theory.semirings -open import ring-theory.subsets-semirings +open import ring-theory.semirings funext univalence truncations +open import ring-theory.subsets-semirings funext univalence truncations ```
diff --git a/src/ring-theory/idempotent-elements-rings.lagda.md b/src/ring-theory/idempotent-elements-rings.lagda.md index 3d3369a849..8f4e32ab0a 100644 --- a/src/ring-theory/idempotent-elements-rings.lagda.md +++ b/src/ring-theory/idempotent-elements-rings.lagda.md @@ -1,18 +1,27 @@ # Idempotent elements in rings ```agda -module ring-theory.idempotent-elements-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module ring-theory.idempotent-elements-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.propositions -open import foundation.sets -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels -open import ring-theory.rings +open import ring-theory.rings funext univalence truncations ```
diff --git a/src/ring-theory/initial-rings.lagda.md b/src/ring-theory/initial-rings.lagda.md index b3287aeae7..96778ef7af 100644 --- a/src/ring-theory/initial-rings.lagda.md +++ b/src/ring-theory/initial-rings.lagda.md @@ -1,18 +1,26 @@ # Initial rings ```agda -module ring-theory.initial-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module ring-theory.initial-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.initial-objects-large-categories +open import category-theory.initial-objects-large-categories funext univalence truncations open import foundation.universe-levels -open import ring-theory.category-of-rings -open import ring-theory.rings +open import ring-theory.category-of-rings funext univalence truncations +open import ring-theory.rings funext univalence truncations ```
diff --git a/src/ring-theory/integer-multiples-of-elements-rings.lagda.md b/src/ring-theory/integer-multiples-of-elements-rings.lagda.md index 9f66654609..a234237b41 100644 --- a/src/ring-theory/integer-multiples-of-elements-rings.lagda.md +++ b/src/ring-theory/integer-multiples-of-elements-rings.lagda.md @@ -1,31 +1,40 @@ # Integer multiples of elements of rings ```agda -module ring-theory.integer-multiples-of-elements-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module ring-theory.integer-multiples-of-elements-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.addition-integers +open import elementary-number-theory.addition-integers funext univalence truncations open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-integers +open import elementary-number-theory.multiplication-integers funext univalence truncations open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.coproduct-types -open import foundation.identity-types -open import foundation.propositions +open import foundation.coproduct-types funext univalence truncations +open import foundation.dependent-products-propositions funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence open import foundation.transport-along-identifications open import foundation.universe-levels -open import group-theory.homomorphisms-abelian-groups -open import group-theory.integer-multiples-of-elements-abelian-groups +open import group-theory.homomorphisms-abelian-groups funext univalence truncations +open import group-theory.integer-multiples-of-elements-abelian-groups funext univalence truncations -open import ring-theory.commuting-elements-rings -open import ring-theory.homomorphisms-rings -open import ring-theory.multiples-of-elements-rings -open import ring-theory.rings +open import ring-theory.commuting-elements-rings funext univalence truncations +open import ring-theory.homomorphisms-rings funext univalence truncations +open import ring-theory.multiples-of-elements-rings funext univalence truncations +open import ring-theory.rings funext univalence truncations ```
diff --git a/src/ring-theory/intersections-ideals-rings.lagda.md b/src/ring-theory/intersections-ideals-rings.lagda.md index 4444ab8716..102b6836dc 100644 --- a/src/ring-theory/intersections-ideals-rings.lagda.md +++ b/src/ring-theory/intersections-ideals-rings.lagda.md @@ -1,22 +1,30 @@ # Intersections of ideals of rings ```agda -module ring-theory.intersections-ideals-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module ring-theory.intersections-ideals-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.intersections-subtypes +open import foundation.intersections-subtypes funext univalence truncations open import foundation.universe-levels -open import order-theory.greatest-lower-bounds-large-posets +open import order-theory.greatest-lower-bounds-large-posets funext univalence truncations -open import ring-theory.ideals-rings -open import ring-theory.poset-of-ideals-rings -open import ring-theory.rings -open import ring-theory.subsets-rings +open import ring-theory.ideals-rings funext univalence truncations +open import ring-theory.poset-of-ideals-rings funext univalence truncations +open import ring-theory.rings funext univalence truncations +open import ring-theory.subsets-rings funext univalence truncations ```
diff --git a/src/ring-theory/intersections-ideals-semirings.lagda.md b/src/ring-theory/intersections-ideals-semirings.lagda.md index e263dc496c..88d1880b54 100644 --- a/src/ring-theory/intersections-ideals-semirings.lagda.md +++ b/src/ring-theory/intersections-ideals-semirings.lagda.md @@ -1,19 +1,27 @@ # Intersections of ideals of semirings ```agda -module ring-theory.intersections-ideals-semirings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module ring-theory.intersections-ideals-semirings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.intersections-subtypes +open import foundation.intersections-subtypes funext univalence truncations open import foundation.universe-levels -open import ring-theory.ideals-semirings -open import ring-theory.semirings -open import ring-theory.subsets-semirings +open import ring-theory.ideals-semirings funext univalence truncations +open import ring-theory.semirings funext univalence truncations +open import ring-theory.subsets-semirings funext univalence truncations ```
diff --git a/src/ring-theory/invariant-basis-property-rings.lagda.md b/src/ring-theory/invariant-basis-property-rings.lagda.md index ae9972819c..db717fb3d1 100644 --- a/src/ring-theory/invariant-basis-property-rings.lagda.md +++ b/src/ring-theory/invariant-basis-property-rings.lagda.md @@ -1,7 +1,15 @@ # The invariant basis property of rings ```agda -module ring-theory.invariant-basis-property-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module ring-theory.invariant-basis-property-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,14 +17,14 @@ module ring-theory.invariant-basis-property-rings where ```agda open import elementary-number-theory.natural-numbers -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import ring-theory.dependent-products-rings -open import ring-theory.isomorphisms-rings -open import ring-theory.rings +open import ring-theory.dependent-products-rings funext univalence truncations +open import ring-theory.isomorphisms-rings funext univalence truncations +open import ring-theory.rings funext univalence truncations -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/ring-theory/invertible-elements-rings.lagda.md b/src/ring-theory/invertible-elements-rings.lagda.md index 5066846791..cb9f6beeb5 100644 --- a/src/ring-theory/invertible-elements-rings.lagda.md +++ b/src/ring-theory/invertible-elements-rings.lagda.md @@ -1,27 +1,37 @@ # Invertible elements in rings ```agda -module ring-theory.invertible-elements-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module ring-theory.invertible-elements-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.contractible-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-cartesian-product-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.propositions +open import foundation.contractible-types funext univalence +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence open import foundation.transport-along-identifications open import foundation.universe-levels -open import group-theory.invertible-elements-monoids +open import group-theory.invertible-elements-monoids funext univalence truncations -open import ring-theory.rings +open import ring-theory.rings funext univalence truncations ```
diff --git a/src/ring-theory/isomorphisms-rings.lagda.md b/src/ring-theory/isomorphisms-rings.lagda.md index 5a982e30d8..9f72f127e9 100644 --- a/src/ring-theory/isomorphisms-rings.lagda.md +++ b/src/ring-theory/isomorphisms-rings.lagda.md @@ -1,47 +1,58 @@ # Isomorphisms of rings ```agda -module ring-theory.isomorphisms-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module ring-theory.isomorphisms-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.isomorphisms-in-large-precategories +open import category-theory.isomorphisms-in-large-precategories funext univalence truncations open import foundation.action-on-identifications-functions -open import foundation.contractible-types +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-function-types -open import foundation.functoriality-dependent-pair-types +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.equality-dependent-function-types funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-function-types funext univalence +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext open import foundation.implicit-function-types -open import foundation.iterated-dependent-product-types -open import foundation.multivariable-homotopies -open import foundation.propositions +open import foundation.iterated-dependent-product-types funext +open import foundation.multivariable-homotopies funext +open import foundation.propositions funext univalence open import foundation.structure-identity-principle open import foundation.subtype-identity-principle -open import foundation.subtypes -open import foundation.torsorial-type-families +open import foundation.subtypes funext univalence truncations +open import foundation.telescopes +open import foundation.torsorial-type-families funext univalence truncations open import foundation.type-arithmetic-cartesian-product-types open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels -open import group-theory.homomorphisms-abelian-groups -open import group-theory.homomorphisms-monoids -open import group-theory.isomorphisms-abelian-groups -open import group-theory.isomorphisms-monoids +open import group-theory.homomorphisms-abelian-groups funext univalence truncations +open import group-theory.homomorphisms-monoids funext univalence truncations +open import group-theory.isomorphisms-abelian-groups funext univalence truncations +open import group-theory.isomorphisms-monoids funext univalence truncations -open import ring-theory.homomorphisms-rings -open import ring-theory.invertible-elements-rings -open import ring-theory.precategory-of-rings -open import ring-theory.rings +open import ring-theory.homomorphisms-rings funext univalence truncations +open import ring-theory.invertible-elements-rings funext univalence truncations +open import ring-theory.precategory-of-rings funext univalence truncations +open import ring-theory.rings funext univalence truncations ```
diff --git a/src/ring-theory/joins-ideals-rings.lagda.md b/src/ring-theory/joins-ideals-rings.lagda.md index cefa31e7f4..46d3eb2381 100644 --- a/src/ring-theory/joins-ideals-rings.lagda.md +++ b/src/ring-theory/joins-ideals-rings.lagda.md @@ -1,26 +1,34 @@ # Joins of ideals of rings ```agda -module ring-theory.joins-ideals-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module ring-theory.joins-ideals-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.unions-subtypes +open import foundation.identity-types funext +open import foundation.unions-subtypes funext univalence truncations open import foundation.universe-levels -open import order-theory.large-suplattices -open import order-theory.least-upper-bounds-large-posets -open import order-theory.similarity-of-elements-large-posets +open import order-theory.large-suplattices funext univalence truncations +open import order-theory.least-upper-bounds-large-posets funext univalence truncations +open import order-theory.similarity-of-elements-large-posets funext univalence truncations -open import ring-theory.ideals-generated-by-subsets-rings -open import ring-theory.ideals-rings -open import ring-theory.poset-of-ideals-rings -open import ring-theory.rings -open import ring-theory.subsets-rings +open import ring-theory.ideals-generated-by-subsets-rings funext univalence truncations +open import ring-theory.ideals-rings funext univalence truncations +open import ring-theory.poset-of-ideals-rings funext univalence truncations +open import ring-theory.rings funext univalence truncations +open import ring-theory.subsets-rings funext univalence truncations ```
diff --git a/src/ring-theory/joins-left-ideals-rings.lagda.md b/src/ring-theory/joins-left-ideals-rings.lagda.md index 9b93c7d3c5..528b326fc9 100644 --- a/src/ring-theory/joins-left-ideals-rings.lagda.md +++ b/src/ring-theory/joins-left-ideals-rings.lagda.md @@ -1,26 +1,34 @@ # Joins of left ideals of rings ```agda -module ring-theory.joins-left-ideals-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module ring-theory.joins-left-ideals-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.unions-subtypes +open import foundation.identity-types funext +open import foundation.unions-subtypes funext univalence truncations open import foundation.universe-levels -open import order-theory.large-suplattices -open import order-theory.least-upper-bounds-large-posets -open import order-theory.similarity-of-elements-large-posets +open import order-theory.large-suplattices funext univalence truncations +open import order-theory.least-upper-bounds-large-posets funext univalence truncations +open import order-theory.similarity-of-elements-large-posets funext univalence truncations -open import ring-theory.left-ideals-generated-by-subsets-rings -open import ring-theory.left-ideals-rings -open import ring-theory.poset-of-left-ideals-rings -open import ring-theory.rings -open import ring-theory.subsets-rings +open import ring-theory.left-ideals-generated-by-subsets-rings funext univalence truncations +open import ring-theory.left-ideals-rings funext univalence truncations +open import ring-theory.poset-of-left-ideals-rings funext univalence truncations +open import ring-theory.rings funext univalence truncations +open import ring-theory.subsets-rings funext univalence truncations ```
diff --git a/src/ring-theory/joins-right-ideals-rings.lagda.md b/src/ring-theory/joins-right-ideals-rings.lagda.md index f1ce158230..efecfca4af 100644 --- a/src/ring-theory/joins-right-ideals-rings.lagda.md +++ b/src/ring-theory/joins-right-ideals-rings.lagda.md @@ -1,26 +1,34 @@ # Joins of right ideals of rings ```agda -module ring-theory.joins-right-ideals-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module ring-theory.joins-right-ideals-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.unions-subtypes +open import foundation.identity-types funext +open import foundation.unions-subtypes funext univalence truncations open import foundation.universe-levels -open import order-theory.large-suplattices -open import order-theory.least-upper-bounds-large-posets -open import order-theory.similarity-of-elements-large-posets +open import order-theory.large-suplattices funext univalence truncations +open import order-theory.least-upper-bounds-large-posets funext univalence truncations +open import order-theory.similarity-of-elements-large-posets funext univalence truncations -open import ring-theory.poset-of-right-ideals-rings -open import ring-theory.right-ideals-generated-by-subsets-rings -open import ring-theory.right-ideals-rings -open import ring-theory.rings -open import ring-theory.subsets-rings +open import ring-theory.poset-of-right-ideals-rings funext univalence truncations +open import ring-theory.right-ideals-generated-by-subsets-rings funext univalence truncations +open import ring-theory.right-ideals-rings funext univalence truncations +open import ring-theory.rings funext univalence truncations +open import ring-theory.subsets-rings funext univalence truncations ```
diff --git a/src/ring-theory/kernels-of-ring-homomorphisms.lagda.md b/src/ring-theory/kernels-of-ring-homomorphisms.lagda.md index 905d2411ee..3676ed3bff 100644 --- a/src/ring-theory/kernels-of-ring-homomorphisms.lagda.md +++ b/src/ring-theory/kernels-of-ring-homomorphisms.lagda.md @@ -1,7 +1,15 @@ # Kernels of ring homomorphisms ```agda -module ring-theory.kernels-of-ring-homomorphisms where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module ring-theory.kernels-of-ring-homomorphisms + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,16 +17,16 @@ module ring-theory.kernels-of-ring-homomorphisms where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import group-theory.kernels-homomorphisms-groups -open import group-theory.subgroups-abelian-groups +open import group-theory.kernels-homomorphisms-groups funext univalence truncations +open import group-theory.subgroups-abelian-groups funext univalence truncations -open import ring-theory.homomorphisms-rings -open import ring-theory.ideals-rings -open import ring-theory.rings -open import ring-theory.subsets-rings +open import ring-theory.homomorphisms-rings funext univalence truncations +open import ring-theory.ideals-rings funext univalence truncations +open import ring-theory.rings funext univalence truncations +open import ring-theory.subsets-rings funext univalence truncations ```
diff --git a/src/ring-theory/left-ideals-generated-by-subsets-rings.lagda.md b/src/ring-theory/left-ideals-generated-by-subsets-rings.lagda.md index 45001b74cb..77bee8519a 100644 --- a/src/ring-theory/left-ideals-generated-by-subsets-rings.lagda.md +++ b/src/ring-theory/left-ideals-generated-by-subsets-rings.lagda.md @@ -1,41 +1,50 @@ # Left ideals generated by subsets of rings ```agda -module ring-theory.left-ideals-generated-by-subsets-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module ring-theory.left-ideals-generated-by-subsets-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.fibers-of-maps -open import foundation.function-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.powersets -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.fibers-of-maps funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.powersets funext univalence truncations +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.transport-along-identifications -open import foundation.unions-subtypes +open import foundation.unions-subtypes funext univalence truncations open import foundation.universe-levels -open import lists.concatenation-lists -open import lists.functoriality-lists +open import lists.concatenation-lists funext univalence truncations +open import lists.functoriality-lists funext univalence truncations open import lists.lists -open import order-theory.galois-connections-large-posets -open import order-theory.least-upper-bounds-large-posets -open import order-theory.order-preserving-maps-large-posets -open import order-theory.order-preserving-maps-large-preorders -open import order-theory.reflective-galois-connections-large-posets +open import order-theory.galois-connections-large-posets funext univalence truncations +open import order-theory.least-upper-bounds-large-posets funext univalence truncations +open import order-theory.order-preserving-maps-large-posets funext univalence truncations +open import order-theory.order-preserving-maps-large-preorders funext univalence truncations +open import order-theory.reflective-galois-connections-large-posets funext univalence truncations -open import ring-theory.left-ideals-rings -open import ring-theory.poset-of-left-ideals-rings -open import ring-theory.rings -open import ring-theory.subsets-rings +open import ring-theory.left-ideals-rings funext univalence truncations +open import ring-theory.poset-of-left-ideals-rings funext univalence truncations +open import ring-theory.rings funext univalence truncations +open import ring-theory.subsets-rings funext univalence truncations ```
diff --git a/src/ring-theory/left-ideals-rings.lagda.md b/src/ring-theory/left-ideals-rings.lagda.md index c0d2710a89..733505d92b 100644 --- a/src/ring-theory/left-ideals-rings.lagda.md +++ b/src/ring-theory/left-ideals-rings.lagda.md @@ -1,25 +1,34 @@ # Left ideals of rings ```agda -module ring-theory.left-ideals-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module ring-theory.left-ideals-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types -open import foundation.propositions +open import foundation.identity-types funext +open import foundation.propositions funext univalence open import foundation.subtype-identity-principle -open import foundation.subtypes -open import foundation.torsorial-type-families +open import foundation.subtypes funext univalence truncations +open import foundation.torsorial-type-families funext univalence truncations open import foundation.universe-levels -open import ring-theory.rings -open import ring-theory.subsets-rings +open import ring-theory.rings funext univalence truncations +open import ring-theory.subsets-rings funext univalence truncations ```
diff --git a/src/ring-theory/local-rings.lagda.md b/src/ring-theory/local-rings.lagda.md index 6ec65472c7..87c54ce3a0 100644 --- a/src/ring-theory/local-rings.lagda.md +++ b/src/ring-theory/local-rings.lagda.md @@ -1,20 +1,29 @@ # Local rings ```agda -module ring-theory.local-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module ring-theory.local-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.disjunction -open import foundation.propositions -open import foundation.sets +open import foundation.dependent-products-propositions funext +open import foundation.disjunction funext univalence truncations +open import foundation.propositions funext univalence +open import foundation.sets funext univalence open import foundation.universe-levels -open import ring-theory.invertible-elements-rings -open import ring-theory.rings +open import ring-theory.invertible-elements-rings funext univalence truncations +open import ring-theory.rings funext univalence truncations ```
diff --git a/src/ring-theory/localizations-rings.lagda.md b/src/ring-theory/localizations-rings.lagda.md index 0c3aeb511a..85e11e25f8 100644 --- a/src/ring-theory/localizations-rings.lagda.md +++ b/src/ring-theory/localizations-rings.lagda.md @@ -1,28 +1,38 @@ # Localizations of rings ```agda -module ring-theory.localizations-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module ring-theory.localizations-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.contractible-maps -open import foundation.contractible-types +open import foundation.contractible-maps funext +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.fibers-of-maps -open import foundation.functoriality-dependent-pair-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.subtypes +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.fibers-of-maps funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels -open import ring-theory.homomorphisms-rings -open import ring-theory.invertible-elements-rings -open import ring-theory.rings -open import ring-theory.subsets-rings +open import ring-theory.homomorphisms-rings funext univalence truncations +open import ring-theory.invertible-elements-rings funext univalence truncations +open import ring-theory.rings funext univalence truncations +open import ring-theory.subsets-rings funext univalence truncations ```
diff --git a/src/ring-theory/modules-rings.lagda.md b/src/ring-theory/modules-rings.lagda.md index dd09b187e4..0f169930ca 100644 --- a/src/ring-theory/modules-rings.lagda.md +++ b/src/ring-theory/modules-rings.lagda.md @@ -1,25 +1,33 @@ # Modules over rings ```agda -module ring-theory.modules-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module ring-theory.modules-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.sets +open import foundation.identity-types funext +open import foundation.sets funext univalence open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.addition-homomorphisms-abelian-groups -open import group-theory.endomorphism-rings-abelian-groups -open import group-theory.homomorphisms-abelian-groups +open import group-theory.abelian-groups funext univalence truncations +open import group-theory.addition-homomorphisms-abelian-groups funext univalence truncations +open import group-theory.endomorphism-rings-abelian-groups funext univalence truncations +open import group-theory.homomorphisms-abelian-groups funext univalence truncations -open import ring-theory.homomorphisms-rings -open import ring-theory.opposite-rings -open import ring-theory.rings +open import ring-theory.homomorphisms-rings funext univalence truncations +open import ring-theory.opposite-rings funext univalence truncations +open import ring-theory.rings funext univalence truncations ```
diff --git a/src/ring-theory/multiples-of-elements-rings.lagda.md b/src/ring-theory/multiples-of-elements-rings.lagda.md index f0bf36215a..230b24f991 100644 --- a/src/ring-theory/multiples-of-elements-rings.lagda.md +++ b/src/ring-theory/multiples-of-elements-rings.lagda.md @@ -1,7 +1,15 @@ # Multiples of elements in rings ```agda -module ring-theory.multiples-of-elements-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module ring-theory.multiples-of-elements-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -11,13 +19,14 @@ open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import foundation.identity-types -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence open import foundation.universe-levels -open import group-theory.multiples-of-elements-abelian-groups +open import group-theory.multiples-of-elements-abelian-groups funext univalence truncations -open import ring-theory.rings +open import ring-theory.rings funext univalence truncations ```
diff --git a/src/ring-theory/nil-ideals-rings.lagda.md b/src/ring-theory/nil-ideals-rings.lagda.md index 22688c8e4c..252ec3db93 100644 --- a/src/ring-theory/nil-ideals-rings.lagda.md +++ b/src/ring-theory/nil-ideals-rings.lagda.md @@ -1,20 +1,29 @@ # Nil ideals of rings ```agda -module ring-theory.nil-ideals-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module ring-theory.nil-ideals-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.propositions funext univalence open import foundation.universe-levels -open import ring-theory.ideals-rings -open import ring-theory.left-ideals-rings -open import ring-theory.nilpotent-elements-rings -open import ring-theory.right-ideals-rings -open import ring-theory.rings +open import ring-theory.ideals-rings funext univalence truncations +open import ring-theory.left-ideals-rings funext univalence truncations +open import ring-theory.nilpotent-elements-rings funext univalence truncations +open import ring-theory.right-ideals-rings funext univalence truncations +open import ring-theory.rings funext univalence truncations ```
diff --git a/src/ring-theory/nilpotent-elements-rings.lagda.md b/src/ring-theory/nilpotent-elements-rings.lagda.md index 96f8512935..1e8c6c936b 100644 --- a/src/ring-theory/nilpotent-elements-rings.lagda.md +++ b/src/ring-theory/nilpotent-elements-rings.lagda.md @@ -1,7 +1,15 @@ # Nilpotent elements in rings ```agda -module ring-theory.nilpotent-elements-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module ring-theory.nilpotent-elements-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,16 +17,17 @@ module ring-theory.nilpotent-elements-rings where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.existential-quantification -open import foundation.identity-types -open import foundation.propositional-truncations -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.existential-quantification funext univalence truncations +open import foundation.identity-types funext +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence open import foundation.universe-levels -open import ring-theory.nilpotent-elements-semirings -open import ring-theory.powers-of-elements-rings -open import ring-theory.rings -open import ring-theory.subsets-rings +open import ring-theory.nilpotent-elements-semirings funext univalence truncations +open import ring-theory.powers-of-elements-rings funext univalence truncations +open import ring-theory.rings funext univalence truncations +open import ring-theory.subsets-rings funext univalence truncations ```
diff --git a/src/ring-theory/nilpotent-elements-semirings.lagda.md b/src/ring-theory/nilpotent-elements-semirings.lagda.md index 434bdf7fb8..d28c0ac2ef 100644 --- a/src/ring-theory/nilpotent-elements-semirings.lagda.md +++ b/src/ring-theory/nilpotent-elements-semirings.lagda.md @@ -1,7 +1,15 @@ # Nilpotent elements in semirings ```agda -module ring-theory.nilpotent-elements-semirings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module ring-theory.nilpotent-elements-semirings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -12,16 +20,17 @@ open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.existential-quantification -open import foundation.identity-types -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.existential-quantification funext univalence truncations +open import foundation.identity-types funext +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels -open import ring-theory.binomial-theorem-semirings -open import ring-theory.powers-of-elements-semirings -open import ring-theory.semirings +open import ring-theory.binomial-theorem-semirings funext univalence truncations +open import ring-theory.powers-of-elements-semirings funext univalence truncations +open import ring-theory.semirings funext univalence truncations ```
diff --git a/src/ring-theory/opposite-rings.lagda.md b/src/ring-theory/opposite-rings.lagda.md index 824b49515c..f1a7fd8c21 100644 --- a/src/ring-theory/opposite-rings.lagda.md +++ b/src/ring-theory/opposite-rings.lagda.md @@ -1,17 +1,25 @@ # Opposite rings ```agda -module ring-theory.opposite-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module ring-theory.opposite-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import ring-theory.rings +open import ring-theory.rings funext univalence truncations ```
diff --git a/src/ring-theory/poset-of-cyclic-rings.lagda.md b/src/ring-theory/poset-of-cyclic-rings.lagda.md index ef3023bcd0..0b99c8e983 100644 --- a/src/ring-theory/poset-of-cyclic-rings.lagda.md +++ b/src/ring-theory/poset-of-cyclic-rings.lagda.md @@ -1,7 +1,15 @@ # The poset of cyclic rings ```agda -module ring-theory.poset-of-cyclic-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module ring-theory.poset-of-cyclic-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,9 +17,9 @@ module ring-theory.poset-of-cyclic-rings where ```agda open import foundation.universe-levels -open import order-theory.large-posets +open import order-theory.large-posets funext univalence truncations -open import ring-theory.category-of-cyclic-rings +open import ring-theory.category-of-cyclic-rings funext univalence truncations ```
diff --git a/src/ring-theory/poset-of-ideals-rings.lagda.md b/src/ring-theory/poset-of-ideals-rings.lagda.md index 7ac68be10d..4a757edccb 100644 --- a/src/ring-theory/poset-of-ideals-rings.lagda.md +++ b/src/ring-theory/poset-of-ideals-rings.lagda.md @@ -1,28 +1,37 @@ # The poset of ideals of a ring ```agda -module ring-theory.poset-of-ideals-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module ring-theory.poset-of-ideals-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.binary-relations +open import foundation.binary-relations funext univalence truncations open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.powersets -open import foundation.propositions -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.identity-types funext +open import foundation.powersets funext univalence truncations +open import foundation.propositions funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels -open import order-theory.large-posets -open import order-theory.large-preorders -open import order-theory.order-preserving-maps-large-posets -open import order-theory.order-preserving-maps-large-preorders -open import order-theory.similarity-of-elements-large-posets +open import order-theory.large-posets funext univalence truncations +open import order-theory.large-preorders funext univalence truncations +open import order-theory.order-preserving-maps-large-posets funext univalence truncations +open import order-theory.order-preserving-maps-large-preorders funext univalence truncations +open import order-theory.similarity-of-elements-large-posets funext univalence truncations -open import ring-theory.ideals-rings -open import ring-theory.rings +open import ring-theory.ideals-rings funext univalence truncations +open import ring-theory.rings funext univalence truncations ```
diff --git a/src/ring-theory/poset-of-left-ideals-rings.lagda.md b/src/ring-theory/poset-of-left-ideals-rings.lagda.md index a34d3bad4a..100667edae 100644 --- a/src/ring-theory/poset-of-left-ideals-rings.lagda.md +++ b/src/ring-theory/poset-of-left-ideals-rings.lagda.md @@ -1,28 +1,37 @@ # The poset of left ideals of a ring ```agda -module ring-theory.poset-of-left-ideals-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module ring-theory.poset-of-left-ideals-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.binary-relations +open import foundation.binary-relations funext univalence truncations open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.powersets -open import foundation.propositions -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.identity-types funext +open import foundation.powersets funext univalence truncations +open import foundation.propositions funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels -open import order-theory.large-posets -open import order-theory.large-preorders -open import order-theory.order-preserving-maps-large-posets -open import order-theory.order-preserving-maps-large-preorders -open import order-theory.similarity-of-elements-large-posets +open import order-theory.large-posets funext univalence truncations +open import order-theory.large-preorders funext univalence truncations +open import order-theory.order-preserving-maps-large-posets funext univalence truncations +open import order-theory.order-preserving-maps-large-preorders funext univalence truncations +open import order-theory.similarity-of-elements-large-posets funext univalence truncations -open import ring-theory.left-ideals-rings -open import ring-theory.rings +open import ring-theory.left-ideals-rings funext univalence truncations +open import ring-theory.rings funext univalence truncations ```
diff --git a/src/ring-theory/poset-of-right-ideals-rings.lagda.md b/src/ring-theory/poset-of-right-ideals-rings.lagda.md index 9ddb7754b7..4cf8dc99b9 100644 --- a/src/ring-theory/poset-of-right-ideals-rings.lagda.md +++ b/src/ring-theory/poset-of-right-ideals-rings.lagda.md @@ -1,28 +1,37 @@ # The poset of right ideals of a ring ```agda -module ring-theory.poset-of-right-ideals-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module ring-theory.poset-of-right-ideals-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.binary-relations +open import foundation.binary-relations funext univalence truncations open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.powersets -open import foundation.propositions -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.identity-types funext +open import foundation.powersets funext univalence truncations +open import foundation.propositions funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels -open import order-theory.large-posets -open import order-theory.large-preorders -open import order-theory.order-preserving-maps-large-posets -open import order-theory.order-preserving-maps-large-preorders -open import order-theory.similarity-of-elements-large-posets +open import order-theory.large-posets funext univalence truncations +open import order-theory.large-preorders funext univalence truncations +open import order-theory.order-preserving-maps-large-posets funext univalence truncations +open import order-theory.order-preserving-maps-large-preorders funext univalence truncations +open import order-theory.similarity-of-elements-large-posets funext univalence truncations -open import ring-theory.right-ideals-rings -open import ring-theory.rings +open import ring-theory.right-ideals-rings funext univalence truncations +open import ring-theory.rings funext univalence truncations ```
diff --git a/src/ring-theory/powers-of-elements-rings.lagda.md b/src/ring-theory/powers-of-elements-rings.lagda.md index e7a4956cc4..86d1fc5155 100644 --- a/src/ring-theory/powers-of-elements-rings.lagda.md +++ b/src/ring-theory/powers-of-elements-rings.lagda.md @@ -1,7 +1,15 @@ # Powers of elements in rings ```agda -module ring-theory.powers-of-elements-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module ring-theory.powers-of-elements-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,17 +18,17 @@ module ring-theory.powers-of-elements-rings where open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.parity-natural-numbers +open import elementary-number-theory.parity-natural-numbers funext univalence truncations open import foundation.action-on-identifications-functions -open import foundation.empty-types -open import foundation.function-types -open import foundation.identity-types +open import foundation.empty-types funext univalence truncations +open import foundation.function-types funext +open import foundation.identity-types funext open import foundation.universe-levels -open import ring-theory.central-elements-rings -open import ring-theory.powers-of-elements-semirings -open import ring-theory.rings +open import ring-theory.central-elements-rings funext univalence truncations +open import ring-theory.powers-of-elements-semirings funext univalence truncations +open import ring-theory.rings funext univalence truncations ```
diff --git a/src/ring-theory/powers-of-elements-semirings.lagda.md b/src/ring-theory/powers-of-elements-semirings.lagda.md index ca2f29b47c..f241b422d0 100644 --- a/src/ring-theory/powers-of-elements-semirings.lagda.md +++ b/src/ring-theory/powers-of-elements-semirings.lagda.md @@ -1,7 +1,15 @@ # Powers of elements in semirings ```agda -module ring-theory.powers-of-elements-semirings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module ring-theory.powers-of-elements-semirings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -11,12 +19,12 @@ open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import group-theory.powers-of-elements-monoids +open import group-theory.powers-of-elements-monoids funext univalence truncations -open import ring-theory.semirings +open import ring-theory.semirings funext univalence truncations ```
diff --git a/src/ring-theory/precategory-of-rings.lagda.md b/src/ring-theory/precategory-of-rings.lagda.md index e22cb72547..b25cbb9cdb 100644 --- a/src/ring-theory/precategory-of-rings.lagda.md +++ b/src/ring-theory/precategory-of-rings.lagda.md @@ -1,19 +1,27 @@ # The precategory of rings ```agda -module ring-theory.precategory-of-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module ring-theory.precategory-of-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.large-precategories -open import category-theory.precategories +open import category-theory.large-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations open import foundation.universe-levels -open import ring-theory.homomorphisms-rings -open import ring-theory.rings +open import ring-theory.homomorphisms-rings funext univalence truncations +open import ring-theory.rings funext univalence truncations ```
diff --git a/src/ring-theory/precategory-of-semirings.lagda.md b/src/ring-theory/precategory-of-semirings.lagda.md index 8b84a0d3e0..b1b27ae290 100644 --- a/src/ring-theory/precategory-of-semirings.lagda.md +++ b/src/ring-theory/precategory-of-semirings.lagda.md @@ -1,19 +1,27 @@ # The precategory of semirings ```agda -module ring-theory.precategory-of-semirings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module ring-theory.precategory-of-semirings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.large-precategories -open import category-theory.precategories +open import category-theory.large-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations open import foundation.universe-levels -open import ring-theory.homomorphisms-semirings -open import ring-theory.semirings +open import ring-theory.homomorphisms-semirings funext univalence truncations +open import ring-theory.semirings funext univalence truncations ```
diff --git a/src/ring-theory/products-ideals-rings.lagda.md b/src/ring-theory/products-ideals-rings.lagda.md index 73cb6e9253..b366405607 100644 --- a/src/ring-theory/products-ideals-rings.lagda.md +++ b/src/ring-theory/products-ideals-rings.lagda.md @@ -1,23 +1,31 @@ # Products of ideals of rings ```agda -module ring-theory.products-ideals-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module ring-theory.products-ideals-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.propositional-truncations +open import foundation.identity-types funext +open import foundation.propositional-truncations funext univalence open import foundation.universe-levels -open import ring-theory.ideals-generated-by-subsets-rings -open import ring-theory.ideals-rings -open import ring-theory.poset-of-ideals-rings -open import ring-theory.products-subsets-rings -open import ring-theory.rings -open import ring-theory.subsets-rings +open import ring-theory.ideals-generated-by-subsets-rings funext univalence truncations +open import ring-theory.ideals-rings funext univalence truncations +open import ring-theory.poset-of-ideals-rings funext univalence truncations +open import ring-theory.products-subsets-rings funext univalence truncations +open import ring-theory.rings funext univalence truncations +open import ring-theory.subsets-rings funext univalence truncations ```
diff --git a/src/ring-theory/products-left-ideals-rings.lagda.md b/src/ring-theory/products-left-ideals-rings.lagda.md index 553c0eacf9..0d7cdac6d7 100644 --- a/src/ring-theory/products-left-ideals-rings.lagda.md +++ b/src/ring-theory/products-left-ideals-rings.lagda.md @@ -1,23 +1,31 @@ # Products of left ideals of rings ```agda -module ring-theory.products-left-ideals-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module ring-theory.products-left-ideals-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.propositional-truncations +open import foundation.identity-types funext +open import foundation.propositional-truncations funext univalence open import foundation.universe-levels -open import ring-theory.left-ideals-generated-by-subsets-rings -open import ring-theory.left-ideals-rings -open import ring-theory.poset-of-left-ideals-rings -open import ring-theory.products-subsets-rings -open import ring-theory.rings -open import ring-theory.subsets-rings +open import ring-theory.left-ideals-generated-by-subsets-rings funext univalence truncations +open import ring-theory.left-ideals-rings funext univalence truncations +open import ring-theory.poset-of-left-ideals-rings funext univalence truncations +open import ring-theory.products-subsets-rings funext univalence truncations +open import ring-theory.rings funext univalence truncations +open import ring-theory.subsets-rings funext univalence truncations ```
diff --git a/src/ring-theory/products-right-ideals-rings.lagda.md b/src/ring-theory/products-right-ideals-rings.lagda.md index 22cf1b4cfe..3257ad7761 100644 --- a/src/ring-theory/products-right-ideals-rings.lagda.md +++ b/src/ring-theory/products-right-ideals-rings.lagda.md @@ -1,23 +1,31 @@ # Products of right ideals of rings ```agda -module ring-theory.products-right-ideals-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module ring-theory.products-right-ideals-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.propositional-truncations +open import foundation.identity-types funext +open import foundation.propositional-truncations funext univalence open import foundation.universe-levels -open import ring-theory.poset-of-right-ideals-rings -open import ring-theory.products-subsets-rings -open import ring-theory.right-ideals-generated-by-subsets-rings -open import ring-theory.right-ideals-rings -open import ring-theory.rings -open import ring-theory.subsets-rings +open import ring-theory.poset-of-right-ideals-rings funext univalence truncations +open import ring-theory.products-subsets-rings funext univalence truncations +open import ring-theory.right-ideals-generated-by-subsets-rings funext univalence truncations +open import ring-theory.right-ideals-rings funext univalence truncations +open import ring-theory.rings funext univalence truncations +open import ring-theory.subsets-rings funext univalence truncations ```
diff --git a/src/ring-theory/products-rings.lagda.md b/src/ring-theory/products-rings.lagda.md index fcebad162a..3c7f5c0ad3 100644 --- a/src/ring-theory/products-rings.lagda.md +++ b/src/ring-theory/products-rings.lagda.md @@ -1,7 +1,15 @@ # Products of rings ```agda -module ring-theory.products-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module ring-theory.products-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,15 +17,15 @@ module ring-theory.products-rings where ```agda open import foundation.dependent-pair-types open import foundation.equality-cartesian-product-types -open import foundation.identity-types -open import foundation.sets +open import foundation.identity-types funext +open import foundation.sets funext univalence open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.groups -open import group-theory.semigroups +open import group-theory.abelian-groups funext univalence truncations +open import group-theory.groups funext univalence truncations +open import group-theory.semigroups funext univalence -open import ring-theory.rings +open import ring-theory.rings funext univalence truncations ```
diff --git a/src/ring-theory/products-subsets-rings.lagda.md b/src/ring-theory/products-subsets-rings.lagda.md index 157d8910ef..ce7141e993 100644 --- a/src/ring-theory/products-subsets-rings.lagda.md +++ b/src/ring-theory/products-subsets-rings.lagda.md @@ -1,21 +1,29 @@ # Products of subsets of rings ```agda -module ring-theory.products-subsets-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module ring-theory.products-subsets-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.propositional-truncations -open import foundation.subtypes -open import foundation.unions-subtypes +open import foundation.identity-types funext +open import foundation.propositional-truncations funext univalence +open import foundation.subtypes funext univalence truncations +open import foundation.unions-subtypes funext univalence truncations open import foundation.universe-levels -open import ring-theory.rings -open import ring-theory.subsets-rings +open import ring-theory.rings funext univalence truncations +open import ring-theory.subsets-rings funext univalence truncations ```
diff --git a/src/ring-theory/quotient-rings.lagda.md b/src/ring-theory/quotient-rings.lagda.md index cf3fdbe28f..bfa7d108d6 100644 --- a/src/ring-theory/quotient-rings.lagda.md +++ b/src/ring-theory/quotient-rings.lagda.md @@ -1,7 +1,15 @@ # Quotient rings ```agda -module ring-theory.quotient-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module ring-theory.quotient-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,13 +17,13 @@ module ring-theory.quotient-rings where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.identity-types +open import foundation.equivalences funext +open import foundation.identity-types funext open import foundation.universe-levels -open import ring-theory.homomorphisms-rings -open import ring-theory.ideals-rings -open import ring-theory.rings +open import ring-theory.homomorphisms-rings funext univalence truncations +open import ring-theory.ideals-rings funext univalence truncations +open import ring-theory.rings funext univalence truncations ```
diff --git a/src/ring-theory/radical-ideals-rings.lagda.md b/src/ring-theory/radical-ideals-rings.lagda.md index 964017ee37..fd07bc5546 100644 --- a/src/ring-theory/radical-ideals-rings.lagda.md +++ b/src/ring-theory/radical-ideals-rings.lagda.md @@ -1,18 +1,27 @@ # Radical ideals of rings ```agda -module ring-theory.radical-ideals-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module ring-theory.radical-ideals-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.propositions funext univalence open import foundation.universe-levels -open import ring-theory.ideals-rings -open import ring-theory.invertible-elements-rings -open import ring-theory.rings +open import ring-theory.ideals-rings funext univalence truncations +open import ring-theory.invertible-elements-rings funext univalence truncations +open import ring-theory.rings funext univalence truncations ```
diff --git a/src/ring-theory/right-ideals-generated-by-subsets-rings.lagda.md b/src/ring-theory/right-ideals-generated-by-subsets-rings.lagda.md index ec913d21e3..0b568ff95e 100644 --- a/src/ring-theory/right-ideals-generated-by-subsets-rings.lagda.md +++ b/src/ring-theory/right-ideals-generated-by-subsets-rings.lagda.md @@ -1,41 +1,50 @@ # Right ideals generated by subsets of rings ```agda -module ring-theory.right-ideals-generated-by-subsets-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module ring-theory.right-ideals-generated-by-subsets-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.fibers-of-maps -open import foundation.function-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.powersets -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.fibers-of-maps funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.powersets funext univalence truncations +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.transport-along-identifications -open import foundation.unions-subtypes +open import foundation.unions-subtypes funext univalence truncations open import foundation.universe-levels -open import lists.concatenation-lists -open import lists.functoriality-lists +open import lists.concatenation-lists funext univalence truncations +open import lists.functoriality-lists funext univalence truncations open import lists.lists -open import order-theory.galois-connections-large-posets -open import order-theory.least-upper-bounds-large-posets -open import order-theory.order-preserving-maps-large-posets -open import order-theory.order-preserving-maps-large-preorders -open import order-theory.reflective-galois-connections-large-posets +open import order-theory.galois-connections-large-posets funext univalence truncations +open import order-theory.least-upper-bounds-large-posets funext univalence truncations +open import order-theory.order-preserving-maps-large-posets funext univalence truncations +open import order-theory.order-preserving-maps-large-preorders funext univalence truncations +open import order-theory.reflective-galois-connections-large-posets funext univalence truncations -open import ring-theory.poset-of-right-ideals-rings -open import ring-theory.right-ideals-rings -open import ring-theory.rings -open import ring-theory.subsets-rings +open import ring-theory.poset-of-right-ideals-rings funext univalence truncations +open import ring-theory.right-ideals-rings funext univalence truncations +open import ring-theory.rings funext univalence truncations +open import ring-theory.subsets-rings funext univalence truncations ```
diff --git a/src/ring-theory/right-ideals-rings.lagda.md b/src/ring-theory/right-ideals-rings.lagda.md index 1da87674fc..888c66ab1e 100644 --- a/src/ring-theory/right-ideals-rings.lagda.md +++ b/src/ring-theory/right-ideals-rings.lagda.md @@ -1,25 +1,34 @@ # Right ideals of rings ```agda -module ring-theory.right-ideals-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module ring-theory.right-ideals-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types -open import foundation.propositions +open import foundation.identity-types funext +open import foundation.propositions funext univalence open import foundation.subtype-identity-principle -open import foundation.subtypes -open import foundation.torsorial-type-families +open import foundation.subtypes funext univalence truncations +open import foundation.torsorial-type-families funext univalence truncations open import foundation.universe-levels -open import ring-theory.rings -open import ring-theory.subsets-rings +open import ring-theory.rings funext univalence truncations +open import ring-theory.subsets-rings funext univalence truncations ```
diff --git a/src/ring-theory/rings.lagda.md b/src/ring-theory/rings.lagda.md index 757f7994ee..209d125c52 100644 --- a/src/ring-theory/rings.lagda.md +++ b/src/ring-theory/rings.lagda.md @@ -1,7 +1,15 @@ # Rings ```agda -module ring-theory.rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module ring-theory.rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -12,33 +20,34 @@ open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.binary-embeddings +open import foundation.binary-embeddings funext open import foundation.binary-equivalences -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalences -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.involutions -open import foundation.negation -open import foundation.propositions -open import foundation.sets +open import foundation.dependent-products-propositions funext +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.involutions funext univalence +open import foundation.negation funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence open import foundation.unital-binary-operations open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.commutative-monoids -open import group-theory.groups -open import group-theory.monoids -open import group-theory.semigroups +open import group-theory.abelian-groups funext univalence truncations +open import group-theory.commutative-monoids funext univalence truncations +open import group-theory.groups funext univalence truncations +open import group-theory.monoids funext univalence truncations +open import group-theory.semigroups funext univalence -open import lists.concatenation-lists +open import lists.concatenation-lists funext univalence truncations open import lists.lists -open import ring-theory.semirings +open import ring-theory.semirings funext univalence truncations ```
diff --git a/src/ring-theory/semirings.lagda.md b/src/ring-theory/semirings.lagda.md index 982869d8d3..093b1b5303 100644 --- a/src/ring-theory/semirings.lagda.md +++ b/src/ring-theory/semirings.lagda.md @@ -1,7 +1,15 @@ # Semirings ```agda -module ring-theory.semirings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module ring-theory.semirings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -12,18 +20,19 @@ open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.negation -open import foundation.propositions -open import foundation.sets +open import foundation.dependent-products-propositions funext +open import foundation.identity-types funext +open import foundation.negation funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence open import foundation.unital-binary-operations open import foundation.universe-levels -open import group-theory.commutative-monoids -open import group-theory.monoids -open import group-theory.semigroups +open import group-theory.commutative-monoids funext univalence truncations +open import group-theory.monoids funext univalence truncations +open import group-theory.semigroups funext univalence ```
diff --git a/src/ring-theory/subsets-rings.lagda.md b/src/ring-theory/subsets-rings.lagda.md index df9a3f2c84..127e2b4e65 100644 --- a/src/ring-theory/subsets-rings.lagda.md +++ b/src/ring-theory/subsets-rings.lagda.md @@ -1,22 +1,31 @@ # Subsets of rings ```agda -module ring-theory.subsets-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module ring-theory.subsets-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.identity-types -open import foundation.propositional-extensionality -open import foundation.propositions -open import foundation.sets -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.identity-types funext +open import foundation.propositional-extensionality funext univalence truncations +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels -open import group-theory.subgroups-abelian-groups +open import group-theory.subgroups-abelian-groups funext univalence truncations -open import ring-theory.rings +open import ring-theory.rings funext univalence truncations ```
diff --git a/src/ring-theory/subsets-semirings.lagda.md b/src/ring-theory/subsets-semirings.lagda.md index 0236a79809..63b8c3d38a 100644 --- a/src/ring-theory/subsets-semirings.lagda.md +++ b/src/ring-theory/subsets-semirings.lagda.md @@ -1,20 +1,29 @@ # Subsets of semirings ```agda -module ring-theory.subsets-semirings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module ring-theory.subsets-semirings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.identity-types -open import foundation.propositional-extensionality -open import foundation.propositions -open import foundation.sets -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.identity-types funext +open import foundation.propositional-extensionality funext univalence truncations +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels -open import ring-theory.semirings +open import ring-theory.semirings funext univalence truncations ```
diff --git a/src/ring-theory/sums-rings.lagda.md b/src/ring-theory/sums-rings.lagda.md index f2f5859aa9..878a296017 100644 --- a/src/ring-theory/sums-rings.lagda.md +++ b/src/ring-theory/sums-rings.lagda.md @@ -1,7 +1,15 @@ # Sums of elements in rings ```agda -module ring-theory.sums-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module ring-theory.sums-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,19 +18,19 @@ module ring-theory.sums-rings where open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.natural-numbers -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.universe-levels -open import linear-algebra.vectors -open import linear-algebra.vectors-on-rings +open import linear-algebra.vectors funext univalence truncations +open import linear-algebra.vectors-on-rings funext univalence truncations -open import ring-theory.rings -open import ring-theory.sums-semirings +open import ring-theory.rings funext univalence truncations +open import ring-theory.sums-semirings funext univalence truncations -open import univalent-combinatorics.coproduct-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.coproduct-types funext univalence truncations +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/ring-theory/sums-semirings.lagda.md b/src/ring-theory/sums-semirings.lagda.md index 3f42f0a446..126e1aeaa8 100644 --- a/src/ring-theory/sums-semirings.lagda.md +++ b/src/ring-theory/sums-semirings.lagda.md @@ -1,7 +1,15 @@ # Sums of elements in semirings ```agda -module ring-theory.sums-semirings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module ring-theory.sums-semirings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -11,21 +19,21 @@ open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.coproduct-types -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types +open import foundation.coproduct-types funext univalence truncations +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.unit-type open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import linear-algebra.vectors -open import linear-algebra.vectors-on-semirings +open import linear-algebra.vectors funext univalence truncations +open import linear-algebra.vectors-on-semirings funext univalence truncations -open import ring-theory.semirings +open import ring-theory.semirings funext univalence truncations -open import univalent-combinatorics.coproduct-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.coproduct-types funext univalence truncations +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/ring-theory/transporting-ring-structure-along-isomorphisms-abelian-groups.lagda.md b/src/ring-theory/transporting-ring-structure-along-isomorphisms-abelian-groups.lagda.md index d69f003772..bfb75fa732 100644 --- a/src/ring-theory/transporting-ring-structure-along-isomorphisms-abelian-groups.lagda.md +++ b/src/ring-theory/transporting-ring-structure-along-isomorphisms-abelian-groups.lagda.md @@ -11,17 +11,17 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.unital-binary-operations open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.isomorphisms-abelian-groups -open import group-theory.semigroups +open import group-theory.abelian-groups funext univalence truncations +open import group-theory.isomorphisms-abelian-groups funext univalence truncations +open import group-theory.semigroups funext univalence -open import ring-theory.homomorphisms-rings -open import ring-theory.isomorphisms-rings -open import ring-theory.rings +open import ring-theory.homomorphisms-rings funext univalence truncations +open import ring-theory.isomorphisms-rings funext univalence truncations +open import ring-theory.rings funext univalence truncations ```
@@ -44,7 +44,14 @@ transported ring structure. ### Transporting the multiplicative structure of a ring along an isomorphism of abelian groups ```agda +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + module _ + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) {l1 l2 : Level} (R : Ring l1) (A : Ab l2) (f : iso-Ab (ab-Ring R) A) where diff --git a/src/ring-theory/trivial-rings.lagda.md b/src/ring-theory/trivial-rings.lagda.md index 4173514622..59af0a1469 100644 --- a/src/ring-theory/trivial-rings.lagda.md +++ b/src/ring-theory/trivial-rings.lagda.md @@ -1,7 +1,15 @@ # Trivial rings ```agda -module ring-theory.trivial-rings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module ring-theory.trivial-rings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,17 +17,19 @@ module ring-theory.trivial-rings where ```agda open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.contractible-types +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.negated-equality -open import foundation.negation -open import foundation.propositions -open import foundation.sets +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.identity-types funext +open import foundation.negated-equality funext univalence truncations +open import foundation.negation funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence open import foundation.universe-levels -open import ring-theory.invertible-elements-rings -open import ring-theory.rings +open import ring-theory.invertible-elements-rings funext univalence truncations +open import ring-theory.rings funext univalence truncations ```
diff --git a/src/set-theory.lagda.md b/src/set-theory.lagda.md index 054f1135dc..9a0826cad6 100644 --- a/src/set-theory.lagda.md +++ b/src/set-theory.lagda.md @@ -42,17 +42,25 @@ theory, and [Russell's paradox](set-theory.russells-paradox.md). ## Modules in the set theory namespace ```agda -module set-theory where - -open import set-theory.baire-space public -open import set-theory.cantor-space public -open import set-theory.cantors-diagonal-argument public -open import set-theory.cardinalities public -open import set-theory.countable-sets public -open import set-theory.cumulative-hierarchy public -open import set-theory.infinite-sets public -open import set-theory.russells-paradox public -open import set-theory.uncountable-sets public +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module set-theory + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where + +open import set-theory.baire-space funext univalence truncations public +open import set-theory.cantor-space funext univalence truncations public +open import set-theory.cantors-diagonal-argument funext univalence truncations public +open import set-theory.cardinalities funext univalence truncations public +open import set-theory.countable-sets funext univalence truncations public +open import set-theory.cumulative-hierarchy funext univalence truncations public +open import set-theory.infinite-sets funext univalence truncations public +open import set-theory.russells-paradox funext univalence truncations public +open import set-theory.uncountable-sets funext univalence truncations public ``` ## References diff --git a/src/set-theory/baire-space.lagda.md b/src/set-theory/baire-space.lagda.md index 6e7075dc17..30e2507689 100644 --- a/src/set-theory/baire-space.lagda.md +++ b/src/set-theory/baire-space.lagda.md @@ -1,32 +1,37 @@ # Baire space ```agda -module set-theory.baire-space where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module set-theory.baire-space + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.equality-natural-numbers +open import elementary-number-theory.equality-natural-numbers funext univalence truncations open import elementary-number-theory.natural-numbers -open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.lawveres-fixed-point-theorem -open import foundation.negation -open import foundation.propositional-truncations -open import foundation.sets +open import foundation.function-types funext +open import foundation.lawveres-fixed-point-theorem funext univalence truncations +open import foundation.negation funext +open import foundation.propositional-truncations funext univalence +open import foundation.sets funext univalence open import foundation.universe-levels open import foundation-core.empty-types open import foundation-core.identity-types -open import foundation-core.propositions -open import set-theory.cantors-diagonal-argument -open import set-theory.countable-sets -open import set-theory.uncountable-sets +open import set-theory.cantors-diagonal-argument funext univalence truncations +open import set-theory.countable-sets funext univalence truncations +open import set-theory.uncountable-sets funext univalence truncations ```
diff --git a/src/set-theory/cantor-space.lagda.md b/src/set-theory/cantor-space.lagda.md index 41ea6e9e47..049bd7b0db 100644 --- a/src/set-theory/cantor-space.lagda.md +++ b/src/set-theory/cantor-space.lagda.md @@ -1,7 +1,15 @@ # Cantor space ```agda -module set-theory.cantor-space where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module set-theory.cantor-space + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,24 +17,24 @@ module set-theory.cantor-space where ```agda open import elementary-number-theory.natural-numbers -open import foundation.booleans -open import foundation.coproduct-types +open import foundation.booleans funext univalence truncations +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.lawveres-fixed-point-theorem -open import foundation.negation -open import foundation.propositional-truncations -open import foundation.sets -open import foundation.tight-apartness-relations +open import foundation.empty-types funext univalence truncations +open import foundation.lawveres-fixed-point-theorem funext univalence truncations +open import foundation.negation funext +open import foundation.propositional-truncations funext univalence +open import foundation.sets funext univalence +open import foundation.tight-apartness-relations funext univalence truncations open import foundation.unit-type open import foundation.universe-levels -open import set-theory.cantors-diagonal-argument -open import set-theory.countable-sets -open import set-theory.uncountable-sets +open import set-theory.cantors-diagonal-argument funext univalence truncations +open import set-theory.countable-sets funext univalence truncations +open import set-theory.uncountable-sets funext univalence truncations -open import univalent-combinatorics.equality-standard-finite-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.equality-standard-finite-types funext univalence truncations +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/set-theory/cantors-diagonal-argument.lagda.md b/src/set-theory/cantors-diagonal-argument.lagda.md index b573aa9ab7..b04cb3c262 100644 --- a/src/set-theory/cantors-diagonal-argument.lagda.md +++ b/src/set-theory/cantors-diagonal-argument.lagda.md @@ -1,7 +1,15 @@ # Cantor's diagonal argument ```agda -module set-theory.cantors-diagonal-argument where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module set-theory.cantors-diagonal-argument + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,32 +18,24 @@ module set-theory.cantors-diagonal-argument where open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.coproduct-types -open import foundation.decidable-propositions -open import foundation.decidable-subtypes -open import foundation.decidable-types +open import foundation.coproduct-types funext univalence truncations +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.discrete-types -open import foundation.double-negation -open import foundation.function-extensionality -open import foundation.identity-types -open import foundation.isolated-elements -open import foundation.logical-equivalences -open import foundation.negated-equality -open import foundation.negation -open import foundation.powersets -open import foundation.propositional-truncations -open import foundation.sets -open import foundation.surjective-maps +open import foundation.discrete-types funext univalence truncations +open import foundation.identity-types funext +open import foundation.negated-equality funext univalence truncations +open import foundation.negation funext +open import foundation.propositional-truncations funext univalence +open import foundation.sets funext univalence +open import foundation.surjective-maps funext univalence truncations open import foundation.universe-levels open import foundation-core.empty-types open import foundation-core.fibers-of-maps open import foundation-core.propositions -open import set-theory.countable-sets -open import set-theory.infinite-sets -open import set-theory.uncountable-sets +open import set-theory.countable-sets funext univalence truncations +open import set-theory.uncountable-sets funext univalence truncations ```
diff --git a/src/set-theory/cardinalities.lagda.md b/src/set-theory/cardinalities.lagda.md index 0ab8653a6f..30e293de34 100644 --- a/src/set-theory/cardinalities.lagda.md +++ b/src/set-theory/cardinalities.lagda.md @@ -1,26 +1,33 @@ # Cardinalities of sets ```agda -module set-theory.cardinalities where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module set-theory.cardinalities + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.binary-relations open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.functoriality-propositional-truncation -open import foundation.identity-types -open import foundation.large-binary-relations -open import foundation.law-of-excluded-middle -open import foundation.mere-embeddings -open import foundation.mere-equivalences -open import foundation.propositional-extensionality -open import foundation.propositions -open import foundation.set-truncations -open import foundation.sets +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.functoriality-propositional-truncation funext univalence truncations +open import foundation.identity-types funext +open import foundation.large-binary-relations funext univalence truncations +open import foundation.law-of-excluded-middle funext univalence truncations +open import foundation.mere-embeddings funext univalence truncations +open import foundation.mere-equivalences funext univalence truncations +open import foundation.propositional-extensionality funext univalence truncations +open import foundation.propositions funext univalence +open import foundation.set-truncations funext univalence +open import foundation.sets funext univalence open import foundation.universe-levels ``` diff --git a/src/set-theory/countable-sets.lagda.md b/src/set-theory/countable-sets.lagda.md index 023911e269..4308914a69 100644 --- a/src/set-theory/countable-sets.lagda.md +++ b/src/set-theory/countable-sets.lagda.md @@ -1,48 +1,58 @@ # Countable sets ```agda -module set-theory.countable-sets where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module set-theory.countable-sets + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.equality-natural-numbers +open import elementary-number-theory.equality-integers funext univalence truncations +open import elementary-number-theory.equality-natural-numbers funext univalence truncations open import elementary-number-theory.integers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.type-arithmetic-natural-numbers +open import elementary-number-theory.type-arithmetic-natural-numbers funext univalence truncations open import foundation.action-on-identifications-functions -open import foundation.coproduct-types -open import foundation.decidable-propositions -open import foundation.decidable-subtypes -open import foundation.decidable-types +open import foundation.coproduct-types funext univalence truncations +open import foundation.decidable-propositions funext univalence truncations +open import foundation.decidable-subtypes funext univalence truncations +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.equality-coproduct-types -open import foundation.equivalences -open import foundation.existential-quantification -open import foundation.function-types -open import foundation.functoriality-cartesian-product-types -open import foundation.functoriality-coproduct-types -open import foundation.maybe -open import foundation.negated-equality -open import foundation.negation -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.raising-universe-levels -open import foundation.retracts-of-types -open import foundation.sets +open import foundation.dependent-products-propositions funext +open import foundation.empty-types funext univalence truncations +open import foundation.equality-coproduct-types funext univalence truncations +open import foundation.equivalences funext +open import foundation.existential-quantification funext univalence truncations +open import foundation.function-types funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.functoriality-coproduct-types funext univalence truncations +open import foundation.maybe funext univalence truncations +open import foundation.negated-equality funext univalence truncations +open import foundation.negation funext +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence +open import foundation.retracts-of-types funext univalence +open import foundation.sets funext univalence open import foundation.shifting-sequences -open import foundation.surjective-maps +open import foundation.surjective-maps funext univalence truncations open import foundation.unit-type open import foundation.universe-levels open import foundation-core.cartesian-product-types open import foundation-core.fibers-of-maps open import foundation-core.identity-types +open import foundation-core.raising-universe-levels -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/set-theory/cumulative-hierarchy.lagda.md b/src/set-theory/cumulative-hierarchy.lagda.md index 4d4ae93868..38ae14e69b 100644 --- a/src/set-theory/cumulative-hierarchy.lagda.md +++ b/src/set-theory/cumulative-hierarchy.lagda.md @@ -1,7 +1,15 @@ # Cumulative hierarchy ```agda -module set-theory.cumulative-hierarchy where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module set-theory.cumulative-hierarchy + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,27 +18,32 @@ module set-theory.cumulative-hierarchy where open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.booleans -open import foundation.cartesian-product-types -open import foundation.constant-type-families -open import foundation.coproduct-types +open import foundation.booleans funext univalence truncations +open import foundation.cartesian-product-types funext univalence +open import foundation.constant-type-families funext +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.existential-quantification -open import foundation.function-types -open import foundation.functoriality-propositional-truncation -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.negation -open import foundation.propositional-extensionality -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.raising-universe-levels -open import foundation.sets +open import foundation.dependent-products-propositions funext +open import foundation.dependent-products-truncated-types funext +open import foundation.empty-types funext univalence truncations +open import foundation.existential-quantification funext univalence truncations +open import foundation.function-types funext +open import foundation.functoriality-propositional-truncation funext univalence truncations +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.negation funext +open import foundation.propositional-extensionality funext univalence truncations +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence +open import foundation.raising-universe-levels-booleans +open import foundation.raising-universe-levels-unit-type +open import foundation.sets funext univalence open import foundation.transport-along-identifications -open import foundation.truncated-types +open import foundation.truncated-types funext univalence open import foundation.unit-type open import foundation.universe-levels + +open import foundation-core.raising-universe-levels ```
diff --git a/src/set-theory/infinite-sets.lagda.md b/src/set-theory/infinite-sets.lagda.md index d94e6be82f..15af8020c4 100644 --- a/src/set-theory/infinite-sets.lagda.md +++ b/src/set-theory/infinite-sets.lagda.md @@ -1,7 +1,15 @@ # Infinite sets ```agda -module set-theory.infinite-sets where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module set-theory.infinite-sets + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,12 +18,13 @@ module set-theory.infinite-sets where open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.mere-embeddings -open import foundation.propositions -open import foundation.sets +open import foundation.dependent-products-propositions funext +open import foundation.mere-embeddings funext univalence truncations +open import foundation.propositions funext univalence +open import foundation.sets funext univalence open import foundation.universe-levels -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/set-theory/russells-paradox.lagda.md b/src/set-theory/russells-paradox.lagda.md index 9ca07432a8..84b4f4bec9 100644 --- a/src/set-theory/russells-paradox.lagda.md +++ b/src/set-theory/russells-paradox.lagda.md @@ -2,25 +2,32 @@ ```agda {-# OPTIONS --lossy-unification #-} - -module set-theory.russells-paradox where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module set-theory.russells-paradox + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.functoriality-cartesian-product-types -open import foundation.identity-types -open import foundation.locally-small-types -open import foundation.negation -open import foundation.small-types -open import foundation.small-universes -open import foundation.surjective-maps -open import foundation.torsorial-type-families +open import foundation.functoriality-cartesian-product-types funext +open import foundation.identity-types funext +open import foundation.locally-small-types funext univalence truncations +open import foundation.negation funext +open import foundation.small-types funext univalence truncations +open import foundation.small-universes funext univalence truncations +open import foundation.surjective-maps funext univalence truncations +open import foundation.torsorial-type-families funext univalence truncations open import foundation.type-arithmetic-cartesian-product-types open import foundation.type-arithmetic-dependent-pair-types -open import foundation.universal-property-equivalences +open import foundation.universal-property-equivalences funext open import foundation.universe-levels open import foundation-core.contractible-types @@ -28,9 +35,9 @@ open import foundation-core.empty-types open import foundation-core.equivalences open import foundation-core.functoriality-dependent-pair-types -open import trees.multisets -open import trees.small-multisets -open import trees.universal-multiset +open import trees.multisets funext univalence truncations +open import trees.small-multisets funext univalence truncations +open import trees.universal-multiset funext univalence truncations ```
diff --git a/src/set-theory/uncountable-sets.lagda.md b/src/set-theory/uncountable-sets.lagda.md index f1cb306d08..5175747b86 100644 --- a/src/set-theory/uncountable-sets.lagda.md +++ b/src/set-theory/uncountable-sets.lagda.md @@ -1,18 +1,27 @@ # Uncountable sets ```agda -module set-theory.uncountable-sets where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module set-theory.uncountable-sets + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.negation -open import foundation.propositions -open import foundation.sets +open import foundation.dependent-products-propositions funext +open import foundation.negation funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence open import foundation.universe-levels -open import set-theory.countable-sets +open import set-theory.countable-sets funext univalence truncations ```
diff --git a/src/species.lagda.md b/src/species.lagda.md index c36d98ea52..f731c579c3 100644 --- a/src/species.lagda.md +++ b/src/species.lagda.md @@ -3,53 +3,61 @@ ## Modules in the species namespace ```agda -module species where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom -open import species.cartesian-exponents-species-of-types public -open import species.cartesian-products-species-of-types public -open import species.cauchy-composition-species-of-types public -open import species.cauchy-composition-species-of-types-in-subuniverses public -open import species.cauchy-exponentials-species-of-types public -open import species.cauchy-exponentials-species-of-types-in-subuniverses public -open import species.cauchy-products-species-of-types public -open import species.cauchy-products-species-of-types-in-subuniverses public -open import species.cauchy-series-species-of-types public -open import species.cauchy-series-species-of-types-in-subuniverses public -open import species.composition-cauchy-series-species-of-types public -open import species.composition-cauchy-series-species-of-types-in-subuniverses public -open import species.coproducts-species-of-types public -open import species.coproducts-species-of-types-in-subuniverses public -open import species.cycle-index-series-species-of-types public -open import species.derivatives-species-of-types public -open import species.dirichlet-exponentials-species-of-types public -open import species.dirichlet-exponentials-species-of-types-in-subuniverses public -open import species.dirichlet-products-species-of-types public -open import species.dirichlet-products-species-of-types-in-subuniverses public -open import species.dirichlet-series-species-of-finite-inhabited-types public -open import species.dirichlet-series-species-of-types public -open import species.dirichlet-series-species-of-types-in-subuniverses public -open import species.equivalences-species-of-types public -open import species.equivalences-species-of-types-in-subuniverses public -open import species.exponentials-cauchy-series-of-types public -open import species.exponentials-cauchy-series-of-types-in-subuniverses public -open import species.hasse-weil-species public -open import species.morphisms-finite-species public -open import species.morphisms-species-of-types public -open import species.pointing-species-of-types public -open import species.precategory-of-finite-species public -open import species.products-cauchy-series-species-of-types public -open import species.products-cauchy-series-species-of-types-in-subuniverses public -open import species.products-dirichlet-series-species-of-finite-inhabited-types public -open import species.products-dirichlet-series-species-of-types public -open import species.products-dirichlet-series-species-of-types-in-subuniverses public -open import species.small-cauchy-composition-species-of-finite-inhabited-types public -open import species.small-cauchy-composition-species-of-types-in-subuniverses public -open import species.species-of-finite-inhabited-types public -open import species.species-of-finite-types public -open import species.species-of-inhabited-types public -open import species.species-of-types public -open import species.species-of-types-in-subuniverses public -open import species.unit-cauchy-composition-species-of-types public -open import species.unit-cauchy-composition-species-of-types-in-subuniverses public -open import species.unlabeled-structures-species public +module species + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where + +open import species.cartesian-exponents-species-of-types funext univalence public +open import species.cartesian-products-species-of-types funext univalence truncations public +open import species.cauchy-composition-species-of-types funext univalence public +open import species.cauchy-composition-species-of-types-in-subuniverses funext univalence public +open import species.cauchy-exponentials-species-of-types funext univalence truncations public +open import species.cauchy-exponentials-species-of-types-in-subuniverses funext univalence truncations public +open import species.cauchy-products-species-of-types funext univalence truncations public +open import species.cauchy-products-species-of-types-in-subuniverses funext univalence truncations public +open import species.cauchy-series-species-of-types funext univalence public +open import species.cauchy-series-species-of-types-in-subuniverses funext univalence public +open import species.composition-cauchy-series-species-of-types funext univalence public +open import species.composition-cauchy-series-species-of-types-in-subuniverses funext univalence public +open import species.coproducts-species-of-types funext univalence truncations public +open import species.coproducts-species-of-types-in-subuniverses funext univalence truncations public +open import species.cycle-index-series-species-of-types funext univalence truncations public +open import species.derivatives-species-of-types funext univalence truncations public +open import species.dirichlet-exponentials-species-of-types funext univalence truncations public +open import species.dirichlet-exponentials-species-of-types-in-subuniverses funext univalence truncations public +open import species.dirichlet-products-species-of-types funext univalence public +open import species.dirichlet-products-species-of-types-in-subuniverses funext univalence public +open import species.dirichlet-series-species-of-finite-inhabited-types funext univalence truncations public +open import species.dirichlet-series-species-of-types funext univalence public +open import species.dirichlet-series-species-of-types-in-subuniverses funext univalence public +open import species.equivalences-species-of-types funext univalence public +open import species.equivalences-species-of-types-in-subuniverses funext univalence public +open import species.exponentials-cauchy-series-of-types funext univalence truncations public +open import species.exponentials-cauchy-series-of-types-in-subuniverses funext univalence truncations public +open import species.hasse-weil-species funext univalence truncations public +open import species.morphisms-finite-species funext univalence truncations public +open import species.morphisms-species-of-types funext univalence truncations public +open import species.pointing-species-of-types funext univalence public +open import species.precategory-of-finite-species funext univalence truncations public +open import species.products-cauchy-series-species-of-types funext univalence truncations public +open import species.products-cauchy-series-species-of-types-in-subuniverses funext univalence truncations public +open import species.products-dirichlet-series-species-of-finite-inhabited-types funext univalence truncations public +open import species.products-dirichlet-series-species-of-types funext univalence public +open import species.products-dirichlet-series-species-of-types-in-subuniverses funext univalence truncations public +open import species.small-cauchy-composition-species-of-finite-inhabited-types funext univalence truncations public +open import species.small-cauchy-composition-species-of-types-in-subuniverses funext univalence truncations public +open import species.species-of-finite-inhabited-types funext univalence truncations public +open import species.species-of-finite-types funext univalence truncations public +open import species.species-of-inhabited-types funext univalence truncations public +open import species.species-of-types funext univalence public +open import species.species-of-types-in-subuniverses funext univalence public +open import species.unit-cauchy-composition-species-of-types funext univalence public +open import species.unit-cauchy-composition-species-of-types-in-subuniverses funext univalence public +open import species.unlabeled-structures-species funext univalence truncations public ``` diff --git a/src/species/cartesian-exponents-species-of-types.lagda.md b/src/species/cartesian-exponents-species-of-types.lagda.md index 8f07241384..4d1270548f 100644 --- a/src/species/cartesian-exponents-species-of-types.lagda.md +++ b/src/species/cartesian-exponents-species-of-types.lagda.md @@ -1,7 +1,13 @@ # Cartesian exponents of species ```agda -module species.cartesian-exponents-species-of-types where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module species.cartesian-exponents-species-of-types + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports @@ -9,7 +15,7 @@ module species.cartesian-exponents-species-of-types where ```agda open import foundation.universe-levels -open import species.species-of-types +open import species.species-of-types funext univalence ```
diff --git a/src/species/cartesian-products-species-of-types.lagda.md b/src/species/cartesian-products-species-of-types.lagda.md index 60e524d6b4..3cb566c6cd 100644 --- a/src/species/cartesian-products-species-of-types.lagda.md +++ b/src/species/cartesian-products-species-of-types.lagda.md @@ -1,21 +1,29 @@ # Cartesian products of species of types ```agda -module species.cartesian-products-species-of-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module species.cartesian-products-species-of-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.cartesian-product-types -open import foundation.equivalences -open import foundation.functoriality-dependent-function-types -open import foundation.universal-property-dependent-pair-types +open import foundation.cartesian-product-types funext univalence +open import foundation.equivalences funext +open import foundation.functoriality-dependent-function-types funext univalence +open import foundation.universal-property-dependent-pair-types funext open import foundation.universe-levels -open import species.cartesian-exponents-species-of-types -open import species.morphisms-species-of-types -open import species.species-of-types +open import species.cartesian-exponents-species-of-types funext univalence +open import species.morphisms-species-of-types funext univalence truncations +open import species.species-of-types funext univalence ```
diff --git a/src/species/cauchy-composition-species-of-types-in-subuniverses.lagda.md b/src/species/cauchy-composition-species-of-types-in-subuniverses.lagda.md index 65183258e0..ee501e8483 100644 --- a/src/species/cauchy-composition-species-of-types-in-subuniverses.lagda.md +++ b/src/species/cauchy-composition-species-of-types-in-subuniverses.lagda.md @@ -1,40 +1,49 @@ # Cauchy composition of species of types in a subuniverse ```agda -module species.cauchy-composition-species-of-types-in-subuniverses where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module species.cauchy-composition-species-of-types-in-subuniverses + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda -open import foundation.cartesian-product-types -open import foundation.contractible-types +open import foundation.cartesian-product-types funext univalence +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext open import foundation.equality-cartesian-product-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-cartesian-product-types -open import foundation.functoriality-dependent-function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.global-subuniverses -open import foundation.homotopies -open import foundation.propositions -open import foundation.relaxed-sigma-decompositions -open import foundation.sigma-closed-subuniverses -open import foundation.sigma-decomposition-subuniverse -open import foundation.subuniverses +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.functoriality-dependent-function-types funext univalence +open import foundation.functoriality-dependent-pair-types funext +open import foundation.global-subuniverses funext univalence +open import foundation.homotopies funext +open import foundation.propositions funext univalence +open import foundation.raising-universe-levels-unit-type +open import foundation.relaxed-sigma-decompositions funext univalence +open import foundation.sigma-closed-subuniverses funext univalence +open import foundation.sigma-decomposition-subuniverse funext univalence +open import foundation.subuniverses funext univalence open import foundation.transport-along-identifications open import foundation.type-arithmetic-cartesian-product-types open import foundation.type-arithmetic-dependent-pair-types -open import foundation.type-theoretic-principle-of-choice +open import foundation.type-theoretic-principle-of-choice funext open import foundation.unit-type -open import foundation.univalence +open import foundation.univalence funext univalence open import foundation.universe-levels -open import species.cauchy-composition-species-of-types -open import species.species-of-types-in-subuniverses -open import species.unit-cauchy-composition-species-of-types -open import species.unit-cauchy-composition-species-of-types-in-subuniverses +open import species.cauchy-composition-species-of-types funext univalence +open import species.species-of-types-in-subuniverses funext univalence +open import species.unit-cauchy-composition-species-of-types funext univalence +open import species.unit-cauchy-composition-species-of-types-in-subuniverses funext univalence ```
diff --git a/src/species/cauchy-composition-species-of-types.lagda.md b/src/species/cauchy-composition-species-of-types.lagda.md index 05943435c9..ee62bdf9a8 100644 --- a/src/species/cauchy-composition-species-of-types.lagda.md +++ b/src/species/cauchy-composition-species-of-types.lagda.md @@ -1,35 +1,42 @@ # Cauchy composition of species of types ```agda -module species.cauchy-composition-species-of-types where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module species.cauchy-composition-species-of-types + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda -open import foundation.cartesian-product-types -open import foundation.contractible-types +open import foundation.cartesian-product-types funext univalence +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.dependent-universal-property-equivalences -open import foundation.discrete-relaxed-sigma-decompositions -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.functoriality-cartesian-product-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.relaxed-sigma-decompositions -open import foundation.trivial-relaxed-sigma-decompositions +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-universal-property-equivalences funext +open import foundation.discrete-relaxed-sigma-decompositions funext univalence +open import foundation.equivalences funext +open import foundation.function-extensionality funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.relaxed-sigma-decompositions funext univalence +open import foundation.trivial-relaxed-sigma-decompositions funext univalence open import foundation.type-arithmetic-cartesian-product-types -open import foundation.type-arithmetic-dependent-function-types +open import foundation.type-arithmetic-dependent-function-types funext univalence open import foundation.type-arithmetic-dependent-pair-types -open import foundation.type-theoretic-principle-of-choice -open import foundation.univalence -open import foundation.universal-property-dependent-pair-types +open import foundation.type-theoretic-principle-of-choice funext +open import foundation.univalence funext univalence +open import foundation.universal-property-dependent-pair-types funext open import foundation.universe-levels -open import species.species-of-types -open import species.unit-cauchy-composition-species-of-types +open import species.species-of-types funext univalence +open import species.unit-cauchy-composition-species-of-types funext univalence ```
diff --git a/src/species/cauchy-exponentials-species-of-types-in-subuniverses.lagda.md b/src/species/cauchy-exponentials-species-of-types-in-subuniverses.lagda.md index a5d3b8b486..a45d8d20d9 100644 --- a/src/species/cauchy-exponentials-species-of-types-in-subuniverses.lagda.md +++ b/src/species/cauchy-exponentials-species-of-types-in-subuniverses.lagda.md @@ -1,40 +1,49 @@ # Cauchy exponentials of species of types in a subuniverse ```agda -module species.cauchy-exponentials-species-of-types-in-subuniverses where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module species.cauchy-exponentials-species-of-types-in-subuniverses + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.cartesian-product-types -open import foundation.coproduct-decompositions -open import foundation.coproduct-types +open import foundation.cartesian-product-types funext univalence +open import foundation.coproduct-decompositions funext univalence truncations +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-cartesian-product-types -open import foundation.functoriality-dependent-function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.global-subuniverses -open import foundation.homotopies -open import foundation.propositions -open import foundation.relaxed-sigma-decompositions -open import foundation.sigma-closed-subuniverses -open import foundation.sigma-decomposition-subuniverse -open import foundation.subuniverses +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.functoriality-dependent-function-types funext univalence +open import foundation.functoriality-dependent-pair-types funext +open import foundation.global-subuniverses funext univalence +open import foundation.homotopies funext +open import foundation.propositions funext univalence +open import foundation.relaxed-sigma-decompositions funext univalence +open import foundation.sigma-closed-subuniverses funext univalence +open import foundation.sigma-decomposition-subuniverse funext univalence +open import foundation.subuniverses funext univalence open import foundation.transport-along-identifications open import foundation.type-arithmetic-cartesian-product-types open import foundation.unit-type -open import foundation.univalence +open import foundation.univalence funext univalence open import foundation.universe-levels -open import species.cauchy-composition-species-of-types-in-subuniverses -open import species.cauchy-exponentials-species-of-types -open import species.cauchy-products-species-of-types-in-subuniverses -open import species.coproducts-species-of-types -open import species.coproducts-species-of-types-in-subuniverses -open import species.species-of-types-in-subuniverses +open import species.cauchy-composition-species-of-types-in-subuniverses funext univalence +open import species.cauchy-exponentials-species-of-types funext univalence truncations +open import species.cauchy-products-species-of-types-in-subuniverses funext univalence truncations +open import species.coproducts-species-of-types funext univalence truncations +open import species.coproducts-species-of-types-in-subuniverses funext univalence truncations +open import species.species-of-types-in-subuniverses funext univalence ```
diff --git a/src/species/cauchy-exponentials-species-of-types.lagda.md b/src/species/cauchy-exponentials-species-of-types.lagda.md index 0a4e3d7d9c..019fac5a4b 100644 --- a/src/species/cauchy-exponentials-species-of-types.lagda.md +++ b/src/species/cauchy-exponentials-species-of-types.lagda.md @@ -1,36 +1,44 @@ # Cauchy exponentials of species of types ```agda -module species.cauchy-exponentials-species-of-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module species.cauchy-exponentials-species-of-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.arithmetic-law-coproduct-and-sigma-decompositions -open import foundation.cartesian-product-types -open import foundation.coproduct-decompositions -open import foundation.dependent-binomial-theorem +open import foundation.arithmetic-law-coproduct-and-sigma-decompositions funext univalence truncations +open import foundation.cartesian-product-types funext univalence +open import foundation.coproduct-decompositions funext univalence truncations +open import foundation.dependent-binomial-theorem funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.functoriality-cartesian-product-types -open import foundation.functoriality-dependent-function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.relaxed-sigma-decompositions +open import foundation.equivalences funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.functoriality-dependent-function-types funext univalence +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.relaxed-sigma-decompositions funext univalence open import foundation.type-arithmetic-cartesian-product-types open import foundation.type-arithmetic-dependent-pair-types open import foundation.unit-type -open import foundation.univalence +open import foundation.univalence funext univalence open import foundation.universe-levels -open import species.cauchy-composition-species-of-types -open import species.cauchy-products-species-of-types -open import species.coproducts-species-of-types -open import species.equivalences-species-of-types -open import species.species-of-types +open import species.cauchy-composition-species-of-types funext univalence +open import species.cauchy-products-species-of-types funext univalence truncations +open import species.coproducts-species-of-types funext univalence truncations +open import species.equivalences-species-of-types funext univalence +open import species.species-of-types funext univalence ```
diff --git a/src/species/cauchy-products-species-of-types-in-subuniverses.lagda.md b/src/species/cauchy-products-species-of-types-in-subuniverses.lagda.md index dc5f62299c..bb0e1cc874 100644 --- a/src/species/cauchy-products-species-of-types-in-subuniverses.lagda.md +++ b/src/species/cauchy-products-species-of-types-in-subuniverses.lagda.md @@ -1,34 +1,43 @@ # Cauchy products of species of types in a subuniverse ```agda -module species.cauchy-products-species-of-types-in-subuniverses where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module species.cauchy-products-species-of-types-in-subuniverses + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.cartesian-product-types -open import foundation.coproduct-decompositions -open import foundation.coproduct-decompositions-subuniverse -open import foundation.coproduct-types +open import foundation.cartesian-product-types funext univalence +open import foundation.coproduct-decompositions funext univalence truncations +open import foundation.coproduct-decompositions-subuniverse funext univalence truncations +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.equivalences -open import foundation.functoriality-dependent-pair-types -open import foundation.global-subuniverses -open import foundation.homotopies -open import foundation.identity-types -open import foundation.propositions -open import foundation.subuniverses +open import foundation.dependent-products-propositions funext +open import foundation.empty-types funext univalence truncations +open import foundation.equivalences funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.global-subuniverses funext univalence +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.subuniverses funext univalence open import foundation.transport-along-identifications open import foundation.type-arithmetic-cartesian-product-types -open import foundation.type-arithmetic-coproduct-types +open import foundation.type-arithmetic-coproduct-types funext univalence truncations open import foundation.type-arithmetic-dependent-pair-types -open import foundation.univalence +open import foundation.univalence funext univalence open import foundation.universe-levels -open import species.cauchy-products-species-of-types -open import species.species-of-types-in-subuniverses +open import species.cauchy-products-species-of-types funext univalence truncations +open import species.species-of-types-in-subuniverses funext univalence ```
diff --git a/src/species/cauchy-products-species-of-types.lagda.md b/src/species/cauchy-products-species-of-types.lagda.md index 1d4560f78f..20cfe9f223 100644 --- a/src/species/cauchy-products-species-of-types.lagda.md +++ b/src/species/cauchy-products-species-of-types.lagda.md @@ -1,18 +1,26 @@ # Cauchy products of species of types ```agda -module species.cauchy-products-species-of-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module species.cauchy-products-species-of-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.cartesian-product-types -open import foundation.coproduct-decompositions +open import foundation.cartesian-product-types funext univalence +open import foundation.coproduct-decompositions funext univalence truncations open import foundation.dependent-pair-types open import foundation.universe-levels -open import species.species-of-types +open import species.species-of-types funext univalence ```
diff --git a/src/species/cauchy-series-species-of-types-in-subuniverses.lagda.md b/src/species/cauchy-series-species-of-types-in-subuniverses.lagda.md index 4e9a36c29a..bba68ac591 100644 --- a/src/species/cauchy-series-species-of-types-in-subuniverses.lagda.md +++ b/src/species/cauchy-series-species-of-types-in-subuniverses.lagda.md @@ -1,26 +1,33 @@ # Cauchy series of species of types in a subuniverse ```agda -module species.cauchy-series-species-of-types-in-subuniverses where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module species.cauchy-series-species-of-types-in-subuniverses + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.functoriality-cartesian-product-types -open import foundation.functoriality-dependent-pair-types -open import foundation.global-subuniverses -open import foundation.postcomposition-functions -open import foundation.propositions -open import foundation.subuniverses +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.global-subuniverses funext univalence +open import foundation.postcomposition-functions funext +open import foundation.propositions funext univalence +open import foundation.subuniverses funext univalence open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels -open import species.cauchy-series-species-of-types -open import species.species-of-types-in-subuniverses +open import species.cauchy-series-species-of-types funext univalence +open import species.species-of-types-in-subuniverses funext univalence ```
diff --git a/src/species/cauchy-series-species-of-types.lagda.md b/src/species/cauchy-series-species-of-types.lagda.md index a7a7a35a51..df2e7138a2 100644 --- a/src/species/cauchy-series-species-of-types.lagda.md +++ b/src/species/cauchy-series-species-of-types.lagda.md @@ -1,21 +1,27 @@ # Cauchy series of species of types ```agda -module species.cauchy-series-species-of-types where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module species.cauchy-series-species-of-types + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.functoriality-cartesian-product-types -open import foundation.functoriality-dependent-pair-types -open import foundation.postcomposition-functions +open import foundation.equivalences funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.postcomposition-functions funext open import foundation.universe-levels -open import species.species-of-types +open import species.species-of-types funext univalence ```
diff --git a/src/species/composition-cauchy-series-species-of-types-in-subuniverses.lagda.md b/src/species/composition-cauchy-series-species-of-types-in-subuniverses.lagda.md index e0eb8cc904..8d930af0d0 100644 --- a/src/species/composition-cauchy-series-species-of-types-in-subuniverses.lagda.md +++ b/src/species/composition-cauchy-series-species-of-types-in-subuniverses.lagda.md @@ -1,24 +1,30 @@ # Composition of Cauchy series of species of types in subuniverses ```agda -module species.composition-cauchy-series-species-of-types-in-subuniverses where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module species.composition-cauchy-series-species-of-types-in-subuniverses + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda -open import foundation.equivalences -open import foundation.global-subuniverses -open import foundation.sigma-closed-subuniverses -open import foundation.subuniverses +open import foundation.equivalences funext +open import foundation.global-subuniverses funext univalence +open import foundation.sigma-closed-subuniverses funext univalence +open import foundation.subuniverses funext univalence open import foundation.universe-levels -open import species.cauchy-composition-species-of-types -open import species.cauchy-composition-species-of-types-in-subuniverses -open import species.cauchy-series-species-of-types -open import species.cauchy-series-species-of-types-in-subuniverses -open import species.composition-cauchy-series-species-of-types -open import species.species-of-types-in-subuniverses +open import species.cauchy-composition-species-of-types funext univalence +open import species.cauchy-composition-species-of-types-in-subuniverses funext univalence +open import species.cauchy-series-species-of-types funext univalence +open import species.cauchy-series-species-of-types-in-subuniverses funext univalence +open import species.composition-cauchy-series-species-of-types funext univalence +open import species.species-of-types-in-subuniverses funext univalence ```
diff --git a/src/species/composition-cauchy-series-species-of-types.lagda.md b/src/species/composition-cauchy-series-species-of-types.lagda.md index 729af0a56f..efbcca1ccb 100644 --- a/src/species/composition-cauchy-series-species-of-types.lagda.md +++ b/src/species/composition-cauchy-series-species-of-types.lagda.md @@ -1,28 +1,34 @@ # Composition of Cauchy series of species of types ```agda -module species.composition-cauchy-series-species-of-types where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module species.composition-cauchy-series-species-of-types + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.functoriality-cartesian-product-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies +open import foundation.equivalences funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext open import foundation.type-arithmetic-dependent-pair-types -open import foundation.type-theoretic-principle-of-choice -open import foundation.univalence -open import foundation.universal-property-cartesian-product-types -open import foundation.universal-property-dependent-pair-types +open import foundation.type-theoretic-principle-of-choice funext +open import foundation.univalence funext univalence +open import foundation.universal-property-cartesian-product-types funext +open import foundation.universal-property-dependent-pair-types funext open import foundation.universe-levels -open import species.cauchy-composition-species-of-types -open import species.cauchy-series-species-of-types -open import species.species-of-types +open import species.cauchy-composition-species-of-types funext univalence +open import species.cauchy-series-species-of-types funext univalence +open import species.species-of-types funext univalence ```
diff --git a/src/species/coproducts-species-of-types-in-subuniverses.lagda.md b/src/species/coproducts-species-of-types-in-subuniverses.lagda.md index 2900441e71..8f1ef3d05f 100644 --- a/src/species/coproducts-species-of-types-in-subuniverses.lagda.md +++ b/src/species/coproducts-species-of-types-in-subuniverses.lagda.md @@ -1,24 +1,32 @@ # Coproducts of species of types in subuniverses ```agda -module species.coproducts-species-of-types-in-subuniverses where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module species.coproducts-species-of-types-in-subuniverses + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.coproduct-types +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.global-subuniverses -open import foundation.homotopies -open import foundation.identity-types -open import foundation.subuniverses +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.global-subuniverses funext univalence +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.subuniverses funext univalence open import foundation.universe-levels -open import species.coproducts-species-of-types -open import species.species-of-types-in-subuniverses +open import species.coproducts-species-of-types funext univalence truncations +open import species.species-of-types-in-subuniverses funext univalence ```
diff --git a/src/species/coproducts-species-of-types.lagda.md b/src/species/coproducts-species-of-types.lagda.md index b38a5e44ee..6000559f57 100644 --- a/src/species/coproducts-species-of-types.lagda.md +++ b/src/species/coproducts-species-of-types.lagda.md @@ -1,22 +1,30 @@ # Coproducts of species of types ```agda -module species.coproducts-species-of-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module species.coproducts-species-of-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.cartesian-product-types -open import foundation.coproduct-types -open import foundation.equivalences -open import foundation.functoriality-dependent-function-types -open import foundation.type-theoretic-principle-of-choice -open import foundation.universal-property-coproduct-types +open import foundation.cartesian-product-types funext univalence +open import foundation.coproduct-types funext univalence truncations +open import foundation.equivalences funext +open import foundation.functoriality-dependent-function-types funext univalence +open import foundation.type-theoretic-principle-of-choice funext +open import foundation.universal-property-coproduct-types funext open import foundation.universe-levels -open import species.morphisms-species-of-types -open import species.species-of-types +open import species.morphisms-species-of-types funext univalence truncations +open import species.species-of-types funext univalence ```
diff --git a/src/species/cycle-index-series-species-of-types.lagda.md b/src/species/cycle-index-series-species-of-types.lagda.md index 36fe229ae9..e760c4f9d5 100644 --- a/src/species/cycle-index-series-species-of-types.lagda.md +++ b/src/species/cycle-index-series-species-of-types.lagda.md @@ -1,7 +1,15 @@ # Cycle index series of species ```agda -module species.cycle-index-series-species-of-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module species.cycle-index-series-species-of-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -12,7 +20,7 @@ open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types open import foundation.universe-levels -open import univalent-combinatorics.cyclic-finite-types +open import univalent-combinatorics.cyclic-finite-types funext univalence truncations ```
diff --git a/src/species/derivatives-species-of-types.lagda.md b/src/species/derivatives-species-of-types.lagda.md index 089dca1f20..4f4383d7a2 100644 --- a/src/species/derivatives-species-of-types.lagda.md +++ b/src/species/derivatives-species-of-types.lagda.md @@ -1,17 +1,25 @@ # Derivatives of species ```agda -module species.derivatives-species-of-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module species.derivatives-species-of-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.coproduct-types +open import foundation.coproduct-types funext univalence truncations open import foundation.unit-type open import foundation.universe-levels -open import species.species-of-types +open import species.species-of-types funext univalence ```
diff --git a/src/species/dirichlet-exponentials-species-of-types-in-subuniverses.lagda.md b/src/species/dirichlet-exponentials-species-of-types-in-subuniverses.lagda.md index caf7c99d4d..0b9d3e7678 100644 --- a/src/species/dirichlet-exponentials-species-of-types-in-subuniverses.lagda.md +++ b/src/species/dirichlet-exponentials-species-of-types-in-subuniverses.lagda.md @@ -1,36 +1,45 @@ # Dirichlet exponentials of species of types in a subuniverse ```agda -module species.dirichlet-exponentials-species-of-types-in-subuniverses where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module species.dirichlet-exponentials-species-of-types-in-subuniverses + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-cartesian-product-types -open import foundation.functoriality-dependent-function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.global-subuniverses -open import foundation.homotopies -open import foundation.pi-decompositions -open import foundation.pi-decompositions-subuniverse +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.functoriality-dependent-function-types funext univalence +open import foundation.functoriality-dependent-pair-types funext +open import foundation.global-subuniverses funext univalence +open import foundation.homotopies funext +open import foundation.pi-decompositions funext univalence +open import foundation.pi-decompositions-subuniverse funext univalence open import foundation.product-decompositions -open import foundation.propositions -open import foundation.subuniverses +open import foundation.propositions funext univalence +open import foundation.subuniverses funext univalence open import foundation.transport-along-identifications open import foundation.type-arithmetic-cartesian-product-types -open import foundation.univalence +open import foundation.univalence funext univalence open import foundation.universe-levels -open import species.coproducts-species-of-types -open import species.coproducts-species-of-types-in-subuniverses -open import species.dirichlet-exponentials-species-of-types -open import species.dirichlet-products-species-of-types-in-subuniverses -open import species.species-of-types-in-subuniverses +open import species.coproducts-species-of-types funext univalence truncations +open import species.coproducts-species-of-types-in-subuniverses funext univalence truncations +open import species.dirichlet-exponentials-species-of-types funext univalence truncations +open import species.dirichlet-products-species-of-types-in-subuniverses funext univalence +open import species.species-of-types-in-subuniverses funext univalence ```
diff --git a/src/species/dirichlet-exponentials-species-of-types.lagda.md b/src/species/dirichlet-exponentials-species-of-types.lagda.md index 4a1ac22104..531b8756e3 100644 --- a/src/species/dirichlet-exponentials-species-of-types.lagda.md +++ b/src/species/dirichlet-exponentials-species-of-types.lagda.md @@ -1,34 +1,42 @@ # Dirichlet exponentials of a species of types ```agda -module species.dirichlet-exponentials-species-of-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module species.dirichlet-exponentials-species-of-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.arithmetic-law-product-and-pi-decompositions -open import foundation.cartesian-product-types -open import foundation.coproduct-decompositions -open import foundation.dependent-binomial-theorem +open import foundation.arithmetic-law-product-and-pi-decompositions funext univalence truncations +open import foundation.cartesian-product-types funext univalence +open import foundation.coproduct-decompositions funext univalence truncations +open import foundation.dependent-binomial-theorem funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.functoriality-cartesian-product-types -open import foundation.functoriality-dependent-function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.pi-decompositions +open import foundation.equivalences funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.functoriality-dependent-function-types funext univalence +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.pi-decompositions funext univalence open import foundation.product-decompositions open import foundation.type-arithmetic-dependent-pair-types -open import foundation.univalence +open import foundation.univalence funext univalence open import foundation.universe-levels -open import species.coproducts-species-of-types -open import species.dirichlet-products-species-of-types -open import species.equivalences-species-of-types -open import species.species-of-types +open import species.coproducts-species-of-types funext univalence truncations +open import species.dirichlet-products-species-of-types funext univalence +open import species.equivalences-species-of-types funext univalence +open import species.species-of-types funext univalence ```
diff --git a/src/species/dirichlet-products-species-of-types-in-subuniverses.lagda.md b/src/species/dirichlet-products-species-of-types-in-subuniverses.lagda.md index 1c966ec39c..4719b90a54 100644 --- a/src/species/dirichlet-products-species-of-types-in-subuniverses.lagda.md +++ b/src/species/dirichlet-products-species-of-types-in-subuniverses.lagda.md @@ -1,33 +1,42 @@ # Dirichlet products of species of types in subuniverses ```agda -module species.dirichlet-products-species-of-types-in-subuniverses where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module species.dirichlet-products-species-of-types-in-subuniverses + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda -open import foundation.cartesian-product-types -open import foundation.contractible-types +open import foundation.cartesian-product-types funext univalence +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.functoriality-dependent-pair-types -open import foundation.global-subuniverses -open import foundation.homotopies -open import foundation.identity-types +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.global-subuniverses funext univalence +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.product-decompositions -open import foundation.product-decompositions-subuniverse -open import foundation.propositions -open import foundation.subuniverses +open import foundation.product-decompositions-subuniverse funext univalence +open import foundation.propositions funext univalence +open import foundation.raising-universe-levels-unit-type +open import foundation.subuniverses funext univalence open import foundation.transport-along-identifications open import foundation.type-arithmetic-cartesian-product-types open import foundation.type-arithmetic-dependent-pair-types open import foundation.unit-type -open import foundation.univalence +open import foundation.univalence funext univalence open import foundation.universe-levels -open import species.dirichlet-products-species-of-types -open import species.species-of-types-in-subuniverses +open import species.dirichlet-products-species-of-types funext univalence +open import species.species-of-types-in-subuniverses funext univalence ```
diff --git a/src/species/dirichlet-products-species-of-types.lagda.md b/src/species/dirichlet-products-species-of-types.lagda.md index ba7ab3e640..a583a0780b 100644 --- a/src/species/dirichlet-products-species-of-types.lagda.md +++ b/src/species/dirichlet-products-species-of-types.lagda.md @@ -1,18 +1,24 @@ # Dirichlet products of species of types ```agda -module species.dirichlet-products-species-of-types where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module species.dirichlet-products-species-of-types + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types open import foundation.product-decompositions open import foundation.universe-levels -open import species.species-of-types +open import species.species-of-types funext univalence ```
diff --git a/src/species/dirichlet-series-species-of-finite-inhabited-types.lagda.md b/src/species/dirichlet-series-species-of-finite-inhabited-types.lagda.md index d5d0a07c20..c436b3c0f5 100644 --- a/src/species/dirichlet-series-species-of-finite-inhabited-types.lagda.md +++ b/src/species/dirichlet-series-species-of-finite-inhabited-types.lagda.md @@ -1,7 +1,15 @@ # Dirichlet series of species of finite inhabited types ```agda -module species.dirichlet-series-species-of-finite-inhabited-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module species.dirichlet-series-species-of-finite-inhabited-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,15 +17,15 @@ module species.dirichlet-series-species-of-finite-inhabited-types where ```agda open import elementary-number-theory.natural-numbers -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types open import foundation.universe-levels -open import species.species-of-finite-inhabited-types +open import species.species-of-finite-inhabited-types funext univalence truncations -open import univalent-combinatorics.cycle-prime-decomposition-natural-numbers -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.inhabited-finite-types +open import univalent-combinatorics.cycle-prime-decomposition-natural-numbers funext univalence truncations +open import univalent-combinatorics.finite-types funext univalence truncations +open import univalent-combinatorics.inhabited-finite-types funext univalence truncations ```
diff --git a/src/species/dirichlet-series-species-of-types-in-subuniverses.lagda.md b/src/species/dirichlet-series-species-of-types-in-subuniverses.lagda.md index 22ff7d6265..4adae61c70 100644 --- a/src/species/dirichlet-series-species-of-types-in-subuniverses.lagda.md +++ b/src/species/dirichlet-series-species-of-types-in-subuniverses.lagda.md @@ -1,18 +1,24 @@ # Dirichlet series of species of types in subuniverses ```agda -module species.dirichlet-series-species-of-types-in-subuniverses where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module species.dirichlet-series-species-of-types-in-subuniverses + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.subuniverses +open import foundation.subuniverses funext univalence open import foundation.universe-levels -open import species.species-of-types-in-subuniverses +open import species.species-of-types-in-subuniverses funext univalence ```
diff --git a/src/species/dirichlet-series-species-of-types.lagda.md b/src/species/dirichlet-series-species-of-types.lagda.md index a3e2595e36..f08c60479f 100644 --- a/src/species/dirichlet-series-species-of-types.lagda.md +++ b/src/species/dirichlet-series-species-of-types.lagda.md @@ -1,17 +1,23 @@ # Dirichlet series of species of types ```agda -module species.dirichlet-series-species-of-types where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module species.dirichlet-series-species-of-types + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types open import foundation.universe-levels -open import species.species-of-types +open import species.species-of-types funext univalence ```
diff --git a/src/species/equivalences-species-of-types-in-subuniverses.lagda.md b/src/species/equivalences-species-of-types-in-subuniverses.lagda.md index e2a0f54a3f..74bf8397a3 100644 --- a/src/species/equivalences-species-of-types-in-subuniverses.lagda.md +++ b/src/species/equivalences-species-of-types-in-subuniverses.lagda.md @@ -1,18 +1,24 @@ # Equivalences of species of types in subuniverses ```agda -module species.equivalences-species-of-types-in-subuniverses where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module species.equivalences-species-of-types-in-subuniverses + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda -open import foundation.equivalences -open import foundation.identity-types -open import foundation.subuniverses +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.subuniverses funext univalence open import foundation.universe-levels -open import species.species-of-types-in-subuniverses +open import species.species-of-types-in-subuniverses funext univalence ```
diff --git a/src/species/equivalences-species-of-types.lagda.md b/src/species/equivalences-species-of-types.lagda.md index a0e35581a6..166eb94c19 100644 --- a/src/species/equivalences-species-of-types.lagda.md +++ b/src/species/equivalences-species-of-types.lagda.md @@ -1,18 +1,24 @@ # Equivalences of species of types ```agda -module species.equivalences-species-of-types where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module species.equivalences-species-of-types + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda -open import foundation.equivalences -open import foundation.identity-types -open import foundation.univalence +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.univalence funext univalence open import foundation.universe-levels -open import species.species-of-types +open import species.species-of-types funext univalence ```
diff --git a/src/species/exponentials-cauchy-series-of-types-in-subuniverses.lagda.md b/src/species/exponentials-cauchy-series-of-types-in-subuniverses.lagda.md index 4f1628ab45..43423d6920 100644 --- a/src/species/exponentials-cauchy-series-of-types-in-subuniverses.lagda.md +++ b/src/species/exponentials-cauchy-series-of-types-in-subuniverses.lagda.md @@ -1,28 +1,36 @@ # Exponential of Cauchy series of species of types in subuniverses ```agda -module species.exponentials-cauchy-series-of-types-in-subuniverses where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module species.exponentials-cauchy-series-of-types-in-subuniverses + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.functoriality-dependent-pair-types -open import foundation.global-subuniverses -open import foundation.sigma-closed-subuniverses -open import foundation.subuniverses +open import foundation.equivalences funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.global-subuniverses funext univalence +open import foundation.sigma-closed-subuniverses funext univalence +open import foundation.subuniverses funext univalence open import foundation.type-arithmetic-cartesian-product-types open import foundation.unit-type open import foundation.universe-levels -open import species.cauchy-composition-species-of-types-in-subuniverses -open import species.cauchy-exponentials-species-of-types-in-subuniverses -open import species.cauchy-series-species-of-types-in-subuniverses -open import species.composition-cauchy-series-species-of-types-in-subuniverses -open import species.species-of-types-in-subuniverses +open import species.cauchy-composition-species-of-types-in-subuniverses funext univalence +open import species.cauchy-exponentials-species-of-types-in-subuniverses funext univalence truncations +open import species.cauchy-series-species-of-types-in-subuniverses funext univalence +open import species.composition-cauchy-series-species-of-types-in-subuniverses funext univalence +open import species.species-of-types-in-subuniverses funext univalence ```
diff --git a/src/species/exponentials-cauchy-series-of-types.lagda.md b/src/species/exponentials-cauchy-series-of-types.lagda.md index 39cbfbf9be..3177a1dd10 100644 --- a/src/species/exponentials-cauchy-series-of-types.lagda.md +++ b/src/species/exponentials-cauchy-series-of-types.lagda.md @@ -1,25 +1,33 @@ # Exponential of Cauchy series of species of types ```agda -module species.exponentials-cauchy-series-of-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module species.exponentials-cauchy-series-of-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.functoriality-dependent-pair-types +open import foundation.equivalences funext +open import foundation.functoriality-dependent-pair-types funext open import foundation.type-arithmetic-cartesian-product-types open import foundation.unit-type open import foundation.universe-levels -open import species.cauchy-composition-species-of-types -open import species.cauchy-exponentials-species-of-types -open import species.cauchy-series-species-of-types -open import species.composition-cauchy-series-species-of-types -open import species.species-of-types +open import species.cauchy-composition-species-of-types funext univalence +open import species.cauchy-exponentials-species-of-types funext univalence truncations +open import species.cauchy-series-species-of-types funext univalence +open import species.composition-cauchy-series-species-of-types funext univalence +open import species.species-of-types funext univalence ```
diff --git a/src/species/hasse-weil-species.lagda.md b/src/species/hasse-weil-species.lagda.md index 4538f31367..09afaa0153 100644 --- a/src/species/hasse-weil-species.lagda.md +++ b/src/species/hasse-weil-species.lagda.md @@ -1,20 +1,28 @@ # Hasse-Weil species ```agda -module species.hasse-weil-species where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module species.hasse-weil-species + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import finite-algebra.commutative-finite-rings -open import finite-algebra.products-commutative-finite-rings +open import finite-algebra.commutative-finite-rings funext univalence truncations +open import finite-algebra.products-commutative-finite-rings funext univalence truncations -open import foundation.cartesian-product-types -open import foundation.equivalences +open import foundation.cartesian-product-types funext univalence +open import foundation.equivalences funext open import foundation.universe-levels -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.finite-types funext univalence truncations ```
diff --git a/src/species/morphisms-finite-species.lagda.md b/src/species/morphisms-finite-species.lagda.md index 52f2991b25..f709af2c84 100644 --- a/src/species/morphisms-finite-species.lagda.md +++ b/src/species/morphisms-finite-species.lagda.md @@ -1,28 +1,37 @@ # Morphisms of finite species ```agda -module species.morphisms-finite-species where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module species.morphisms-finite-species + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types -open import foundation.equivalences -open import foundation.function-types +open import foundation.dependent-products-propositions funext +open import foundation.equality-dependent-function-types funext +open import foundation.equivalences funext +open import foundation.function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets -open import foundation.torsorial-type-families +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.torsorial-type-families funext univalence truncations open import foundation.universe-levels -open import species.species-of-finite-types +open import species.species-of-finite-types funext univalence truncations -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.finite-types funext univalence truncations ```
diff --git a/src/species/morphisms-species-of-types.lagda.md b/src/species/morphisms-species-of-types.lagda.md index 713b51777c..ae56a96e5d 100644 --- a/src/species/morphisms-species-of-types.lagda.md +++ b/src/species/morphisms-species-of-types.lagda.md @@ -1,23 +1,31 @@ # Morphisms of species of types ```agda -module species.morphisms-species-of-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module species.morphisms-species-of-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.equality-dependent-function-types -open import foundation.equivalences -open import foundation.function-types +open import foundation.equality-dependent-function-types funext +open import foundation.equivalences funext +open import foundation.function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types -open import foundation.torsorial-type-families +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext +open import foundation.torsorial-type-families funext univalence truncations open import foundation.universe-levels -open import species.species-of-types +open import species.species-of-types funext univalence ```
diff --git a/src/species/pointing-species-of-types.lagda.md b/src/species/pointing-species-of-types.lagda.md index 6761bb997f..05e754d0e7 100644 --- a/src/species/pointing-species-of-types.lagda.md +++ b/src/species/pointing-species-of-types.lagda.md @@ -1,16 +1,22 @@ # Pointing of species of types ```agda -module species.pointing-species-of-types where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module species.pointing-species-of-types + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.universe-levels -open import species.species-of-types +open import species.species-of-types funext univalence ```
diff --git a/src/species/precategory-of-finite-species.lagda.md b/src/species/precategory-of-finite-species.lagda.md index d2de76dfc8..14c999446b 100644 --- a/src/species/precategory-of-finite-species.lagda.md +++ b/src/species/precategory-of-finite-species.lagda.md @@ -1,18 +1,26 @@ # The precategory of finite species ```agda -module species.precategory-of-finite-species where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module species.precategory-of-finite-species + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.large-precategories +open import category-theory.large-precategories funext univalence truncations open import foundation.universe-levels -open import species.morphisms-finite-species -open import species.species-of-finite-types +open import species.morphisms-finite-species funext univalence truncations +open import species.species-of-finite-types funext univalence truncations ```
diff --git a/src/species/products-cauchy-series-species-of-types-in-subuniverses.lagda.md b/src/species/products-cauchy-series-species-of-types-in-subuniverses.lagda.md index 946d2dd088..0092231329 100644 --- a/src/species/products-cauchy-series-species-of-types-in-subuniverses.lagda.md +++ b/src/species/products-cauchy-series-species-of-types-in-subuniverses.lagda.md @@ -1,26 +1,34 @@ # Products of Cauchy series of species of types in subuniverses ```agda -module species.products-cauchy-series-species-of-types-in-subuniverses where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module species.products-cauchy-series-species-of-types-in-subuniverses + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.cartesian-product-types -open import foundation.coproduct-types -open import foundation.equivalences -open import foundation.functoriality-cartesian-product-types -open import foundation.global-subuniverses -open import foundation.subuniverses +open import foundation.cartesian-product-types funext univalence +open import foundation.coproduct-types funext univalence truncations +open import foundation.equivalences funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.global-subuniverses funext univalence +open import foundation.subuniverses funext univalence open import foundation.universe-levels -open import species.cauchy-products-species-of-types -open import species.cauchy-products-species-of-types-in-subuniverses -open import species.cauchy-series-species-of-types -open import species.cauchy-series-species-of-types-in-subuniverses -open import species.products-cauchy-series-species-of-types -open import species.species-of-types-in-subuniverses +open import species.cauchy-products-species-of-types funext univalence truncations +open import species.cauchy-products-species-of-types-in-subuniverses funext univalence truncations +open import species.cauchy-series-species-of-types funext univalence +open import species.cauchy-series-species-of-types-in-subuniverses funext univalence +open import species.products-cauchy-series-species-of-types funext univalence truncations +open import species.species-of-types-in-subuniverses funext univalence ```
diff --git a/src/species/products-cauchy-series-species-of-types.lagda.md b/src/species/products-cauchy-series-species-of-types.lagda.md index 347682538c..1005cb60a7 100644 --- a/src/species/products-cauchy-series-species-of-types.lagda.md +++ b/src/species/products-cauchy-series-species-of-types.lagda.md @@ -1,27 +1,35 @@ # Products of Cauchy series of species of types ```agda -module species.products-cauchy-series-species-of-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module species.products-cauchy-series-species-of-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.cartesian-product-types -open import foundation.coproduct-types +open import foundation.cartesian-product-types funext univalence +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.functoriality-cartesian-product-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies +open import foundation.equivalences funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext open import foundation.type-arithmetic-dependent-pair-types -open import foundation.univalence -open import foundation.universal-property-coproduct-types +open import foundation.univalence funext univalence +open import foundation.universal-property-coproduct-types funext open import foundation.universe-levels -open import species.cauchy-products-species-of-types -open import species.cauchy-series-species-of-types -open import species.species-of-types +open import species.cauchy-products-species-of-types funext univalence truncations +open import species.cauchy-series-species-of-types funext univalence +open import species.species-of-types funext univalence ```
diff --git a/src/species/products-dirichlet-series-species-of-finite-inhabited-types.lagda.md b/src/species/products-dirichlet-series-species-of-finite-inhabited-types.lagda.md index 26fac97788..bba8343a6c 100644 --- a/src/species/products-dirichlet-series-species-of-finite-inhabited-types.lagda.md +++ b/src/species/products-dirichlet-series-species-of-finite-inhabited-types.lagda.md @@ -1,17 +1,25 @@ # Products of Dirichlet series of species of finite inhabited types ```agda -module species.products-dirichlet-series-species-of-finite-inhabited-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module species.products-dirichlet-series-species-of-finite-inhabited-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.universe-levels -open import species.dirichlet-series-species-of-finite-inhabited-types -open import species.species-of-finite-inhabited-types +open import species.dirichlet-series-species-of-finite-inhabited-types funext univalence truncations +open import species.species-of-finite-inhabited-types funext univalence truncations ```
diff --git a/src/species/products-dirichlet-series-species-of-types-in-subuniverses.lagda.md b/src/species/products-dirichlet-series-species-of-types-in-subuniverses.lagda.md index 0618179c6c..d0f6dbcc89 100644 --- a/src/species/products-dirichlet-series-species-of-types-in-subuniverses.lagda.md +++ b/src/species/products-dirichlet-series-species-of-types-in-subuniverses.lagda.md @@ -1,29 +1,37 @@ # Products of Dirichlet series of species of types in subuniverses ```agda -module species.products-dirichlet-series-species-of-types-in-subuniverses where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module species.products-dirichlet-series-species-of-types-in-subuniverses + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.cartesian-product-types -open import foundation.coproduct-types +open import foundation.cartesian-product-types funext univalence +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.functoriality-cartesian-product-types -open import foundation.functoriality-dependent-pair-types -open import foundation.global-subuniverses -open import foundation.homotopies -open import foundation.postcomposition-functions -open import foundation.subuniverses +open import foundation.equivalences funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.global-subuniverses funext univalence +open import foundation.homotopies funext +open import foundation.postcomposition-functions funext +open import foundation.subuniverses funext univalence open import foundation.type-arithmetic-dependent-pair-types -open import foundation.universal-property-cartesian-product-types +open import foundation.universal-property-cartesian-product-types funext open import foundation.universe-levels -open import species.dirichlet-products-species-of-types-in-subuniverses -open import species.dirichlet-series-species-of-types-in-subuniverses -open import species.species-of-types-in-subuniverses +open import species.dirichlet-products-species-of-types-in-subuniverses funext univalence +open import species.dirichlet-series-species-of-types-in-subuniverses funext univalence +open import species.species-of-types-in-subuniverses funext univalence ```
diff --git a/src/species/products-dirichlet-series-species-of-types.lagda.md b/src/species/products-dirichlet-series-species-of-types.lagda.md index 1b015bd412..ca8259962e 100644 --- a/src/species/products-dirichlet-series-species-of-types.lagda.md +++ b/src/species/products-dirichlet-series-species-of-types.lagda.md @@ -1,27 +1,33 @@ # Products of Dirichlet series of species of types ```agda -module species.products-dirichlet-series-species-of-types where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module species.products-dirichlet-series-species-of-types + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.functoriality-cartesian-product-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies -open import foundation.postcomposition-functions +open import foundation.equivalences funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext +open import foundation.postcomposition-functions funext open import foundation.type-arithmetic-dependent-pair-types -open import foundation.univalence -open import foundation.universal-property-cartesian-product-types +open import foundation.univalence funext univalence +open import foundation.universal-property-cartesian-product-types funext open import foundation.universe-levels -open import species.dirichlet-products-species-of-types -open import species.dirichlet-series-species-of-types -open import species.species-of-types +open import species.dirichlet-products-species-of-types funext univalence +open import species.dirichlet-series-species-of-types funext univalence +open import species.species-of-types funext univalence ```
diff --git a/src/species/small-cauchy-composition-species-of-finite-inhabited-types.lagda.md b/src/species/small-cauchy-composition-species-of-finite-inhabited-types.lagda.md index 32e27e77d0..feabf3fb3b 100644 --- a/src/species/small-cauchy-composition-species-of-finite-inhabited-types.lagda.md +++ b/src/species/small-cauchy-composition-species-of-finite-inhabited-types.lagda.md @@ -2,41 +2,51 @@ ```agda {-# OPTIONS --lossy-unification #-} +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom -module species.small-cauchy-composition-species-of-finite-inhabited-types where +module species.small-cauchy-composition-species-of-finite-inhabited-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.contractible-types -open import foundation.decidable-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-cartesian-product-types -open import foundation.functoriality-dependent-pair-types -open import foundation.identity-types -open import foundation.inhabited-types -open import foundation.propositions -open import foundation.relaxed-sigma-decompositions -open import foundation.sigma-closed-subuniverses -open import foundation.sigma-decomposition-subuniverse -open import foundation.subuniverses +open import foundation.contractible-types funext univalence +open import foundation.decidable-types funext univalence truncations +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.identity-types funext +open import foundation.inhabited-types funext univalence truncations +open import foundation.propositions funext univalence +open import foundation.raising-universe-levels-unit-type +open import foundation.relaxed-sigma-decompositions funext univalence +open import foundation.sigma-closed-subuniverses funext univalence +open import foundation.sigma-decomposition-subuniverse funext univalence +open import foundation.subuniverses funext univalence open import foundation.type-arithmetic-cartesian-product-types open import foundation.unit-type open import foundation.universe-levels -open import species.small-cauchy-composition-species-of-types-in-subuniverses -open import species.species-of-finite-inhabited-types +open import species.small-cauchy-composition-species-of-types-in-subuniverses funext univalence truncations +open import species.species-of-finite-inhabited-types funext univalence truncations -open import univalent-combinatorics.cartesian-product-types -open import univalent-combinatorics.decidable-propositions -open import univalent-combinatorics.dependent-function-types -open import univalent-combinatorics.dependent-pair-types -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.inhabited-finite-types -open import univalent-combinatorics.sigma-decompositions -open import univalent-combinatorics.small-types +open import univalent-combinatorics.cartesian-product-types funext univalence truncations +open import univalent-combinatorics.decidable-propositions funext univalence truncations +open import univalent-combinatorics.dependent-function-types funext univalence truncations +open import univalent-combinatorics.dependent-pair-types funext univalence truncations +open import univalent-combinatorics.finite-types funext univalence truncations +open import univalent-combinatorics.inhabited-finite-types funext univalence truncations +open import univalent-combinatorics.sigma-decompositions funext univalence truncations +open import univalent-combinatorics.small-types funext univalence truncations ```
diff --git a/src/species/small-cauchy-composition-species-of-types-in-subuniverses.lagda.md b/src/species/small-cauchy-composition-species-of-types-in-subuniverses.lagda.md index 78eac4cbc1..fceaf1f924 100644 --- a/src/species/small-cauchy-composition-species-of-types-in-subuniverses.lagda.md +++ b/src/species/small-cauchy-composition-species-of-types-in-subuniverses.lagda.md @@ -1,38 +1,49 @@ # Small Cauchy composition of species types in subuniverses ```agda -module species.small-cauchy-composition-species-of-types-in-subuniverses where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module species.small-cauchy-composition-species-of-types-in-subuniverses + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.cartesian-product-types -open import foundation.contractible-types +open import foundation.cartesian-product-types funext univalence +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext open import foundation.equality-cartesian-product-types -open import foundation.equivalences -open import foundation.functoriality-cartesian-product-types -open import foundation.functoriality-dependent-function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.relaxed-sigma-decompositions -open import foundation.sigma-closed-subuniverses -open import foundation.sigma-decomposition-subuniverse -open import foundation.small-types -open import foundation.subuniverses +open import foundation.equivalences funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.functoriality-dependent-function-types funext univalence +open import foundation.functoriality-dependent-pair-types funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.raising-universe-levels-unit-type +open import foundation.relaxed-sigma-decompositions funext univalence +open import foundation.sigma-closed-subuniverses funext univalence +open import foundation.sigma-decomposition-subuniverse funext univalence +open import foundation.small-types funext univalence truncations +open import foundation.subuniverses funext univalence open import foundation.transport-along-identifications open import foundation.type-arithmetic-cartesian-product-types open import foundation.type-arithmetic-dependent-pair-types -open import foundation.type-theoretic-principle-of-choice +open import foundation.type-theoretic-principle-of-choice funext open import foundation.unit-type -open import foundation.univalence +open import foundation.univalence funext univalence open import foundation.universe-levels -open import species.cauchy-composition-species-of-types -open import species.species-of-types-in-subuniverses -open import species.unit-cauchy-composition-species-of-types +open import species.cauchy-composition-species-of-types funext univalence +open import species.species-of-types-in-subuniverses funext univalence +open import species.unit-cauchy-composition-species-of-types funext univalence ```
diff --git a/src/species/species-of-finite-inhabited-types.lagda.md b/src/species/species-of-finite-inhabited-types.lagda.md index fa9ba4bc14..ca52e7d70f 100644 --- a/src/species/species-of-finite-inhabited-types.lagda.md +++ b/src/species/species-of-finite-inhabited-types.lagda.md @@ -1,7 +1,15 @@ # Species of finite inhabited types ```agda -module species.species-of-finite-inhabited-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module species.species-of-finite-inhabited-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,10 +17,10 @@ module species.species-of-finite-inhabited-types where ```agda open import foundation.universe-levels -open import species.species-of-types-in-subuniverses +open import species.species-of-types-in-subuniverses funext univalence -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.inhabited-finite-types +open import univalent-combinatorics.finite-types funext univalence truncations +open import univalent-combinatorics.inhabited-finite-types funext univalence truncations ```
diff --git a/src/species/species-of-finite-types.lagda.md b/src/species/species-of-finite-types.lagda.md index 24eb4eb3b3..0c4f21c875 100644 --- a/src/species/species-of-finite-types.lagda.md +++ b/src/species/species-of-finite-types.lagda.md @@ -1,7 +1,15 @@ # Species of finite types ```agda -module species.species-of-finite-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module species.species-of-finite-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,9 +17,9 @@ module species.species-of-finite-types where ```agda open import foundation.universe-levels -open import species.species-of-types-in-subuniverses +open import species.species-of-types-in-subuniverses funext univalence -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.finite-types funext univalence truncations ```
diff --git a/src/species/species-of-inhabited-types.lagda.md b/src/species/species-of-inhabited-types.lagda.md index 92c51b4adf..69cd6982fc 100644 --- a/src/species/species-of-inhabited-types.lagda.md +++ b/src/species/species-of-inhabited-types.lagda.md @@ -1,17 +1,25 @@ # Species of inhabited types ```agda -module species.species-of-inhabited-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module species.species-of-inhabited-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.inhabited-types +open import foundation.inhabited-types funext univalence truncations open import foundation.unit-type open import foundation.universe-levels -open import species.species-of-types-in-subuniverses +open import species.species-of-types-in-subuniverses funext univalence ```
diff --git a/src/species/species-of-types-in-subuniverses.lagda.md b/src/species/species-of-types-in-subuniverses.lagda.md index 1ef1c85fec..9631e70885 100644 --- a/src/species/species-of-types-in-subuniverses.lagda.md +++ b/src/species/species-of-types-in-subuniverses.lagda.md @@ -1,23 +1,30 @@ # Species of types in subuniverses ```agda -module species.species-of-types-in-subuniverses where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module species.species-of-types-in-subuniverses + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.propositions -open import foundation.subuniverses +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.propositions funext univalence +open import foundation.subuniverses funext univalence open import foundation.transport-along-identifications open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels -open import species.species-of-types +open import species.species-of-types funext univalence ```
diff --git a/src/species/species-of-types.lagda.md b/src/species/species-of-types.lagda.md index e300981b9b..9428a9b81f 100644 --- a/src/species/species-of-types.lagda.md +++ b/src/species/species-of-types.lagda.md @@ -1,16 +1,22 @@ # Species of types ```agda -module species.species-of-types where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module species.species-of-types + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda -open import foundation.cartesian-product-types -open import foundation.equivalences +open import foundation.cartesian-product-types funext univalence +open import foundation.equivalences funext open import foundation.transport-along-identifications -open import foundation.univalence +open import foundation.univalence funext univalence open import foundation.universe-levels ``` diff --git a/src/species/unit-cauchy-composition-species-of-types-in-subuniverses.lagda.md b/src/species/unit-cauchy-composition-species-of-types-in-subuniverses.lagda.md index 030f8440d0..b7a96bac07 100644 --- a/src/species/unit-cauchy-composition-species-of-types-in-subuniverses.lagda.md +++ b/src/species/unit-cauchy-composition-species-of-types-in-subuniverses.lagda.md @@ -1,19 +1,26 @@ # The unit of Cauchy composition of species of types in subuniverses ```agda -module species.unit-cauchy-composition-species-of-types-in-subuniverses where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module species.unit-cauchy-composition-species-of-types-in-subuniverses + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda -open import foundation.contractible-types +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.global-subuniverses -open import foundation.subuniverses +open import foundation.dependent-products-contractible-types funext +open import foundation.global-subuniverses funext univalence +open import foundation.subuniverses funext univalence open import foundation.universe-levels -open import species.species-of-types-in-subuniverses +open import species.species-of-types-in-subuniverses funext univalence ```
diff --git a/src/species/unit-cauchy-composition-species-of-types.lagda.md b/src/species/unit-cauchy-composition-species-of-types.lagda.md index 15884d5b45..d2bb150b00 100644 --- a/src/species/unit-cauchy-composition-species-of-types.lagda.md +++ b/src/species/unit-cauchy-composition-species-of-types.lagda.md @@ -1,16 +1,23 @@ # The unit of Cauchy composition of types ```agda -module species.unit-cauchy-composition-species-of-types where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module species.unit-cauchy-composition-species-of-types + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda -open import foundation.contractible-types +open import foundation.contractible-types funext univalence +open import foundation.dependent-products-contractible-types funext open import foundation.universe-levels -open import species.species-of-types +open import species.species-of-types funext univalence ```
diff --git a/src/species/unlabeled-structures-species.lagda.md b/src/species/unlabeled-structures-species.lagda.md index 2ed30b8522..03519a14c1 100644 --- a/src/species/unlabeled-structures-species.lagda.md +++ b/src/species/unlabeled-structures-species.lagda.md @@ -1,7 +1,15 @@ # Unlabeled structures of finite species ```agda -module species.unlabeled-structures-species where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module species.unlabeled-structures-species + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -12,9 +20,9 @@ open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types open import foundation.universe-levels -open import species.species-of-types +open import species.species-of-types funext univalence -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.finite-types funext univalence truncations ```
diff --git a/src/structured-types.lagda.md b/src/structured-types.lagda.md index 081ebda794..8d18a7e7d2 100644 --- a/src/structured-types.lagda.md +++ b/src/structured-types.lagda.md @@ -7,83 +7,91 @@ ## Modules in the structured types namespace ```agda -module structured-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom -open import structured-types.cartesian-products-types-equipped-with-endomorphisms public -open import structured-types.central-h-spaces public -open import structured-types.commuting-squares-of-pointed-homotopies public -open import structured-types.commuting-squares-of-pointed-maps public -open import structured-types.commuting-triangles-of-pointed-maps public -open import structured-types.conjugation-pointed-types public -open import structured-types.constant-pointed-maps public -open import structured-types.contractible-pointed-types public -open import structured-types.cyclic-types public -open import structured-types.dependent-products-h-spaces public +module structured-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where + +open import structured-types.cartesian-products-types-equipped-with-endomorphisms funext univalence public +open import structured-types.central-h-spaces funext public +open import structured-types.commuting-squares-of-pointed-homotopies funext univalence truncations public +open import structured-types.commuting-squares-of-pointed-maps funext univalence truncations public +open import structured-types.commuting-triangles-of-pointed-maps funext univalence truncations public +open import structured-types.conjugation-pointed-types funext univalence truncations public +open import structured-types.constant-pointed-maps funext univalence truncations public +open import structured-types.contractible-pointed-types funext univalence public +open import structured-types.cyclic-types funext univalence truncations public +open import structured-types.dependent-products-h-spaces funext univalence truncations public open import structured-types.dependent-products-pointed-types public -open import structured-types.dependent-products-wild-monoids public -open import structured-types.dependent-types-equipped-with-automorphisms public -open import structured-types.equivalences-h-spaces public -open import structured-types.equivalences-pointed-arrows public -open import structured-types.equivalences-types-equipped-with-automorphisms public -open import structured-types.equivalences-types-equipped-with-endomorphisms public -open import structured-types.faithful-pointed-maps public -open import structured-types.fibers-of-pointed-maps public -open import structured-types.finite-multiplication-magmas public -open import structured-types.function-h-spaces public -open import structured-types.function-magmas public -open import structured-types.function-wild-monoids public -open import structured-types.h-spaces public -open import structured-types.initial-pointed-type-equipped-with-automorphism public -open import structured-types.involutive-type-of-h-space-structures public -open import structured-types.involutive-types public -open import structured-types.iterated-cartesian-products-types-equipped-with-endomorphisms public -open import structured-types.iterated-pointed-cartesian-product-types public -open import structured-types.magmas public -open import structured-types.mere-equivalences-types-equipped-with-endomorphisms public -open import structured-types.morphisms-h-spaces public -open import structured-types.morphisms-magmas public -open import structured-types.morphisms-pointed-arrows public -open import structured-types.morphisms-twisted-pointed-arrows public -open import structured-types.morphisms-types-equipped-with-automorphisms public -open import structured-types.morphisms-types-equipped-with-endomorphisms public -open import structured-types.morphisms-wild-monoids public -open import structured-types.noncoherent-h-spaces public -open import structured-types.opposite-pointed-spans public -open import structured-types.pointed-2-homotopies public -open import structured-types.pointed-cartesian-product-types public -open import structured-types.pointed-dependent-functions public +open import structured-types.dependent-products-wild-monoids funext univalence truncations public +open import structured-types.dependent-types-equipped-with-automorphisms funext univalence truncations public +open import structured-types.equivalences-h-spaces funext univalence truncations public +open import structured-types.equivalences-pointed-arrows funext univalence truncations public +open import structured-types.equivalences-types-equipped-with-automorphisms funext univalence truncations public +open import structured-types.equivalences-types-equipped-with-endomorphisms funext univalence truncations public +open import structured-types.faithful-pointed-maps funext univalence truncations public +open import structured-types.fibers-of-pointed-maps funext univalence truncations public +open import structured-types.finite-multiplication-magmas funext univalence truncations public +open import structured-types.function-h-spaces funext univalence truncations public +open import structured-types.function-magmas funext univalence public +open import structured-types.function-wild-monoids funext univalence truncations public +open import structured-types.h-spaces funext univalence truncations public +open import structured-types.initial-pointed-type-equipped-with-automorphism funext univalence truncations public +open import structured-types.involutive-type-of-h-space-structures funext univalence truncations public +open import structured-types.involutive-types funext univalence truncations public +open import structured-types.iterated-cartesian-products-types-equipped-with-endomorphisms funext univalence public +open import structured-types.iterated-pointed-cartesian-product-types funext univalence truncations public +open import structured-types.magmas funext univalence public +open import structured-types.mere-equivalences-types-equipped-with-endomorphisms funext univalence truncations public +open import structured-types.morphisms-h-spaces funext univalence truncations public +open import structured-types.morphisms-magmas funext univalence public +open import structured-types.morphisms-pointed-arrows funext univalence truncations public +open import structured-types.morphisms-twisted-pointed-arrows funext univalence truncations public +open import structured-types.morphisms-types-equipped-with-automorphisms funext univalence truncations public +open import structured-types.morphisms-types-equipped-with-endomorphisms funext univalence truncations public +open import structured-types.morphisms-wild-monoids funext univalence truncations public +open import structured-types.noncoherent-h-spaces funext public +open import structured-types.opposite-pointed-spans funext univalence truncations public +open import structured-types.pointed-2-homotopies funext univalence truncations public +open import structured-types.pointed-cartesian-product-types funext univalence truncations public +open import structured-types.pointed-dependent-functions funext public open import structured-types.pointed-dependent-pair-types public -open import structured-types.pointed-equivalences public +open import structured-types.pointed-equivalences funext univalence truncations public open import structured-types.pointed-families-of-types public -open import structured-types.pointed-homotopies public -open import structured-types.pointed-isomorphisms public -open import structured-types.pointed-maps public -open import structured-types.pointed-retractions public -open import structured-types.pointed-sections public -open import structured-types.pointed-span-diagrams public -open import structured-types.pointed-spans public +open import structured-types.pointed-homotopies funext univalence truncations public +open import structured-types.pointed-isomorphisms funext univalence truncations public +open import structured-types.pointed-maps funext univalence truncations public +open import structured-types.pointed-retractions funext univalence truncations public +open import structured-types.pointed-sections funext univalence truncations public +open import structured-types.pointed-span-diagrams funext univalence truncations public +open import structured-types.pointed-spans funext univalence truncations public open import structured-types.pointed-types public -open import structured-types.pointed-types-equipped-with-automorphisms public -open import structured-types.pointed-unit-type public -open import structured-types.pointed-universal-property-contractible-types public -open import structured-types.postcomposition-pointed-maps public -open import structured-types.precomposition-pointed-maps public -open import structured-types.sets-equipped-with-automorphisms public -open import structured-types.small-pointed-types public -open import structured-types.symmetric-elements-involutive-types public -open import structured-types.symmetric-h-spaces public -open import structured-types.transposition-pointed-span-diagrams public -open import structured-types.types-equipped-with-automorphisms public -open import structured-types.types-equipped-with-endomorphisms public -open import structured-types.uniform-pointed-homotopies public -open import structured-types.universal-property-pointed-equivalences public +open import structured-types.pointed-types-equipped-with-automorphisms funext univalence truncations public +open import structured-types.pointed-unit-type funext univalence truncations public +open import structured-types.pointed-universal-property-contractible-types funext univalence truncations public +open import structured-types.postcomposition-pointed-maps funext univalence truncations public +open import structured-types.precomposition-pointed-maps funext univalence truncations public +open import structured-types.sets-equipped-with-automorphisms funext univalence public +open import structured-types.small-pointed-types funext univalence truncations public +open import structured-types.symmetric-elements-involutive-types funext univalence truncations public +open import structured-types.symmetric-h-spaces funext univalence truncations public +open import structured-types.transposition-pointed-span-diagrams funext univalence truncations public +open import structured-types.types-equipped-with-automorphisms funext univalence public +open import structured-types.types-equipped-with-endomorphisms funext univalence public +open import structured-types.uniform-pointed-homotopies funext univalence truncations public +open import structured-types.universal-property-pointed-equivalences funext univalence truncations public open import structured-types.unpointed-maps public -open import structured-types.whiskering-pointed-2-homotopies-concatenation public -open import structured-types.whiskering-pointed-homotopies-composition public -open import structured-types.wild-category-of-pointed-types public -open import structured-types.wild-groups public -open import structured-types.wild-loops public -open import structured-types.wild-monoids public -open import structured-types.wild-quasigroups public -open import structured-types.wild-semigroups public +open import structured-types.whiskering-pointed-2-homotopies-concatenation funext univalence truncations public +open import structured-types.whiskering-pointed-homotopies-composition funext univalence truncations public +open import structured-types.wild-category-of-pointed-types funext univalence truncations public +open import structured-types.wild-groups funext univalence truncations public +open import structured-types.wild-loops funext univalence truncations public +open import structured-types.wild-monoids funext univalence truncations public +open import structured-types.wild-quasigroups funext univalence public +open import structured-types.wild-semigroups funext univalence public ``` diff --git a/src/structured-types/cartesian-products-types-equipped-with-endomorphisms.lagda.md b/src/structured-types/cartesian-products-types-equipped-with-endomorphisms.lagda.md index e8593cf7cf..6dff896779 100644 --- a/src/structured-types/cartesian-products-types-equipped-with-endomorphisms.lagda.md +++ b/src/structured-types/cartesian-products-types-equipped-with-endomorphisms.lagda.md @@ -1,18 +1,24 @@ # Cartesian products of types equipped with endomorphisms ```agda -module structured-types.cartesian-products-types-equipped-with-endomorphisms where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module structured-types.cartesian-products-types-equipped-with-endomorphisms + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.functoriality-cartesian-product-types +open import foundation.functoriality-cartesian-product-types funext open import foundation.universe-levels -open import structured-types.types-equipped-with-endomorphisms +open import structured-types.types-equipped-with-endomorphisms funext univalence ```
diff --git a/src/structured-types/central-h-spaces.lagda.md b/src/structured-types/central-h-spaces.lagda.md index c0ea967513..12bad56d7d 100644 --- a/src/structured-types/central-h-spaces.lagda.md +++ b/src/structured-types/central-h-spaces.lagda.md @@ -1,13 +1,17 @@ # Central H-spaces ```agda -module structured-types.central-h-spaces where +open import foundation.function-extensionality-axiom + +module structured-types.central-h-spaces + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.equivalences +open import foundation.equivalences funext open import foundation.universe-levels open import structured-types.pointed-types diff --git a/src/structured-types/commuting-squares-of-pointed-homotopies.lagda.md b/src/structured-types/commuting-squares-of-pointed-homotopies.lagda.md index 0bd38407d8..a5d1f8ddb7 100644 --- a/src/structured-types/commuting-squares-of-pointed-homotopies.lagda.md +++ b/src/structured-types/commuting-squares-of-pointed-homotopies.lagda.md @@ -1,7 +1,15 @@ # Commuting squares of pointed homotopies ```agda -module structured-types.commuting-squares-of-pointed-homotopies where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module structured-types.commuting-squares-of-pointed-homotopies + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,10 +17,10 @@ module structured-types.commuting-squares-of-pointed-homotopies where ```agda open import foundation.universe-levels -open import structured-types.pointed-2-homotopies -open import structured-types.pointed-dependent-functions +open import structured-types.pointed-2-homotopies funext univalence truncations +open import structured-types.pointed-dependent-functions funext open import structured-types.pointed-families-of-types -open import structured-types.pointed-homotopies +open import structured-types.pointed-homotopies funext univalence truncations open import structured-types.pointed-types ``` diff --git a/src/structured-types/commuting-squares-of-pointed-maps.lagda.md b/src/structured-types/commuting-squares-of-pointed-maps.lagda.md index ed8779ac44..07b2a48dc0 100644 --- a/src/structured-types/commuting-squares-of-pointed-maps.lagda.md +++ b/src/structured-types/commuting-squares-of-pointed-maps.lagda.md @@ -1,25 +1,33 @@ # Commuting squares of pointed maps ```agda -module structured-types.commuting-squares-of-pointed-maps where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module structured-types.commuting-squares-of-pointed-maps + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-identifications -open import foundation.commuting-squares-of-maps +open import foundation.commuting-squares-of-identifications funext +open import foundation.commuting-squares-of-maps funext univalence open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.identity-types +open import foundation.function-types funext +open import foundation.identity-types funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import structured-types.pointed-homotopies -open import structured-types.pointed-maps +open import structured-types.pointed-homotopies funext univalence truncations +open import structured-types.pointed-maps funext univalence truncations open import structured-types.pointed-types -open import structured-types.whiskering-pointed-homotopies-composition +open import structured-types.whiskering-pointed-homotopies-composition funext univalence truncations ```
diff --git a/src/structured-types/commuting-triangles-of-pointed-maps.lagda.md b/src/structured-types/commuting-triangles-of-pointed-maps.lagda.md index 34a14fabd0..e372b44ecd 100644 --- a/src/structured-types/commuting-triangles-of-pointed-maps.lagda.md +++ b/src/structured-types/commuting-triangles-of-pointed-maps.lagda.md @@ -1,7 +1,15 @@ # Commuting triangles of pointed maps ```agda -module structured-types.commuting-triangles-of-pointed-maps where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module structured-types.commuting-triangles-of-pointed-maps + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,10 +17,10 @@ module structured-types.commuting-triangles-of-pointed-maps where ```agda open import foundation.universe-levels -open import structured-types.pointed-homotopies -open import structured-types.pointed-maps +open import structured-types.pointed-homotopies funext univalence truncations +open import structured-types.pointed-maps funext univalence truncations open import structured-types.pointed-types -open import structured-types.whiskering-pointed-homotopies-composition +open import structured-types.whiskering-pointed-homotopies-composition funext univalence truncations ```
diff --git a/src/structured-types/conjugation-pointed-types.lagda.md b/src/structured-types/conjugation-pointed-types.lagda.md index fb95e9ed66..9ade3c569a 100644 --- a/src/structured-types/conjugation-pointed-types.lagda.md +++ b/src/structured-types/conjugation-pointed-types.lagda.md @@ -1,7 +1,15 @@ # Conjugation of pointed types ```agda -module structured-types.conjugation-pointed-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module structured-types.conjugation-pointed-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,18 +17,18 @@ module structured-types.conjugation-pointed-types where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.universe-levels -open import structured-types.pointed-homotopies -open import structured-types.pointed-maps +open import structured-types.pointed-homotopies funext univalence truncations +open import structured-types.pointed-maps funext univalence truncations open import structured-types.pointed-types -open import synthetic-homotopy-theory.conjugation-loops -open import synthetic-homotopy-theory.functoriality-loop-spaces -open import synthetic-homotopy-theory.loop-spaces +open import synthetic-homotopy-theory.conjugation-loops funext univalence truncations +open import synthetic-homotopy-theory.functoriality-loop-spaces funext univalence truncations +open import synthetic-homotopy-theory.loop-spaces funext univalence truncations ```
diff --git a/src/structured-types/constant-pointed-maps.lagda.md b/src/structured-types/constant-pointed-maps.lagda.md index 327fb4e80a..6e295677ec 100644 --- a/src/structured-types/constant-pointed-maps.lagda.md +++ b/src/structured-types/constant-pointed-maps.lagda.md @@ -1,18 +1,26 @@ # Constant pointed maps ```agda -module structured-types.constant-pointed-maps where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module structured-types.constant-pointed-maps + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.constant-maps +open import foundation.constant-maps funext univalence truncations open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import structured-types.pointed-maps +open import structured-types.pointed-maps funext univalence truncations open import structured-types.pointed-types ``` diff --git a/src/structured-types/contractible-pointed-types.lagda.md b/src/structured-types/contractible-pointed-types.lagda.md index 67d5b144e8..cb8b665f44 100644 --- a/src/structured-types/contractible-pointed-types.lagda.md +++ b/src/structured-types/contractible-pointed-types.lagda.md @@ -1,14 +1,22 @@ # Contractible pointed types ```agda -module structured-types.contractible-pointed-types where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module structured-types.contractible-pointed-types + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda -open import foundation.contractible-types -open import foundation.propositions +open import foundation.contractible-types funext univalence +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.propositions funext univalence open import foundation.universe-levels open import structured-types.pointed-types diff --git a/src/structured-types/cyclic-types.lagda.md b/src/structured-types/cyclic-types.lagda.md index dcd59c7116..9531fa61f6 100644 --- a/src/structured-types/cyclic-types.lagda.md +++ b/src/structured-types/cyclic-types.lagda.md @@ -1,22 +1,31 @@ # Cyclic types ```agda -module structured-types.cyclic-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module structured-types.cyclic-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.automorphisms +open import foundation.automorphisms funext univalence open import foundation.dependent-pair-types -open import foundation.iterating-automorphisms -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.sets -open import foundation.surjective-maps +open import foundation.dependent-products-propositions funext +open import foundation.iterating-automorphisms funext univalence truncations +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.surjective-maps funext univalence truncations open import foundation.universe-levels -open import structured-types.sets-equipped-with-automorphisms +open import structured-types.sets-equipped-with-automorphisms funext univalence ```
diff --git a/src/structured-types/dependent-products-h-spaces.lagda.md b/src/structured-types/dependent-products-h-spaces.lagda.md index 535481be7f..ca5ab7c5d0 100644 --- a/src/structured-types/dependent-products-h-spaces.lagda.md +++ b/src/structured-types/dependent-products-h-spaces.lagda.md @@ -1,7 +1,15 @@ # Dependent products of H-spaces ```agda -module structured-types.dependent-products-h-spaces where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module structured-types.dependent-products-h-spaces + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,13 +17,13 @@ module structured-types.dependent-products-h-spaces where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-extensionality -open import foundation.identity-types +open import foundation.function-extensionality funext +open import foundation.identity-types funext open import foundation.unital-binary-operations open import foundation.universe-levels open import structured-types.dependent-products-pointed-types -open import structured-types.h-spaces +open import structured-types.h-spaces funext univalence truncations open import structured-types.pointed-types ``` diff --git a/src/structured-types/dependent-products-wild-monoids.lagda.md b/src/structured-types/dependent-products-wild-monoids.lagda.md index 183ccb58a5..c4cc72f4ab 100644 --- a/src/structured-types/dependent-products-wild-monoids.lagda.md +++ b/src/structured-types/dependent-products-wild-monoids.lagda.md @@ -1,7 +1,15 @@ # Dependent products of wild monoids ```agda -module structured-types.dependent-products-wild-monoids where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module structured-types.dependent-products-wild-monoids + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,16 +17,16 @@ module structured-types.dependent-products-wild-monoids where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-extensionality -open import foundation.homotopies -open import foundation.identity-types +open import foundation.function-extensionality funext +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.unit-type open import foundation.universe-levels -open import structured-types.dependent-products-h-spaces -open import structured-types.h-spaces +open import structured-types.dependent-products-h-spaces funext univalence truncations +open import structured-types.h-spaces funext univalence truncations open import structured-types.pointed-types -open import structured-types.wild-monoids +open import structured-types.wild-monoids funext univalence truncations ```
diff --git a/src/structured-types/dependent-types-equipped-with-automorphisms.lagda.md b/src/structured-types/dependent-types-equipped-with-automorphisms.lagda.md index 5cc34bb515..f95cfbb816 100644 --- a/src/structured-types/dependent-types-equipped-with-automorphisms.lagda.md +++ b/src/structured-types/dependent-types-equipped-with-automorphisms.lagda.md @@ -1,27 +1,35 @@ # Dependent types equipped with automorphisms ```agda -module structured-types.dependent-types-equipped-with-automorphisms where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module structured-types.dependent-types-equipped-with-automorphisms + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.commuting-squares-of-maps +open import foundation.commuting-squares-of-maps funext univalence open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types -open import foundation.equivalence-extensionality -open import foundation.equivalences -open import foundation.function-types +open import foundation.equality-dependent-function-types funext +open import foundation.equivalence-extensionality funext +open import foundation.equivalences funext +open import foundation.function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.identity-types +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.structure-identity-principle -open import foundation.torsorial-type-families -open import foundation.univalence +open import foundation.torsorial-type-families funext univalence truncations +open import foundation.univalence funext univalence open import foundation.universe-levels -open import structured-types.types-equipped-with-automorphisms +open import structured-types.types-equipped-with-automorphisms funext univalence ```
diff --git a/src/structured-types/equivalences-h-spaces.lagda.md b/src/structured-types/equivalences-h-spaces.lagda.md index 3a8285ea5c..fb896ac5de 100644 --- a/src/structured-types/equivalences-h-spaces.lagda.md +++ b/src/structured-types/equivalences-h-spaces.lagda.md @@ -1,31 +1,39 @@ # Equivalences of H-spaces ```agda -module structured-types.equivalences-h-spaces where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module structured-types.equivalences-h-spaces + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.action-on-higher-identifications-functions +open import foundation.action-on-higher-identifications-functions funext open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-identifications -open import foundation.commuting-triangles-of-identifications +open import foundation.commuting-squares-of-identifications funext +open import foundation.commuting-triangles-of-identifications funext open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.path-algebra +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.path-algebra funext open import foundation.universe-levels -open import foundation.whiskering-identifications-concatenation +open import foundation.whiskering-identifications-concatenation funext -open import group-theory.homomorphisms-semigroups +open import group-theory.homomorphisms-semigroups funext univalence truncations -open import structured-types.h-spaces -open import structured-types.morphisms-h-spaces -open import structured-types.pointed-equivalences -open import structured-types.pointed-maps +open import structured-types.h-spaces funext univalence truncations +open import structured-types.morphisms-h-spaces funext univalence truncations +open import structured-types.pointed-equivalences funext univalence truncations +open import structured-types.pointed-maps funext univalence truncations open import structured-types.pointed-types ``` diff --git a/src/structured-types/equivalences-pointed-arrows.lagda.md b/src/structured-types/equivalences-pointed-arrows.lagda.md index 0d1aacbfd7..8fb21cf683 100644 --- a/src/structured-types/equivalences-pointed-arrows.lagda.md +++ b/src/structured-types/equivalences-pointed-arrows.lagda.md @@ -1,23 +1,31 @@ # Equivalences of pointed arrows ```agda -module structured-types.equivalences-pointed-arrows where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module structured-types.equivalences-pointed-arrows + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.equivalences-arrows -open import foundation.function-types -open import foundation.identity-types +open import foundation.equivalences funext +open import foundation.equivalences-arrows funext univalence truncations +open import foundation.function-types funext +open import foundation.identity-types funext open import foundation.universe-levels -open import structured-types.commuting-squares-of-pointed-maps -open import structured-types.pointed-equivalences -open import structured-types.pointed-homotopies -open import structured-types.pointed-maps +open import structured-types.commuting-squares-of-pointed-maps funext univalence truncations +open import structured-types.pointed-equivalences funext univalence truncations +open import structured-types.pointed-homotopies funext univalence truncations +open import structured-types.pointed-maps funext univalence truncations open import structured-types.pointed-types ``` diff --git a/src/structured-types/equivalences-types-equipped-with-automorphisms.lagda.md b/src/structured-types/equivalences-types-equipped-with-automorphisms.lagda.md index a9d7268372..8ca8c9ac05 100644 --- a/src/structured-types/equivalences-types-equipped-with-automorphisms.lagda.md +++ b/src/structured-types/equivalences-types-equipped-with-automorphisms.lagda.md @@ -1,26 +1,34 @@ # Equivalences of types equipped with automorphisms ```agda -module structured-types.equivalences-types-equipped-with-automorphisms where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module structured-types.equivalences-types-equipped-with-automorphisms + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.commuting-squares-of-maps +open import foundation.commuting-squares-of-maps funext univalence open import foundation.dependent-pair-types -open import foundation.equivalence-extensionality -open import foundation.equivalences +open import foundation.equivalence-extensionality funext +open import foundation.equivalences funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.structure-identity-principle -open import foundation.torsorial-type-families -open import foundation.univalence +open import foundation.torsorial-type-families funext univalence truncations +open import foundation.univalence funext univalence open import foundation.universe-levels -open import structured-types.equivalences-types-equipped-with-endomorphisms -open import structured-types.morphisms-types-equipped-with-automorphisms -open import structured-types.types-equipped-with-automorphisms +open import structured-types.equivalences-types-equipped-with-endomorphisms funext univalence truncations +open import structured-types.morphisms-types-equipped-with-automorphisms funext univalence truncations +open import structured-types.types-equipped-with-automorphisms funext univalence ```
diff --git a/src/structured-types/equivalences-types-equipped-with-endomorphisms.lagda.md b/src/structured-types/equivalences-types-equipped-with-endomorphisms.lagda.md index 3b8b45fb50..5654ef8365 100644 --- a/src/structured-types/equivalences-types-equipped-with-endomorphisms.lagda.md +++ b/src/structured-types/equivalences-types-equipped-with-endomorphisms.lagda.md @@ -1,32 +1,41 @@ # Equivalences of types equipped with endomorphisms ```agda -module structured-types.equivalences-types-equipped-with-endomorphisms where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module structured-types.equivalences-types-equipped-with-endomorphisms + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-maps -open import foundation.contractible-types +open import foundation.commuting-squares-of-maps funext univalence +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types +open import foundation.dependent-products-contractible-types funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext open import foundation.structure-identity-principle open import foundation.subtype-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext univalence truncations open import foundation.type-arithmetic-dependent-pair-types -open import foundation.univalence +open import foundation.univalence funext univalence open import foundation.universe-levels -open import structured-types.morphisms-types-equipped-with-endomorphisms -open import structured-types.types-equipped-with-endomorphisms +open import structured-types.morphisms-types-equipped-with-endomorphisms funext univalence truncations +open import structured-types.types-equipped-with-endomorphisms funext univalence ```
diff --git a/src/structured-types/faithful-pointed-maps.lagda.md b/src/structured-types/faithful-pointed-maps.lagda.md index eeb654cf27..ea98d54019 100644 --- a/src/structured-types/faithful-pointed-maps.lagda.md +++ b/src/structured-types/faithful-pointed-maps.lagda.md @@ -1,18 +1,26 @@ # Faithful pointed maps ```agda -module structured-types.faithful-pointed-maps where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module structured-types.faithful-pointed-maps + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.faithful-maps -open import foundation.identity-types +open import foundation.faithful-maps funext +open import foundation.identity-types funext open import foundation.universe-levels -open import structured-types.pointed-maps +open import structured-types.pointed-maps funext univalence truncations open import structured-types.pointed-types ``` diff --git a/src/structured-types/fibers-of-pointed-maps.lagda.md b/src/structured-types/fibers-of-pointed-maps.lagda.md index 3564027bd2..37c806e131 100644 --- a/src/structured-types/fibers-of-pointed-maps.lagda.md +++ b/src/structured-types/fibers-of-pointed-maps.lagda.md @@ -1,17 +1,25 @@ # Fibers of pointed maps ```agda -module structured-types.fibers-of-pointed-maps where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module structured-types.fibers-of-pointed-maps + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.fibers-of-maps +open import foundation.fibers-of-maps funext open import foundation.universe-levels -open import structured-types.pointed-maps +open import structured-types.pointed-maps funext univalence truncations open import structured-types.pointed-types ``` diff --git a/src/structured-types/finite-multiplication-magmas.lagda.md b/src/structured-types/finite-multiplication-magmas.lagda.md index 6c31a6bd9a..ea9ff86e68 100644 --- a/src/structured-types/finite-multiplication-magmas.lagda.md +++ b/src/structured-types/finite-multiplication-magmas.lagda.md @@ -1,7 +1,15 @@ # Finite multiplication in magmas ```agda -module structured-types.finite-multiplication-magmas where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module structured-types.finite-multiplication-magmas + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,16 +17,16 @@ module structured-types.finite-multiplication-magmas where ```agda open import elementary-number-theory.natural-numbers -open import foundation.coproduct-types -open import foundation.equivalences -open import foundation.function-types +open import foundation.coproduct-types funext univalence truncations +open import foundation.equivalences funext +open import foundation.function-types funext open import foundation.unit-type open import foundation.universe-levels -open import structured-types.magmas +open import structured-types.magmas funext univalence -open import univalent-combinatorics.counting -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.counting funext univalence truncations +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/structured-types/function-h-spaces.lagda.md b/src/structured-types/function-h-spaces.lagda.md index 05b8a63e3c..4b529087b5 100644 --- a/src/structured-types/function-h-spaces.lagda.md +++ b/src/structured-types/function-h-spaces.lagda.md @@ -1,18 +1,26 @@ # Function H-spaces ```agda -module structured-types.function-h-spaces where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module structured-types.function-h-spaces + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.unital-binary-operations open import foundation.universe-levels -open import structured-types.dependent-products-h-spaces -open import structured-types.h-spaces +open import structured-types.dependent-products-h-spaces funext univalence truncations +open import structured-types.h-spaces funext univalence truncations open import structured-types.pointed-types ``` diff --git a/src/structured-types/function-magmas.lagda.md b/src/structured-types/function-magmas.lagda.md index e5eef3f42a..6f3fd41008 100644 --- a/src/structured-types/function-magmas.lagda.md +++ b/src/structured-types/function-magmas.lagda.md @@ -1,7 +1,13 @@ # Function magmas ```agda -module structured-types.function-magmas where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module structured-types.function-magmas + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports @@ -10,7 +16,7 @@ module structured-types.function-magmas where open import foundation.dependent-pair-types open import foundation.universe-levels -open import structured-types.magmas +open import structured-types.magmas funext univalence ```
diff --git a/src/structured-types/function-wild-monoids.lagda.md b/src/structured-types/function-wild-monoids.lagda.md index 154a0e8116..a95c5374a8 100644 --- a/src/structured-types/function-wild-monoids.lagda.md +++ b/src/structured-types/function-wild-monoids.lagda.md @@ -1,19 +1,27 @@ # Function wild monoids ```agda -module structured-types.function-wild-monoids where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module structured-types.function-wild-monoids + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import structured-types.dependent-products-wild-monoids -open import structured-types.h-spaces +open import structured-types.dependent-products-wild-monoids funext univalence truncations +open import structured-types.h-spaces funext univalence truncations open import structured-types.pointed-types -open import structured-types.wild-monoids +open import structured-types.wild-monoids funext univalence truncations ```
diff --git a/src/structured-types/h-spaces.lagda.md b/src/structured-types/h-spaces.lagda.md index be217b8539..302a53cce0 100644 --- a/src/structured-types/h-spaces.lagda.md +++ b/src/structured-types/h-spaces.lagda.md @@ -1,7 +1,15 @@ # H-spaces ```agda -module structured-types.h-spaces where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module structured-types.h-spaces + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,24 +18,24 @@ module structured-types.h-spaces where open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalences +open import foundation.equivalences funext open import foundation.evaluation-functions -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.identity-types +open import foundation.function-extensionality funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.identity-types funext open import foundation.type-arithmetic-dependent-pair-types open import foundation.unital-binary-operations open import foundation.universe-levels -open import foundation.whiskering-identifications-concatenation +open import foundation.whiskering-identifications-concatenation funext -open import foundation-core.endomorphisms +open import foundation-core.endomorphisms funext univalence -open import structured-types.magmas -open import structured-types.noncoherent-h-spaces -open import structured-types.pointed-homotopies -open import structured-types.pointed-maps -open import structured-types.pointed-sections +open import structured-types.magmas funext univalence +open import structured-types.noncoherent-h-spaces funext +open import structured-types.pointed-homotopies funext univalence truncations +open import structured-types.pointed-maps funext univalence truncations +open import structured-types.pointed-sections funext univalence truncations open import structured-types.pointed-types ``` diff --git a/src/structured-types/initial-pointed-type-equipped-with-automorphism.lagda.md b/src/structured-types/initial-pointed-type-equipped-with-automorphism.lagda.md index cab4124961..5726b8a6c9 100644 --- a/src/structured-types/initial-pointed-type-equipped-with-automorphism.lagda.md +++ b/src/structured-types/initial-pointed-type-equipped-with-automorphism.lagda.md @@ -1,7 +1,15 @@ # The initial pointed type equipped with an automorphism ```agda -module structured-types.initial-pointed-type-equipped-with-automorphism where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module structured-types.initial-pointed-type-equipped-with-automorphism + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -11,18 +19,19 @@ open import elementary-number-theory.integers open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.contractible-types -open import foundation.coproduct-types +open import foundation.contractible-types funext univalence +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.homotopies -open import foundation.identity-types -open import foundation.iterating-automorphisms -open import foundation.transposition-identifications-along-equivalences +open import foundation.dependent-products-contractible-types funext +open import foundation.equivalences funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.iterating-automorphisms funext univalence truncations +open import foundation.transposition-identifications-along-equivalences funext open import foundation.unit-type open import foundation.universe-levels -open import structured-types.pointed-types-equipped-with-automorphisms +open import structured-types.pointed-types-equipped-with-automorphisms funext univalence truncations ```
diff --git a/src/structured-types/involutive-type-of-h-space-structures.lagda.md b/src/structured-types/involutive-type-of-h-space-structures.lagda.md index a9109305c2..2ec8e75d98 100644 --- a/src/structured-types/involutive-type-of-h-space-structures.lagda.md +++ b/src/structured-types/involutive-type-of-h-space-structures.lagda.md @@ -1,7 +1,15 @@ # The involutive type of H-space structures on a pointed type ```agda -module structured-types.involutive-type-of-h-space-structures where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module structured-types.involutive-type-of-h-space-structures + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,25 +17,26 @@ module structured-types.involutive-type-of-h-space-structures where ```agda open import foundation.action-on-identifications-functions open import foundation.binary-transport -open import foundation.constant-maps -open import foundation.contractible-types +open import foundation.constant-maps funext univalence truncations +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types -open import foundation.equivalences -open import foundation.functoriality-dependent-pair-types +open import foundation.dependent-products-contractible-types funext +open import foundation.equality-dependent-function-types funext +open import foundation.equivalences funext +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext open import foundation.structure-identity-principle -open import foundation.symmetric-identity-types -open import foundation.torsorial-type-families +open import foundation.symmetric-identity-types funext univalence truncations +open import foundation.torsorial-type-families funext univalence truncations open import foundation.universe-levels -open import structured-types.constant-pointed-maps +open import structured-types.constant-pointed-maps funext univalence truncations open import structured-types.pointed-types -open import univalent-combinatorics.2-element-types +open import univalent-combinatorics.2-element-types funext univalence truncations ```
diff --git a/src/structured-types/involutive-types.lagda.md b/src/structured-types/involutive-types.lagda.md index 14c1459d5d..5822323628 100644 --- a/src/structured-types/involutive-types.lagda.md +++ b/src/structured-types/involutive-types.lagda.md @@ -1,17 +1,25 @@ # Involutive types ```agda -module structured-types.involutive-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module structured-types.involutive-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences +open import foundation.equivalences funext open import foundation.universe-levels -open import univalent-combinatorics.2-element-types +open import univalent-combinatorics.2-element-types funext univalence truncations ```
diff --git a/src/structured-types/iterated-cartesian-products-types-equipped-with-endomorphisms.lagda.md b/src/structured-types/iterated-cartesian-products-types-equipped-with-endomorphisms.lagda.md index 58ed426a9e..160999c52a 100644 --- a/src/structured-types/iterated-cartesian-products-types-equipped-with-endomorphisms.lagda.md +++ b/src/structured-types/iterated-cartesian-products-types-equipped-with-endomorphisms.lagda.md @@ -13,8 +13,8 @@ open import foundation.universe-levels open import lists.lists -open import structured-types.cartesian-products-types-equipped-with-endomorphisms -open import structured-types.types-equipped-with-endomorphisms +open import structured-types.cartesian-products-types-equipped-with-endomorphisms funext univalence +open import structured-types.types-equipped-with-endomorphisms funext univalence ```
diff --git a/src/structured-types/iterated-pointed-cartesian-product-types.lagda.md b/src/structured-types/iterated-pointed-cartesian-product-types.lagda.md index 085abff691..b16077eb7e 100644 --- a/src/structured-types/iterated-pointed-cartesian-product-types.lagda.md +++ b/src/structured-types/iterated-pointed-cartesian-product-types.lagda.md @@ -1,19 +1,28 @@ # Iterated cartesian products of pointed types ```agda -module structured-types.iterated-pointed-cartesian-product-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module structured-types.iterated-pointed-cartesian-product-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types +open import foundation.raising-universe-levels-unit-type open import foundation.unit-type open import foundation.universe-levels open import lists.lists -open import structured-types.pointed-cartesian-product-types +open import structured-types.pointed-cartesian-product-types funext univalence truncations open import structured-types.pointed-types ``` diff --git a/src/structured-types/magmas.lagda.md b/src/structured-types/magmas.lagda.md index 13372059eb..d7880df4c7 100644 --- a/src/structured-types/magmas.lagda.md +++ b/src/structured-types/magmas.lagda.md @@ -1,15 +1,21 @@ # Magmas ```agda -module structured-types.magmas where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module structured-types.magmas + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.unital-binary-operations open import foundation.universe-levels ``` diff --git a/src/structured-types/mere-equivalences-types-equipped-with-endomorphisms.lagda.md b/src/structured-types/mere-equivalences-types-equipped-with-endomorphisms.lagda.md index 0d43b47932..f60de9c767 100644 --- a/src/structured-types/mere-equivalences-types-equipped-with-endomorphisms.lagda.md +++ b/src/structured-types/mere-equivalences-types-equipped-with-endomorphisms.lagda.md @@ -1,25 +1,34 @@ # Mere equivalences of types equipped with endomorphisms ```agda -module structured-types.mere-equivalences-types-equipped-with-endomorphisms where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module structured-types.mere-equivalences-types-equipped-with-endomorphisms + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types -open import foundation.propositional-truncations -open import foundation.propositions +open import foundation.identity-types funext +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence open import foundation.subtype-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext univalence truncations open import foundation.universe-levels -open import structured-types.equivalences-types-equipped-with-endomorphisms -open import structured-types.types-equipped-with-endomorphisms +open import structured-types.equivalences-types-equipped-with-endomorphisms funext univalence truncations +open import structured-types.types-equipped-with-endomorphisms funext univalence ```
diff --git a/src/structured-types/morphisms-h-spaces.lagda.md b/src/structured-types/morphisms-h-spaces.lagda.md index 15fe75ebf3..cc3fef9b14 100644 --- a/src/structured-types/morphisms-h-spaces.lagda.md +++ b/src/structured-types/morphisms-h-spaces.lagda.md @@ -1,29 +1,37 @@ # Morphisms of H-spaces ```agda -module structured-types.morphisms-h-spaces where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module structured-types.morphisms-h-spaces + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.action-on-higher-identifications-functions +open import foundation.action-on-higher-identifications-functions funext open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-identifications -open import foundation.commuting-triangles-of-identifications +open import foundation.commuting-squares-of-identifications funext +open import foundation.commuting-triangles-of-identifications funext open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.path-algebra +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.path-algebra funext open import foundation.universe-levels -open import foundation.whiskering-identifications-concatenation +open import foundation.whiskering-identifications-concatenation funext -open import group-theory.homomorphisms-semigroups +open import group-theory.homomorphisms-semigroups funext univalence truncations -open import structured-types.h-spaces -open import structured-types.pointed-maps +open import structured-types.h-spaces funext univalence truncations +open import structured-types.pointed-maps funext univalence truncations open import structured-types.pointed-types ``` diff --git a/src/structured-types/morphisms-magmas.lagda.md b/src/structured-types/morphisms-magmas.lagda.md index e5d3920e3b..55f86d8ee6 100644 --- a/src/structured-types/morphisms-magmas.lagda.md +++ b/src/structured-types/morphisms-magmas.lagda.md @@ -1,17 +1,23 @@ # Morphisms of magmas ```agda -module structured-types.morphisms-magmas where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module structured-types.morphisms-magmas + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import structured-types.magmas +open import structured-types.magmas funext univalence ```
diff --git a/src/structured-types/morphisms-pointed-arrows.lagda.md b/src/structured-types/morphisms-pointed-arrows.lagda.md index a7f8e2d3fe..0a57c59873 100644 --- a/src/structured-types/morphisms-pointed-arrows.lagda.md +++ b/src/structured-types/morphisms-pointed-arrows.lagda.md @@ -1,42 +1,51 @@ # Morphisms of pointed arrows ```agda -module structured-types.morphisms-pointed-arrows where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module structured-types.morphisms-pointed-arrows + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-homotopies -open import foundation.commuting-squares-of-identifications -open import foundation.commuting-triangles-of-identifications -open import foundation.contractible-types +open import foundation.commuting-squares-of-homotopies funext +open import foundation.commuting-squares-of-identifications funext +open import foundation.commuting-triangles-of-identifications funext +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.functoriality-dependent-pair-types +open import foundation.dependent-products-contractible-types funext +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopy-induction -open import foundation.morphisms-arrows -open import foundation.path-algebra +open import foundation.homotopy-induction funext +open import foundation.morphisms-arrows funext +open import foundation.path-algebra funext open import foundation.structure-identity-principle open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import foundation-core.commuting-squares-of-maps +open import foundation-core.commuting-squares-of-maps funext open import foundation-core.equivalences open import foundation-core.function-types open import foundation-core.homotopies open import foundation-core.identity-types open import foundation-core.torsorial-type-families -open import structured-types.commuting-squares-of-pointed-homotopies -open import structured-types.commuting-squares-of-pointed-maps -open import structured-types.pointed-2-homotopies -open import structured-types.pointed-homotopies -open import structured-types.pointed-maps +open import structured-types.commuting-squares-of-pointed-homotopies funext univalence truncations +open import structured-types.commuting-squares-of-pointed-maps funext univalence truncations +open import structured-types.pointed-2-homotopies funext univalence truncations +open import structured-types.pointed-homotopies funext univalence truncations +open import structured-types.pointed-maps funext univalence truncations open import structured-types.pointed-types -open import structured-types.whiskering-pointed-2-homotopies-concatenation -open import structured-types.whiskering-pointed-homotopies-composition +open import structured-types.whiskering-pointed-2-homotopies-concatenation funext univalence truncations +open import structured-types.whiskering-pointed-homotopies-composition funext univalence truncations ```
diff --git a/src/structured-types/morphisms-twisted-pointed-arrows.lagda.md b/src/structured-types/morphisms-twisted-pointed-arrows.lagda.md index 42373c4872..6756ef24ca 100644 --- a/src/structured-types/morphisms-twisted-pointed-arrows.lagda.md +++ b/src/structured-types/morphisms-twisted-pointed-arrows.lagda.md @@ -1,20 +1,28 @@ # Morphisms of twisted pointed arrows ```agda -module structured-types.morphisms-twisted-pointed-arrows where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module structured-types.morphisms-twisted-pointed-arrows + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.identity-types +open import foundation.function-types funext +open import foundation.identity-types funext open import foundation.morphisms-twisted-arrows open import foundation.universe-levels -open import structured-types.pointed-homotopies -open import structured-types.pointed-maps +open import structured-types.pointed-homotopies funext univalence truncations +open import structured-types.pointed-maps funext univalence truncations open import structured-types.pointed-types ``` diff --git a/src/structured-types/morphisms-types-equipped-with-automorphisms.lagda.md b/src/structured-types/morphisms-types-equipped-with-automorphisms.lagda.md index 2f74c32b78..0833ef9d91 100644 --- a/src/structured-types/morphisms-types-equipped-with-automorphisms.lagda.md +++ b/src/structured-types/morphisms-types-equipped-with-automorphisms.lagda.md @@ -1,20 +1,28 @@ # Morphisms of types equipped with automorphisms ```agda -module structured-types.morphisms-types-equipped-with-automorphisms where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module structured-types.morphisms-types-equipped-with-automorphisms + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.commuting-squares-of-maps -open import foundation.equivalences -open import foundation.identity-types -open import foundation.torsorial-type-families +open import foundation.commuting-squares-of-maps funext univalence +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.torsorial-type-families funext univalence truncations open import foundation.universe-levels -open import structured-types.morphisms-types-equipped-with-endomorphisms -open import structured-types.types-equipped-with-automorphisms +open import structured-types.morphisms-types-equipped-with-endomorphisms funext univalence truncations +open import structured-types.types-equipped-with-automorphisms funext univalence ```
diff --git a/src/structured-types/morphisms-types-equipped-with-endomorphisms.lagda.md b/src/structured-types/morphisms-types-equipped-with-endomorphisms.lagda.md index 3215246b06..148f819dac 100644 --- a/src/structured-types/morphisms-types-equipped-with-endomorphisms.lagda.md +++ b/src/structured-types/morphisms-types-equipped-with-endomorphisms.lagda.md @@ -1,27 +1,36 @@ # Morphisms of types equipped with endomorphisms ```agda -module structured-types.morphisms-types-equipped-with-endomorphisms where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module structured-types.morphisms-types-equipped-with-endomorphisms + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.commuting-squares-of-maps -open import foundation.contractible-types +open import foundation.commuting-squares-of-maps funext univalence +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.functoriality-dependent-pair-types +open import foundation.dependent-products-contractible-types funext +open import foundation.equivalences funext +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext open import foundation.structure-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext univalence truncations open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import structured-types.types-equipped-with-endomorphisms +open import structured-types.types-equipped-with-endomorphisms funext univalence ```
diff --git a/src/structured-types/morphisms-wild-monoids.lagda.md b/src/structured-types/morphisms-wild-monoids.lagda.md index 93df4f6dd1..6578c47948 100644 --- a/src/structured-types/morphisms-wild-monoids.lagda.md +++ b/src/structured-types/morphisms-wild-monoids.lagda.md @@ -1,21 +1,29 @@ # Morphisms of wild monoids ```agda -module structured-types.morphisms-wild-monoids where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module structured-types.morphisms-wild-monoids + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import group-theory.homomorphisms-semigroups +open import group-theory.homomorphisms-semigroups funext univalence truncations -open import structured-types.morphisms-h-spaces -open import structured-types.pointed-maps -open import structured-types.wild-monoids +open import structured-types.morphisms-h-spaces funext univalence truncations +open import structured-types.pointed-maps funext univalence truncations +open import structured-types.wild-monoids funext univalence truncations ```
diff --git a/src/structured-types/noncoherent-h-spaces.lagda.md b/src/structured-types/noncoherent-h-spaces.lagda.md index bf3ba3b5d1..efc52f9f69 100644 --- a/src/structured-types/noncoherent-h-spaces.lagda.md +++ b/src/structured-types/noncoherent-h-spaces.lagda.md @@ -1,14 +1,18 @@ # Noncoherent H-spaces ```agda -module structured-types.noncoherent-h-spaces where +open import foundation.function-extensionality-axiom + +module structured-types.noncoherent-h-spaces + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.unital-binary-operations open import foundation.universe-levels diff --git a/src/structured-types/opposite-pointed-spans.lagda.md b/src/structured-types/opposite-pointed-spans.lagda.md index 2c29bc256f..28496e2094 100644 --- a/src/structured-types/opposite-pointed-spans.lagda.md +++ b/src/structured-types/opposite-pointed-spans.lagda.md @@ -1,7 +1,15 @@ # Opposite pointed spans ```agda -module structured-types.opposite-pointed-spans where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module structured-types.opposite-pointed-spans + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,7 +18,7 @@ module structured-types.opposite-pointed-spans where open import foundation.dependent-pair-types open import foundation.universe-levels -open import structured-types.pointed-spans +open import structured-types.pointed-spans funext univalence truncations open import structured-types.pointed-types ``` diff --git a/src/structured-types/pointed-2-homotopies.lagda.md b/src/structured-types/pointed-2-homotopies.lagda.md index 7b40b04004..8f25fc2ae5 100644 --- a/src/structured-types/pointed-2-homotopies.lagda.md +++ b/src/structured-types/pointed-2-homotopies.lagda.md @@ -1,7 +1,15 @@ # Pointed `2`-homotopies ```agda -module structured-types.pointed-2-homotopies where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module structured-types.pointed-2-homotopies + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,27 +17,28 @@ module structured-types.pointed-2-homotopies where ```agda open import foundation.action-on-identifications-functions open import foundation.binary-equivalences -open import foundation.commuting-triangles-of-identifications -open import foundation.contractible-types +open import foundation.commuting-triangles-of-identifications funext +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.functoriality-dependent-pair-types +open import foundation.dependent-products-contractible-types funext +open import foundation.equivalences funext +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types -open import foundation.path-algebra +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext +open import foundation.path-algebra funext open import foundation.structure-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext univalence truncations open import foundation.universe-levels -open import foundation.whiskering-identifications-concatenation +open import foundation.whiskering-identifications-concatenation funext -open import structured-types.pointed-dependent-functions +open import structured-types.pointed-dependent-functions funext open import structured-types.pointed-families-of-types -open import structured-types.pointed-homotopies -open import structured-types.pointed-maps +open import structured-types.pointed-homotopies funext univalence truncations +open import structured-types.pointed-maps funext univalence truncations open import structured-types.pointed-types -open import structured-types.uniform-pointed-homotopies +open import structured-types.uniform-pointed-homotopies funext univalence truncations ```
diff --git a/src/structured-types/pointed-cartesian-product-types.lagda.md b/src/structured-types/pointed-cartesian-product-types.lagda.md index 6e40cdb641..46e7333e7a 100644 --- a/src/structured-types/pointed-cartesian-product-types.lagda.md +++ b/src/structured-types/pointed-cartesian-product-types.lagda.md @@ -1,21 +1,29 @@ # Pointed cartesian product types ```agda -module structured-types.pointed-cartesian-product-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module structured-types.pointed-cartesian-product-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types open import foundation.equality-cartesian-product-types -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.universe-levels -open import structured-types.pointed-maps +open import structured-types.pointed-maps funext univalence truncations open import structured-types.pointed-types ``` diff --git a/src/structured-types/pointed-dependent-functions.lagda.md b/src/structured-types/pointed-dependent-functions.lagda.md index 7df9e3085d..d6e97715dd 100644 --- a/src/structured-types/pointed-dependent-functions.lagda.md +++ b/src/structured-types/pointed-dependent-functions.lagda.md @@ -1,16 +1,20 @@ # Pointed dependent functions ```agda -module structured-types.pointed-dependent-functions where +open import foundation.function-extensionality-axiom + +module structured-types.pointed-dependent-functions + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.fibers-of-maps -open import foundation.function-types -open import foundation.identity-types +open import foundation.fibers-of-maps funext +open import foundation.function-types funext +open import foundation.identity-types funext open import foundation.universe-levels open import structured-types.pointed-families-of-types diff --git a/src/structured-types/pointed-equivalences.lagda.md b/src/structured-types/pointed-equivalences.lagda.md index 0a852924d2..5c5696ee5d 100644 --- a/src/structured-types/pointed-equivalences.lagda.md +++ b/src/structured-types/pointed-equivalences.lagda.md @@ -1,7 +1,15 @@ # Pointed equivalences ```agda -module structured-types.pointed-equivalences where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module structured-types.pointed-equivalences + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,41 +17,34 @@ module structured-types.pointed-equivalences where ```agda open import foundation.action-on-identifications-functions open import foundation.binary-equivalences -open import foundation.cartesian-product-types -open import foundation.commuting-squares-of-identifications -open import foundation.contractible-maps -open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalences -open import foundation.fibers-of-maps -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.path-algebra -open import foundation.propositions -open import foundation.retractions -open import foundation.sections +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.path-algebra funext +open import foundation.propositions funext univalence +open import foundation.retractions funext +open import foundation.sections funext open import foundation.structure-identity-principle -open import foundation.torsorial-type-families -open import foundation.transposition-identifications-along-equivalences +open import foundation.torsorial-type-families funext univalence truncations open import foundation.type-arithmetic-dependent-pair-types -open import foundation.univalence +open import foundation.univalence funext univalence open import foundation.universe-levels -open import foundation.whiskering-identifications-concatenation +open import foundation.whiskering-identifications-concatenation funext -open import structured-types.pointed-homotopies -open import structured-types.pointed-maps -open import structured-types.pointed-retractions -open import structured-types.pointed-sections +open import structured-types.pointed-homotopies funext univalence truncations +open import structured-types.pointed-maps funext univalence truncations +open import structured-types.pointed-retractions funext univalence truncations +open import structured-types.pointed-sections funext univalence truncations open import structured-types.pointed-types -open import structured-types.postcomposition-pointed-maps -open import structured-types.precomposition-pointed-maps -open import structured-types.universal-property-pointed-equivalences -open import structured-types.whiskering-pointed-homotopies-composition +open import structured-types.postcomposition-pointed-maps funext univalence truncations +open import structured-types.precomposition-pointed-maps funext univalence truncations +open import structured-types.universal-property-pointed-equivalences funext univalence truncations +open import structured-types.whiskering-pointed-homotopies-composition funext univalence truncations ```
diff --git a/src/structured-types/pointed-homotopies.lagda.md b/src/structured-types/pointed-homotopies.lagda.md index ad8f346c7d..0305726ccc 100644 --- a/src/structured-types/pointed-homotopies.lagda.md +++ b/src/structured-types/pointed-homotopies.lagda.md @@ -1,38 +1,40 @@ # Pointed homotopies ```agda -module structured-types.pointed-homotopies where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module structured-types.pointed-homotopies + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.action-on-higher-identifications-functions -open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions open import foundation.binary-equivalences -open import foundation.commuting-triangles-of-identifications -open import foundation.contractible-types +open import foundation.commuting-triangles-of-identifications funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types -open import foundation.path-algebra +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext open import foundation.structure-identity-principle open import foundation.universe-levels -open import foundation.whiskering-homotopies-composition -open import foundation.whiskering-identifications-concatenation +open import foundation.whiskering-identifications-concatenation funext open import foundation-core.torsorial-type-families -open import structured-types.pointed-dependent-functions +open import structured-types.pointed-dependent-functions funext open import structured-types.pointed-families-of-types -open import structured-types.pointed-maps +open import structured-types.pointed-maps funext univalence truncations open import structured-types.pointed-types ``` diff --git a/src/structured-types/pointed-isomorphisms.lagda.md b/src/structured-types/pointed-isomorphisms.lagda.md index f38534a262..f5ab32398e 100644 --- a/src/structured-types/pointed-isomorphisms.lagda.md +++ b/src/structured-types/pointed-isomorphisms.lagda.md @@ -1,30 +1,40 @@ # Pointed isomorphisms ```agda -module structured-types.pointed-isomorphisms where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module structured-types.pointed-isomorphisms + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.cartesian-product-types -open import foundation.contractible-maps -open import foundation.contractible-types +open import foundation.cartesian-product-types funext univalence +open import foundation.contractible-maps funext +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.propositions -open import foundation.retractions -open import foundation.sections +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.propositions funext univalence +open import foundation.retractions funext +open import foundation.sections funext open import foundation.structure-identity-principle open import foundation.universe-levels -open import structured-types.pointed-equivalences -open import structured-types.pointed-homotopies -open import structured-types.pointed-maps -open import structured-types.pointed-retractions -open import structured-types.pointed-sections +open import structured-types.pointed-equivalences funext univalence truncations +open import structured-types.pointed-homotopies funext univalence truncations +open import structured-types.pointed-maps funext univalence truncations +open import structured-types.pointed-retractions funext univalence truncations +open import structured-types.pointed-sections funext univalence truncations open import structured-types.pointed-types ``` diff --git a/src/structured-types/pointed-maps.lagda.md b/src/structured-types/pointed-maps.lagda.md index 1a8de69535..a2186567b2 100644 --- a/src/structured-types/pointed-maps.lagda.md +++ b/src/structured-types/pointed-maps.lagda.md @@ -1,7 +1,15 @@ # Pointed maps ```agda -module structured-types.pointed-maps where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module structured-types.pointed-maps + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,14 +17,14 @@ module structured-types.pointed-maps where ```agda open import foundation.action-on-identifications-dependent-functions open import foundation.action-on-identifications-functions -open import foundation.constant-maps +open import foundation.constant-maps funext univalence truncations open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.identity-types +open import foundation.function-types funext +open import foundation.identity-types funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import structured-types.pointed-dependent-functions +open import structured-types.pointed-dependent-functions funext open import structured-types.pointed-families-of-types open import structured-types.pointed-types ``` diff --git a/src/structured-types/pointed-retractions.lagda.md b/src/structured-types/pointed-retractions.lagda.md index d4b837ac66..dcde79b153 100644 --- a/src/structured-types/pointed-retractions.lagda.md +++ b/src/structured-types/pointed-retractions.lagda.md @@ -1,24 +1,32 @@ # Pointed retractions of pointed maps ```agda -module structured-types.pointed-retractions where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module structured-types.pointed-retractions + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-identifications +open import foundation.commuting-squares-of-identifications funext open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels open import foundation-core.contractible-maps open import foundation-core.contractible-types open import foundation-core.retractions -open import structured-types.pointed-homotopies -open import structured-types.pointed-maps +open import structured-types.pointed-homotopies funext univalence truncations +open import structured-types.pointed-maps funext univalence truncations open import structured-types.pointed-types ``` diff --git a/src/structured-types/pointed-sections.lagda.md b/src/structured-types/pointed-sections.lagda.md index a3dfdb69f3..cae7541da4 100644 --- a/src/structured-types/pointed-sections.lagda.md +++ b/src/structured-types/pointed-sections.lagda.md @@ -1,19 +1,27 @@ # Pointed sections of pointed maps ```agda -module structured-types.pointed-sections where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module structured-types.pointed-sections + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.sections +open import foundation.identity-types funext +open import foundation.sections funext open import foundation.universe-levels -open import structured-types.pointed-homotopies -open import structured-types.pointed-maps +open import structured-types.pointed-homotopies funext univalence truncations +open import structured-types.pointed-maps funext univalence truncations open import structured-types.pointed-types ``` diff --git a/src/structured-types/pointed-span-diagrams.lagda.md b/src/structured-types/pointed-span-diagrams.lagda.md index 95f98ce716..4b897a1259 100644 --- a/src/structured-types/pointed-span-diagrams.lagda.md +++ b/src/structured-types/pointed-span-diagrams.lagda.md @@ -1,20 +1,28 @@ # Pointed span diagrams ```agda -module structured-types.pointed-span-diagrams where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module structured-types.pointed-span-diagrams + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.morphisms-arrows +open import foundation.identity-types funext +open import foundation.morphisms-arrows funext open import foundation.universe-levels -open import structured-types.morphisms-pointed-arrows -open import structured-types.pointed-maps -open import structured-types.pointed-spans +open import structured-types.morphisms-pointed-arrows funext univalence truncations +open import structured-types.pointed-maps funext univalence truncations +open import structured-types.pointed-spans funext univalence truncations open import structured-types.pointed-types ``` diff --git a/src/structured-types/pointed-spans.lagda.md b/src/structured-types/pointed-spans.lagda.md index 125e01bee5..60418b3125 100644 --- a/src/structured-types/pointed-spans.lagda.md +++ b/src/structured-types/pointed-spans.lagda.md @@ -1,19 +1,27 @@ # Pointed spans ```agda -module structured-types.pointed-spans where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module structured-types.pointed-spans + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.spans open import foundation.universe-levels -open import structured-types.pointed-maps +open import structured-types.pointed-maps funext univalence truncations open import structured-types.pointed-types ``` diff --git a/src/structured-types/pointed-types-equipped-with-automorphisms.lagda.md b/src/structured-types/pointed-types-equipped-with-automorphisms.lagda.md index b97e8e7ae3..96765cfeca 100644 --- a/src/structured-types/pointed-types-equipped-with-automorphisms.lagda.md +++ b/src/structured-types/pointed-types-equipped-with-automorphisms.lagda.md @@ -1,26 +1,35 @@ # Pointed types equipped with automorphisms ```agda -module structured-types.pointed-types-equipped-with-automorphisms where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module structured-types.pointed-types-equipped-with-automorphisms + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.automorphisms -open import foundation.cartesian-product-types -open import foundation.contractible-types +open import foundation.automorphisms funext univalence +open import foundation.cartesian-product-types funext univalence +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types +open import foundation.dependent-products-contractible-types funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext open import foundation.structure-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext univalence truncations open import foundation.universe-levels open import structured-types.pointed-types diff --git a/src/structured-types/pointed-unit-type.lagda.md b/src/structured-types/pointed-unit-type.lagda.md index af2130cf0b..6315ebdba3 100644 --- a/src/structured-types/pointed-unit-type.lagda.md +++ b/src/structured-types/pointed-unit-type.lagda.md @@ -1,19 +1,27 @@ # The pointed unit type ```agda -module structured-types.pointed-unit-type where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module structured-types.pointed-unit-type + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.unit-type open import foundation.universe-levels -open import structured-types.pointed-homotopies -open import structured-types.pointed-maps +open import structured-types.pointed-homotopies funext univalence truncations +open import structured-types.pointed-maps funext univalence truncations open import structured-types.pointed-types ``` diff --git a/src/structured-types/pointed-universal-property-contractible-types.lagda.md b/src/structured-types/pointed-universal-property-contractible-types.lagda.md index 296b91ee4b..4bdd2f405c 100644 --- a/src/structured-types/pointed-universal-property-contractible-types.lagda.md +++ b/src/structured-types/pointed-universal-property-contractible-types.lagda.md @@ -1,24 +1,33 @@ # Universal property of contractible types with respect to pointed types and maps ```agda -module structured-types.pointed-universal-property-contractible-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module structured-types.pointed-universal-property-contractible-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.contractible-types +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.functoriality-dependent-pair-types -open import foundation.identity-types -open import foundation.torsorial-type-families +open import foundation.dependent-products-contractible-types funext +open import foundation.equivalences funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.identity-types funext +open import foundation.torsorial-type-families funext univalence truncations open import foundation.type-arithmetic-dependent-pair-types -open import foundation.universal-property-contractible-types +open import foundation.universal-property-contractible-types funext open import foundation.universe-levels -open import structured-types.pointed-maps +open import structured-types.pointed-maps funext univalence truncations open import structured-types.pointed-types ``` diff --git a/src/structured-types/postcomposition-pointed-maps.lagda.md b/src/structured-types/postcomposition-pointed-maps.lagda.md index 03629c2259..00084cead6 100644 --- a/src/structured-types/postcomposition-pointed-maps.lagda.md +++ b/src/structured-types/postcomposition-pointed-maps.lagda.md @@ -1,7 +1,15 @@ # Postcomposition of pointed maps ```agda -module structured-types.postcomposition-pointed-maps where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module structured-types.postcomposition-pointed-maps + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,7 +17,7 @@ module structured-types.postcomposition-pointed-maps where ```agda open import foundation.universe-levels -open import structured-types.pointed-maps +open import structured-types.pointed-maps funext univalence truncations open import structured-types.pointed-types ``` diff --git a/src/structured-types/precomposition-pointed-maps.lagda.md b/src/structured-types/precomposition-pointed-maps.lagda.md index da91cbc088..3aa379b860 100644 --- a/src/structured-types/precomposition-pointed-maps.lagda.md +++ b/src/structured-types/precomposition-pointed-maps.lagda.md @@ -1,7 +1,15 @@ # Precomposition of pointed maps ```agda -module structured-types.precomposition-pointed-maps where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module structured-types.precomposition-pointed-maps + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,7 +17,7 @@ module structured-types.precomposition-pointed-maps where ```agda open import foundation.universe-levels -open import structured-types.pointed-maps +open import structured-types.pointed-maps funext univalence truncations open import structured-types.pointed-types ``` diff --git a/src/structured-types/sets-equipped-with-automorphisms.lagda.md b/src/structured-types/sets-equipped-with-automorphisms.lagda.md index 2d0431fa3f..03a9c3a828 100644 --- a/src/structured-types/sets-equipped-with-automorphisms.lagda.md +++ b/src/structured-types/sets-equipped-with-automorphisms.lagda.md @@ -1,17 +1,23 @@ # Sets equipped with automorphisms ```agda -module structured-types.sets-equipped-with-automorphisms where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module structured-types.sets-equipped-with-automorphisms + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda -open import foundation.automorphisms +open import foundation.automorphisms funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.sets +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.sets funext univalence open import foundation.universe-levels ``` diff --git a/src/structured-types/small-pointed-types.lagda.md b/src/structured-types/small-pointed-types.lagda.md index c1ee5d36fa..1c18da50e4 100644 --- a/src/structured-types/small-pointed-types.lagda.md +++ b/src/structured-types/small-pointed-types.lagda.md @@ -1,22 +1,32 @@ # Small pointed types ```agda -module structured-types.small-pointed-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module structured-types.small-pointed-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.contractible-types +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.functoriality-dependent-pair-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.small-types +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.small-types funext univalence truncations open import foundation.universe-levels -open import structured-types.pointed-equivalences +open import structured-types.pointed-equivalences funext univalence truncations open import structured-types.pointed-types ``` diff --git a/src/structured-types/symmetric-elements-involutive-types.lagda.md b/src/structured-types/symmetric-elements-involutive-types.lagda.md index d9f5ee8705..6f0b766430 100644 --- a/src/structured-types/symmetric-elements-involutive-types.lagda.md +++ b/src/structured-types/symmetric-elements-involutive-types.lagda.md @@ -1,7 +1,15 @@ # Symmetric elements of involutive types ```agda -module structured-types.symmetric-elements-involutive-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module structured-types.symmetric-elements-involutive-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,9 +17,9 @@ module structured-types.symmetric-elements-involutive-types where ```agda open import foundation.universe-levels -open import structured-types.involutive-types +open import structured-types.involutive-types funext univalence truncations -open import univalent-combinatorics.2-element-types +open import univalent-combinatorics.2-element-types funext univalence truncations ```
diff --git a/src/structured-types/symmetric-h-spaces.lagda.md b/src/structured-types/symmetric-h-spaces.lagda.md index 95d5e73667..fb033a3cd0 100644 --- a/src/structured-types/symmetric-h-spaces.lagda.md +++ b/src/structured-types/symmetric-h-spaces.lagda.md @@ -1,19 +1,27 @@ # Symmetric H-spaces ```agda -module structured-types.symmetric-h-spaces where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module structured-types.symmetric-h-spaces + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.symmetric-operations +open import foundation.symmetric-operations funext univalence truncations open import foundation.universe-levels -open import structured-types.involutive-type-of-h-space-structures +open import structured-types.involutive-type-of-h-space-structures funext univalence truncations open import structured-types.pointed-types -open import structured-types.symmetric-elements-involutive-types +open import structured-types.symmetric-elements-involutive-types funext univalence truncations ```
diff --git a/src/structured-types/transposition-pointed-span-diagrams.lagda.md b/src/structured-types/transposition-pointed-span-diagrams.lagda.md index 3b21a8cd57..07380ad1ff 100644 --- a/src/structured-types/transposition-pointed-span-diagrams.lagda.md +++ b/src/structured-types/transposition-pointed-span-diagrams.lagda.md @@ -1,7 +1,15 @@ # Transposition of pointed span diagrams ```agda -module structured-types.transposition-pointed-span-diagrams where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module structured-types.transposition-pointed-span-diagrams + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,8 +18,8 @@ module structured-types.transposition-pointed-span-diagrams where open import foundation.dependent-pair-types open import foundation.universe-levels -open import structured-types.opposite-pointed-spans -open import structured-types.pointed-span-diagrams +open import structured-types.opposite-pointed-spans funext univalence truncations +open import structured-types.pointed-span-diagrams funext univalence truncations ```
diff --git a/src/structured-types/types-equipped-with-automorphisms.lagda.md b/src/structured-types/types-equipped-with-automorphisms.lagda.md index 56e43e8efd..63a050d613 100644 --- a/src/structured-types/types-equipped-with-automorphisms.lagda.md +++ b/src/structured-types/types-equipped-with-automorphisms.lagda.md @@ -1,18 +1,24 @@ # Types equipped with automorphisms ```agda -module structured-types.types-equipped-with-automorphisms where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module structured-types.types-equipped-with-automorphisms + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda -open import foundation.automorphisms +open import foundation.automorphisms funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences +open import foundation.equivalences funext open import foundation.universe-levels -open import structured-types.types-equipped-with-endomorphisms +open import structured-types.types-equipped-with-endomorphisms funext univalence ```
diff --git a/src/structured-types/types-equipped-with-endomorphisms.lagda.md b/src/structured-types/types-equipped-with-endomorphisms.lagda.md index f9e9a9b3d5..217362dd91 100644 --- a/src/structured-types/types-equipped-with-endomorphisms.lagda.md +++ b/src/structured-types/types-equipped-with-endomorphisms.lagda.md @@ -1,17 +1,25 @@ # Types equipped with endomorphisms ```agda -module structured-types.types-equipped-with-endomorphisms where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module structured-types.types-equipped-with-endomorphisms + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.endomorphisms -open import foundation.function-types +open import foundation.raising-universe-levels-unit-type open import foundation.unit-type open import foundation.universe-levels + +open import foundation-core.endomorphisms funext univalence +open import foundation-core.function-types ```
diff --git a/src/structured-types/uniform-pointed-homotopies.lagda.md b/src/structured-types/uniform-pointed-homotopies.lagda.md index eb98f22918..d02a94b23c 100644 --- a/src/structured-types/uniform-pointed-homotopies.lagda.md +++ b/src/structured-types/uniform-pointed-homotopies.lagda.md @@ -1,27 +1,35 @@ # Uniform pointed homotopies ```agda -module structured-types.uniform-pointed-homotopies where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module structured-types.uniform-pointed-homotopies + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.commuting-triangles-of-identifications +open import foundation.commuting-triangles-of-identifications funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types +open import foundation.equivalences funext +open import foundation.function-extensionality funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.structure-identity-principle open import foundation.universe-levels -open import structured-types.pointed-dependent-functions +open import structured-types.pointed-dependent-functions funext open import structured-types.pointed-families-of-types -open import structured-types.pointed-homotopies -open import structured-types.pointed-maps +open import structured-types.pointed-homotopies funext univalence truncations +open import structured-types.pointed-maps funext univalence truncations open import structured-types.pointed-types ``` diff --git a/src/structured-types/universal-property-pointed-equivalences.lagda.md b/src/structured-types/universal-property-pointed-equivalences.lagda.md index 1ed069812f..16c65e7562 100644 --- a/src/structured-types/universal-property-pointed-equivalences.lagda.md +++ b/src/structured-types/universal-property-pointed-equivalences.lagda.md @@ -1,18 +1,26 @@ # The universal property of pointed equivalences ```agda -module structured-types.universal-property-pointed-equivalences where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module structured-types.universal-property-pointed-equivalences + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.equivalences +open import foundation.equivalences funext open import foundation.universe-levels -open import structured-types.pointed-maps +open import structured-types.pointed-maps funext univalence truncations open import structured-types.pointed-types -open import structured-types.precomposition-pointed-maps +open import structured-types.precomposition-pointed-maps funext univalence truncations ```
diff --git a/src/structured-types/whiskering-pointed-2-homotopies-concatenation.lagda.md b/src/structured-types/whiskering-pointed-2-homotopies-concatenation.lagda.md index 7e99884c46..5c7fc89f5f 100644 --- a/src/structured-types/whiskering-pointed-2-homotopies-concatenation.lagda.md +++ b/src/structured-types/whiskering-pointed-2-homotopies-concatenation.lagda.md @@ -1,24 +1,32 @@ # Whiskering pointed homotopies with respect to concatenation ```agda -module structured-types.whiskering-pointed-2-homotopies-concatenation where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module structured-types.whiskering-pointed-2-homotopies-concatenation + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-triangles-of-identifications +open import foundation.commuting-triangles-of-identifications funext open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.path-algebra +open import foundation.identity-types funext +open import foundation.path-algebra funext open import foundation.universe-levels -open import foundation.whiskering-homotopies-concatenation -open import foundation.whiskering-identifications-concatenation +open import foundation.whiskering-homotopies-concatenation funext +open import foundation.whiskering-identifications-concatenation funext -open import structured-types.pointed-2-homotopies -open import structured-types.pointed-homotopies -open import structured-types.pointed-maps +open import structured-types.pointed-2-homotopies funext univalence truncations +open import structured-types.pointed-homotopies funext univalence truncations +open import structured-types.pointed-maps funext univalence truncations open import structured-types.pointed-types ``` diff --git a/src/structured-types/whiskering-pointed-homotopies-composition.lagda.md b/src/structured-types/whiskering-pointed-homotopies-composition.lagda.md index ce71678ce6..3253e9b0bc 100644 --- a/src/structured-types/whiskering-pointed-homotopies-composition.lagda.md +++ b/src/structured-types/whiskering-pointed-homotopies-composition.lagda.md @@ -1,7 +1,15 @@ # Whiskering of pointed homotopies with respect to composition of pointed maps ```agda -module structured-types.whiskering-pointed-homotopies-composition where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module structured-types.whiskering-pointed-homotopies-composition + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,19 +17,19 @@ module structured-types.whiskering-pointed-homotopies-composition where ```agda open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-identifications -open import foundation.commuting-triangles-of-identifications +open import foundation.commuting-squares-of-identifications funext +open import foundation.commuting-triangles-of-identifications funext open import foundation.dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import foundation.whiskering-identifications-concatenation +open import foundation.whiskering-identifications-concatenation funext -open import structured-types.pointed-2-homotopies +open import structured-types.pointed-2-homotopies funext univalence truncations open import structured-types.pointed-families-of-types -open import structured-types.pointed-homotopies -open import structured-types.pointed-maps +open import structured-types.pointed-homotopies funext univalence truncations +open import structured-types.pointed-maps funext univalence truncations open import structured-types.pointed-types ``` diff --git a/src/structured-types/wild-category-of-pointed-types.lagda.md b/src/structured-types/wild-category-of-pointed-types.lagda.md index 3ff1429d27..6048a78b95 100644 --- a/src/structured-types/wild-category-of-pointed-types.lagda.md +++ b/src/structured-types/wild-category-of-pointed-types.lagda.md @@ -2,8 +2,15 @@ ```agda {-# OPTIONS --guardedness #-} - -module structured-types.wild-category-of-pointed-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module structured-types.wild-category-of-pointed-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -11,29 +18,29 @@ module structured-types.wild-category-of-pointed-types where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.universe-levels -open import foundation.whiskering-identifications-concatenation +open import foundation.whiskering-identifications-concatenation funext -open import globular-types.discrete-reflexive-globular-types +open import globular-types.discrete-reflexive-globular-types funext univalence truncations open import globular-types.globular-types open import globular-types.large-globular-types -open import globular-types.large-reflexive-globular-types -open import globular-types.large-transitive-globular-types -open import globular-types.reflexive-globular-types -open import globular-types.transitive-globular-types +open import globular-types.large-reflexive-globular-types funext univalence truncations +open import globular-types.large-transitive-globular-types funext univalence truncations +open import globular-types.reflexive-globular-types funext univalence truncations +open import globular-types.transitive-globular-types funext univalence truncations -open import structured-types.pointed-2-homotopies -open import structured-types.pointed-dependent-functions +open import structured-types.pointed-2-homotopies funext univalence truncations +open import structured-types.pointed-dependent-functions funext open import structured-types.pointed-families-of-types -open import structured-types.pointed-homotopies -open import structured-types.pointed-maps +open import structured-types.pointed-homotopies funext univalence truncations +open import structured-types.pointed-maps funext univalence truncations open import structured-types.pointed-types -open import structured-types.uniform-pointed-homotopies +open import structured-types.uniform-pointed-homotopies funext univalence truncations -open import wild-category-theory.noncoherent-large-omega-precategories -open import wild-category-theory.noncoherent-omega-precategories +open import wild-category-theory.noncoherent-large-omega-precategories funext univalence truncations +open import wild-category-theory.noncoherent-omega-precategories funext univalence truncations ```
diff --git a/src/structured-types/wild-groups.lagda.md b/src/structured-types/wild-groups.lagda.md index a743c1d556..27391030bd 100644 --- a/src/structured-types/wild-groups.lagda.md +++ b/src/structured-types/wild-groups.lagda.md @@ -1,7 +1,15 @@ # Wild groups ```agda -module structured-types.wild-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module structured-types.wild-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -11,7 +19,7 @@ open import foundation.binary-equivalences open import foundation.dependent-pair-types open import foundation.universe-levels -open import structured-types.wild-monoids +open import structured-types.wild-monoids funext univalence truncations ```
diff --git a/src/structured-types/wild-loops.lagda.md b/src/structured-types/wild-loops.lagda.md index 0abc01f7c2..2b6ee43b4a 100644 --- a/src/structured-types/wild-loops.lagda.md +++ b/src/structured-types/wild-loops.lagda.md @@ -1,23 +1,31 @@ # Wild loops ```agda -module structured-types.wild-loops where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module structured-types.wild-loops + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.automorphisms +open import foundation.automorphisms funext univalence open import foundation.binary-equivalences open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.identity-types +open import foundation.equivalences funext +open import foundation.identity-types funext open import foundation.universe-levels -open import structured-types.h-spaces -open import structured-types.magmas +open import structured-types.h-spaces funext univalence truncations +open import structured-types.magmas funext univalence open import structured-types.pointed-types -open import structured-types.wild-quasigroups +open import structured-types.wild-quasigroups funext univalence ```
diff --git a/src/structured-types/wild-monoids.lagda.md b/src/structured-types/wild-monoids.lagda.md index 250cabb823..46652bc34e 100644 --- a/src/structured-types/wild-monoids.lagda.md +++ b/src/structured-types/wild-monoids.lagda.md @@ -1,7 +1,15 @@ # Wild monoids ```agda -module structured-types.wild-monoids where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module structured-types.wild-monoids + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,11 +17,11 @@ module structured-types.wild-monoids where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.unit-type open import foundation.universe-levels -open import structured-types.h-spaces +open import structured-types.h-spaces funext univalence truncations open import structured-types.pointed-types ``` diff --git a/src/structured-types/wild-quasigroups.lagda.md b/src/structured-types/wild-quasigroups.lagda.md index a9e84acf35..7ff10d525d 100644 --- a/src/structured-types/wild-quasigroups.lagda.md +++ b/src/structured-types/wild-quasigroups.lagda.md @@ -1,19 +1,25 @@ # Wild quasigroups ```agda -module structured-types.wild-quasigroups where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module structured-types.wild-quasigroups + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda -open import foundation.automorphisms +open import foundation.automorphisms funext univalence open import foundation.binary-equivalences open import foundation.dependent-pair-types -open import foundation.equivalences +open import foundation.equivalences funext open import foundation.universe-levels -open import structured-types.magmas +open import structured-types.magmas funext univalence ```
diff --git a/src/structured-types/wild-semigroups.lagda.md b/src/structured-types/wild-semigroups.lagda.md index f1a0642256..0946e71b53 100644 --- a/src/structured-types/wild-semigroups.lagda.md +++ b/src/structured-types/wild-semigroups.lagda.md @@ -1,17 +1,23 @@ # Wild semigroups ```agda -module structured-types.wild-semigroups where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module structured-types.wild-semigroups + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import structured-types.magmas +open import structured-types.magmas funext univalence ```
diff --git a/src/synthetic-category-theory.lagda.md b/src/synthetic-category-theory.lagda.md index 5ff89a2169..008fdfeb48 100644 --- a/src/synthetic-category-theory.lagda.md +++ b/src/synthetic-category-theory.lagda.md @@ -23,13 +23,19 @@ Some core principles of higher category theory include: ## Modules in the synthetic category theory namespace ```agda -module synthetic-category-theory where - -open import synthetic-category-theory.cone-diagrams-synthetic-categories public -open import synthetic-category-theory.cospans-synthetic-categories public -open import synthetic-category-theory.equivalences-synthetic-categories public -open import synthetic-category-theory.invertible-functors-synthetic-categories public -open import synthetic-category-theory.pullbacks-synthetic-categories public +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-category-theory + (funext : function-extensionality) + (univalence : univalence-axiom) + where + +open import synthetic-category-theory.cone-diagrams-synthetic-categories funext univalence public +open import synthetic-category-theory.cospans-synthetic-categories funext univalence public +open import synthetic-category-theory.equivalences-synthetic-categories funext univalence public +open import synthetic-category-theory.invertible-functors-synthetic-categories funext univalence public +open import synthetic-category-theory.pullbacks-synthetic-categories funext univalence public open import synthetic-category-theory.retractions-synthetic-categories public open import synthetic-category-theory.sections-synthetic-categories public open import synthetic-category-theory.synthetic-categories public diff --git a/src/synthetic-category-theory/cone-diagrams-synthetic-categories.lagda.md b/src/synthetic-category-theory/cone-diagrams-synthetic-categories.lagda.md index 793041a163..56ebd7c048 100644 --- a/src/synthetic-category-theory/cone-diagrams-synthetic-categories.lagda.md +++ b/src/synthetic-category-theory/cone-diagrams-synthetic-categories.lagda.md @@ -2,20 +2,25 @@ ```agda {-# OPTIONS --guardedness #-} +open import foundation-core.univalence +open import foundation.function-extensionality-axiom -module synthetic-category-theory.cone-diagrams-synthetic-categories where +module synthetic-category-theory.cone-diagrams-synthetic-categories + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types open import foundation.universe-levels open import globular-types.globular-types -open import synthetic-category-theory.cospans-synthetic-categories +open import synthetic-category-theory.cospans-synthetic-categories funext univalence open import synthetic-category-theory.synthetic-categories ``` diff --git a/src/synthetic-category-theory/cospans-synthetic-categories.lagda.md b/src/synthetic-category-theory/cospans-synthetic-categories.lagda.md index d4385ae17e..92c97d7cb0 100644 --- a/src/synthetic-category-theory/cospans-synthetic-categories.lagda.md +++ b/src/synthetic-category-theory/cospans-synthetic-categories.lagda.md @@ -2,20 +2,25 @@ ```agda {-# OPTIONS --guardedness #-} +open import foundation-core.univalence +open import foundation.function-extensionality-axiom -module synthetic-category-theory.cospans-synthetic-categories where +module synthetic-category-theory.cospans-synthetic-categories + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types open import foundation.universe-levels open import globular-types.globular-types -open import synthetic-category-theory.equivalences-synthetic-categories +open import synthetic-category-theory.equivalences-synthetic-categories funext univalence open import synthetic-category-theory.synthetic-categories ``` diff --git a/src/synthetic-category-theory/equivalences-synthetic-categories.lagda.md b/src/synthetic-category-theory/equivalences-synthetic-categories.lagda.md index e616153e9f..04e557d541 100644 --- a/src/synthetic-category-theory/equivalences-synthetic-categories.lagda.md +++ b/src/synthetic-category-theory/equivalences-synthetic-categories.lagda.md @@ -2,14 +2,19 @@ ```agda {-# OPTIONS --guardedness #-} +open import foundation-core.univalence +open import foundation.function-extensionality-axiom -module synthetic-category-theory.equivalences-synthetic-categories where +module synthetic-category-theory.equivalences-synthetic-categories + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types open import foundation.universe-levels diff --git a/src/synthetic-category-theory/invertible-functors-synthetic-categories.lagda.md b/src/synthetic-category-theory/invertible-functors-synthetic-categories.lagda.md index 79a237ffc1..708a6876b7 100644 --- a/src/synthetic-category-theory/invertible-functors-synthetic-categories.lagda.md +++ b/src/synthetic-category-theory/invertible-functors-synthetic-categories.lagda.md @@ -2,20 +2,25 @@ ```agda {-# OPTIONS --guardedness #-} +open import foundation-core.univalence +open import foundation.function-extensionality-axiom -module synthetic-category-theory.invertible-functors-synthetic-categories where +module synthetic-category-theory.invertible-functors-synthetic-categories + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types open import foundation.universe-levels open import globular-types.globular-types -open import synthetic-category-theory.equivalences-synthetic-categories +open import synthetic-category-theory.equivalences-synthetic-categories funext univalence open import synthetic-category-theory.retractions-synthetic-categories open import synthetic-category-theory.sections-synthetic-categories open import synthetic-category-theory.synthetic-categories diff --git a/src/synthetic-category-theory/pullbacks-synthetic-categories.lagda.md b/src/synthetic-category-theory/pullbacks-synthetic-categories.lagda.md index c57580a72d..92486d3869 100644 --- a/src/synthetic-category-theory/pullbacks-synthetic-categories.lagda.md +++ b/src/synthetic-category-theory/pullbacks-synthetic-categories.lagda.md @@ -2,22 +2,27 @@ ```agda {-# OPTIONS --guardedness #-} +open import foundation-core.univalence +open import foundation.function-extensionality-axiom -module synthetic-category-theory.pullbacks-synthetic-categories where +module synthetic-category-theory.pullbacks-synthetic-categories + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types open import foundation.universe-levels open import globular-types.globular-types -open import synthetic-category-theory.cone-diagrams-synthetic-categories -open import synthetic-category-theory.cospans-synthetic-categories -open import synthetic-category-theory.equivalences-synthetic-categories +open import synthetic-category-theory.cone-diagrams-synthetic-categories funext univalence +open import synthetic-category-theory.cospans-synthetic-categories funext univalence +open import synthetic-category-theory.equivalences-synthetic-categories funext univalence open import synthetic-category-theory.synthetic-categories ``` diff --git a/src/synthetic-category-theory/retractions-synthetic-categories.lagda.md b/src/synthetic-category-theory/retractions-synthetic-categories.lagda.md index 9eefe32176..9c81fdcf53 100644 --- a/src/synthetic-category-theory/retractions-synthetic-categories.lagda.md +++ b/src/synthetic-category-theory/retractions-synthetic-categories.lagda.md @@ -9,12 +9,9 @@ module synthetic-category-theory.retractions-synthetic-categories where
Imports ```agda -open import foundation.cartesian-product-types open import foundation.dependent-pair-types open import foundation.universe-levels -open import globular-types.globular-types - open import synthetic-category-theory.synthetic-categories ``` diff --git a/src/synthetic-category-theory/sections-synthetic-categories.lagda.md b/src/synthetic-category-theory/sections-synthetic-categories.lagda.md index e24866c194..12556a69e2 100644 --- a/src/synthetic-category-theory/sections-synthetic-categories.lagda.md +++ b/src/synthetic-category-theory/sections-synthetic-categories.lagda.md @@ -9,12 +9,9 @@ module synthetic-category-theory.sections-synthetic-categories where
Imports ```agda -open import foundation.cartesian-product-types open import foundation.dependent-pair-types open import foundation.universe-levels -open import globular-types.globular-types - open import synthetic-category-theory.synthetic-categories ``` diff --git a/src/synthetic-category-theory/synthetic-categories.lagda.md b/src/synthetic-category-theory/synthetic-categories.lagda.md index 5deaf488e8..cc5990a41f 100644 --- a/src/synthetic-category-theory/synthetic-categories.lagda.md +++ b/src/synthetic-category-theory/synthetic-categories.lagda.md @@ -9,7 +9,6 @@ module synthetic-category-theory.synthetic-categories where
Imports ```agda -open import foundation.dependent-pair-types open import foundation.universe-levels open import globular-types.globular-types diff --git a/src/synthetic-homotopy-theory.lagda.md b/src/synthetic-homotopy-theory.lagda.md index f05ba2976d..d142709fa4 100644 --- a/src/synthetic-homotopy-theory.lagda.md +++ b/src/synthetic-homotopy-theory.lagda.md @@ -7,137 +7,145 @@ ## Modules in the synthetic homotopy theory namespace ```agda -module synthetic-homotopy-theory where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom -open import synthetic-homotopy-theory.0-acyclic-maps public -open import synthetic-homotopy-theory.0-acyclic-types public -open import synthetic-homotopy-theory.1-acyclic-types public -open import synthetic-homotopy-theory.acyclic-maps public -open import synthetic-homotopy-theory.acyclic-types public -open import synthetic-homotopy-theory.category-of-connected-set-bundles-circle public -open import synthetic-homotopy-theory.cavallos-trick public -open import synthetic-homotopy-theory.circle public -open import synthetic-homotopy-theory.cocartesian-morphisms-arrows public -open import synthetic-homotopy-theory.cocones-under-pointed-span-diagrams public -open import synthetic-homotopy-theory.cocones-under-sequential-diagrams public -open import synthetic-homotopy-theory.cocones-under-spans public -open import synthetic-homotopy-theory.codiagonals-of-maps public -open import synthetic-homotopy-theory.coequalizers public -open import synthetic-homotopy-theory.cofibers-of-maps public -open import synthetic-homotopy-theory.cofibers-of-pointed-maps public -open import synthetic-homotopy-theory.coforks public -open import synthetic-homotopy-theory.coforks-cocones-under-sequential-diagrams public -open import synthetic-homotopy-theory.conjugation-loops public -open import synthetic-homotopy-theory.connected-set-bundles-circle public -open import synthetic-homotopy-theory.connective-prespectra public -open import synthetic-homotopy-theory.connective-spectra public -open import synthetic-homotopy-theory.dependent-cocones-under-sequential-diagrams public -open import synthetic-homotopy-theory.dependent-cocones-under-spans public -open import synthetic-homotopy-theory.dependent-coforks public -open import synthetic-homotopy-theory.dependent-descent-circle public -open import synthetic-homotopy-theory.dependent-pullback-property-pushouts public -open import synthetic-homotopy-theory.dependent-pushout-products public -open import synthetic-homotopy-theory.dependent-sequential-diagrams public -open import synthetic-homotopy-theory.dependent-suspension-structures public -open import synthetic-homotopy-theory.dependent-universal-property-coequalizers public -open import synthetic-homotopy-theory.dependent-universal-property-pushouts public -open import synthetic-homotopy-theory.dependent-universal-property-sequential-colimits public -open import synthetic-homotopy-theory.dependent-universal-property-suspensions public -open import synthetic-homotopy-theory.descent-circle public -open import synthetic-homotopy-theory.descent-circle-constant-families public -open import synthetic-homotopy-theory.descent-circle-dependent-pair-types public -open import synthetic-homotopy-theory.descent-circle-equivalence-types public -open import synthetic-homotopy-theory.descent-circle-function-types public -open import synthetic-homotopy-theory.descent-circle-subtypes public -open import synthetic-homotopy-theory.descent-data-equivalence-types-over-pushouts public -open import synthetic-homotopy-theory.descent-data-function-types-over-pushouts public -open import synthetic-homotopy-theory.descent-data-identity-types-over-pushouts public -open import synthetic-homotopy-theory.descent-data-pushouts public -open import synthetic-homotopy-theory.descent-data-sequential-colimits public -open import synthetic-homotopy-theory.descent-property-pushouts public -open import synthetic-homotopy-theory.descent-property-sequential-colimits public -open import synthetic-homotopy-theory.double-loop-spaces public -open import synthetic-homotopy-theory.eckmann-hilton-argument public -open import synthetic-homotopy-theory.equifibered-sequential-diagrams public -open import synthetic-homotopy-theory.equivalences-cocones-under-equivalences-sequential-diagrams public -open import synthetic-homotopy-theory.equivalences-coforks-under-equivalences-double-arrows public -open import synthetic-homotopy-theory.equivalences-dependent-sequential-diagrams public -open import synthetic-homotopy-theory.equivalences-descent-data-pushouts public -open import synthetic-homotopy-theory.equivalences-sequential-diagrams public -open import synthetic-homotopy-theory.families-descent-data-pushouts public -open import synthetic-homotopy-theory.families-descent-data-sequential-colimits public -open import synthetic-homotopy-theory.flattening-lemma-coequalizers public -open import synthetic-homotopy-theory.flattening-lemma-pushouts public -open import synthetic-homotopy-theory.flattening-lemma-sequential-colimits public -open import synthetic-homotopy-theory.free-loops public -open import synthetic-homotopy-theory.functoriality-loop-spaces public -open import synthetic-homotopy-theory.functoriality-sequential-colimits public -open import synthetic-homotopy-theory.functoriality-suspensions public -open import synthetic-homotopy-theory.groups-of-loops-in-1-types public -open import synthetic-homotopy-theory.hatchers-acyclic-type public -open import synthetic-homotopy-theory.homotopy-groups public -open import synthetic-homotopy-theory.identity-systems-descent-data-pushouts public -open import synthetic-homotopy-theory.induction-principle-pushouts public -open import synthetic-homotopy-theory.infinite-complex-projective-space public -open import synthetic-homotopy-theory.infinite-cyclic-types public -open import synthetic-homotopy-theory.interval-type public -open import synthetic-homotopy-theory.iterated-loop-spaces public -open import synthetic-homotopy-theory.iterated-suspensions-of-pointed-types public -open import synthetic-homotopy-theory.join-powers-of-types public -open import synthetic-homotopy-theory.joins-of-maps public -open import synthetic-homotopy-theory.joins-of-types public -open import synthetic-homotopy-theory.left-half-smash-products public -open import synthetic-homotopy-theory.loop-homotopy-circle public -open import synthetic-homotopy-theory.loop-spaces public -open import synthetic-homotopy-theory.maps-of-prespectra public -open import synthetic-homotopy-theory.mere-spheres public -open import synthetic-homotopy-theory.morphisms-cocones-under-morphisms-sequential-diagrams public -open import synthetic-homotopy-theory.morphisms-coforks-under-morphisms-double-arrows public -open import synthetic-homotopy-theory.morphisms-dependent-sequential-diagrams public -open import synthetic-homotopy-theory.morphisms-descent-data-circle public -open import synthetic-homotopy-theory.morphisms-descent-data-pushouts public -open import synthetic-homotopy-theory.morphisms-sequential-diagrams public -open import synthetic-homotopy-theory.multiplication-circle public -open import synthetic-homotopy-theory.null-cocones-under-pointed-span-diagrams public -open import synthetic-homotopy-theory.plus-principle public -open import synthetic-homotopy-theory.powers-of-loops public -open import synthetic-homotopy-theory.premanifolds public -open import synthetic-homotopy-theory.prespectra public -open import synthetic-homotopy-theory.pullback-property-pushouts public -open import synthetic-homotopy-theory.pushout-products public -open import synthetic-homotopy-theory.pushouts public -open import synthetic-homotopy-theory.pushouts-of-pointed-types public -open import synthetic-homotopy-theory.recursion-principle-pushouts public -open import synthetic-homotopy-theory.retracts-of-sequential-diagrams public -open import synthetic-homotopy-theory.rewriting-pushouts public -open import synthetic-homotopy-theory.sections-descent-circle public -open import synthetic-homotopy-theory.sections-descent-data-pushouts public -open import synthetic-homotopy-theory.sequential-colimits public -open import synthetic-homotopy-theory.sequential-diagrams public -open import synthetic-homotopy-theory.sequentially-compact-types public -open import synthetic-homotopy-theory.shifts-sequential-diagrams public -open import synthetic-homotopy-theory.smash-products-of-pointed-types public -open import synthetic-homotopy-theory.spectra public -open import synthetic-homotopy-theory.sphere-prespectrum public -open import synthetic-homotopy-theory.spheres public -open import synthetic-homotopy-theory.suspension-prespectra public -open import synthetic-homotopy-theory.suspension-structures public -open import synthetic-homotopy-theory.suspensions-of-pointed-types public -open import synthetic-homotopy-theory.suspensions-of-propositions public -open import synthetic-homotopy-theory.suspensions-of-types public -open import synthetic-homotopy-theory.tangent-spheres public -open import synthetic-homotopy-theory.total-cocones-families-sequential-diagrams public -open import synthetic-homotopy-theory.total-sequential-diagrams public -open import synthetic-homotopy-theory.triple-loop-spaces public -open import synthetic-homotopy-theory.truncated-acyclic-maps public -open import synthetic-homotopy-theory.truncated-acyclic-types public -open import synthetic-homotopy-theory.universal-cover-circle public -open import synthetic-homotopy-theory.universal-property-circle public -open import synthetic-homotopy-theory.universal-property-coequalizers public -open import synthetic-homotopy-theory.universal-property-pushouts public -open import synthetic-homotopy-theory.universal-property-sequential-colimits public -open import synthetic-homotopy-theory.universal-property-suspensions public -open import synthetic-homotopy-theory.universal-property-suspensions-of-pointed-types public -open import synthetic-homotopy-theory.wedges-of-pointed-types public -open import synthetic-homotopy-theory.zigzags-sequential-diagrams public +module synthetic-homotopy-theory + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where + +open import synthetic-homotopy-theory.0-acyclic-maps funext univalence truncations public +open import synthetic-homotopy-theory.0-acyclic-types funext univalence truncations public +open import synthetic-homotopy-theory.1-acyclic-types funext univalence truncations public +open import synthetic-homotopy-theory.acyclic-maps funext univalence truncations public +open import synthetic-homotopy-theory.acyclic-types funext univalence truncations public +open import synthetic-homotopy-theory.category-of-connected-set-bundles-circle funext univalence truncations public +open import synthetic-homotopy-theory.cavallos-trick funext univalence truncations public +open import synthetic-homotopy-theory.circle funext univalence truncations public +open import synthetic-homotopy-theory.cocartesian-morphisms-arrows funext univalence truncations public +open import synthetic-homotopy-theory.cocones-under-pointed-span-diagrams funext univalence truncations public +open import synthetic-homotopy-theory.cocones-under-sequential-diagrams funext univalence truncations public +open import synthetic-homotopy-theory.cocones-under-spans funext public +open import synthetic-homotopy-theory.codiagonals-of-maps funext univalence truncations public +open import synthetic-homotopy-theory.coequalizers funext univalence truncations public +open import synthetic-homotopy-theory.cofibers-of-maps funext univalence truncations public +open import synthetic-homotopy-theory.cofibers-of-pointed-maps funext univalence truncations public +open import synthetic-homotopy-theory.coforks funext univalence truncations public +open import synthetic-homotopy-theory.coforks-cocones-under-sequential-diagrams funext univalence truncations public +open import synthetic-homotopy-theory.conjugation-loops funext univalence truncations public +open import synthetic-homotopy-theory.connected-set-bundles-circle funext univalence truncations public +open import synthetic-homotopy-theory.connective-prespectra funext univalence truncations public +open import synthetic-homotopy-theory.connective-spectra funext univalence truncations public +open import synthetic-homotopy-theory.dependent-cocones-under-sequential-diagrams funext univalence truncations public +open import synthetic-homotopy-theory.dependent-cocones-under-spans funext univalence truncations public +open import synthetic-homotopy-theory.dependent-coforks funext univalence truncations public +open import synthetic-homotopy-theory.dependent-descent-circle funext univalence truncations public +open import synthetic-homotopy-theory.dependent-pullback-property-pushouts funext univalence truncations public +open import synthetic-homotopy-theory.dependent-pushout-products funext univalence truncations public +open import synthetic-homotopy-theory.dependent-sequential-diagrams funext univalence public +open import synthetic-homotopy-theory.dependent-suspension-structures funext univalence truncations public +open import synthetic-homotopy-theory.dependent-universal-property-coequalizers funext univalence truncations public +open import synthetic-homotopy-theory.dependent-universal-property-pushouts funext univalence truncations public +open import synthetic-homotopy-theory.dependent-universal-property-sequential-colimits funext univalence truncations public +open import synthetic-homotopy-theory.dependent-universal-property-suspensions funext univalence truncations public +open import synthetic-homotopy-theory.descent-circle funext univalence truncations public +open import synthetic-homotopy-theory.descent-circle-constant-families funext univalence truncations public +open import synthetic-homotopy-theory.descent-circle-dependent-pair-types funext univalence truncations public +open import synthetic-homotopy-theory.descent-circle-equivalence-types funext univalence truncations public +open import synthetic-homotopy-theory.descent-circle-function-types funext univalence truncations public +open import synthetic-homotopy-theory.descent-circle-subtypes funext univalence truncations public +open import synthetic-homotopy-theory.descent-data-equivalence-types-over-pushouts funext univalence truncations public +open import synthetic-homotopy-theory.descent-data-function-types-over-pushouts funext univalence truncations public +open import synthetic-homotopy-theory.descent-data-identity-types-over-pushouts funext univalence truncations public +open import synthetic-homotopy-theory.descent-data-pushouts funext public +open import synthetic-homotopy-theory.descent-data-sequential-colimits funext univalence truncations public +open import synthetic-homotopy-theory.descent-property-pushouts funext univalence truncations public +open import synthetic-homotopy-theory.descent-property-sequential-colimits funext univalence truncations public +open import synthetic-homotopy-theory.double-loop-spaces funext univalence truncations public +open import synthetic-homotopy-theory.eckmann-hilton-argument funext univalence truncations public +open import synthetic-homotopy-theory.equifibered-sequential-diagrams funext univalence public +open import synthetic-homotopy-theory.equivalences-cocones-under-equivalences-sequential-diagrams funext univalence truncations public +open import synthetic-homotopy-theory.equivalences-coforks-under-equivalences-double-arrows funext univalence truncations public +open import synthetic-homotopy-theory.equivalences-dependent-sequential-diagrams funext univalence truncations public +open import synthetic-homotopy-theory.equivalences-descent-data-pushouts funext univalence truncations public +open import synthetic-homotopy-theory.equivalences-sequential-diagrams funext univalence truncations public +open import synthetic-homotopy-theory.families-descent-data-pushouts funext univalence truncations public +open import synthetic-homotopy-theory.families-descent-data-sequential-colimits funext univalence truncations public +open import synthetic-homotopy-theory.flattening-lemma-coequalizers funext univalence truncations public +open import synthetic-homotopy-theory.flattening-lemma-pushouts funext univalence truncations public +open import synthetic-homotopy-theory.flattening-lemma-sequential-colimits funext univalence truncations public +open import synthetic-homotopy-theory.free-loops funext univalence truncations public +open import synthetic-homotopy-theory.functoriality-loop-spaces funext univalence truncations public +open import synthetic-homotopy-theory.functoriality-sequential-colimits funext univalence truncations public +open import synthetic-homotopy-theory.functoriality-suspensions funext univalence truncations public +open import synthetic-homotopy-theory.groups-of-loops-in-1-types funext univalence truncations public +open import synthetic-homotopy-theory.hatchers-acyclic-type funext univalence truncations public +open import synthetic-homotopy-theory.homotopy-groups funext univalence truncations public +open import synthetic-homotopy-theory.identity-systems-descent-data-pushouts funext univalence truncations public +open import synthetic-homotopy-theory.induction-principle-pushouts funext univalence truncations public +open import synthetic-homotopy-theory.infinite-complex-projective-space funext univalence truncations public +open import synthetic-homotopy-theory.infinite-cyclic-types funext univalence truncations public +open import synthetic-homotopy-theory.interval-type funext univalence public +open import synthetic-homotopy-theory.iterated-loop-spaces funext univalence truncations public +open import synthetic-homotopy-theory.iterated-suspensions-of-pointed-types funext univalence truncations public +open import synthetic-homotopy-theory.join-powers-of-types funext univalence truncations public +open import synthetic-homotopy-theory.joins-of-maps funext univalence truncations public +open import synthetic-homotopy-theory.joins-of-types funext univalence truncations public +open import synthetic-homotopy-theory.left-half-smash-products funext univalence truncations public +open import synthetic-homotopy-theory.loop-homotopy-circle funext univalence truncations public +open import synthetic-homotopy-theory.loop-spaces funext univalence truncations public +open import synthetic-homotopy-theory.maps-of-prespectra funext univalence truncations public +open import synthetic-homotopy-theory.mere-spheres funext univalence truncations public +open import synthetic-homotopy-theory.morphisms-cocones-under-morphisms-sequential-diagrams funext univalence truncations public +open import synthetic-homotopy-theory.morphisms-coforks-under-morphisms-double-arrows funext univalence truncations public +open import synthetic-homotopy-theory.morphisms-dependent-sequential-diagrams funext univalence public +open import synthetic-homotopy-theory.morphisms-descent-data-circle funext univalence truncations public +open import synthetic-homotopy-theory.morphisms-descent-data-pushouts funext univalence truncations public +open import synthetic-homotopy-theory.morphisms-sequential-diagrams funext univalence truncations public +open import synthetic-homotopy-theory.multiplication-circle funext univalence truncations public +open import synthetic-homotopy-theory.null-cocones-under-pointed-span-diagrams funext univalence truncations public +open import synthetic-homotopy-theory.plus-principle funext univalence truncations public +open import synthetic-homotopy-theory.powers-of-loops funext univalence truncations public +open import synthetic-homotopy-theory.premanifolds funext univalence truncations public +open import synthetic-homotopy-theory.prespectra funext univalence truncations public +open import synthetic-homotopy-theory.pullback-property-pushouts funext univalence truncations public +open import synthetic-homotopy-theory.pushout-products funext univalence truncations public +open import synthetic-homotopy-theory.pushouts funext univalence truncations public +open import synthetic-homotopy-theory.pushouts-of-pointed-types funext univalence truncations public +open import synthetic-homotopy-theory.recursion-principle-pushouts funext univalence truncations public +open import synthetic-homotopy-theory.retracts-of-sequential-diagrams funext univalence truncations public +open import synthetic-homotopy-theory.rewriting-pushouts funext univalence truncations public +open import synthetic-homotopy-theory.sections-descent-circle funext univalence truncations public +open import synthetic-homotopy-theory.sections-descent-data-pushouts funext univalence truncations public +open import synthetic-homotopy-theory.sequential-colimits funext univalence truncations public +open import synthetic-homotopy-theory.sequential-diagrams funext univalence public +open import synthetic-homotopy-theory.sequentially-compact-types funext univalence truncations public +open import synthetic-homotopy-theory.shifts-sequential-diagrams funext univalence truncations public +open import synthetic-homotopy-theory.smash-products-of-pointed-types funext univalence truncations public +open import synthetic-homotopy-theory.spectra funext univalence truncations public +open import synthetic-homotopy-theory.sphere-prespectrum funext univalence truncations public +open import synthetic-homotopy-theory.spheres funext univalence truncations public +open import synthetic-homotopy-theory.suspension-prespectra funext univalence truncations public +open import synthetic-homotopy-theory.suspension-structures funext univalence truncations public +open import synthetic-homotopy-theory.suspensions-of-pointed-types funext univalence truncations public +open import synthetic-homotopy-theory.suspensions-of-propositions funext univalence truncations public +open import synthetic-homotopy-theory.suspensions-of-types funext univalence truncations public +open import synthetic-homotopy-theory.tangent-spheres funext univalence truncations public +open import synthetic-homotopy-theory.total-cocones-families-sequential-diagrams funext univalence truncations public +open import synthetic-homotopy-theory.total-sequential-diagrams funext univalence truncations public +open import synthetic-homotopy-theory.triple-loop-spaces funext univalence truncations public +open import synthetic-homotopy-theory.truncated-acyclic-maps funext univalence truncations public +open import synthetic-homotopy-theory.truncated-acyclic-types funext univalence truncations public +open import synthetic-homotopy-theory.universal-cover-circle funext univalence truncations public +open import synthetic-homotopy-theory.universal-property-circle funext univalence truncations public +open import synthetic-homotopy-theory.universal-property-coequalizers funext univalence truncations public +open import synthetic-homotopy-theory.universal-property-pushouts funext univalence truncations public +open import synthetic-homotopy-theory.universal-property-sequential-colimits funext univalence truncations public +open import synthetic-homotopy-theory.universal-property-suspensions funext univalence truncations public +open import synthetic-homotopy-theory.universal-property-suspensions-of-pointed-types funext univalence truncations public +open import synthetic-homotopy-theory.wedges-of-pointed-types funext univalence truncations public +open import synthetic-homotopy-theory.zigzags-sequential-diagrams funext univalence truncations public ``` diff --git a/src/synthetic-homotopy-theory/0-acyclic-maps.lagda.md b/src/synthetic-homotopy-theory/0-acyclic-maps.lagda.md index aaa7ec0e76..be3fb92ff3 100644 --- a/src/synthetic-homotopy-theory/0-acyclic-maps.lagda.md +++ b/src/synthetic-homotopy-theory/0-acyclic-maps.lagda.md @@ -1,19 +1,28 @@ # `0`-acyclic maps ```agda -module synthetic-homotopy-theory.0-acyclic-maps where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.0-acyclic-maps + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.epimorphisms-with-respect-to-sets -open import foundation.propositions -open import foundation.surjective-maps +open import foundation.dependent-products-propositions funext +open import foundation.epimorphisms-with-respect-to-sets funext univalence truncations +open import foundation.propositions funext univalence +open import foundation.surjective-maps funext univalence truncations open import foundation.truncation-levels open import foundation.universe-levels -open import synthetic-homotopy-theory.truncated-acyclic-maps +open import synthetic-homotopy-theory.truncated-acyclic-maps funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/0-acyclic-types.lagda.md b/src/synthetic-homotopy-theory/0-acyclic-types.lagda.md index cdfaabba69..2c5661669f 100644 --- a/src/synthetic-homotopy-theory/0-acyclic-types.lagda.md +++ b/src/synthetic-homotopy-theory/0-acyclic-types.lagda.md @@ -1,25 +1,35 @@ # `0`-acyclic types ```agda -module synthetic-homotopy-theory.0-acyclic-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.0-acyclic-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.contractible-types +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.functoriality-propositional-truncation -open import foundation.inhabited-types -open import foundation.propositional-truncations -open import foundation.propositions +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.functoriality-propositional-truncation funext univalence truncations +open import foundation.inhabited-types funext univalence truncations +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence open import foundation.truncation-levels open import foundation.unit-type open import foundation.universe-levels -open import synthetic-homotopy-theory.0-acyclic-maps -open import synthetic-homotopy-theory.truncated-acyclic-maps -open import synthetic-homotopy-theory.truncated-acyclic-types +open import synthetic-homotopy-theory.0-acyclic-maps funext univalence truncations +open import synthetic-homotopy-theory.truncated-acyclic-maps funext univalence truncations +open import synthetic-homotopy-theory.truncated-acyclic-types funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/1-acyclic-types.lagda.md b/src/synthetic-homotopy-theory/1-acyclic-types.lagda.md index 9c3c160c3d..efa59dd44a 100644 --- a/src/synthetic-homotopy-theory/1-acyclic-types.lagda.md +++ b/src/synthetic-homotopy-theory/1-acyclic-types.lagda.md @@ -1,34 +1,43 @@ # `1`-acyclic types ```agda -module synthetic-homotopy-theory.1-acyclic-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.1-acyclic-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.0-connected-types +open import foundation.0-connected-types funext univalence truncations open import foundation.binary-transport -open import foundation.constant-maps -open import foundation.contractible-types +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.diagonal-maps-of-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.identity-types -open import foundation.inhabited-types -open import foundation.injective-maps -open import foundation.propositions -open import foundation.set-truncations -open import foundation.sets -open import foundation.truncated-types +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.dependent-products-truncated-types funext +open import foundation.diagonal-maps-of-types funext +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.inhabited-types funext univalence truncations +open import foundation.injective-maps funext +open import foundation.propositions funext univalence +open import foundation.set-truncations funext univalence +open import foundation.sets funext univalence +open import foundation.truncated-types funext univalence open import foundation.truncation-levels open import foundation.universe-levels -open import synthetic-homotopy-theory.0-acyclic-types -open import synthetic-homotopy-theory.loop-spaces -open import synthetic-homotopy-theory.truncated-acyclic-maps -open import synthetic-homotopy-theory.truncated-acyclic-types +open import synthetic-homotopy-theory.0-acyclic-types funext univalence truncations +open import synthetic-homotopy-theory.loop-spaces funext univalence truncations +open import synthetic-homotopy-theory.truncated-acyclic-maps funext univalence truncations +open import synthetic-homotopy-theory.truncated-acyclic-types funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/acyclic-maps.lagda.md b/src/synthetic-homotopy-theory/acyclic-maps.lagda.md index 60423d0894..d943dac927 100644 --- a/src/synthetic-homotopy-theory/acyclic-maps.lagda.md +++ b/src/synthetic-homotopy-theory/acyclic-maps.lagda.md @@ -1,54 +1,64 @@ # Acyclic maps ```agda -module synthetic-homotopy-theory.acyclic-maps where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.acyclic-maps + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types -open import foundation.cones-over-cospan-diagrams -open import foundation.constant-maps -open import foundation.contractible-maps -open import foundation.contractible-types -open import foundation.dependent-epimorphisms +open import foundation.cartesian-product-types funext univalence +open import foundation.cones-over-cospan-diagrams funext +open import foundation.constant-maps funext univalence truncations +open import foundation.contractible-maps funext +open import foundation.contractible-types funext univalence +open import foundation.dependent-epimorphisms funext univalence truncations open import foundation.dependent-pair-types -open import foundation.dependent-universal-property-equivalences -open import foundation.diagonal-maps-of-types -open import foundation.embeddings -open import foundation.epimorphisms -open import foundation.equivalences -open import foundation.fibers-of-maps -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.functoriality-dependent-function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.functoriality-fibers-of-maps -open import foundation.homotopies -open import foundation.identity-types -open import foundation.inhabited-types -open import foundation.precomposition-dependent-functions -open import foundation.precomposition-functions -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.pullbacks -open import foundation.retracts-of-maps -open import foundation.torsorial-type-families +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.dependent-universal-property-equivalences funext +open import foundation.diagonal-maps-of-types funext +open import foundation.embeddings funext +open import foundation.epimorphisms funext univalence truncations +open import foundation.equivalences funext +open import foundation.fibers-of-maps funext +open import foundation.function-extensionality funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-function-types funext univalence +open import foundation.functoriality-dependent-pair-types funext +open import foundation.functoriality-fibers-of-maps funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.inhabited-types funext univalence truncations +open import foundation.precomposition-dependent-functions funext +open import foundation.precomposition-functions funext +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence +open import foundation.pullbacks funext univalence truncations +open import foundation.retracts-of-maps funext univalence +open import foundation.torsorial-type-families funext univalence truncations open import foundation.type-arithmetic-dependent-pair-types -open import foundation.type-arithmetic-unit-type +open import foundation.type-arithmetic-unit-type funext open import foundation.unit-type -open import foundation.universal-property-cartesian-product-types -open import foundation.universal-property-dependent-pair-types +open import foundation.universal-property-cartesian-product-types funext +open import foundation.universal-property-dependent-pair-types funext open import foundation.universe-levels -open import synthetic-homotopy-theory.acyclic-types -open import synthetic-homotopy-theory.cocones-under-spans -open import synthetic-homotopy-theory.codiagonals-of-maps -open import synthetic-homotopy-theory.pushouts -open import synthetic-homotopy-theory.suspensions-of-types -open import synthetic-homotopy-theory.universal-property-pushouts +open import synthetic-homotopy-theory.acyclic-types funext univalence truncations +open import synthetic-homotopy-theory.cocones-under-spans funext +open import synthetic-homotopy-theory.codiagonals-of-maps funext univalence truncations +open import synthetic-homotopy-theory.pushouts funext univalence truncations +open import synthetic-homotopy-theory.suspensions-of-types funext univalence truncations +open import synthetic-homotopy-theory.universal-property-pushouts funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/acyclic-types.lagda.md b/src/synthetic-homotopy-theory/acyclic-types.lagda.md index 35473b70bf..c0c1ab336f 100644 --- a/src/synthetic-homotopy-theory/acyclic-types.lagda.md +++ b/src/synthetic-homotopy-theory/acyclic-types.lagda.md @@ -1,21 +1,31 @@ # Acyclic types ```agda -module synthetic-homotopy-theory.acyclic-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.acyclic-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.contractible-types -open import foundation.equivalences -open import foundation.propositions -open import foundation.retracts-of-types +open import foundation.contractible-types funext univalence +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.propositions funext univalence +open import foundation.retracts-of-types funext univalence open import foundation.unit-type open import foundation.universe-levels -open import synthetic-homotopy-theory.functoriality-suspensions -open import synthetic-homotopy-theory.suspensions-of-types +open import synthetic-homotopy-theory.functoriality-suspensions funext univalence truncations +open import synthetic-homotopy-theory.suspensions-of-types funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/category-of-connected-set-bundles-circle.lagda.md b/src/synthetic-homotopy-theory/category-of-connected-set-bundles-circle.lagda.md index c03b92fe6a..80cdeb353b 100644 --- a/src/synthetic-homotopy-theory/category-of-connected-set-bundles-circle.lagda.md +++ b/src/synthetic-homotopy-theory/category-of-connected-set-bundles-circle.lagda.md @@ -1,20 +1,28 @@ # The category of connected set bundles over the circle ```agda -module synthetic-homotopy-theory.category-of-connected-set-bundles-circle where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.category-of-connected-set-bundles-circle + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.full-large-subcategories -open import category-theory.large-categories +open import category-theory.full-large-subcategories funext univalence truncations +open import category-theory.large-categories funext univalence truncations -open import foundation.category-of-families-of-sets +open import foundation.category-of-families-of-sets funext univalence truncations open import foundation.universe-levels -open import synthetic-homotopy-theory.circle -open import synthetic-homotopy-theory.connected-set-bundles-circle +open import synthetic-homotopy-theory.circle funext univalence truncations +open import synthetic-homotopy-theory.connected-set-bundles-circle funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/cavallos-trick.lagda.md b/src/synthetic-homotopy-theory/cavallos-trick.lagda.md index 54d3a7e599..15fa98f8a4 100644 --- a/src/synthetic-homotopy-theory/cavallos-trick.lagda.md +++ b/src/synthetic-homotopy-theory/cavallos-trick.lagda.md @@ -1,7 +1,15 @@ # Cavallo's trick ```agda -module synthetic-homotopy-theory.cavallos-trick where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.cavallos-trick + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,15 +17,15 @@ module synthetic-homotopy-theory.cavallos-trick where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.sections +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.sections funext open import foundation.universe-levels -open import foundation.whiskering-identifications-concatenation +open import foundation.whiskering-identifications-concatenation funext -open import structured-types.pointed-homotopies -open import structured-types.pointed-maps +open import structured-types.pointed-homotopies funext univalence truncations +open import structured-types.pointed-maps funext univalence truncations open import structured-types.pointed-types ``` diff --git a/src/synthetic-homotopy-theory/circle.lagda.md b/src/synthetic-homotopy-theory/circle.lagda.md index 0340db0b69..ac38dbf2d5 100644 --- a/src/synthetic-homotopy-theory/circle.lagda.md +++ b/src/synthetic-homotopy-theory/circle.lagda.md @@ -1,48 +1,58 @@ # The circle ```agda -module synthetic-homotopy-theory.circle where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.circle + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.0-connected-types +open import foundation.0-connected-types funext univalence truncations open import foundation.action-on-identifications-dependent-functions open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-identifications -open import foundation.contractible-types -open import foundation.coproduct-types -open import foundation.dependent-identifications +open import foundation.commuting-squares-of-identifications funext +open import foundation.contractible-types funext univalence +open import foundation.coproduct-types funext univalence truncations +open import foundation.dependent-identifications funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.mere-equality -open import foundation.negated-equality -open import foundation.negation -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.retractions -open import foundation.sections +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.mere-equality funext univalence truncations +open import foundation.negated-equality funext univalence truncations +open import foundation.negation funext +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence +open import foundation.retractions funext +open import foundation.sections funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import foundation.whiskering-identifications-concatenation +open import foundation.whiskering-identifications-concatenation funext -open import higher-group-theory.higher-groups +open import higher-group-theory.higher-groups funext univalence truncations open import structured-types.pointed-types -open import synthetic-homotopy-theory.dependent-suspension-structures -open import synthetic-homotopy-theory.free-loops -open import synthetic-homotopy-theory.spheres -open import synthetic-homotopy-theory.suspension-structures -open import synthetic-homotopy-theory.suspensions-of-types -open import synthetic-homotopy-theory.universal-cover-circle -open import synthetic-homotopy-theory.universal-property-circle +open import synthetic-homotopy-theory.dependent-suspension-structures funext univalence truncations +open import synthetic-homotopy-theory.free-loops funext univalence truncations +open import synthetic-homotopy-theory.spheres funext univalence truncations +open import synthetic-homotopy-theory.suspension-structures funext univalence truncations +open import synthetic-homotopy-theory.suspensions-of-types funext univalence truncations +open import synthetic-homotopy-theory.universal-cover-circle funext univalence truncations +open import synthetic-homotopy-theory.universal-property-circle funext univalence truncations -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/cocartesian-morphisms-arrows.lagda.md b/src/synthetic-homotopy-theory/cocartesian-morphisms-arrows.lagda.md index 9e34713e9c..6bf975cc4d 100644 --- a/src/synthetic-homotopy-theory/cocartesian-morphisms-arrows.lagda.md +++ b/src/synthetic-homotopy-theory/cocartesian-morphisms-arrows.lagda.md @@ -1,21 +1,30 @@ # Cocartesian morphisms of arrows ```agda -module synthetic-homotopy-theory.cocartesian-morphisms-arrows where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.cocartesian-morphisms-arrows + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.commuting-squares-of-maps +open import foundation.commuting-squares-of-maps funext univalence open import foundation.dependent-pair-types -open import foundation.morphisms-arrows -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.morphisms-arrows funext +open import foundation.propositions funext univalence open import foundation.universe-levels -open import synthetic-homotopy-theory.cocones-under-spans -open import synthetic-homotopy-theory.pushouts -open import synthetic-homotopy-theory.universal-property-pushouts +open import synthetic-homotopy-theory.cocones-under-spans funext +open import synthetic-homotopy-theory.pushouts funext univalence truncations +open import synthetic-homotopy-theory.universal-property-pushouts funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/cocones-under-pointed-span-diagrams.lagda.md b/src/synthetic-homotopy-theory/cocones-under-pointed-span-diagrams.lagda.md index cec36cef2d..e59ebf1dd3 100644 --- a/src/synthetic-homotopy-theory/cocones-under-pointed-span-diagrams.lagda.md +++ b/src/synthetic-homotopy-theory/cocones-under-pointed-span-diagrams.lagda.md @@ -1,7 +1,15 @@ # Cocones under pointed span diagrams ```agda -module synthetic-homotopy-theory.cocones-under-pointed-span-diagrams where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.cocones-under-pointed-span-diagrams + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,15 +17,15 @@ module synthetic-homotopy-theory.cocones-under-pointed-span-diagrams where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.universe-levels -open import structured-types.commuting-squares-of-pointed-maps -open import structured-types.pointed-maps +open import structured-types.commuting-squares-of-pointed-maps funext univalence truncations +open import structured-types.pointed-maps funext univalence truncations open import structured-types.pointed-types -open import synthetic-homotopy-theory.cocones-under-spans +open import synthetic-homotopy-theory.cocones-under-spans funext ```
diff --git a/src/synthetic-homotopy-theory/cocones-under-sequential-diagrams.lagda.md b/src/synthetic-homotopy-theory/cocones-under-sequential-diagrams.lagda.md index ca4adb47b0..01424da8ee 100644 --- a/src/synthetic-homotopy-theory/cocones-under-sequential-diagrams.lagda.md +++ b/src/synthetic-homotopy-theory/cocones-under-sequential-diagrams.lagda.md @@ -1,7 +1,15 @@ # Cocones under sequential diagrams ```agda -module synthetic-homotopy-theory.cocones-under-sequential-diagrams where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.cocones-under-sequential-diagrams + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,25 +17,25 @@ module synthetic-homotopy-theory.cocones-under-sequential-diagrams where ```agda open import elementary-number-theory.natural-numbers -open import foundation.binary-homotopies -open import foundation.commuting-squares-of-homotopies -open import foundation.commuting-triangles-of-maps +open import foundation.binary-homotopies funext +open import foundation.commuting-squares-of-homotopies funext +open import foundation.commuting-triangles-of-maps funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types +open import foundation.equivalences funext +open import foundation.function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.postcomposition-functions +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.postcomposition-functions funext open import foundation.structure-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext univalence truncations open import foundation.transport-along-identifications open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import synthetic-homotopy-theory.dependent-sequential-diagrams -open import synthetic-homotopy-theory.equifibered-sequential-diagrams -open import synthetic-homotopy-theory.sequential-diagrams +open import synthetic-homotopy-theory.dependent-sequential-diagrams funext univalence +open import synthetic-homotopy-theory.equifibered-sequential-diagrams funext univalence +open import synthetic-homotopy-theory.sequential-diagrams funext univalence ```
diff --git a/src/synthetic-homotopy-theory/cocones-under-spans.lagda.md b/src/synthetic-homotopy-theory/cocones-under-spans.lagda.md index b3ac5c1716..4952ff5fdf 100644 --- a/src/synthetic-homotopy-theory/cocones-under-spans.lagda.md +++ b/src/synthetic-homotopy-theory/cocones-under-spans.lagda.md @@ -1,7 +1,11 @@ # Cocones under spans ```agda -module synthetic-homotopy-theory.cocones-under-spans where +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.cocones-under-spans + (funext : function-extensionality) + where ```
Imports @@ -9,17 +13,17 @@ module synthetic-homotopy-theory.cocones-under-spans where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-extensionality +open import foundation.function-extensionality funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.morphisms-arrows -open import foundation.span-diagrams +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.morphisms-arrows funext +open import foundation.span-diagrams funext open import foundation.structure-identity-principle open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import foundation-core.commuting-squares-of-maps +open import foundation-core.commuting-squares-of-maps funext open import foundation-core.contractible-types open import foundation-core.equality-dependent-pair-types open import foundation-core.equivalences diff --git a/src/synthetic-homotopy-theory/codiagonals-of-maps.lagda.md b/src/synthetic-homotopy-theory/codiagonals-of-maps.lagda.md index b483d3e9a8..4ab3792c03 100644 --- a/src/synthetic-homotopy-theory/codiagonals-of-maps.lagda.md +++ b/src/synthetic-homotopy-theory/codiagonals-of-maps.lagda.md @@ -1,27 +1,36 @@ # Codiagonals of maps ```agda -module synthetic-homotopy-theory.codiagonals-of-maps where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.codiagonals-of-maps + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.contractible-types +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.fibers-of-maps -open import foundation.function-types -open import foundation.homotopies -open import foundation.torsorial-type-families +open import foundation.dependent-products-contractible-types funext +open import foundation.equivalences funext +open import foundation.fibers-of-maps funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.torsorial-type-families funext univalence truncations open import foundation.unit-type open import foundation.universe-levels -open import synthetic-homotopy-theory.cocones-under-spans -open import synthetic-homotopy-theory.pushouts -open import synthetic-homotopy-theory.suspension-structures -open import synthetic-homotopy-theory.suspensions-of-types -open import synthetic-homotopy-theory.universal-property-pushouts +open import synthetic-homotopy-theory.cocones-under-spans funext +open import synthetic-homotopy-theory.pushouts funext univalence truncations +open import synthetic-homotopy-theory.suspension-structures funext univalence truncations +open import synthetic-homotopy-theory.suspensions-of-types funext univalence truncations +open import synthetic-homotopy-theory.universal-property-pushouts funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/coequalizers.lagda.md b/src/synthetic-homotopy-theory/coequalizers.lagda.md index a89b394839..2df213835e 100644 --- a/src/synthetic-homotopy-theory/coequalizers.lagda.md +++ b/src/synthetic-homotopy-theory/coequalizers.lagda.md @@ -1,23 +1,31 @@ # Coequalizers ```agda -module synthetic-homotopy-theory.coequalizers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.coequalizers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.double-arrows -open import foundation.equivalences -open import foundation.identity-types +open import foundation.equivalences funext +open import foundation.identity-types funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import synthetic-homotopy-theory.coforks -open import synthetic-homotopy-theory.dependent-cocones-under-spans -open import synthetic-homotopy-theory.dependent-universal-property-coequalizers -open import synthetic-homotopy-theory.pushouts -open import synthetic-homotopy-theory.universal-property-coequalizers +open import synthetic-homotopy-theory.coforks funext univalence truncations +open import synthetic-homotopy-theory.dependent-cocones-under-spans funext univalence truncations +open import synthetic-homotopy-theory.dependent-universal-property-coequalizers funext univalence truncations +open import synthetic-homotopy-theory.pushouts funext univalence truncations +open import synthetic-homotopy-theory.universal-property-coequalizers funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/cofibers-of-maps.lagda.md b/src/synthetic-homotopy-theory/cofibers-of-maps.lagda.md index 09fde243e6..5dba711b71 100644 --- a/src/synthetic-homotopy-theory/cofibers-of-maps.lagda.md +++ b/src/synthetic-homotopy-theory/cofibers-of-maps.lagda.md @@ -1,28 +1,36 @@ # Cofibers of maps ```agda -module synthetic-homotopy-theory.cofibers-of-maps where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.cofibers-of-maps + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.constant-maps -open import foundation.contractible-types +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences +open import foundation.dependent-products-contractible-types funext +open import foundation.equivalences funext open import foundation.unit-type open import foundation.universe-levels -open import structured-types.pointed-maps +open import structured-types.pointed-maps funext univalence truncations open import structured-types.pointed-types -open import structured-types.pointed-unit-type +open import structured-types.pointed-unit-type funext univalence truncations -open import synthetic-homotopy-theory.cocones-under-spans -open import synthetic-homotopy-theory.dependent-cocones-under-spans -open import synthetic-homotopy-theory.dependent-universal-property-pushouts -open import synthetic-homotopy-theory.pushouts -open import synthetic-homotopy-theory.universal-property-pushouts +open import synthetic-homotopy-theory.cocones-under-spans funext +open import synthetic-homotopy-theory.dependent-cocones-under-spans funext univalence truncations +open import synthetic-homotopy-theory.dependent-universal-property-pushouts funext univalence truncations +open import synthetic-homotopy-theory.pushouts funext univalence truncations +open import synthetic-homotopy-theory.universal-property-pushouts funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/cofibers-of-pointed-maps.lagda.md b/src/synthetic-homotopy-theory/cofibers-of-pointed-maps.lagda.md index 87be7c63e3..58bb047abc 100644 --- a/src/synthetic-homotopy-theory/cofibers-of-pointed-maps.lagda.md +++ b/src/synthetic-homotopy-theory/cofibers-of-pointed-maps.lagda.md @@ -1,31 +1,28 @@ # Cofibers of pointed maps ```agda -module synthetic-homotopy-theory.cofibers-of-pointed-maps where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.cofibers-of-pointed-maps + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.constant-maps -open import foundation.contractible-types -open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.unit-type open import foundation.universe-levels -open import structured-types.pointed-maps +open import structured-types.pointed-maps funext univalence truncations open import structured-types.pointed-types -open import structured-types.pointed-unit-type - -open import synthetic-homotopy-theory.cocones-under-pointed-span-diagrams -open import synthetic-homotopy-theory.cocones-under-spans -open import synthetic-homotopy-theory.cofibers-of-maps -open import synthetic-homotopy-theory.dependent-cocones-under-spans -open import synthetic-homotopy-theory.dependent-universal-property-pushouts -open import synthetic-homotopy-theory.pushouts -open import synthetic-homotopy-theory.pushouts-of-pointed-types -open import synthetic-homotopy-theory.universal-property-pushouts +open import structured-types.pointed-unit-type funext univalence truncations + +open import synthetic-homotopy-theory.cocones-under-pointed-span-diagrams funext univalence truncations +open import synthetic-homotopy-theory.pushouts-of-pointed-types funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/coforks-cocones-under-sequential-diagrams.lagda.md b/src/synthetic-homotopy-theory/coforks-cocones-under-sequential-diagrams.lagda.md index 0efd91005f..81baf0a141 100644 --- a/src/synthetic-homotopy-theory/coforks-cocones-under-sequential-diagrams.lagda.md +++ b/src/synthetic-homotopy-theory/coforks-cocones-under-sequential-diagrams.lagda.md @@ -1,7 +1,15 @@ # Correspondence between cocones under sequential diagrams and certain coforks ```agda -module synthetic-homotopy-theory.coforks-cocones-under-sequential-diagrams where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.coforks-cocones-under-sequential-diagrams + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,33 +17,33 @@ module synthetic-homotopy-theory.coforks-cocones-under-sequential-diagrams where ```agda open import elementary-number-theory.natural-numbers -open import foundation.commuting-prisms-of-maps -open import foundation.commuting-triangles-of-maps +open import foundation.commuting-prisms-of-maps funext univalence +open import foundation.commuting-triangles-of-maps funext univalence open import foundation.dependent-pair-types open import foundation.double-arrows -open import foundation.equivalences -open import foundation.equivalences-double-arrows -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies -open import foundation.morphisms-double-arrows -open import foundation.retractions -open import foundation.sections +open import foundation.equivalences funext +open import foundation.equivalences-double-arrows funext univalence truncations +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext +open import foundation.morphisms-double-arrows funext univalence +open import foundation.retractions funext +open import foundation.sections funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import foundation.whiskering-homotopies-concatenation - -open import synthetic-homotopy-theory.cocones-under-sequential-diagrams -open import synthetic-homotopy-theory.coforks -open import synthetic-homotopy-theory.dependent-cocones-under-sequential-diagrams -open import synthetic-homotopy-theory.dependent-coforks -open import synthetic-homotopy-theory.equivalences-cocones-under-equivalences-sequential-diagrams -open import synthetic-homotopy-theory.equivalences-coforks-under-equivalences-double-arrows -open import synthetic-homotopy-theory.equivalences-sequential-diagrams -open import synthetic-homotopy-theory.morphisms-cocones-under-morphisms-sequential-diagrams -open import synthetic-homotopy-theory.morphisms-coforks-under-morphisms-double-arrows -open import synthetic-homotopy-theory.morphisms-sequential-diagrams -open import synthetic-homotopy-theory.sequential-diagrams +open import foundation.whiskering-homotopies-concatenation funext + +open import synthetic-homotopy-theory.cocones-under-sequential-diagrams funext univalence truncations +open import synthetic-homotopy-theory.coforks funext univalence truncations +open import synthetic-homotopy-theory.dependent-cocones-under-sequential-diagrams funext univalence truncations +open import synthetic-homotopy-theory.dependent-coforks funext univalence truncations +open import synthetic-homotopy-theory.equivalences-cocones-under-equivalences-sequential-diagrams funext univalence truncations +open import synthetic-homotopy-theory.equivalences-coforks-under-equivalences-double-arrows funext univalence truncations +open import synthetic-homotopy-theory.equivalences-sequential-diagrams funext univalence truncations +open import synthetic-homotopy-theory.morphisms-cocones-under-morphisms-sequential-diagrams funext univalence truncations +open import synthetic-homotopy-theory.morphisms-coforks-under-morphisms-double-arrows funext univalence truncations +open import synthetic-homotopy-theory.morphisms-sequential-diagrams funext univalence truncations +open import synthetic-homotopy-theory.sequential-diagrams funext univalence ```
diff --git a/src/synthetic-homotopy-theory/coforks.lagda.md b/src/synthetic-homotopy-theory/coforks.lagda.md index fa5ea65e19..41d7e30ce8 100644 --- a/src/synthetic-homotopy-theory/coforks.lagda.md +++ b/src/synthetic-homotopy-theory/coforks.lagda.md @@ -1,38 +1,47 @@ # Coforks ```agda -module synthetic-homotopy-theory.coforks where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.coforks + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.codiagonal-maps-of-types -open import foundation.commuting-squares-of-maps -open import foundation.commuting-triangles-of-maps -open import foundation.contractible-types -open import foundation.coproduct-types +open import foundation.commuting-squares-of-maps funext univalence +open import foundation.commuting-triangles-of-maps funext univalence +open import foundation.contractible-types funext univalence +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types funext open import foundation.double-arrows -open import foundation.equivalences -open import foundation.equivalences-double-arrows -open import foundation.equivalences-span-diagrams -open import foundation.function-types -open import foundation.functoriality-coproduct-types -open import foundation.functoriality-dependent-pair-types +open import foundation.equivalences funext +open import foundation.equivalences-double-arrows funext univalence truncations +open import foundation.equivalences-span-diagrams funext univalence truncations +open import foundation.function-types funext +open import foundation.functoriality-coproduct-types funext univalence truncations +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types -open import foundation.morphisms-double-arrows -open import foundation.morphisms-span-diagrams -open import foundation.span-diagrams +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext +open import foundation.morphisms-double-arrows funext univalence +open import foundation.morphisms-span-diagrams funext univalence truncations +open import foundation.span-diagrams funext open import foundation.structure-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext univalence truncations open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import synthetic-homotopy-theory.cocones-under-spans +open import synthetic-homotopy-theory.cocones-under-spans funext ```
diff --git a/src/synthetic-homotopy-theory/conjugation-loops.lagda.md b/src/synthetic-homotopy-theory/conjugation-loops.lagda.md index 589c5d457d..5b0f48b44f 100644 --- a/src/synthetic-homotopy-theory/conjugation-loops.lagda.md +++ b/src/synthetic-homotopy-theory/conjugation-loops.lagda.md @@ -1,21 +1,29 @@ # Conjugation of loops ```agda -module synthetic-homotopy-theory.conjugation-loops where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.conjugation-loops + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.universe-levels -open import structured-types.pointed-homotopies -open import structured-types.pointed-maps +open import structured-types.pointed-homotopies funext univalence truncations +open import structured-types.pointed-maps funext univalence truncations -open import synthetic-homotopy-theory.loop-spaces +open import synthetic-homotopy-theory.loop-spaces funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/connected-set-bundles-circle.lagda.md b/src/synthetic-homotopy-theory/connected-set-bundles-circle.lagda.md index 46a02e248f..044ff0f0cb 100644 --- a/src/synthetic-homotopy-theory/connected-set-bundles-circle.lagda.md +++ b/src/synthetic-homotopy-theory/connected-set-bundles-circle.lagda.md @@ -1,32 +1,41 @@ # Connected set bundles over the circle ```agda -module synthetic-homotopy-theory.connected-set-bundles-circle where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.connected-set-bundles-circle + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.0-connected-types -open import foundation.automorphisms +open import foundation.0-connected-types funext univalence truncations +open import foundation.automorphisms funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.identity-types -open import foundation.inhabited-types -open import foundation.mere-equality -open import foundation.propositions -open import foundation.sets -open import foundation.subtypes -open import foundation.surjective-maps +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.inhabited-types funext univalence truncations +open import foundation.mere-equality funext univalence truncations +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.subtypes funext univalence truncations +open import foundation.surjective-maps funext univalence truncations open import foundation.transport-along-identifications open import foundation.universe-levels -open import higher-group-theory.transitive-higher-group-actions +open import higher-group-theory.transitive-higher-group-actions funext univalence truncations -open import structured-types.sets-equipped-with-automorphisms +open import structured-types.sets-equipped-with-automorphisms funext univalence -open import synthetic-homotopy-theory.circle +open import synthetic-homotopy-theory.circle funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/connective-prespectra.lagda.md b/src/synthetic-homotopy-theory/connective-prespectra.lagda.md index db0ebe5577..2e4e42269e 100644 --- a/src/synthetic-homotopy-theory/connective-prespectra.lagda.md +++ b/src/synthetic-homotopy-theory/connective-prespectra.lagda.md @@ -1,7 +1,15 @@ # Connective prespectra ```agda -module synthetic-homotopy-theory.connective-prespectra where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.connective-prespectra + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,23 +17,24 @@ module synthetic-homotopy-theory.connective-prespectra where ```agda open import elementary-number-theory.natural-numbers -open import foundation.connected-types +open import foundation.connected-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.identity-types -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence open import foundation.truncation-levels open import foundation.universe-levels -open import structured-types.pointed-equivalences -open import structured-types.pointed-maps +open import structured-types.pointed-equivalences funext univalence truncations +open import structured-types.pointed-maps funext univalence truncations open import structured-types.pointed-types -open import synthetic-homotopy-theory.loop-spaces -open import synthetic-homotopy-theory.prespectra -open import synthetic-homotopy-theory.suspensions-of-pointed-types -open import synthetic-homotopy-theory.suspensions-of-types +open import synthetic-homotopy-theory.loop-spaces funext univalence truncations +open import synthetic-homotopy-theory.prespectra funext univalence truncations +open import synthetic-homotopy-theory.suspensions-of-pointed-types funext univalence truncations +open import synthetic-homotopy-theory.suspensions-of-types funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/connective-spectra.lagda.md b/src/synthetic-homotopy-theory/connective-spectra.lagda.md index 939ec9243c..f9a59674a4 100644 --- a/src/synthetic-homotopy-theory/connective-spectra.lagda.md +++ b/src/synthetic-homotopy-theory/connective-spectra.lagda.md @@ -1,7 +1,15 @@ # Connective spectra ```agda -module synthetic-homotopy-theory.connective-spectra where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.connective-spectra + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,25 +17,26 @@ module synthetic-homotopy-theory.connective-spectra where ```agda open import elementary-number-theory.natural-numbers -open import foundation.connected-types +open import foundation.connected-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.identity-types -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence open import foundation.truncation-levels open import foundation.universe-levels -open import structured-types.pointed-equivalences -open import structured-types.pointed-maps +open import structured-types.pointed-equivalences funext univalence truncations +open import structured-types.pointed-maps funext univalence truncations open import structured-types.pointed-types -open import synthetic-homotopy-theory.connective-prespectra -open import synthetic-homotopy-theory.loop-spaces -open import synthetic-homotopy-theory.prespectra -open import synthetic-homotopy-theory.spectra -open import synthetic-homotopy-theory.suspensions-of-pointed-types -open import synthetic-homotopy-theory.suspensions-of-types +open import synthetic-homotopy-theory.connective-prespectra funext univalence truncations +open import synthetic-homotopy-theory.loop-spaces funext univalence truncations +open import synthetic-homotopy-theory.prespectra funext univalence truncations +open import synthetic-homotopy-theory.spectra funext univalence truncations +open import synthetic-homotopy-theory.suspensions-of-pointed-types funext univalence truncations +open import synthetic-homotopy-theory.suspensions-of-types funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/dependent-cocones-under-sequential-diagrams.lagda.md b/src/synthetic-homotopy-theory/dependent-cocones-under-sequential-diagrams.lagda.md index debb9262d7..b9867b8f4b 100644 --- a/src/synthetic-homotopy-theory/dependent-cocones-under-sequential-diagrams.lagda.md +++ b/src/synthetic-homotopy-theory/dependent-cocones-under-sequential-diagrams.lagda.md @@ -1,7 +1,15 @@ # Dependent cocones under sequential diagrams ```agda -module synthetic-homotopy-theory.dependent-cocones-under-sequential-diagrams where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.dependent-cocones-under-sequential-diagrams + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -11,27 +19,27 @@ open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-dependent-functions open import foundation.action-on-identifications-functions -open import foundation.binary-homotopies -open import foundation.commuting-triangles-of-maps -open import foundation.constant-type-families +open import foundation.binary-homotopies funext +open import foundation.commuting-triangles-of-maps funext univalence +open import foundation.constant-type-families funext open import foundation.dependent-homotopies -open import foundation.dependent-identifications +open import foundation.dependent-identifications funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-function-types -open import foundation.functoriality-dependent-pair-types +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-function-types funext univalence +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.identity-types +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.structure-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext univalence truncations open import foundation.transport-along-identifications open import foundation.universe-levels -open import synthetic-homotopy-theory.cocones-under-sequential-diagrams -open import synthetic-homotopy-theory.dependent-coforks -open import synthetic-homotopy-theory.sequential-diagrams +open import synthetic-homotopy-theory.cocones-under-sequential-diagrams funext univalence truncations +open import synthetic-homotopy-theory.dependent-coforks funext univalence truncations +open import synthetic-homotopy-theory.sequential-diagrams funext univalence ```
diff --git a/src/synthetic-homotopy-theory/dependent-cocones-under-spans.lagda.md b/src/synthetic-homotopy-theory/dependent-cocones-under-spans.lagda.md index cfba684dd3..42bed8c513 100644 --- a/src/synthetic-homotopy-theory/dependent-cocones-under-spans.lagda.md +++ b/src/synthetic-homotopy-theory/dependent-cocones-under-spans.lagda.md @@ -1,7 +1,15 @@ # Dependent cocones under spans ```agda -module synthetic-homotopy-theory.dependent-cocones-under-spans where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.dependent-cocones-under-spans + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,35 +17,36 @@ module synthetic-homotopy-theory.dependent-cocones-under-spans where ```agda open import foundation.action-on-identifications-dependent-functions open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-identifications -open import foundation.commuting-squares-of-maps -open import foundation.constant-type-families -open import foundation.contractible-types +open import foundation.commuting-squares-of-identifications funext +open import foundation.commuting-squares-of-maps funext univalence +open import foundation.constant-type-families funext +open import foundation.contractible-types funext univalence open import foundation.dependent-homotopies -open import foundation.dependent-identifications +open import foundation.dependent-identifications funext open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types +open import foundation.dependent-products-contractible-types funext +open import foundation.equality-dependent-pair-types funext +open import foundation.equivalences funext +open import foundation.function-extensionality funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types -open import foundation.retractions -open import foundation.sections -open import foundation.span-diagrams +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext +open import foundation.retractions funext +open import foundation.sections funext +open import foundation.span-diagrams funext open import foundation.structure-identity-principle -open import foundation.torsorial-type-families -open import foundation.transport-along-higher-identifications +open import foundation.torsorial-type-families funext univalence truncations +open import foundation.transport-along-higher-identifications funext open import foundation.transport-along-identifications open import foundation.universe-levels open import foundation.whiskering-homotopies-composition open import foundation-core.injective-maps -open import synthetic-homotopy-theory.cocones-under-spans +open import synthetic-homotopy-theory.cocones-under-spans funext ```
diff --git a/src/synthetic-homotopy-theory/dependent-coforks.lagda.md b/src/synthetic-homotopy-theory/dependent-coforks.lagda.md index 39b40000f5..861983a445 100644 --- a/src/synthetic-homotopy-theory/dependent-coforks.lagda.md +++ b/src/synthetic-homotopy-theory/dependent-coforks.lagda.md @@ -1,7 +1,15 @@ # Dependent coforks ```agda -module synthetic-homotopy-theory.dependent-coforks where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.dependent-coforks + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,29 +17,29 @@ module synthetic-homotopy-theory.dependent-coforks where ```agda open import foundation.action-on-identifications-dependent-functions open import foundation.action-on-identifications-functions -open import foundation.commuting-triangles-of-maps -open import foundation.constant-type-families -open import foundation.coproduct-types -open import foundation.dependent-identifications +open import foundation.commuting-triangles-of-maps funext univalence +open import foundation.constant-type-families funext +open import foundation.coproduct-types funext univalence truncations +open import foundation.dependent-identifications funext open import foundation.dependent-pair-types open import foundation.double-arrows -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-function-types -open import foundation.functoriality-dependent-pair-types +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-function-types funext univalence +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext open import foundation.structure-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext univalence truncations open import foundation.transport-along-identifications open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import foundation.whiskering-identifications-concatenation +open import foundation.whiskering-identifications-concatenation funext -open import synthetic-homotopy-theory.coforks -open import synthetic-homotopy-theory.dependent-cocones-under-spans +open import synthetic-homotopy-theory.coforks funext univalence truncations +open import synthetic-homotopy-theory.dependent-cocones-under-spans funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/dependent-descent-circle.lagda.md b/src/synthetic-homotopy-theory/dependent-descent-circle.lagda.md index a847a0abfa..97a344acb8 100644 --- a/src/synthetic-homotopy-theory/dependent-descent-circle.lagda.md +++ b/src/synthetic-homotopy-theory/dependent-descent-circle.lagda.md @@ -1,28 +1,37 @@ # Dependent descent for the circle ```agda -module synthetic-homotopy-theory.dependent-descent-circle where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.dependent-descent-circle + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.commuting-squares-of-maps -open import foundation.contractible-types +open import foundation.commuting-squares-of-maps funext univalence +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.identity-types -open import foundation.torsorial-type-families +open import foundation.dependent-products-contractible-types funext +open import foundation.equality-dependent-pair-types funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.torsorial-type-families funext univalence truncations open import foundation.transport-along-identifications -open import foundation.univalence +open import foundation.univalence funext univalence open import foundation.universe-levels -open import structured-types.dependent-types-equipped-with-automorphisms +open import structured-types.dependent-types-equipped-with-automorphisms funext univalence truncations -open import synthetic-homotopy-theory.descent-circle -open import synthetic-homotopy-theory.free-loops +open import synthetic-homotopy-theory.descent-circle funext univalence truncations +open import synthetic-homotopy-theory.free-loops funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/dependent-pullback-property-pushouts.lagda.md b/src/synthetic-homotopy-theory/dependent-pullback-property-pushouts.lagda.md index 977930ff08..b379b5e30c 100644 --- a/src/synthetic-homotopy-theory/dependent-pullback-property-pushouts.lagda.md +++ b/src/synthetic-homotopy-theory/dependent-pullback-property-pushouts.lagda.md @@ -1,7 +1,15 @@ # The dependent pullback property of pushouts ```agda -module synthetic-homotopy-theory.dependent-pullback-property-pushouts where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.dependent-pullback-property-pushouts + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,26 +17,26 @@ module synthetic-homotopy-theory.dependent-pullback-property-pushouts where ```agda open import foundation.action-on-identifications-dependent-functions open import foundation.action-on-identifications-functions -open import foundation.cones-over-cospan-diagrams -open import foundation.constant-type-families +open import foundation.cones-over-cospan-diagrams funext +open import foundation.constant-type-families funext open import foundation.dependent-pair-types -open import foundation.dependent-sums-pullbacks -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.precomposition-functions -open import foundation.pullbacks +open import foundation.dependent-sums-pullbacks funext +open import foundation.function-extensionality funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.precomposition-functions funext +open import foundation.pullbacks funext univalence truncations open import foundation.transport-along-identifications -open import foundation.type-theoretic-principle-of-choice +open import foundation.type-theoretic-principle-of-choice funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import orthogonal-factorization-systems.lifts-families-of-elements -open import orthogonal-factorization-systems.precomposition-lifts-families-of-elements +open import orthogonal-factorization-systems.lifts-families-of-elements funext +open import orthogonal-factorization-systems.precomposition-lifts-families-of-elements funext univalence -open import synthetic-homotopy-theory.cocones-under-spans -open import synthetic-homotopy-theory.pullback-property-pushouts +open import synthetic-homotopy-theory.cocones-under-spans funext +open import synthetic-homotopy-theory.pullback-property-pushouts funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/dependent-pushout-products.lagda.md b/src/synthetic-homotopy-theory/dependent-pushout-products.lagda.md index 265ce6a2c9..763af4aebf 100644 --- a/src/synthetic-homotopy-theory/dependent-pushout-products.lagda.md +++ b/src/synthetic-homotopy-theory/dependent-pushout-products.lagda.md @@ -1,22 +1,31 @@ # Dependent pushout-products ```agda -module synthetic-homotopy-theory.dependent-pushout-products where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.dependent-pushout-products + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.contractible-types +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies +open import foundation.dependent-products-contractible-types funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext open import foundation.universe-levels -open import synthetic-homotopy-theory.cocones-under-spans -open import synthetic-homotopy-theory.pushouts -open import synthetic-homotopy-theory.universal-property-pushouts +open import synthetic-homotopy-theory.cocones-under-spans funext +open import synthetic-homotopy-theory.pushouts funext univalence truncations +open import synthetic-homotopy-theory.universal-property-pushouts funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/dependent-sequential-diagrams.lagda.md b/src/synthetic-homotopy-theory/dependent-sequential-diagrams.lagda.md index 04bd1a9b0a..6003d73014 100644 --- a/src/synthetic-homotopy-theory/dependent-sequential-diagrams.lagda.md +++ b/src/synthetic-homotopy-theory/dependent-sequential-diagrams.lagda.md @@ -1,7 +1,13 @@ # Dependent sequential diagrams ```agda -module synthetic-homotopy-theory.dependent-sequential-diagrams where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.dependent-sequential-diagrams + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports @@ -10,11 +16,11 @@ module synthetic-homotopy-theory.dependent-sequential-diagrams where open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.homotopies +open import foundation.function-types funext +open import foundation.homotopies funext open import foundation.universe-levels -open import synthetic-homotopy-theory.sequential-diagrams +open import synthetic-homotopy-theory.sequential-diagrams funext univalence ```
diff --git a/src/synthetic-homotopy-theory/dependent-suspension-structures.lagda.md b/src/synthetic-homotopy-theory/dependent-suspension-structures.lagda.md index 8000b52d60..35ea8ded9a 100644 --- a/src/synthetic-homotopy-theory/dependent-suspension-structures.lagda.md +++ b/src/synthetic-homotopy-theory/dependent-suspension-structures.lagda.md @@ -1,32 +1,40 @@ # Dependent suspension structures ```agda -module synthetic-homotopy-theory.dependent-suspension-structures where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.dependent-suspension-structures + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-identifications -open import foundation.constant-maps -open import foundation.dependent-identifications +open import foundation.commuting-squares-of-identifications funext +open import foundation.constant-maps funext univalence truncations +open import foundation.dependent-identifications funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.injective-maps +open import foundation.equivalences funext +open import foundation.function-extensionality funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.injective-maps funext open import foundation.structure-identity-principle open import foundation.transport-along-identifications open import foundation.unit-type -open import foundation.universal-property-unit-type +open import foundation.universal-property-unit-type funext open import foundation.universe-levels -open import synthetic-homotopy-theory.dependent-cocones-under-spans -open import synthetic-homotopy-theory.suspension-structures +open import synthetic-homotopy-theory.dependent-cocones-under-spans funext univalence truncations +open import synthetic-homotopy-theory.suspension-structures funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/dependent-universal-property-coequalizers.lagda.md b/src/synthetic-homotopy-theory/dependent-universal-property-coequalizers.lagda.md index ba60811fcb..442259776a 100644 --- a/src/synthetic-homotopy-theory/dependent-universal-property-coequalizers.lagda.md +++ b/src/synthetic-homotopy-theory/dependent-universal-property-coequalizers.lagda.md @@ -1,26 +1,35 @@ # The dependent universal property of coequalizers ```agda -module synthetic-homotopy-theory.dependent-universal-property-coequalizers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.dependent-universal-property-coequalizers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.contractible-maps -open import foundation.contractible-types +open import foundation.contractible-maps funext +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types funext open import foundation.double-arrows -open import foundation.equivalences -open import foundation.fibers-of-maps -open import foundation.functoriality-dependent-pair-types +open import foundation.equivalences funext +open import foundation.fibers-of-maps funext +open import foundation.functoriality-dependent-pair-types funext open import foundation.universe-levels -open import synthetic-homotopy-theory.coforks -open import synthetic-homotopy-theory.dependent-cocones-under-spans -open import synthetic-homotopy-theory.dependent-coforks -open import synthetic-homotopy-theory.dependent-universal-property-pushouts -open import synthetic-homotopy-theory.universal-property-coequalizers +open import synthetic-homotopy-theory.coforks funext univalence truncations +open import synthetic-homotopy-theory.dependent-cocones-under-spans funext univalence truncations +open import synthetic-homotopy-theory.dependent-coforks funext univalence truncations +open import synthetic-homotopy-theory.dependent-universal-property-pushouts funext univalence truncations +open import synthetic-homotopy-theory.universal-property-coequalizers funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/dependent-universal-property-pushouts.lagda.md b/src/synthetic-homotopy-theory/dependent-universal-property-pushouts.lagda.md index 22394d4c95..a32a382cde 100644 --- a/src/synthetic-homotopy-theory/dependent-universal-property-pushouts.lagda.md +++ b/src/synthetic-homotopy-theory/dependent-universal-property-pushouts.lagda.md @@ -1,34 +1,43 @@ # The dependent universal property of pushouts ```agda -module synthetic-homotopy-theory.dependent-universal-property-pushouts where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.dependent-universal-property-pushouts + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-dependent-functions -open import foundation.contractible-maps -open import foundation.contractible-types +open import foundation.contractible-maps funext +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types -open import foundation.equivalences -open import foundation.fibers-of-maps -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.retractions -open import foundation.standard-pullbacks +open import foundation.dependent-products-contractible-types funext +open import foundation.equality-dependent-pair-types funext +open import foundation.equivalences funext +open import foundation.fibers-of-maps funext +open import foundation.function-extensionality funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.retractions funext +open import foundation.standard-pullbacks funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import synthetic-homotopy-theory.cocones-under-spans -open import synthetic-homotopy-theory.dependent-cocones-under-spans -open import synthetic-homotopy-theory.dependent-pullback-property-pushouts -open import synthetic-homotopy-theory.induction-principle-pushouts -open import synthetic-homotopy-theory.universal-property-pushouts +open import synthetic-homotopy-theory.cocones-under-spans funext +open import synthetic-homotopy-theory.dependent-cocones-under-spans funext univalence truncations +open import synthetic-homotopy-theory.dependent-pullback-property-pushouts funext univalence truncations +open import synthetic-homotopy-theory.induction-principle-pushouts funext univalence truncations +open import synthetic-homotopy-theory.universal-property-pushouts funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/dependent-universal-property-sequential-colimits.lagda.md b/src/synthetic-homotopy-theory/dependent-universal-property-sequential-colimits.lagda.md index 449c744b8e..731a7e572e 100644 --- a/src/synthetic-homotopy-theory/dependent-universal-property-sequential-colimits.lagda.md +++ b/src/synthetic-homotopy-theory/dependent-universal-property-sequential-colimits.lagda.md @@ -1,38 +1,47 @@ # The dependent universal property of sequential colimits ```agda -module synthetic-homotopy-theory.dependent-universal-property-sequential-colimits where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.dependent-universal-property-sequential-colimits + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-triangles-of-maps -open import foundation.contractible-maps -open import foundation.contractible-types +open import foundation.commuting-triangles-of-maps funext univalence +open import foundation.contractible-maps funext +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.fibers-of-maps -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.precomposition-dependent-functions -open import foundation.precomposition-functions +open import foundation.dependent-products-contractible-types funext +open import foundation.equivalences funext +open import foundation.fibers-of-maps funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.precomposition-dependent-functions funext +open import foundation.precomposition-functions funext open import foundation.subtype-identity-principle -open import foundation.universal-property-equivalences +open import foundation.universal-property-equivalences funext open import foundation.universe-levels -open import synthetic-homotopy-theory.cocones-under-sequential-diagrams -open import synthetic-homotopy-theory.coforks -open import synthetic-homotopy-theory.coforks-cocones-under-sequential-diagrams -open import synthetic-homotopy-theory.dependent-cocones-under-sequential-diagrams -open import synthetic-homotopy-theory.dependent-coforks -open import synthetic-homotopy-theory.dependent-universal-property-coequalizers -open import synthetic-homotopy-theory.sequential-diagrams -open import synthetic-homotopy-theory.universal-property-coequalizers -open import synthetic-homotopy-theory.universal-property-sequential-colimits +open import synthetic-homotopy-theory.cocones-under-sequential-diagrams funext univalence truncations +open import synthetic-homotopy-theory.coforks funext univalence truncations +open import synthetic-homotopy-theory.coforks-cocones-under-sequential-diagrams funext univalence truncations +open import synthetic-homotopy-theory.dependent-cocones-under-sequential-diagrams funext univalence truncations +open import synthetic-homotopy-theory.dependent-coforks funext univalence truncations +open import synthetic-homotopy-theory.dependent-universal-property-coequalizers funext univalence truncations +open import synthetic-homotopy-theory.sequential-diagrams funext univalence +open import synthetic-homotopy-theory.universal-property-coequalizers funext univalence truncations +open import synthetic-homotopy-theory.universal-property-sequential-colimits funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/dependent-universal-property-suspensions.lagda.md b/src/synthetic-homotopy-theory/dependent-universal-property-suspensions.lagda.md index 0b545c7c69..0360d19894 100644 --- a/src/synthetic-homotopy-theory/dependent-universal-property-suspensions.lagda.md +++ b/src/synthetic-homotopy-theory/dependent-universal-property-suspensions.lagda.md @@ -1,24 +1,32 @@ # Dependent universal property of suspensions ```agda -module synthetic-homotopy-theory.dependent-universal-property-suspensions where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.dependent-universal-property-suspensions + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-dependent-functions -open import foundation.constant-maps +open import foundation.constant-maps funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.homotopies +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.homotopies funext open import foundation.unit-type open import foundation.universe-levels -open import synthetic-homotopy-theory.dependent-cocones-under-spans -open import synthetic-homotopy-theory.dependent-suspension-structures -open import synthetic-homotopy-theory.suspension-structures +open import synthetic-homotopy-theory.dependent-cocones-under-spans funext univalence truncations +open import synthetic-homotopy-theory.dependent-suspension-structures funext univalence truncations +open import synthetic-homotopy-theory.suspension-structures funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/descent-circle-constant-families.lagda.md b/src/synthetic-homotopy-theory/descent-circle-constant-families.lagda.md index 8ae23e0e55..1075df8f84 100644 --- a/src/synthetic-homotopy-theory/descent-circle-constant-families.lagda.md +++ b/src/synthetic-homotopy-theory/descent-circle-constant-families.lagda.md @@ -1,20 +1,28 @@ # Descent data for constant type families over the circle ```agda -module synthetic-homotopy-theory.descent-circle-constant-families where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.descent-circle-constant-families + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.constant-type-families +open import foundation.constant-type-families funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.identity-types +open import foundation.equivalences funext +open import foundation.identity-types funext open import foundation.universe-levels -open import synthetic-homotopy-theory.descent-circle -open import synthetic-homotopy-theory.free-loops +open import synthetic-homotopy-theory.descent-circle funext univalence truncations +open import synthetic-homotopy-theory.free-loops funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/descent-circle-dependent-pair-types.lagda.md b/src/synthetic-homotopy-theory/descent-circle-dependent-pair-types.lagda.md index b9abaf71f4..f9a11682ec 100644 --- a/src/synthetic-homotopy-theory/descent-circle-dependent-pair-types.lagda.md +++ b/src/synthetic-homotopy-theory/descent-circle-dependent-pair-types.lagda.md @@ -1,21 +1,29 @@ # Descent data for families of dependent pair types over the circle ```agda -module synthetic-homotopy-theory.descent-circle-dependent-pair-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.descent-circle-dependent-pair-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types -open import foundation.functoriality-dependent-pair-types -open import foundation.identity-types +open import foundation.equality-dependent-pair-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.identity-types funext open import foundation.universe-levels -open import synthetic-homotopy-theory.dependent-descent-circle -open import synthetic-homotopy-theory.descent-circle -open import synthetic-homotopy-theory.free-loops +open import synthetic-homotopy-theory.dependent-descent-circle funext univalence truncations +open import synthetic-homotopy-theory.descent-circle funext univalence truncations +open import synthetic-homotopy-theory.free-loops funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/descent-circle-equivalence-types.lagda.md b/src/synthetic-homotopy-theory/descent-circle-equivalence-types.lagda.md index cec4371a5e..98fadc2f58 100644 --- a/src/synthetic-homotopy-theory/descent-circle-equivalence-types.lagda.md +++ b/src/synthetic-homotopy-theory/descent-circle-equivalence-types.lagda.md @@ -1,27 +1,36 @@ # Descent data for families of equivalence types over the circle ```agda -module synthetic-homotopy-theory.descent-circle-equivalence-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.descent-circle-equivalence-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.contractible-types +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.functoriality-dependent-pair-types +open import foundation.dependent-products-contractible-types funext +open import foundation.equivalences funext +open import foundation.functoriality-dependent-pair-types funext open import foundation.universe-levels -open import synthetic-homotopy-theory.dependent-descent-circle -open import synthetic-homotopy-theory.descent-circle -open import synthetic-homotopy-theory.descent-circle-dependent-pair-types -open import synthetic-homotopy-theory.descent-circle-function-types -open import synthetic-homotopy-theory.descent-circle-subtypes -open import synthetic-homotopy-theory.free-loops -open import synthetic-homotopy-theory.morphisms-descent-data-circle -open import synthetic-homotopy-theory.sections-descent-circle -open import synthetic-homotopy-theory.universal-property-circle +open import synthetic-homotopy-theory.dependent-descent-circle funext univalence truncations +open import synthetic-homotopy-theory.descent-circle funext univalence truncations +open import synthetic-homotopy-theory.descent-circle-dependent-pair-types funext univalence truncations +open import synthetic-homotopy-theory.descent-circle-function-types funext univalence truncations +open import synthetic-homotopy-theory.descent-circle-subtypes funext univalence truncations +open import synthetic-homotopy-theory.free-loops funext univalence truncations +open import synthetic-homotopy-theory.morphisms-descent-data-circle funext univalence truncations +open import synthetic-homotopy-theory.sections-descent-circle funext univalence truncations +open import synthetic-homotopy-theory.universal-property-circle funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/descent-circle-function-types.lagda.md b/src/synthetic-homotopy-theory/descent-circle-function-types.lagda.md index 447911b467..fc6b8fb183 100644 --- a/src/synthetic-homotopy-theory/descent-circle-function-types.lagda.md +++ b/src/synthetic-homotopy-theory/descent-circle-function-types.lagda.md @@ -1,34 +1,42 @@ # Descent data for families of function types over the circle ```agda -module synthetic-homotopy-theory.descent-circle-function-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.descent-circle-function-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.commuting-squares-of-maps -open import foundation.commuting-triangles-of-maps +open import foundation.commuting-squares-of-maps funext univalence +open import foundation.commuting-triangles-of-maps funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.functoriality-function-types -open import foundation.homotopies +open import foundation.equivalences funext +open import foundation.function-extensionality funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.functoriality-function-types funext univalence +open import foundation.homotopies funext open import foundation.homotopy-algebra -open import foundation.identity-types -open import foundation.postcomposition-functions +open import foundation.identity-types funext +open import foundation.postcomposition-functions funext open import foundation.transport-along-identifications -open import foundation.universal-property-equivalences +open import foundation.universal-property-equivalences funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import synthetic-homotopy-theory.descent-circle -open import synthetic-homotopy-theory.free-loops -open import synthetic-homotopy-theory.morphisms-descent-data-circle -open import synthetic-homotopy-theory.sections-descent-circle -open import synthetic-homotopy-theory.universal-property-circle +open import synthetic-homotopy-theory.descent-circle funext univalence truncations +open import synthetic-homotopy-theory.free-loops funext univalence truncations +open import synthetic-homotopy-theory.morphisms-descent-data-circle funext univalence truncations +open import synthetic-homotopy-theory.sections-descent-circle funext univalence truncations +open import synthetic-homotopy-theory.universal-property-circle funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/descent-circle-subtypes.lagda.md b/src/synthetic-homotopy-theory/descent-circle-subtypes.lagda.md index 8b2ed00fc2..662933f910 100644 --- a/src/synthetic-homotopy-theory/descent-circle-subtypes.lagda.md +++ b/src/synthetic-homotopy-theory/descent-circle-subtypes.lagda.md @@ -1,29 +1,38 @@ # Subtypes of descent data for the circle ```agda -module synthetic-homotopy-theory.descent-circle-subtypes where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.descent-circle-subtypes + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.functoriality-dependent-pair-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.type-arithmetic-cartesian-product-types open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels -open import synthetic-homotopy-theory.dependent-descent-circle -open import synthetic-homotopy-theory.descent-circle -open import synthetic-homotopy-theory.descent-circle-dependent-pair-types -open import synthetic-homotopy-theory.free-loops -open import synthetic-homotopy-theory.sections-descent-circle -open import synthetic-homotopy-theory.universal-property-circle +open import synthetic-homotopy-theory.dependent-descent-circle funext univalence truncations +open import synthetic-homotopy-theory.descent-circle funext univalence truncations +open import synthetic-homotopy-theory.descent-circle-dependent-pair-types funext univalence truncations +open import synthetic-homotopy-theory.free-loops funext univalence truncations +open import synthetic-homotopy-theory.sections-descent-circle funext univalence truncations +open import synthetic-homotopy-theory.universal-property-circle funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/descent-circle.lagda.md b/src/synthetic-homotopy-theory/descent-circle.lagda.md index 8adc5c7904..8800d2e9e1 100644 --- a/src/synthetic-homotopy-theory/descent-circle.lagda.md +++ b/src/synthetic-homotopy-theory/descent-circle.lagda.md @@ -1,34 +1,42 @@ # The descent property of the circle ```agda -module synthetic-homotopy-theory.descent-circle where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.descent-circle + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.automorphisms -open import foundation.commuting-squares-of-maps -open import foundation.commuting-triangles-of-maps -open import foundation.contractible-maps -open import foundation.contractible-types +open import foundation.automorphisms funext univalence +open import foundation.commuting-squares-of-maps funext univalence +open import foundation.commuting-triangles-of-maps funext univalence +open import foundation.contractible-maps funext +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.fibers-of-maps -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.identity-types -open import foundation.torsorial-type-families +open import foundation.dependent-products-contractible-types funext +open import foundation.equivalences funext +open import foundation.fibers-of-maps funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.identity-types funext +open import foundation.torsorial-type-families funext univalence truncations open import foundation.transport-along-identifications -open import foundation.univalence +open import foundation.univalence funext univalence open import foundation.universe-levels -open import structured-types.equivalences-types-equipped-with-automorphisms -open import structured-types.types-equipped-with-automorphisms +open import structured-types.equivalences-types-equipped-with-automorphisms funext univalence truncations +open import structured-types.types-equipped-with-automorphisms funext univalence -open import synthetic-homotopy-theory.free-loops -open import synthetic-homotopy-theory.universal-property-circle +open import synthetic-homotopy-theory.free-loops funext univalence truncations +open import synthetic-homotopy-theory.universal-property-circle funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/descent-data-equivalence-types-over-pushouts.lagda.md b/src/synthetic-homotopy-theory/descent-data-equivalence-types-over-pushouts.lagda.md index 7095433e23..179a57151d 100644 --- a/src/synthetic-homotopy-theory/descent-data-equivalence-types-over-pushouts.lagda.md +++ b/src/synthetic-homotopy-theory/descent-data-equivalence-types-over-pushouts.lagda.md @@ -2,40 +2,48 @@ ```agda {-# OPTIONS --lossy-unification #-} - -module synthetic-homotopy-theory.descent-data-equivalence-types-over-pushouts where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.descent-data-equivalence-types-over-pushouts + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.commuting-squares-of-maps -open import foundation.commuting-triangles-of-maps -open import foundation.contractible-maps -open import foundation.contractible-types +open import foundation.commuting-squares-of-maps funext univalence +open import foundation.commuting-triangles-of-maps funext univalence +open import foundation.contractible-maps funext +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalence-extensionality -open import foundation.equivalences -open import foundation.fibers-of-maps -open import foundation.function-types -open import foundation.functoriality-dependent-function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies +open import foundation.dependent-products-contractible-types funext +open import foundation.equivalence-extensionality funext +open import foundation.equivalences funext +open import foundation.fibers-of-maps funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-function-types funext univalence +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext open import foundation.homotopy-algebra -open import foundation.postcomposition-functions -open import foundation.span-diagrams +open import foundation.postcomposition-functions funext +open import foundation.span-diagrams funext open import foundation.transport-along-identifications -open import foundation.universal-property-equivalences +open import foundation.universal-property-equivalences funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import synthetic-homotopy-theory.cocones-under-spans -open import synthetic-homotopy-theory.descent-data-pushouts -open import synthetic-homotopy-theory.equivalences-descent-data-pushouts -open import synthetic-homotopy-theory.families-descent-data-pushouts -open import synthetic-homotopy-theory.morphisms-descent-data-pushouts -open import synthetic-homotopy-theory.sections-descent-data-pushouts -open import synthetic-homotopy-theory.universal-property-pushouts +open import synthetic-homotopy-theory.cocones-under-spans funext +open import synthetic-homotopy-theory.descent-data-pushouts funext +open import synthetic-homotopy-theory.equivalences-descent-data-pushouts funext univalence truncations +open import synthetic-homotopy-theory.families-descent-data-pushouts funext univalence truncations +open import synthetic-homotopy-theory.morphisms-descent-data-pushouts funext univalence truncations +open import synthetic-homotopy-theory.sections-descent-data-pushouts funext univalence truncations +open import synthetic-homotopy-theory.universal-property-pushouts funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/descent-data-function-types-over-pushouts.lagda.md b/src/synthetic-homotopy-theory/descent-data-function-types-over-pushouts.lagda.md index ac284b320a..3a8c22e8a2 100644 --- a/src/synthetic-homotopy-theory/descent-data-function-types-over-pushouts.lagda.md +++ b/src/synthetic-homotopy-theory/descent-data-function-types-over-pushouts.lagda.md @@ -2,40 +2,48 @@ ```agda {-# OPTIONS --lossy-unification #-} - -module synthetic-homotopy-theory.descent-data-function-types-over-pushouts where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.descent-data-function-types-over-pushouts + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.commuting-squares-of-maps -open import foundation.commuting-triangles-of-maps -open import foundation.contractible-maps -open import foundation.contractible-types +open import foundation.commuting-squares-of-maps funext univalence +open import foundation.commuting-triangles-of-maps funext univalence +open import foundation.contractible-maps funext +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.fibers-of-maps -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.functoriality-dependent-function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies +open import foundation.dependent-products-contractible-types funext +open import foundation.equivalences funext +open import foundation.fibers-of-maps funext +open import foundation.function-extensionality funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-function-types funext univalence +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext open import foundation.homotopy-algebra -open import foundation.postcomposition-functions -open import foundation.span-diagrams +open import foundation.postcomposition-functions funext +open import foundation.span-diagrams funext open import foundation.transport-along-identifications -open import foundation.universal-property-equivalences +open import foundation.universal-property-equivalences funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import synthetic-homotopy-theory.cocones-under-spans -open import synthetic-homotopy-theory.descent-data-pushouts -open import synthetic-homotopy-theory.equivalences-descent-data-pushouts -open import synthetic-homotopy-theory.families-descent-data-pushouts -open import synthetic-homotopy-theory.morphisms-descent-data-pushouts -open import synthetic-homotopy-theory.sections-descent-data-pushouts -open import synthetic-homotopy-theory.universal-property-pushouts +open import synthetic-homotopy-theory.cocones-under-spans funext +open import synthetic-homotopy-theory.descent-data-pushouts funext +open import synthetic-homotopy-theory.equivalences-descent-data-pushouts funext univalence truncations +open import synthetic-homotopy-theory.families-descent-data-pushouts funext univalence truncations +open import synthetic-homotopy-theory.morphisms-descent-data-pushouts funext univalence truncations +open import synthetic-homotopy-theory.sections-descent-data-pushouts funext univalence truncations +open import synthetic-homotopy-theory.universal-property-pushouts funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/descent-data-identity-types-over-pushouts.lagda.md b/src/synthetic-homotopy-theory/descent-data-identity-types-over-pushouts.lagda.md index 6244d587ce..7e998f7258 100644 --- a/src/synthetic-homotopy-theory/descent-data-identity-types-over-pushouts.lagda.md +++ b/src/synthetic-homotopy-theory/descent-data-identity-types-over-pushouts.lagda.md @@ -2,24 +2,31 @@ ```agda {-# OPTIONS --lossy-unification #-} - -module synthetic-homotopy-theory.descent-data-identity-types-over-pushouts where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.descent-data-identity-types-over-pushouts + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.identity-types -open import foundation.span-diagrams +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.span-diagrams funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import synthetic-homotopy-theory.cocones-under-spans -open import synthetic-homotopy-theory.descent-data-pushouts -open import synthetic-homotopy-theory.equivalences-descent-data-pushouts -open import synthetic-homotopy-theory.families-descent-data-pushouts +open import synthetic-homotopy-theory.cocones-under-spans funext +open import synthetic-homotopy-theory.descent-data-pushouts funext +open import synthetic-homotopy-theory.equivalences-descent-data-pushouts funext univalence truncations +open import synthetic-homotopy-theory.families-descent-data-pushouts funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/descent-data-pushouts.lagda.md b/src/synthetic-homotopy-theory/descent-data-pushouts.lagda.md index 020d2dcefb..3126961282 100644 --- a/src/synthetic-homotopy-theory/descent-data-pushouts.lagda.md +++ b/src/synthetic-homotopy-theory/descent-data-pushouts.lagda.md @@ -1,20 +1,24 @@ # Descent data for pushouts ```agda -module synthetic-homotopy-theory.descent-data-pushouts where +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.descent-data-pushouts + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.span-diagrams +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.span-diagrams funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import synthetic-homotopy-theory.cocones-under-spans +open import synthetic-homotopy-theory.cocones-under-spans funext ```
diff --git a/src/synthetic-homotopy-theory/descent-data-sequential-colimits.lagda.md b/src/synthetic-homotopy-theory/descent-data-sequential-colimits.lagda.md index d498ebe3db..428bfc02a7 100644 --- a/src/synthetic-homotopy-theory/descent-data-sequential-colimits.lagda.md +++ b/src/synthetic-homotopy-theory/descent-data-sequential-colimits.lagda.md @@ -1,7 +1,15 @@ # Descent data for sequential colimits ```agda -module synthetic-homotopy-theory.descent-data-sequential-colimits where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.descent-data-sequential-colimits + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,15 +18,15 @@ module synthetic-homotopy-theory.descent-data-sequential-colimits where open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.equivalences +open import foundation.equivalences funext open import foundation.universe-levels -open import synthetic-homotopy-theory.cocones-under-sequential-diagrams -open import synthetic-homotopy-theory.dependent-sequential-diagrams -open import synthetic-homotopy-theory.equifibered-sequential-diagrams -open import synthetic-homotopy-theory.equivalences-dependent-sequential-diagrams -open import synthetic-homotopy-theory.morphisms-dependent-sequential-diagrams -open import synthetic-homotopy-theory.sequential-diagrams +open import synthetic-homotopy-theory.cocones-under-sequential-diagrams funext univalence truncations +open import synthetic-homotopy-theory.dependent-sequential-diagrams funext univalence +open import synthetic-homotopy-theory.equifibered-sequential-diagrams funext univalence +open import synthetic-homotopy-theory.equivalences-dependent-sequential-diagrams funext univalence truncations +open import synthetic-homotopy-theory.morphisms-dependent-sequential-diagrams funext univalence +open import synthetic-homotopy-theory.sequential-diagrams funext univalence ```
diff --git a/src/synthetic-homotopy-theory/descent-property-pushouts.lagda.md b/src/synthetic-homotopy-theory/descent-property-pushouts.lagda.md index 6d1f56638f..5ac86e4781 100644 --- a/src/synthetic-homotopy-theory/descent-property-pushouts.lagda.md +++ b/src/synthetic-homotopy-theory/descent-property-pushouts.lagda.md @@ -1,32 +1,41 @@ # Descent property of pushouts ```agda -module synthetic-homotopy-theory.descent-property-pushouts where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.descent-property-pushouts + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.commuting-triangles-of-maps -open import foundation.contractible-maps -open import foundation.contractible-types +open import foundation.commuting-triangles-of-maps funext univalence +open import foundation.contractible-maps funext +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types -open import foundation.equivalences -open import foundation.fibers-of-maps -open import foundation.function-extensionality -open import foundation.functoriality-dependent-function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.identity-types -open import foundation.span-diagrams -open import foundation.univalence +open import foundation.dependent-products-contractible-types funext +open import foundation.equality-dependent-pair-types funext +open import foundation.equivalences funext +open import foundation.fibers-of-maps funext +open import foundation.function-extensionality funext +open import foundation.functoriality-dependent-function-types funext univalence +open import foundation.functoriality-dependent-pair-types funext +open import foundation.identity-types funext +open import foundation.span-diagrams funext +open import foundation.univalence funext univalence open import foundation.universe-levels -open import synthetic-homotopy-theory.cocones-under-spans -open import synthetic-homotopy-theory.descent-data-pushouts -open import synthetic-homotopy-theory.equivalences-descent-data-pushouts -open import synthetic-homotopy-theory.families-descent-data-pushouts -open import synthetic-homotopy-theory.universal-property-pushouts +open import synthetic-homotopy-theory.cocones-under-spans funext +open import synthetic-homotopy-theory.descent-data-pushouts funext +open import synthetic-homotopy-theory.equivalences-descent-data-pushouts funext univalence truncations +open import synthetic-homotopy-theory.families-descent-data-pushouts funext univalence truncations +open import synthetic-homotopy-theory.universal-property-pushouts funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/descent-property-sequential-colimits.lagda.md b/src/synthetic-homotopy-theory/descent-property-sequential-colimits.lagda.md index 20b9c33dc7..1372029601 100644 --- a/src/synthetic-homotopy-theory/descent-property-sequential-colimits.lagda.md +++ b/src/synthetic-homotopy-theory/descent-property-sequential-colimits.lagda.md @@ -1,7 +1,15 @@ # Descent property of sequential colimits ```agda -module synthetic-homotopy-theory.descent-property-sequential-colimits where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.descent-property-sequential-colimits + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,21 +17,21 @@ module synthetic-homotopy-theory.descent-property-sequential-colimits where ```agda open import elementary-number-theory.natural-numbers -open import foundation.binary-homotopies -open import foundation.commuting-triangles-of-maps +open import foundation.binary-homotopies funext +open import foundation.commuting-triangles-of-maps funext univalence open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types -open import foundation.equivalences -open import foundation.functoriality-dependent-function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.identity-types -open import foundation.univalence +open import foundation.equality-dependent-pair-types funext +open import foundation.equivalences funext +open import foundation.functoriality-dependent-function-types funext univalence +open import foundation.functoriality-dependent-pair-types funext +open import foundation.identity-types funext +open import foundation.univalence funext univalence open import foundation.universe-levels -open import synthetic-homotopy-theory.cocones-under-sequential-diagrams -open import synthetic-homotopy-theory.descent-data-sequential-colimits -open import synthetic-homotopy-theory.sequential-diagrams -open import synthetic-homotopy-theory.universal-property-sequential-colimits +open import synthetic-homotopy-theory.cocones-under-sequential-diagrams funext univalence truncations +open import synthetic-homotopy-theory.descent-data-sequential-colimits funext univalence truncations +open import synthetic-homotopy-theory.sequential-diagrams funext univalence +open import synthetic-homotopy-theory.universal-property-sequential-colimits funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/double-loop-spaces.lagda.md b/src/synthetic-homotopy-theory/double-loop-spaces.lagda.md index 03c7e352fa..e58ce88527 100644 --- a/src/synthetic-homotopy-theory/double-loop-spaces.lagda.md +++ b/src/synthetic-homotopy-theory/double-loop-spaces.lagda.md @@ -1,26 +1,34 @@ # Double loop spaces ```agda -module synthetic-homotopy-theory.double-loop-spaces where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.double-loop-spaces + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-identifications +open import foundation.commuting-squares-of-identifications funext open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.path-algebra +open import foundation.identity-types funext +open import foundation.path-algebra funext open import foundation.universe-levels -open import foundation.whiskering-identifications-concatenation +open import foundation.whiskering-identifications-concatenation funext -open import structured-types.pointed-equivalences +open import structured-types.pointed-equivalences funext univalence truncations open import structured-types.pointed-types -open import synthetic-homotopy-theory.functoriality-loop-spaces -open import synthetic-homotopy-theory.iterated-loop-spaces -open import synthetic-homotopy-theory.loop-spaces +open import synthetic-homotopy-theory.functoriality-loop-spaces funext univalence truncations +open import synthetic-homotopy-theory.iterated-loop-spaces funext univalence truncations +open import synthetic-homotopy-theory.loop-spaces funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/eckmann-hilton-argument.lagda.md b/src/synthetic-homotopy-theory/eckmann-hilton-argument.lagda.md index bef7699d56..e73964f90f 100644 --- a/src/synthetic-homotopy-theory/eckmann-hilton-argument.lagda.md +++ b/src/synthetic-homotopy-theory/eckmann-hilton-argument.lagda.md @@ -1,33 +1,41 @@ # The Eckmann-Hilton argument ```agda -module synthetic-homotopy-theory.eckmann-hilton-argument where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.eckmann-hilton-argument + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-homotopies +open import foundation.commuting-squares-of-homotopies funext open import foundation.dependent-pair-types -open import foundation.homotopies +open import foundation.homotopies funext open import foundation.homotopy-algebra -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.interchange-law -open import foundation.path-algebra -open import foundation.transport-along-higher-identifications +open import foundation.path-algebra funext +open import foundation.transport-along-higher-identifications funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import foundation.whiskering-homotopies-concatenation -open import foundation.whiskering-identifications-concatenation +open import foundation.whiskering-homotopies-concatenation funext +open import foundation.whiskering-identifications-concatenation funext -open import structured-types.pointed-equivalences +open import structured-types.pointed-equivalences funext univalence truncations open import structured-types.pointed-types -open import synthetic-homotopy-theory.double-loop-spaces -open import synthetic-homotopy-theory.functoriality-loop-spaces -open import synthetic-homotopy-theory.loop-spaces -open import synthetic-homotopy-theory.triple-loop-spaces +open import synthetic-homotopy-theory.double-loop-spaces funext univalence truncations +open import synthetic-homotopy-theory.functoriality-loop-spaces funext univalence truncations +open import synthetic-homotopy-theory.loop-spaces funext univalence truncations +open import synthetic-homotopy-theory.triple-loop-spaces funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/equifibered-sequential-diagrams.lagda.md b/src/synthetic-homotopy-theory/equifibered-sequential-diagrams.lagda.md index 07cb2a030f..4f3cfdffb5 100644 --- a/src/synthetic-homotopy-theory/equifibered-sequential-diagrams.lagda.md +++ b/src/synthetic-homotopy-theory/equifibered-sequential-diagrams.lagda.md @@ -1,7 +1,13 @@ # Equifibered sequential diagrams ```agda -module synthetic-homotopy-theory.equifibered-sequential-diagrams where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.equifibered-sequential-diagrams + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports @@ -10,11 +16,11 @@ module synthetic-homotopy-theory.equifibered-sequential-diagrams where open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.equivalences +open import foundation.equivalences funext open import foundation.universe-levels -open import synthetic-homotopy-theory.dependent-sequential-diagrams -open import synthetic-homotopy-theory.sequential-diagrams +open import synthetic-homotopy-theory.dependent-sequential-diagrams funext univalence +open import synthetic-homotopy-theory.sequential-diagrams funext univalence ```
diff --git a/src/synthetic-homotopy-theory/equivalences-cocones-under-equivalences-sequential-diagrams.lagda.md b/src/synthetic-homotopy-theory/equivalences-cocones-under-equivalences-sequential-diagrams.lagda.md index c8954be17c..7ca2a7c247 100644 --- a/src/synthetic-homotopy-theory/equivalences-cocones-under-equivalences-sequential-diagrams.lagda.md +++ b/src/synthetic-homotopy-theory/equivalences-cocones-under-equivalences-sequential-diagrams.lagda.md @@ -1,7 +1,15 @@ # Equivalences of cocones under sequential diagrams ```agda -module synthetic-homotopy-theory.equivalences-cocones-under-equivalences-sequential-diagrams where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.equivalences-cocones-under-equivalences-sequential-diagrams + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,16 +17,16 @@ module synthetic-homotopy-theory.equivalences-cocones-under-equivalences-sequent ```agda open import elementary-number-theory.natural-numbers -open import foundation.commuting-prisms-of-maps -open import foundation.commuting-squares-of-maps +open import foundation.commuting-prisms-of-maps funext univalence +open import foundation.commuting-squares-of-maps funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences +open import foundation.equivalences funext open import foundation.universe-levels -open import synthetic-homotopy-theory.cocones-under-sequential-diagrams -open import synthetic-homotopy-theory.equivalences-sequential-diagrams -open import synthetic-homotopy-theory.morphisms-cocones-under-morphisms-sequential-diagrams -open import synthetic-homotopy-theory.sequential-diagrams +open import synthetic-homotopy-theory.cocones-under-sequential-diagrams funext univalence truncations +open import synthetic-homotopy-theory.equivalences-sequential-diagrams funext univalence truncations +open import synthetic-homotopy-theory.morphisms-cocones-under-morphisms-sequential-diagrams funext univalence truncations +open import synthetic-homotopy-theory.sequential-diagrams funext univalence ```
diff --git a/src/synthetic-homotopy-theory/equivalences-coforks-under-equivalences-double-arrows.lagda.md b/src/synthetic-homotopy-theory/equivalences-coforks-under-equivalences-double-arrows.lagda.md index a5fa74bee9..b68a514fe6 100644 --- a/src/synthetic-homotopy-theory/equivalences-coforks-under-equivalences-double-arrows.lagda.md +++ b/src/synthetic-homotopy-theory/equivalences-coforks-under-equivalences-double-arrows.lagda.md @@ -1,25 +1,33 @@ # Equivalences of coforks ```agda -module synthetic-homotopy-theory.equivalences-coforks-under-equivalences-double-arrows where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.equivalences-coforks-under-equivalences-double-arrows + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.commuting-squares-of-maps +open import foundation.commuting-squares-of-maps funext univalence open import foundation.dependent-pair-types open import foundation.double-arrows -open import foundation.equivalences -open import foundation.equivalences-arrows -open import foundation.equivalences-double-arrows -open import foundation.homotopies -open import foundation.morphisms-arrows +open import foundation.equivalences funext +open import foundation.equivalences-arrows funext univalence truncations +open import foundation.equivalences-double-arrows funext univalence truncations +open import foundation.homotopies funext +open import foundation.morphisms-arrows funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import synthetic-homotopy-theory.coforks -open import synthetic-homotopy-theory.morphisms-coforks-under-morphisms-double-arrows +open import synthetic-homotopy-theory.coforks funext univalence truncations +open import synthetic-homotopy-theory.morphisms-coforks-under-morphisms-double-arrows funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/equivalences-dependent-sequential-diagrams.lagda.md b/src/synthetic-homotopy-theory/equivalences-dependent-sequential-diagrams.lagda.md index 54b42eb7ca..4d639cd934 100644 --- a/src/synthetic-homotopy-theory/equivalences-dependent-sequential-diagrams.lagda.md +++ b/src/synthetic-homotopy-theory/equivalences-dependent-sequential-diagrams.lagda.md @@ -1,7 +1,15 @@ # Equivalances of dependent sequential diagrams ```agda -module synthetic-homotopy-theory.equivalences-dependent-sequential-diagrams where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.equivalences-dependent-sequential-diagrams + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,22 +17,22 @@ module synthetic-homotopy-theory.equivalences-dependent-sequential-diagrams wher ```agda open import elementary-number-theory.natural-numbers -open import foundation.commuting-squares-of-maps +open import foundation.commuting-squares-of-maps funext univalence open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types -open import foundation.equivalences +open import foundation.equality-dependent-function-types funext +open import foundation.equivalences funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext open import foundation.structure-identity-principle -open import foundation.torsorial-type-families -open import foundation.univalence +open import foundation.torsorial-type-families funext univalence truncations +open import foundation.univalence funext univalence open import foundation.universe-levels -open import synthetic-homotopy-theory.dependent-sequential-diagrams -open import synthetic-homotopy-theory.morphisms-dependent-sequential-diagrams -open import synthetic-homotopy-theory.sequential-diagrams +open import synthetic-homotopy-theory.dependent-sequential-diagrams funext univalence +open import synthetic-homotopy-theory.morphisms-dependent-sequential-diagrams funext univalence +open import synthetic-homotopy-theory.sequential-diagrams funext univalence ```
diff --git a/src/synthetic-homotopy-theory/equivalences-descent-data-pushouts.lagda.md b/src/synthetic-homotopy-theory/equivalences-descent-data-pushouts.lagda.md index a95a4a12a1..5176b5016c 100644 --- a/src/synthetic-homotopy-theory/equivalences-descent-data-pushouts.lagda.md +++ b/src/synthetic-homotopy-theory/equivalences-descent-data-pushouts.lagda.md @@ -1,29 +1,37 @@ # Equivalences of descent data for pushouts ```agda -module synthetic-homotopy-theory.equivalences-descent-data-pushouts where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.equivalences-descent-data-pushouts + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.commuting-squares-of-maps +open import foundation.commuting-squares-of-maps funext univalence open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types -open import foundation.equivalence-extensionality -open import foundation.equivalences +open import foundation.equality-dependent-function-types funext +open import foundation.equivalence-extensionality funext +open import foundation.equivalences funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types -open import foundation.span-diagrams +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext +open import foundation.span-diagrams funext open import foundation.structure-identity-principle -open import foundation.torsorial-type-families -open import foundation.univalence +open import foundation.torsorial-type-families funext univalence truncations +open import foundation.univalence funext univalence open import foundation.universe-levels -open import synthetic-homotopy-theory.descent-data-pushouts -open import synthetic-homotopy-theory.morphisms-descent-data-pushouts +open import synthetic-homotopy-theory.descent-data-pushouts funext +open import synthetic-homotopy-theory.morphisms-descent-data-pushouts funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/equivalences-sequential-diagrams.lagda.md b/src/synthetic-homotopy-theory/equivalences-sequential-diagrams.lagda.md index b82afe8957..05ee23e890 100644 --- a/src/synthetic-homotopy-theory/equivalences-sequential-diagrams.lagda.md +++ b/src/synthetic-homotopy-theory/equivalences-sequential-diagrams.lagda.md @@ -1,7 +1,15 @@ # Equivalences of sequential diagrams ```agda -module synthetic-homotopy-theory.equivalences-sequential-diagrams where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.equivalences-sequential-diagrams + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,23 +17,23 @@ module synthetic-homotopy-theory.equivalences-sequential-diagrams where ```agda open import elementary-number-theory.natural-numbers -open import foundation.commuting-squares-of-maps +open import foundation.commuting-squares-of-maps funext univalence open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types -open import foundation.equivalences -open import foundation.function-types +open import foundation.equality-dependent-function-types funext +open import foundation.equivalences funext +open import foundation.function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext open import foundation.structure-identity-principle -open import foundation.torsorial-type-families -open import foundation.univalence +open import foundation.torsorial-type-families funext univalence truncations +open import foundation.univalence funext univalence open import foundation.universe-levels -open import synthetic-homotopy-theory.morphisms-sequential-diagrams -open import synthetic-homotopy-theory.retracts-of-sequential-diagrams -open import synthetic-homotopy-theory.sequential-diagrams +open import synthetic-homotopy-theory.morphisms-sequential-diagrams funext univalence truncations +open import synthetic-homotopy-theory.retracts-of-sequential-diagrams funext univalence truncations +open import synthetic-homotopy-theory.sequential-diagrams funext univalence ```
diff --git a/src/synthetic-homotopy-theory/families-descent-data-pushouts.lagda.md b/src/synthetic-homotopy-theory/families-descent-data-pushouts.lagda.md index 0a68a9200c..2706355130 100644 --- a/src/synthetic-homotopy-theory/families-descent-data-pushouts.lagda.md +++ b/src/synthetic-homotopy-theory/families-descent-data-pushouts.lagda.md @@ -1,22 +1,30 @@ # Families with descent data for pushouts ```agda -module synthetic-homotopy-theory.families-descent-data-pushouts where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.families-descent-data-pushouts + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.commuting-squares-of-maps +open import foundation.commuting-squares-of-maps funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.span-diagrams +open import foundation.equivalences funext +open import foundation.span-diagrams funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import synthetic-homotopy-theory.cocones-under-spans -open import synthetic-homotopy-theory.descent-data-pushouts -open import synthetic-homotopy-theory.equivalences-descent-data-pushouts +open import synthetic-homotopy-theory.cocones-under-spans funext +open import synthetic-homotopy-theory.descent-data-pushouts funext +open import synthetic-homotopy-theory.equivalences-descent-data-pushouts funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/families-descent-data-sequential-colimits.lagda.md b/src/synthetic-homotopy-theory/families-descent-data-sequential-colimits.lagda.md index 4343695a69..b18f5910de 100644 --- a/src/synthetic-homotopy-theory/families-descent-data-sequential-colimits.lagda.md +++ b/src/synthetic-homotopy-theory/families-descent-data-sequential-colimits.lagda.md @@ -1,7 +1,15 @@ # Families with descent data for sequential colimits ```agda -module synthetic-homotopy-theory.families-descent-data-sequential-colimits where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.families-descent-data-sequential-colimits + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,16 +17,16 @@ module synthetic-homotopy-theory.families-descent-data-sequential-colimits where ```agda open import elementary-number-theory.natural-numbers -open import foundation.commuting-squares-of-maps +open import foundation.commuting-squares-of-maps funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences +open import foundation.equivalences funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import synthetic-homotopy-theory.cocones-under-sequential-diagrams -open import synthetic-homotopy-theory.dependent-sequential-diagrams -open import synthetic-homotopy-theory.descent-data-sequential-colimits -open import synthetic-homotopy-theory.sequential-diagrams +open import synthetic-homotopy-theory.cocones-under-sequential-diagrams funext univalence truncations +open import synthetic-homotopy-theory.dependent-sequential-diagrams funext univalence +open import synthetic-homotopy-theory.descent-data-sequential-colimits funext univalence truncations +open import synthetic-homotopy-theory.sequential-diagrams funext univalence ```
diff --git a/src/synthetic-homotopy-theory/flattening-lemma-coequalizers.lagda.md b/src/synthetic-homotopy-theory/flattening-lemma-coequalizers.lagda.md index 552c91b146..a4e40cfa6f 100644 --- a/src/synthetic-homotopy-theory/flattening-lemma-coequalizers.lagda.md +++ b/src/synthetic-homotopy-theory/flattening-lemma-coequalizers.lagda.md @@ -1,30 +1,38 @@ # The flattening lemma for coequalizers ```agda -module synthetic-homotopy-theory.flattening-lemma-coequalizers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.flattening-lemma-coequalizers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.coproduct-types +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types open import foundation.double-arrows -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.transport-along-identifications -open import foundation.type-arithmetic-coproduct-types +open import foundation.type-arithmetic-coproduct-types funext univalence truncations open import foundation.universe-levels -open import synthetic-homotopy-theory.coforks -open import synthetic-homotopy-theory.dependent-universal-property-coequalizers -open import synthetic-homotopy-theory.flattening-lemma-pushouts -open import synthetic-homotopy-theory.universal-property-coequalizers -open import synthetic-homotopy-theory.universal-property-pushouts +open import synthetic-homotopy-theory.coforks funext univalence truncations +open import synthetic-homotopy-theory.dependent-universal-property-coequalizers funext univalence truncations +open import synthetic-homotopy-theory.flattening-lemma-pushouts funext univalence truncations +open import synthetic-homotopy-theory.universal-property-coequalizers funext univalence truncations +open import synthetic-homotopy-theory.universal-property-pushouts funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/flattening-lemma-pushouts.lagda.md b/src/synthetic-homotopy-theory/flattening-lemma-pushouts.lagda.md index a5842aaa89..40bb05c981 100644 --- a/src/synthetic-homotopy-theory/flattening-lemma-pushouts.lagda.md +++ b/src/synthetic-homotopy-theory/flattening-lemma-pushouts.lagda.md @@ -1,36 +1,44 @@ # The flattening lemma for pushouts ```agda -module synthetic-homotopy-theory.flattening-lemma-pushouts where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.flattening-lemma-pushouts + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-cubes-of-maps -open import foundation.commuting-squares-of-maps -open import foundation.commuting-triangles-of-maps +open import foundation.commuting-cubes-of-maps funext univalence +open import foundation.commuting-squares-of-maps funext univalence +open import foundation.commuting-triangles-of-maps funext univalence open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.functoriality-dependent-function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.span-diagrams +open import foundation.equality-dependent-pair-types funext +open import foundation.equivalences funext +open import foundation.function-extensionality funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-function-types funext univalence +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.span-diagrams funext open import foundation.transport-along-identifications -open import foundation.universal-property-dependent-pair-types +open import foundation.universal-property-dependent-pair-types funext open import foundation.universe-levels -open import synthetic-homotopy-theory.cocones-under-spans -open import synthetic-homotopy-theory.dependent-cocones-under-spans -open import synthetic-homotopy-theory.dependent-universal-property-pushouts -open import synthetic-homotopy-theory.descent-data-pushouts -open import synthetic-homotopy-theory.equivalences-descent-data-pushouts -open import synthetic-homotopy-theory.universal-property-pushouts +open import synthetic-homotopy-theory.cocones-under-spans funext +open import synthetic-homotopy-theory.dependent-cocones-under-spans funext univalence truncations +open import synthetic-homotopy-theory.dependent-universal-property-pushouts funext univalence truncations +open import synthetic-homotopy-theory.descent-data-pushouts funext +open import synthetic-homotopy-theory.equivalences-descent-data-pushouts funext univalence truncations +open import synthetic-homotopy-theory.universal-property-pushouts funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/flattening-lemma-sequential-colimits.lagda.md b/src/synthetic-homotopy-theory/flattening-lemma-sequential-colimits.lagda.md index 1e014f974d..5a0599966b 100644 --- a/src/synthetic-homotopy-theory/flattening-lemma-sequential-colimits.lagda.md +++ b/src/synthetic-homotopy-theory/flattening-lemma-sequential-colimits.lagda.md @@ -1,7 +1,15 @@ # The flattening lemma for sequential colimits ```agda -module synthetic-homotopy-theory.flattening-lemma-sequential-colimits where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.flattening-lemma-sequential-colimits + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,26 +18,26 @@ module synthetic-homotopy-theory.flattening-lemma-sequential-colimits where open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.equivalences-double-arrows -open import foundation.function-types -open import foundation.homotopies +open import foundation.equivalences funext +open import foundation.equivalences-double-arrows funext univalence truncations +open import foundation.function-types funext +open import foundation.homotopies funext open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import synthetic-homotopy-theory.cocones-under-sequential-diagrams -open import synthetic-homotopy-theory.coforks -open import synthetic-homotopy-theory.coforks-cocones-under-sequential-diagrams -open import synthetic-homotopy-theory.dependent-universal-property-sequential-colimits -open import synthetic-homotopy-theory.equivalences-coforks-under-equivalences-double-arrows -open import synthetic-homotopy-theory.families-descent-data-sequential-colimits -open import synthetic-homotopy-theory.flattening-lemma-coequalizers -open import synthetic-homotopy-theory.sequential-diagrams -open import synthetic-homotopy-theory.total-cocones-families-sequential-diagrams -open import synthetic-homotopy-theory.total-sequential-diagrams -open import synthetic-homotopy-theory.universal-property-coequalizers -open import synthetic-homotopy-theory.universal-property-sequential-colimits +open import synthetic-homotopy-theory.cocones-under-sequential-diagrams funext univalence truncations +open import synthetic-homotopy-theory.coforks funext univalence truncations +open import synthetic-homotopy-theory.coforks-cocones-under-sequential-diagrams funext univalence truncations +open import synthetic-homotopy-theory.dependent-universal-property-sequential-colimits funext univalence truncations +open import synthetic-homotopy-theory.equivalences-coforks-under-equivalences-double-arrows funext univalence truncations +open import synthetic-homotopy-theory.families-descent-data-sequential-colimits funext univalence truncations +open import synthetic-homotopy-theory.flattening-lemma-coequalizers funext univalence truncations +open import synthetic-homotopy-theory.sequential-diagrams funext univalence +open import synthetic-homotopy-theory.total-cocones-families-sequential-diagrams funext univalence truncations +open import synthetic-homotopy-theory.total-sequential-diagrams funext univalence truncations +open import synthetic-homotopy-theory.universal-property-coequalizers funext univalence truncations +open import synthetic-homotopy-theory.universal-property-sequential-colimits funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/free-loops.lagda.md b/src/synthetic-homotopy-theory/free-loops.lagda.md index 2ca408cc36..2fd9a6a70e 100644 --- a/src/synthetic-homotopy-theory/free-loops.lagda.md +++ b/src/synthetic-homotopy-theory/free-loops.lagda.md @@ -1,22 +1,31 @@ # Free loops ```agda -module synthetic-homotopy-theory.free-loops where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.free-loops + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.constant-type-families -open import foundation.contractible-types +open import foundation.constant-type-families funext +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.functoriality-dependent-pair-types +open import foundation.dependent-products-contractible-types funext +open import foundation.equivalences funext +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.structure-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext univalence truncations open import foundation.transport-along-identifications open import foundation.universe-levels ``` diff --git a/src/synthetic-homotopy-theory/functoriality-loop-spaces.lagda.md b/src/synthetic-homotopy-theory/functoriality-loop-spaces.lagda.md index 32cc8a5ffa..19e7570876 100644 --- a/src/synthetic-homotopy-theory/functoriality-loop-spaces.lagda.md +++ b/src/synthetic-homotopy-theory/functoriality-loop-spaces.lagda.md @@ -1,7 +1,15 @@ # Functoriality of the loop space operation ```agda -module synthetic-homotopy-theory.functoriality-loop-spaces where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.functoriality-loop-spaces + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,21 +17,21 @@ module synthetic-homotopy-theory.functoriality-loop-spaces where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalences -open import foundation.faithful-maps -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.faithful-maps funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.universe-levels -open import structured-types.faithful-pointed-maps -open import structured-types.pointed-equivalences -open import structured-types.pointed-homotopies -open import structured-types.pointed-maps +open import structured-types.faithful-pointed-maps funext univalence truncations +open import structured-types.pointed-equivalences funext univalence truncations +open import structured-types.pointed-homotopies funext univalence truncations +open import structured-types.pointed-maps funext univalence truncations open import structured-types.pointed-types -open import synthetic-homotopy-theory.loop-spaces +open import synthetic-homotopy-theory.loop-spaces funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/functoriality-sequential-colimits.lagda.md b/src/synthetic-homotopy-theory/functoriality-sequential-colimits.lagda.md index e978bc0554..33edefe404 100644 --- a/src/synthetic-homotopy-theory/functoriality-sequential-colimits.lagda.md +++ b/src/synthetic-homotopy-theory/functoriality-sequential-colimits.lagda.md @@ -1,7 +1,15 @@ # Functoriality of sequential colimits ```agda -module synthetic-homotopy-theory.functoriality-sequential-colimits where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.functoriality-sequential-colimits + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,28 +18,26 @@ module synthetic-homotopy-theory.functoriality-sequential-colimits where open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.commuting-prisms-of-maps -open import foundation.commuting-squares-of-homotopies -open import foundation.commuting-squares-of-maps +open import foundation.commuting-prisms-of-maps funext univalence +open import foundation.commuting-squares-of-homotopies funext +open import foundation.commuting-squares-of-maps funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies -open import foundation.retractions -open import foundation.retracts-of-types -open import foundation.sections +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.retractions funext +open import foundation.retracts-of-types funext univalence +open import foundation.sections funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import synthetic-homotopy-theory.cocones-under-sequential-diagrams -open import synthetic-homotopy-theory.equivalences-sequential-diagrams -open import synthetic-homotopy-theory.morphisms-sequential-diagrams -open import synthetic-homotopy-theory.retracts-of-sequential-diagrams -open import synthetic-homotopy-theory.sequential-colimits -open import synthetic-homotopy-theory.sequential-diagrams -open import synthetic-homotopy-theory.universal-property-sequential-colimits +open import synthetic-homotopy-theory.cocones-under-sequential-diagrams funext univalence truncations +open import synthetic-homotopy-theory.equivalences-sequential-diagrams funext univalence truncations +open import synthetic-homotopy-theory.morphisms-sequential-diagrams funext univalence truncations +open import synthetic-homotopy-theory.retracts-of-sequential-diagrams funext univalence truncations +open import synthetic-homotopy-theory.sequential-colimits funext univalence truncations +open import synthetic-homotopy-theory.sequential-diagrams funext univalence +open import synthetic-homotopy-theory.universal-property-sequential-colimits funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/functoriality-suspensions.lagda.md b/src/synthetic-homotopy-theory/functoriality-suspensions.lagda.md index c5706895d6..9806e1b096 100644 --- a/src/synthetic-homotopy-theory/functoriality-suspensions.lagda.md +++ b/src/synthetic-homotopy-theory/functoriality-suspensions.lagda.md @@ -1,27 +1,35 @@ # Functoriality of suspensions ```agda -module synthetic-homotopy-theory.functoriality-suspensions where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.functoriality-suspensions + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-identifications +open import foundation.commuting-squares-of-identifications funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.retractions -open import foundation.retracts-of-types -open import foundation.sections +open import foundation.equivalences funext +open import foundation.function-extensionality funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.retractions funext +open import foundation.retracts-of-types funext univalence +open import foundation.sections funext open import foundation.universe-levels -open import synthetic-homotopy-theory.suspension-structures -open import synthetic-homotopy-theory.suspensions-of-types +open import synthetic-homotopy-theory.suspension-structures funext univalence truncations +open import synthetic-homotopy-theory.suspensions-of-types funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/groups-of-loops-in-1-types.lagda.md b/src/synthetic-homotopy-theory/groups-of-loops-in-1-types.lagda.md index cfa1ef495a..d2a8be0830 100644 --- a/src/synthetic-homotopy-theory/groups-of-loops-in-1-types.lagda.md +++ b/src/synthetic-homotopy-theory/groups-of-loops-in-1-types.lagda.md @@ -1,24 +1,32 @@ # Groups of loops in `1`-types ```agda -module synthetic-homotopy-theory.groups-of-loops-in-1-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.groups-of-loops-in-1-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.1-types +open import foundation.1-types funext univalence open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.sets +open import foundation.identity-types funext +open import foundation.sets funext univalence open import foundation.universe-levels -open import group-theory.groups -open import group-theory.semigroups +open import group-theory.groups funext univalence truncations +open import group-theory.semigroups funext univalence open import structured-types.pointed-types -open import synthetic-homotopy-theory.loop-spaces +open import synthetic-homotopy-theory.loop-spaces funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/hatchers-acyclic-type.lagda.md b/src/synthetic-homotopy-theory/hatchers-acyclic-type.lagda.md index 10609483e0..40b4b08104 100644 --- a/src/synthetic-homotopy-theory/hatchers-acyclic-type.lagda.md +++ b/src/synthetic-homotopy-theory/hatchers-acyclic-type.lagda.md @@ -1,7 +1,15 @@ # Hatcher's acyclic type ```agda -module synthetic-homotopy-theory.hatchers-acyclic-type where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.hatchers-acyclic-type + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,33 +17,34 @@ module synthetic-homotopy-theory.hatchers-acyclic-type where ```agda open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types -open import foundation.commuting-squares-of-identifications -open import foundation.contractible-types +open import foundation.cartesian-product-types funext univalence +open import foundation.commuting-squares-of-identifications funext +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.functoriality-cartesian-product-types -open import foundation.functoriality-dependent-pair-types +open import foundation.dependent-products-contractible-types funext +open import foundation.equivalences funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types -open import foundation.path-algebra +open import foundation.identity-types funext +open import foundation.path-algebra funext open import foundation.structure-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext univalence truncations open import foundation.type-arithmetic-cartesian-product-types open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels -open import structured-types.pointed-maps +open import structured-types.pointed-maps funext univalence truncations open import structured-types.pointed-types -open import structured-types.pointed-universal-property-contractible-types - -open import synthetic-homotopy-theory.acyclic-types -open import synthetic-homotopy-theory.eckmann-hilton-argument -open import synthetic-homotopy-theory.functoriality-loop-spaces -open import synthetic-homotopy-theory.loop-spaces -open import synthetic-homotopy-theory.powers-of-loops -open import synthetic-homotopy-theory.suspensions-of-pointed-types -open import synthetic-homotopy-theory.universal-property-suspensions-of-pointed-types +open import structured-types.pointed-universal-property-contractible-types funext univalence truncations + +open import synthetic-homotopy-theory.acyclic-types funext univalence truncations +open import synthetic-homotopy-theory.eckmann-hilton-argument funext univalence truncations +open import synthetic-homotopy-theory.functoriality-loop-spaces funext univalence truncations +open import synthetic-homotopy-theory.loop-spaces funext univalence truncations +open import synthetic-homotopy-theory.powers-of-loops funext univalence truncations +open import synthetic-homotopy-theory.suspensions-of-pointed-types funext univalence truncations +open import synthetic-homotopy-theory.universal-property-suspensions-of-pointed-types funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/homotopy-groups.lagda.md b/src/synthetic-homotopy-theory/homotopy-groups.lagda.md index 5d30f801f9..7f1adc7722 100644 --- a/src/synthetic-homotopy-theory/homotopy-groups.lagda.md +++ b/src/synthetic-homotopy-theory/homotopy-groups.lagda.md @@ -1,7 +1,15 @@ # Homotopy groups ```agda -module synthetic-homotopy-theory.homotopy-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.homotopy-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,20 +17,17 @@ module synthetic-homotopy-theory.homotopy-groups where ```agda open import elementary-number-theory.natural-numbers -open import foundation.connected-components open import foundation.dependent-pair-types -open import foundation.set-truncations -open import foundation.sets -open import foundation.truncation-levels -open import foundation.truncations +open import foundation.set-truncations funext univalence +open import foundation.sets funext univalence open import foundation.universe-levels -open import group-theory.concrete-groups -open import group-theory.homotopy-automorphism-groups +open import group-theory.concrete-groups funext univalence truncations +open import group-theory.homotopy-automorphism-groups funext univalence truncations open import structured-types.pointed-types -open import synthetic-homotopy-theory.iterated-loop-spaces +open import synthetic-homotopy-theory.iterated-loop-spaces funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/identity-systems-descent-data-pushouts.lagda.md b/src/synthetic-homotopy-theory/identity-systems-descent-data-pushouts.lagda.md index ed4ca2232d..a8de5de7c6 100644 --- a/src/synthetic-homotopy-theory/identity-systems-descent-data-pushouts.lagda.md +++ b/src/synthetic-homotopy-theory/identity-systems-descent-data-pushouts.lagda.md @@ -2,44 +2,52 @@ ```agda {-# OPTIONS --lossy-unification #-} - -module synthetic-homotopy-theory.identity-systems-descent-data-pushouts where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.identity-systems-descent-data-pushouts + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.commuting-squares-of-maps -open import foundation.contractible-types +open import foundation.commuting-squares-of-maps funext univalence +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types +open import foundation.dependent-products-contractible-types funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies +open import foundation.homotopies funext open import foundation.identity-systems -open import foundation.identity-types -open import foundation.sections +open import foundation.identity-types funext +open import foundation.sections funext open import foundation.singleton-induction -open import foundation.span-diagrams -open import foundation.torsorial-type-families -open import foundation.transposition-identifications-along-equivalences -open import foundation.universal-property-dependent-pair-types -open import foundation.universal-property-identity-types +open import foundation.span-diagrams funext +open import foundation.torsorial-type-families funext univalence truncations +open import foundation.transposition-identifications-along-equivalences funext +open import foundation.universal-property-dependent-pair-types funext +open import foundation.universal-property-identity-types funext univalence truncations open import foundation.universe-levels -open import synthetic-homotopy-theory.cocones-under-spans -open import synthetic-homotopy-theory.dependent-universal-property-pushouts -open import synthetic-homotopy-theory.descent-data-equivalence-types-over-pushouts -open import synthetic-homotopy-theory.descent-data-identity-types-over-pushouts -open import synthetic-homotopy-theory.descent-data-pushouts -open import synthetic-homotopy-theory.descent-property-pushouts -open import synthetic-homotopy-theory.equivalences-descent-data-pushouts -open import synthetic-homotopy-theory.families-descent-data-pushouts -open import synthetic-homotopy-theory.flattening-lemma-pushouts -open import synthetic-homotopy-theory.morphisms-descent-data-pushouts -open import synthetic-homotopy-theory.sections-descent-data-pushouts -open import synthetic-homotopy-theory.universal-property-pushouts +open import synthetic-homotopy-theory.cocones-under-spans funext +open import synthetic-homotopy-theory.dependent-universal-property-pushouts funext univalence truncations +open import synthetic-homotopy-theory.descent-data-equivalence-types-over-pushouts funext univalence truncations +open import synthetic-homotopy-theory.descent-data-identity-types-over-pushouts funext univalence truncations +open import synthetic-homotopy-theory.descent-data-pushouts funext +open import synthetic-homotopy-theory.descent-property-pushouts funext univalence truncations +open import synthetic-homotopy-theory.equivalences-descent-data-pushouts funext univalence truncations +open import synthetic-homotopy-theory.families-descent-data-pushouts funext univalence truncations +open import synthetic-homotopy-theory.flattening-lemma-pushouts funext univalence truncations +open import synthetic-homotopy-theory.morphisms-descent-data-pushouts funext univalence truncations +open import synthetic-homotopy-theory.sections-descent-data-pushouts funext univalence truncations +open import synthetic-homotopy-theory.universal-property-pushouts funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/induction-principle-pushouts.lagda.md b/src/synthetic-homotopy-theory/induction-principle-pushouts.lagda.md index f18ec14ff3..7a037c94ec 100644 --- a/src/synthetic-homotopy-theory/induction-principle-pushouts.lagda.md +++ b/src/synthetic-homotopy-theory/induction-principle-pushouts.lagda.md @@ -1,19 +1,27 @@ # The induction principle of pushouts ```agda -module synthetic-homotopy-theory.induction-principle-pushouts where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.induction-principle-pushouts + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.sections +open import foundation.identity-types funext +open import foundation.sections funext open import foundation.universe-levels -open import synthetic-homotopy-theory.cocones-under-spans -open import synthetic-homotopy-theory.dependent-cocones-under-spans +open import synthetic-homotopy-theory.cocones-under-spans funext +open import synthetic-homotopy-theory.dependent-cocones-under-spans funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/infinite-complex-projective-space.lagda.md b/src/synthetic-homotopy-theory/infinite-complex-projective-space.lagda.md index 3492b6e4ea..121e3a9856 100644 --- a/src/synthetic-homotopy-theory/infinite-complex-projective-space.lagda.md +++ b/src/synthetic-homotopy-theory/infinite-complex-projective-space.lagda.md @@ -1,18 +1,26 @@ # The infinite complex projective space ```agda -module synthetic-homotopy-theory.infinite-complex-projective-space where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.infinite-complex-projective-space + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.set-truncations +open import foundation.equivalences funext +open import foundation.set-truncations funext univalence open import foundation.universe-levels -open import synthetic-homotopy-theory.circle +open import synthetic-homotopy-theory.circle funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/infinite-cyclic-types.lagda.md b/src/synthetic-homotopy-theory/infinite-cyclic-types.lagda.md index bab47be956..3ac966f302 100644 --- a/src/synthetic-homotopy-theory/infinite-cyclic-types.lagda.md +++ b/src/synthetic-homotopy-theory/infinite-cyclic-types.lagda.md @@ -1,44 +1,55 @@ # Infinite cyclic types ```agda -module synthetic-homotopy-theory.infinite-cyclic-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.infinite-cyclic-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.addition-integers +open import elementary-number-theory.addition-integers funext univalence truncations +open import elementary-number-theory.group-of-integers funext univalence truncations open import elementary-number-theory.integers open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.contractible-maps -open import foundation.contractible-types +open import foundation.contractible-maps funext +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.functoriality-dependent-function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.raising-universe-levels -open import foundation.torsorial-type-families +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-function-types funext univalence +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence +open import foundation.torsorial-type-families funext univalence truncations open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels -open import structured-types.equivalences-types-equipped-with-endomorphisms -open import structured-types.initial-pointed-type-equipped-with-automorphism -open import structured-types.mere-equivalences-types-equipped-with-endomorphisms +open import foundation-core.raising-universe-levels + +open import structured-types.equivalences-types-equipped-with-endomorphisms funext univalence truncations +open import structured-types.initial-pointed-type-equipped-with-automorphism funext univalence truncations +open import structured-types.mere-equivalences-types-equipped-with-endomorphisms funext univalence truncations open import structured-types.pointed-types -open import structured-types.pointed-types-equipped-with-automorphisms -open import structured-types.types-equipped-with-endomorphisms +open import structured-types.pointed-types-equipped-with-automorphisms funext univalence truncations +open import structured-types.types-equipped-with-endomorphisms funext univalence -open import synthetic-homotopy-theory.loop-spaces +open import synthetic-homotopy-theory.loop-spaces funext univalence truncations -open import univalent-combinatorics.cyclic-finite-types +open import univalent-combinatorics.cyclic-finite-types funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/interval-type.lagda.md b/src/synthetic-homotopy-theory/interval-type.lagda.md index eb421618ba..298c6e3dfc 100644 --- a/src/synthetic-homotopy-theory/interval-type.lagda.md +++ b/src/synthetic-homotopy-theory/interval-type.lagda.md @@ -1,7 +1,13 @@ # The interval ```agda -module synthetic-homotopy-theory.interval-type where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.interval-type + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports @@ -9,14 +15,15 @@ module synthetic-homotopy-theory.interval-type where ```agda open import foundation.action-on-identifications-dependent-functions open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-identifications -open import foundation.contractible-types -open import foundation.dependent-identifications +open import foundation.commuting-squares-of-identifications funext +open import foundation.contractible-types funext univalence +open import foundation.dependent-identifications funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.homotopies -open import foundation.identity-types +open import foundation.dependent-products-contractible-types funext +open import foundation.equivalences funext +open import foundation.function-extensionality funext +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.structure-identity-principle open import foundation.transport-along-identifications open import foundation.universe-levels diff --git a/src/synthetic-homotopy-theory/iterated-loop-spaces.lagda.md b/src/synthetic-homotopy-theory/iterated-loop-spaces.lagda.md index 22f8b3630e..23f746ff0e 100644 --- a/src/synthetic-homotopy-theory/iterated-loop-spaces.lagda.md +++ b/src/synthetic-homotopy-theory/iterated-loop-spaces.lagda.md @@ -1,7 +1,15 @@ # Iterated loop spaces ```agda -module synthetic-homotopy-theory.iterated-loop-spaces where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.iterated-loop-spaces + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,13 +17,13 @@ module synthetic-homotopy-theory.iterated-loop-spaces where ```agda open import elementary-number-theory.natural-numbers -open import foundation.iterating-functions +open import foundation.iterating-functions funext univalence truncations open import foundation.universe-levels -open import structured-types.h-spaces +open import structured-types.h-spaces funext univalence truncations open import structured-types.pointed-types -open import synthetic-homotopy-theory.loop-spaces +open import synthetic-homotopy-theory.loop-spaces funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/iterated-suspensions-of-pointed-types.lagda.md b/src/synthetic-homotopy-theory/iterated-suspensions-of-pointed-types.lagda.md index 831ae41a13..eef6d1c725 100644 --- a/src/synthetic-homotopy-theory/iterated-suspensions-of-pointed-types.lagda.md +++ b/src/synthetic-homotopy-theory/iterated-suspensions-of-pointed-types.lagda.md @@ -1,7 +1,15 @@ # Iterated suspensions of pointed types ```agda -module synthetic-homotopy-theory.iterated-suspensions-of-pointed-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.iterated-suspensions-of-pointed-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,12 +17,12 @@ module synthetic-homotopy-theory.iterated-suspensions-of-pointed-types where ```agda open import elementary-number-theory.natural-numbers -open import foundation.iterating-functions +open import foundation.iterating-functions funext univalence truncations open import foundation.universe-levels open import structured-types.pointed-types -open import synthetic-homotopy-theory.suspensions-of-pointed-types +open import synthetic-homotopy-theory.suspensions-of-pointed-types funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/join-powers-of-types.lagda.md b/src/synthetic-homotopy-theory/join-powers-of-types.lagda.md index 3229530426..49c4b2ba2a 100644 --- a/src/synthetic-homotopy-theory/join-powers-of-types.lagda.md +++ b/src/synthetic-homotopy-theory/join-powers-of-types.lagda.md @@ -1,7 +1,15 @@ # Join powers of types ```agda -module synthetic-homotopy-theory.join-powers-of-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.join-powers-of-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,11 +17,11 @@ module synthetic-homotopy-theory.join-powers-of-types where ```agda open import elementary-number-theory.natural-numbers -open import foundation.empty-types -open import foundation.iterating-functions +open import foundation.empty-types funext univalence truncations +open import foundation.iterating-functions funext univalence truncations open import foundation.universe-levels -open import synthetic-homotopy-theory.joins-of-types +open import synthetic-homotopy-theory.joins-of-types funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/joins-of-maps.lagda.md b/src/synthetic-homotopy-theory/joins-of-maps.lagda.md index d31b23c331..c3a2fb57c8 100644 --- a/src/synthetic-homotopy-theory/joins-of-maps.lagda.md +++ b/src/synthetic-homotopy-theory/joins-of-maps.lagda.md @@ -1,22 +1,31 @@ # Joins of maps ```agda -module synthetic-homotopy-theory.joins-of-maps where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.joins-of-maps + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.contractible-types +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.homotopies -open import foundation.standard-pullbacks +open import foundation.dependent-products-contractible-types funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.standard-pullbacks funext open import foundation.universe-levels -open import synthetic-homotopy-theory.cocones-under-spans -open import synthetic-homotopy-theory.pushouts -open import synthetic-homotopy-theory.universal-property-pushouts +open import synthetic-homotopy-theory.cocones-under-spans funext +open import synthetic-homotopy-theory.pushouts funext univalence truncations +open import synthetic-homotopy-theory.universal-property-pushouts funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/joins-of-types.lagda.md b/src/synthetic-homotopy-theory/joins-of-types.lagda.md index 8b6ea38172..0d0868f5b3 100644 --- a/src/synthetic-homotopy-theory/joins-of-types.lagda.md +++ b/src/synthetic-homotopy-theory/joins-of-types.lagda.md @@ -1,36 +1,46 @@ # Joins of types ```agda -module synthetic-homotopy-theory.joins-of-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.joins-of-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types -open import foundation.contractible-types +open import foundation.cartesian-product-types funext univalence +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.disjunction -open import foundation.empty-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.propositions +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.disjunction funext univalence truncations +open import foundation.empty-types funext univalence truncations +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.propositions funext univalence open import foundation.type-arithmetic-cartesian-product-types open import foundation.type-arithmetic-dependent-pair-types -open import foundation.type-arithmetic-empty-type -open import foundation.type-arithmetic-unit-type +open import foundation.type-arithmetic-empty-type funext univalence truncations +open import foundation.type-arithmetic-unit-type funext open import foundation.unit-type open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import synthetic-homotopy-theory.cocones-under-spans -open import synthetic-homotopy-theory.dependent-cocones-under-spans -open import synthetic-homotopy-theory.pushouts -open import synthetic-homotopy-theory.universal-property-pushouts +open import synthetic-homotopy-theory.cocones-under-spans funext +open import synthetic-homotopy-theory.dependent-cocones-under-spans funext univalence truncations +open import synthetic-homotopy-theory.pushouts funext univalence truncations +open import synthetic-homotopy-theory.universal-property-pushouts funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/left-half-smash-products.lagda.md b/src/synthetic-homotopy-theory/left-half-smash-products.lagda.md index 73c0d3f6e8..7c500b69be 100644 --- a/src/synthetic-homotopy-theory/left-half-smash-products.lagda.md +++ b/src/synthetic-homotopy-theory/left-half-smash-products.lagda.md @@ -1,19 +1,27 @@ # Left half-smash products ```agda -module synthetic-homotopy-theory.left-half-smash-products where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.left-half-smash-products + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types open import foundation.universe-levels open import structured-types.pointed-types -open import synthetic-homotopy-theory.cofibers-of-maps +open import synthetic-homotopy-theory.cofibers-of-maps funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/loop-homotopy-circle.lagda.md b/src/synthetic-homotopy-theory/loop-homotopy-circle.lagda.md index 492b1150f2..1c9b2ad86e 100644 --- a/src/synthetic-homotopy-theory/loop-homotopy-circle.lagda.md +++ b/src/synthetic-homotopy-theory/loop-homotopy-circle.lagda.md @@ -1,27 +1,27 @@ # The loop homotopy on the circle ```agda -module synthetic-homotopy-theory.loop-homotopy-circle where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.loop-homotopy-circle + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.action-on-identifications-functions -open import foundation.dependent-pair-types -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.negated-equality -open import foundation.negation -open import foundation.transport-along-identifications -open import foundation.universe-levels - -open import structured-types.pointed-homotopies -open import structured-types.pointed-maps - -open import synthetic-homotopy-theory.circle +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.negated-equality funext univalence truncations +open import foundation.negation funext + +open import synthetic-homotopy-theory.circle funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/loop-spaces.lagda.md b/src/synthetic-homotopy-theory/loop-spaces.lagda.md index d150a83996..cd5a0604eb 100644 --- a/src/synthetic-homotopy-theory/loop-spaces.lagda.md +++ b/src/synthetic-homotopy-theory/loop-spaces.lagda.md @@ -1,22 +1,30 @@ # Loop spaces ```agda -module synthetic-homotopy-theory.loop-spaces where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.loop-spaces + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.identity-types +open import foundation.equivalences funext +open import foundation.identity-types funext open import foundation.universe-levels -open import structured-types.h-spaces -open import structured-types.magmas -open import structured-types.pointed-equivalences +open import structured-types.h-spaces funext univalence truncations +open import structured-types.magmas funext univalence +open import structured-types.pointed-equivalences funext univalence truncations open import structured-types.pointed-types -open import structured-types.wild-quasigroups +open import structured-types.wild-quasigroups funext univalence ```
diff --git a/src/synthetic-homotopy-theory/maps-of-prespectra.lagda.md b/src/synthetic-homotopy-theory/maps-of-prespectra.lagda.md index 4f3e139b27..aeb87ff871 100644 --- a/src/synthetic-homotopy-theory/maps-of-prespectra.lagda.md +++ b/src/synthetic-homotopy-theory/maps-of-prespectra.lagda.md @@ -2,8 +2,15 @@ ```agda {-# OPTIONS --guardedness #-} - -module synthetic-homotopy-theory.maps-of-prespectra where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.maps-of-prespectra + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -13,17 +20,17 @@ open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.homotopies +open import foundation.homotopies funext open import foundation.universe-levels -open import structured-types.commuting-squares-of-pointed-maps -open import structured-types.pointed-homotopies -open import structured-types.pointed-maps -open import structured-types.whiskering-pointed-homotopies-composition -open import structured-types.wild-category-of-pointed-types +open import structured-types.commuting-squares-of-pointed-maps funext univalence truncations +open import structured-types.pointed-homotopies funext univalence truncations +open import structured-types.pointed-maps funext univalence truncations +open import structured-types.whiskering-pointed-homotopies-composition funext univalence truncations +open import structured-types.wild-category-of-pointed-types funext univalence truncations -open import synthetic-homotopy-theory.functoriality-loop-spaces -open import synthetic-homotopy-theory.prespectra +open import synthetic-homotopy-theory.functoriality-loop-spaces funext univalence truncations +open import synthetic-homotopy-theory.prespectra funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/mere-spheres.lagda.md b/src/synthetic-homotopy-theory/mere-spheres.lagda.md index 70a895594b..b035c8d485 100644 --- a/src/synthetic-homotopy-theory/mere-spheres.lagda.md +++ b/src/synthetic-homotopy-theory/mere-spheres.lagda.md @@ -1,7 +1,15 @@ # Mere spheres ```agda -module synthetic-homotopy-theory.mere-spheres where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.mere-spheres + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports
 @@ -10,11 +18,12 @@ module synthetic-homotopy-theory.mere-spheres where open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.mere-equivalences -open import foundation.propositions +open import foundation.mere-equivalences funext univalence truncations +open import foundation.propositions funext univalence +open import foundation.dependent-products-propositions funext open import foundation.universe-levels -open import synthetic-homotopy-theory.spheres +open import synthetic-homotopy-theory.spheres funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/morphisms-cocones-under-morphisms-sequential-diagrams.lagda.md b/src/synthetic-homotopy-theory/morphisms-cocones-under-morphisms-sequential-diagrams.lagda.md index ab2a8b89e3..0e83217d53 100644 --- a/src/synthetic-homotopy-theory/morphisms-cocones-under-morphisms-sequential-diagrams.lagda.md +++ b/src/synthetic-homotopy-theory/morphisms-cocones-under-morphisms-sequential-diagrams.lagda.md @@ -1,7 +1,15 @@ # Morphisms of cocones under morphisms of sequential diagrams ```agda -module synthetic-homotopy-theory.morphisms-cocones-under-morphisms-sequential-diagrams where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.morphisms-cocones-under-morphisms-sequential-diagrams + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,14 +17,14 @@ module synthetic-homotopy-theory.morphisms-cocones-under-morphisms-sequential-di ```agda open import elementary-number-theory.natural-numbers -open import foundation.commuting-prisms-of-maps -open import foundation.commuting-squares-of-maps +open import foundation.commuting-prisms-of-maps funext univalence +open import foundation.commuting-squares-of-maps funext univalence open import foundation.dependent-pair-types open import foundation.universe-levels -open import synthetic-homotopy-theory.cocones-under-sequential-diagrams -open import synthetic-homotopy-theory.morphisms-sequential-diagrams -open import synthetic-homotopy-theory.sequential-diagrams +open import synthetic-homotopy-theory.cocones-under-sequential-diagrams funext univalence truncations +open import synthetic-homotopy-theory.morphisms-sequential-diagrams funext univalence truncations +open import synthetic-homotopy-theory.sequential-diagrams funext univalence ```
diff --git a/src/synthetic-homotopy-theory/morphisms-coforks-under-morphisms-double-arrows.lagda.md b/src/synthetic-homotopy-theory/morphisms-coforks-under-morphisms-double-arrows.lagda.md index 05c6762c56..dddd499633 100644 --- a/src/synthetic-homotopy-theory/morphisms-coforks-under-morphisms-double-arrows.lagda.md +++ b/src/synthetic-homotopy-theory/morphisms-coforks-under-morphisms-double-arrows.lagda.md @@ -1,22 +1,30 @@ # Morphisms of coforks ```agda -module synthetic-homotopy-theory.morphisms-coforks-under-morphisms-double-arrows where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.morphisms-coforks-under-morphisms-double-arrows + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.commuting-squares-of-maps +open import foundation.commuting-squares-of-maps funext univalence open import foundation.dependent-pair-types open import foundation.double-arrows -open import foundation.homotopies -open import foundation.morphisms-arrows -open import foundation.morphisms-double-arrows +open import foundation.homotopies funext +open import foundation.morphisms-arrows funext +open import foundation.morphisms-double-arrows funext univalence open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import synthetic-homotopy-theory.coforks +open import synthetic-homotopy-theory.coforks funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/morphisms-dependent-sequential-diagrams.lagda.md b/src/synthetic-homotopy-theory/morphisms-dependent-sequential-diagrams.lagda.md index 129a0c0eca..4a5f8e6f3b 100644 --- a/src/synthetic-homotopy-theory/morphisms-dependent-sequential-diagrams.lagda.md +++ b/src/synthetic-homotopy-theory/morphisms-dependent-sequential-diagrams.lagda.md @@ -1,7 +1,13 @@ # Morphisms of dependent sequential diagrams ```agda -module synthetic-homotopy-theory.morphisms-dependent-sequential-diagrams where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.morphisms-dependent-sequential-diagrams + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports @@ -9,12 +15,12 @@ module synthetic-homotopy-theory.morphisms-dependent-sequential-diagrams where ```agda open import elementary-number-theory.natural-numbers -open import foundation.commuting-squares-of-maps +open import foundation.commuting-squares-of-maps funext univalence open import foundation.dependent-pair-types open import foundation.universe-levels -open import synthetic-homotopy-theory.dependent-sequential-diagrams -open import synthetic-homotopy-theory.sequential-diagrams +open import synthetic-homotopy-theory.dependent-sequential-diagrams funext univalence +open import synthetic-homotopy-theory.sequential-diagrams funext univalence ```
diff --git a/src/synthetic-homotopy-theory/morphisms-descent-data-circle.lagda.md b/src/synthetic-homotopy-theory/morphisms-descent-data-circle.lagda.md index d579804e93..35a7e182dd 100644 --- a/src/synthetic-homotopy-theory/morphisms-descent-data-circle.lagda.md +++ b/src/synthetic-homotopy-theory/morphisms-descent-data-circle.lagda.md @@ -1,18 +1,26 @@ # Morphisms of descent data of the circle ```agda -module synthetic-homotopy-theory.morphisms-descent-data-circle where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.morphisms-descent-data-circle + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.commuting-squares-of-maps +open import foundation.commuting-squares-of-maps funext univalence open import foundation.universe-levels -open import structured-types.morphisms-types-equipped-with-automorphisms +open import structured-types.morphisms-types-equipped-with-automorphisms funext univalence truncations -open import synthetic-homotopy-theory.descent-circle +open import synthetic-homotopy-theory.descent-circle funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/morphisms-descent-data-pushouts.lagda.md b/src/synthetic-homotopy-theory/morphisms-descent-data-pushouts.lagda.md index 27f747d90f..37e712131a 100644 --- a/src/synthetic-homotopy-theory/morphisms-descent-data-pushouts.lagda.md +++ b/src/synthetic-homotopy-theory/morphisms-descent-data-pushouts.lagda.md @@ -1,29 +1,37 @@ # Morphisms of descent data for pushouts ```agda -module synthetic-homotopy-theory.morphisms-descent-data-pushouts where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.morphisms-descent-data-pushouts + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.commuting-squares-of-homotopies -open import foundation.commuting-squares-of-maps +open import foundation.commuting-squares-of-homotopies funext +open import foundation.commuting-squares-of-maps funext univalence open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types -open import foundation.equivalences -open import foundation.function-types +open import foundation.equality-dependent-function-types funext +open import foundation.equivalences funext +open import foundation.function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types -open import foundation.span-diagrams +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext +open import foundation.span-diagrams funext open import foundation.structure-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext univalence truncations open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import synthetic-homotopy-theory.descent-data-pushouts +open import synthetic-homotopy-theory.descent-data-pushouts funext ```
diff --git a/src/synthetic-homotopy-theory/morphisms-sequential-diagrams.lagda.md b/src/synthetic-homotopy-theory/morphisms-sequential-diagrams.lagda.md index a094834153..bc40043061 100644 --- a/src/synthetic-homotopy-theory/morphisms-sequential-diagrams.lagda.md +++ b/src/synthetic-homotopy-theory/morphisms-sequential-diagrams.lagda.md @@ -1,7 +1,15 @@ # Morphisms of sequential diagrams ```agda -module synthetic-homotopy-theory.morphisms-sequential-diagrams where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.morphisms-sequential-diagrams + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,24 +17,24 @@ module synthetic-homotopy-theory.morphisms-sequential-diagrams where ```agda open import elementary-number-theory.natural-numbers -open import foundation.binary-homotopies -open import foundation.commuting-squares-of-homotopies -open import foundation.commuting-squares-of-maps +open import foundation.binary-homotopies funext +open import foundation.commuting-squares-of-homotopies funext +open import foundation.commuting-squares-of-maps funext univalence open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types -open import foundation.equivalences -open import foundation.function-types +open import foundation.equality-dependent-function-types funext +open import foundation.equivalences funext +open import foundation.function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext open import foundation.structure-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext univalence truncations open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import synthetic-homotopy-theory.dependent-sequential-diagrams -open import synthetic-homotopy-theory.sequential-diagrams +open import synthetic-homotopy-theory.dependent-sequential-diagrams funext univalence +open import synthetic-homotopy-theory.sequential-diagrams funext univalence ```
diff --git a/src/synthetic-homotopy-theory/multiplication-circle.lagda.md b/src/synthetic-homotopy-theory/multiplication-circle.lagda.md index cb1de4f9ff..35b2083297 100644 --- a/src/synthetic-homotopy-theory/multiplication-circle.lagda.md +++ b/src/synthetic-homotopy-theory/multiplication-circle.lagda.md @@ -1,7 +1,15 @@ # The multiplication operation on the circle ```agda -module synthetic-homotopy-theory.multiplication-circle where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.multiplication-circle + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,20 +17,16 @@ module synthetic-homotopy-theory.multiplication-circle where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.negated-equality -open import foundation.negation +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import structured-types.pointed-homotopies -open import structured-types.pointed-maps +open import structured-types.pointed-homotopies funext univalence truncations +open import structured-types.pointed-maps funext univalence truncations -open import synthetic-homotopy-theory.circle -open import synthetic-homotopy-theory.loop-homotopy-circle +open import synthetic-homotopy-theory.circle funext univalence truncations +open import synthetic-homotopy-theory.loop-homotopy-circle funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/null-cocones-under-pointed-span-diagrams.lagda.md b/src/synthetic-homotopy-theory/null-cocones-under-pointed-span-diagrams.lagda.md index 277a8788fb..c235ba7ff5 100644 --- a/src/synthetic-homotopy-theory/null-cocones-under-pointed-span-diagrams.lagda.md +++ b/src/synthetic-homotopy-theory/null-cocones-under-pointed-span-diagrams.lagda.md @@ -1,28 +1,36 @@ # Null cocones under pointed span diagrams ```agda -module synthetic-homotopy-theory.null-cocones-under-pointed-span-diagrams where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.null-cocones-under-pointed-span-diagrams + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-maps +open import foundation.commuting-squares-of-maps funext univalence open import foundation.dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.universe-levels -open import foundation.whiskering-identifications-concatenation +open import foundation.whiskering-identifications-concatenation funext -open import structured-types.commuting-squares-of-pointed-maps -open import structured-types.constant-pointed-maps -open import structured-types.pointed-homotopies -open import structured-types.pointed-maps -open import structured-types.pointed-span-diagrams +open import structured-types.commuting-squares-of-pointed-maps funext univalence truncations +open import structured-types.constant-pointed-maps funext univalence truncations +open import structured-types.pointed-homotopies funext univalence truncations +open import structured-types.pointed-maps funext univalence truncations +open import structured-types.pointed-span-diagrams funext univalence truncations open import structured-types.pointed-types -open import synthetic-homotopy-theory.cocones-under-pointed-span-diagrams +open import synthetic-homotopy-theory.cocones-under-pointed-span-diagrams funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/plus-principle.lagda.md b/src/synthetic-homotopy-theory/plus-principle.lagda.md index 30af8ac24a..52f18619fe 100644 --- a/src/synthetic-homotopy-theory/plus-principle.lagda.md +++ b/src/synthetic-homotopy-theory/plus-principle.lagda.md @@ -1,18 +1,27 @@ # The plus-principle ```agda -module synthetic-homotopy-theory.plus-principle where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.plus-principle + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.connected-types -open import foundation.contractible-types +open import foundation.connected-types funext univalence truncations +open import foundation.contractible-types funext univalence +open import foundation.dependent-products-contractible-types funext open import foundation.truncation-levels open import foundation.universe-levels -open import synthetic-homotopy-theory.acyclic-types +open import synthetic-homotopy-theory.acyclic-types funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/powers-of-loops.lagda.md b/src/synthetic-homotopy-theory/powers-of-loops.lagda.md index 37c127d6f1..48e2646ca0 100644 --- a/src/synthetic-homotopy-theory/powers-of-loops.lagda.md +++ b/src/synthetic-homotopy-theory/powers-of-loops.lagda.md @@ -1,7 +1,15 @@ # Powers of loops ```agda -module synthetic-homotopy-theory.powers-of-loops where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.powers-of-loops + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -13,18 +21,18 @@ open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.equivalences -open import foundation.identity-types -open import foundation.iterating-automorphisms -open import foundation.iterating-functions +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.iterating-automorphisms funext univalence truncations +open import foundation.iterating-functions funext univalence truncations open import foundation.universe-levels -open import foundation.whiskering-identifications-concatenation +open import foundation.whiskering-identifications-concatenation funext -open import structured-types.pointed-maps +open import structured-types.pointed-maps funext univalence truncations open import structured-types.pointed-types -open import synthetic-homotopy-theory.functoriality-loop-spaces -open import synthetic-homotopy-theory.loop-spaces +open import synthetic-homotopy-theory.functoriality-loop-spaces funext univalence truncations +open import synthetic-homotopy-theory.loop-spaces funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/premanifolds.lagda.md b/src/synthetic-homotopy-theory/premanifolds.lagda.md index 9702bfc037..70b7b8f36d 100644 --- a/src/synthetic-homotopy-theory/premanifolds.lagda.md +++ b/src/synthetic-homotopy-theory/premanifolds.lagda.md @@ -1,7 +1,15 @@ # Premanifolds ```agda -module synthetic-homotopy-theory.premanifolds where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.premanifolds + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,17 +17,17 @@ module synthetic-homotopy-theory.premanifolds where ```agda open import elementary-number-theory.natural-numbers -open import foundation.commuting-squares-of-maps +open import foundation.commuting-squares-of-maps funext univalence open import foundation.dependent-pair-types -open import foundation.mere-equivalences +open import foundation.mere-equivalences funext univalence truncations open import foundation.unit-type open import foundation.universe-levels -open import synthetic-homotopy-theory.cocones-under-spans -open import synthetic-homotopy-theory.mere-spheres -open import synthetic-homotopy-theory.pushouts -open import synthetic-homotopy-theory.spheres -open import synthetic-homotopy-theory.tangent-spheres +open import synthetic-homotopy-theory.cocones-under-spans funext +open import synthetic-homotopy-theory.mere-spheres funext univalence truncations +open import synthetic-homotopy-theory.pushouts funext univalence truncations +open import synthetic-homotopy-theory.spheres funext univalence truncations +open import synthetic-homotopy-theory.tangent-spheres funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/prespectra.lagda.md b/src/synthetic-homotopy-theory/prespectra.lagda.md index b4318725d3..33db969e6f 100644 --- a/src/synthetic-homotopy-theory/prespectra.lagda.md +++ b/src/synthetic-homotopy-theory/prespectra.lagda.md @@ -1,7 +1,15 @@ # Prespectra ```agda -module synthetic-homotopy-theory.prespectra where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.prespectra + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,16 +18,16 @@ module synthetic-homotopy-theory.prespectra where open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import structured-types.pointed-maps +open import structured-types.pointed-maps funext univalence truncations open import structured-types.pointed-types -open import synthetic-homotopy-theory.loop-spaces -open import synthetic-homotopy-theory.suspensions-of-pointed-types -open import synthetic-homotopy-theory.suspensions-of-types -open import synthetic-homotopy-theory.universal-property-suspensions-of-pointed-types +open import synthetic-homotopy-theory.loop-spaces funext univalence truncations +open import synthetic-homotopy-theory.suspensions-of-pointed-types funext univalence truncations +open import synthetic-homotopy-theory.suspensions-of-types funext univalence truncations +open import synthetic-homotopy-theory.universal-property-suspensions-of-pointed-types funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/pullback-property-pushouts.lagda.md b/src/synthetic-homotopy-theory/pullback-property-pushouts.lagda.md index 73103fae01..cd06f7d05c 100644 --- a/src/synthetic-homotopy-theory/pullback-property-pushouts.lagda.md +++ b/src/synthetic-homotopy-theory/pullback-property-pushouts.lagda.md @@ -1,21 +1,29 @@ # The pullback property of pushouts ```agda -module synthetic-homotopy-theory.pullback-property-pushouts where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.pullback-property-pushouts + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.commuting-squares-of-maps -open import foundation.cones-over-cospan-diagrams +open import foundation.commuting-squares-of-maps funext univalence +open import foundation.cones-over-cospan-diagrams funext open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.precomposition-functions -open import foundation.pullbacks +open import foundation.function-types funext +open import foundation.precomposition-functions funext +open import foundation.pullbacks funext univalence truncations open import foundation.universe-levels -open import synthetic-homotopy-theory.cocones-under-spans +open import synthetic-homotopy-theory.cocones-under-spans funext ```
diff --git a/src/synthetic-homotopy-theory/pushout-products.lagda.md b/src/synthetic-homotopy-theory/pushout-products.lagda.md index 5756497b68..e358929b0d 100644 --- a/src/synthetic-homotopy-theory/pushout-products.lagda.md +++ b/src/synthetic-homotopy-theory/pushout-products.lagda.md @@ -1,23 +1,32 @@ # Pushout-products ```agda -module synthetic-homotopy-theory.pushout-products where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.pushout-products + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.cartesian-product-types -open import foundation.contractible-types +open import foundation.cartesian-product-types funext univalence +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.functoriality-cartesian-product-types -open import foundation.homotopies +open import foundation.dependent-products-contractible-types funext +open import foundation.function-types funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.homotopies funext open import foundation.universe-levels -open import synthetic-homotopy-theory.cocones-under-spans -open import synthetic-homotopy-theory.pushouts -open import synthetic-homotopy-theory.universal-property-pushouts +open import synthetic-homotopy-theory.cocones-under-spans funext +open import synthetic-homotopy-theory.pushouts funext univalence truncations +open import synthetic-homotopy-theory.universal-property-pushouts funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/pushouts-of-pointed-types.lagda.md b/src/synthetic-homotopy-theory/pushouts-of-pointed-types.lagda.md index 53105ba5b8..45ba67408a 100644 --- a/src/synthetic-homotopy-theory/pushouts-of-pointed-types.lagda.md +++ b/src/synthetic-homotopy-theory/pushouts-of-pointed-types.lagda.md @@ -1,7 +1,15 @@ # Pushouts of pointed types ```agda -module synthetic-homotopy-theory.pushouts-of-pointed-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.pushouts-of-pointed-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,14 +17,14 @@ module synthetic-homotopy-theory.pushouts-of-pointed-types where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import structured-types.pointed-maps +open import structured-types.pointed-maps funext univalence truncations open import structured-types.pointed-types -open import synthetic-homotopy-theory.cocones-under-pointed-span-diagrams -open import synthetic-homotopy-theory.pushouts +open import synthetic-homotopy-theory.cocones-under-pointed-span-diagrams funext univalence truncations +open import synthetic-homotopy-theory.pushouts funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/pushouts.lagda.md b/src/synthetic-homotopy-theory/pushouts.lagda.md index 1b5112681f..d966cf2ec2 100644 --- a/src/synthetic-homotopy-theory/pushouts.lagda.md +++ b/src/synthetic-homotopy-theory/pushouts.lagda.md @@ -1,7 +1,15 @@ # Pushouts ```agda -module synthetic-homotopy-theory.pushouts where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.pushouts + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,31 +17,32 @@ module synthetic-homotopy-theory.pushouts where ```agda open import foundation.action-on-identifications-dependent-functions open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-maps -open import foundation.constant-type-families +open import foundation.commuting-squares-of-maps funext univalence +open import foundation.constant-type-families funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.fibers-of-maps -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.propositions -open import foundation.retractions -open import foundation.sections -open import foundation.transport-along-homotopies +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.fibers-of-maps funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.retractions funext +open import foundation.sections funext +open import foundation.transport-along-homotopies funext open import foundation.transport-along-identifications open import foundation.universe-levels open import foundation.whiskering-homotopies-composition open import reflection.erasing-equality -open import synthetic-homotopy-theory.cocones-under-spans -open import synthetic-homotopy-theory.dependent-cocones-under-spans -open import synthetic-homotopy-theory.dependent-universal-property-pushouts -open import synthetic-homotopy-theory.flattening-lemma-pushouts -open import synthetic-homotopy-theory.induction-principle-pushouts -open import synthetic-homotopy-theory.universal-property-pushouts +open import synthetic-homotopy-theory.cocones-under-spans funext +open import synthetic-homotopy-theory.dependent-cocones-under-spans funext univalence truncations +open import synthetic-homotopy-theory.dependent-universal-property-pushouts funext univalence truncations +open import synthetic-homotopy-theory.flattening-lemma-pushouts funext univalence truncations +open import synthetic-homotopy-theory.induction-principle-pushouts funext univalence truncations +open import synthetic-homotopy-theory.universal-property-pushouts funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/recursion-principle-pushouts.lagda.md b/src/synthetic-homotopy-theory/recursion-principle-pushouts.lagda.md index af0fa511a5..7486652ca2 100644 --- a/src/synthetic-homotopy-theory/recursion-principle-pushouts.lagda.md +++ b/src/synthetic-homotopy-theory/recursion-principle-pushouts.lagda.md @@ -1,19 +1,27 @@ # The recursion principle of pushouts ```agda -module synthetic-homotopy-theory.recursion-principle-pushouts where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.recursion-principle-pushouts + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.sections +open import foundation.identity-types funext +open import foundation.sections funext open import foundation.universe-levels -open import synthetic-homotopy-theory.cocones-under-spans -open import synthetic-homotopy-theory.dependent-cocones-under-spans +open import synthetic-homotopy-theory.cocones-under-spans funext +open import synthetic-homotopy-theory.dependent-cocones-under-spans funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/retracts-of-sequential-diagrams.lagda.md b/src/synthetic-homotopy-theory/retracts-of-sequential-diagrams.lagda.md index 13ad9399bb..01ee8d8fa3 100644 --- a/src/synthetic-homotopy-theory/retracts-of-sequential-diagrams.lagda.md +++ b/src/synthetic-homotopy-theory/retracts-of-sequential-diagrams.lagda.md @@ -1,7 +1,15 @@ # Retracts of sequential diagrams ```agda -module synthetic-homotopy-theory.retracts-of-sequential-diagrams where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.retracts-of-sequential-diagrams + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,20 +17,20 @@ module synthetic-homotopy-theory.retracts-of-sequential-diagrams where ```agda open import elementary-number-theory.natural-numbers -open import foundation.commuting-squares-of-maps +open import foundation.commuting-squares-of-maps funext univalence open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types -open import foundation.retractions -open import foundation.retracts-of-types +open import foundation.equality-dependent-function-types funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext +open import foundation.retractions funext +open import foundation.retracts-of-types funext univalence open import foundation.universe-levels -open import synthetic-homotopy-theory.morphisms-sequential-diagrams -open import synthetic-homotopy-theory.sequential-diagrams +open import synthetic-homotopy-theory.morphisms-sequential-diagrams funext univalence truncations +open import synthetic-homotopy-theory.sequential-diagrams funext univalence ```
diff --git a/src/synthetic-homotopy-theory/rewriting-pushouts.lagda.md b/src/synthetic-homotopy-theory/rewriting-pushouts.lagda.md index 5b471fe9ff..7ac563d17e 100644 --- a/src/synthetic-homotopy-theory/rewriting-pushouts.lagda.md +++ b/src/synthetic-homotopy-theory/rewriting-pushouts.lagda.md @@ -2,22 +2,29 @@ ```agda {-# OPTIONS --rewriting #-} - -module synthetic-homotopy-theory.rewriting-pushouts where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.rewriting-pushouts + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.homotopies -open import foundation.identity-types +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.universe-levels open import reflection.rewriting -open import synthetic-homotopy-theory.cocones-under-spans -open import synthetic-homotopy-theory.dependent-cocones-under-spans -open import synthetic-homotopy-theory.pushouts +open import synthetic-homotopy-theory.cocones-under-spans funext +open import synthetic-homotopy-theory.dependent-cocones-under-spans funext univalence truncations +open import synthetic-homotopy-theory.pushouts funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/sections-descent-circle.lagda.md b/src/synthetic-homotopy-theory/sections-descent-circle.lagda.md index 77c8924b1c..a074a3eb95 100644 --- a/src/synthetic-homotopy-theory/sections-descent-circle.lagda.md +++ b/src/synthetic-homotopy-theory/sections-descent-circle.lagda.md @@ -1,7 +1,15 @@ # Sections of families over the circle ```agda -module synthetic-homotopy-theory.sections-descent-circle where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.sections-descent-circle + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,27 +17,28 @@ module synthetic-homotopy-theory.sections-descent-circle where ```agda open import foundation.action-on-identifications-dependent-functions open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-maps -open import foundation.commuting-triangles-of-identifications -open import foundation.commuting-triangles-of-maps -open import foundation.contractible-maps -open import foundation.contractible-types -open import foundation.dependent-identifications +open import foundation.commuting-squares-of-maps funext univalence +open import foundation.commuting-triangles-of-identifications funext +open import foundation.commuting-triangles-of-maps funext univalence +open import foundation.contractible-maps funext +open import foundation.contractible-types funext univalence +open import foundation.dependent-identifications funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.fibers-of-maps -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types +open import foundation.dependent-products-contractible-types funext +open import foundation.equivalences funext +open import foundation.fibers-of-maps funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.path-algebra +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.path-algebra funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import synthetic-homotopy-theory.descent-circle -open import synthetic-homotopy-theory.free-loops -open import synthetic-homotopy-theory.universal-property-circle +open import synthetic-homotopy-theory.descent-circle funext univalence truncations +open import synthetic-homotopy-theory.free-loops funext univalence truncations +open import synthetic-homotopy-theory.universal-property-circle funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/sections-descent-data-pushouts.lagda.md b/src/synthetic-homotopy-theory/sections-descent-data-pushouts.lagda.md index 583235db13..bb2c22ac99 100644 --- a/src/synthetic-homotopy-theory/sections-descent-data-pushouts.lagda.md +++ b/src/synthetic-homotopy-theory/sections-descent-data-pushouts.lagda.md @@ -1,7 +1,15 @@ # Sections of descent data for pushouts ```agda -module synthetic-homotopy-theory.sections-descent-data-pushouts where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.sections-descent-data-pushouts + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,31 +17,32 @@ module synthetic-homotopy-theory.sections-descent-data-pushouts where ```agda open import foundation.action-on-identifications-dependent-functions open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-identifications -open import foundation.commuting-triangles-of-maps -open import foundation.contractible-maps -open import foundation.contractible-types +open import foundation.commuting-squares-of-identifications funext +open import foundation.commuting-triangles-of-maps funext univalence +open import foundation.contractible-maps funext +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalences -open import foundation.fibers-of-maps -open import foundation.functoriality-dependent-function-types -open import foundation.functoriality-dependent-pair-types +open import foundation.dependent-products-contractible-types funext +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.fibers-of-maps funext +open import foundation.functoriality-dependent-function-types funext univalence +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types -open import foundation.span-diagrams +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext +open import foundation.span-diagrams funext open import foundation.structure-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext univalence truncations open import foundation.universe-levels -open import synthetic-homotopy-theory.cocones-under-spans -open import synthetic-homotopy-theory.dependent-cocones-under-spans -open import synthetic-homotopy-theory.dependent-universal-property-pushouts -open import synthetic-homotopy-theory.descent-data-pushouts -open import synthetic-homotopy-theory.families-descent-data-pushouts -open import synthetic-homotopy-theory.universal-property-pushouts +open import synthetic-homotopy-theory.cocones-under-spans funext +open import synthetic-homotopy-theory.dependent-cocones-under-spans funext univalence truncations +open import synthetic-homotopy-theory.dependent-universal-property-pushouts funext univalence truncations +open import synthetic-homotopy-theory.descent-data-pushouts funext +open import synthetic-homotopy-theory.families-descent-data-pushouts funext univalence truncations +open import synthetic-homotopy-theory.universal-property-pushouts funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/sequential-colimits.lagda.md b/src/synthetic-homotopy-theory/sequential-colimits.lagda.md index e0767413bd..213a3051e8 100644 --- a/src/synthetic-homotopy-theory/sequential-colimits.lagda.md +++ b/src/synthetic-homotopy-theory/sequential-colimits.lagda.md @@ -1,7 +1,15 @@ # Sequential colimits ```agda -module synthetic-homotopy-theory.sequential-colimits where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.sequential-colimits + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,23 +17,24 @@ module synthetic-homotopy-theory.sequential-colimits where ```agda open import elementary-number-theory.natural-numbers -open import foundation.commuting-triangles-of-maps +open import foundation.commuting-triangles-of-maps funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-function-types funext univalence +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext +open import foundation.propositions funext univalence open import foundation.universe-levels -open import synthetic-homotopy-theory.cocones-under-sequential-diagrams -open import synthetic-homotopy-theory.coequalizers -open import synthetic-homotopy-theory.coforks-cocones-under-sequential-diagrams -open import synthetic-homotopy-theory.dependent-cocones-under-sequential-diagrams -open import synthetic-homotopy-theory.dependent-universal-property-sequential-colimits -open import synthetic-homotopy-theory.sequential-diagrams -open import synthetic-homotopy-theory.universal-property-sequential-colimits +open import synthetic-homotopy-theory.cocones-under-sequential-diagrams funext univalence truncations +open import synthetic-homotopy-theory.coequalizers funext univalence truncations +open import synthetic-homotopy-theory.coforks-cocones-under-sequential-diagrams funext univalence truncations +open import synthetic-homotopy-theory.dependent-cocones-under-sequential-diagrams funext univalence truncations +open import synthetic-homotopy-theory.dependent-universal-property-sequential-colimits funext univalence truncations +open import synthetic-homotopy-theory.sequential-diagrams funext univalence +open import synthetic-homotopy-theory.universal-property-sequential-colimits funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/sequential-diagrams.lagda.md b/src/synthetic-homotopy-theory/sequential-diagrams.lagda.md index 44b7e094cb..436355915a 100644 --- a/src/synthetic-homotopy-theory/sequential-diagrams.lagda.md +++ b/src/synthetic-homotopy-theory/sequential-diagrams.lagda.md @@ -1,7 +1,13 @@ # Sequential diagrams ```agda -module synthetic-homotopy-theory.sequential-diagrams where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.sequential-diagrams + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports @@ -9,9 +15,10 @@ module synthetic-homotopy-theory.sequential-diagrams where ```agda open import elementary-number-theory.natural-numbers -open import foundation.contractible-types +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences +open import foundation.dependent-products-contractible-types funext +open import foundation.equivalences funext open import foundation.universe-levels ``` diff --git a/src/synthetic-homotopy-theory/sequentially-compact-types.lagda.md b/src/synthetic-homotopy-theory/sequentially-compact-types.lagda.md index bd20d04559..872f887d53 100644 --- a/src/synthetic-homotopy-theory/sequentially-compact-types.lagda.md +++ b/src/synthetic-homotopy-theory/sequentially-compact-types.lagda.md @@ -1,18 +1,27 @@ # Sequentially compact types ```agda -module synthetic-homotopy-theory.sequentially-compact-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.sequentially-compact-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.propositions funext univalence open import foundation.universe-levels -open import synthetic-homotopy-theory.cocones-under-sequential-diagrams -open import synthetic-homotopy-theory.sequential-diagrams -open import synthetic-homotopy-theory.universal-property-sequential-colimits +open import synthetic-homotopy-theory.cocones-under-sequential-diagrams funext univalence truncations +open import synthetic-homotopy-theory.sequential-diagrams funext univalence +open import synthetic-homotopy-theory.universal-property-sequential-colimits funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/shifts-sequential-diagrams.lagda.md b/src/synthetic-homotopy-theory/shifts-sequential-diagrams.lagda.md index c7c6e22f6f..e40b1f87ee 100644 --- a/src/synthetic-homotopy-theory/shifts-sequential-diagrams.lagda.md +++ b/src/synthetic-homotopy-theory/shifts-sequential-diagrams.lagda.md @@ -1,7 +1,15 @@ # Shifts of sequential diagrams ```agda -module synthetic-homotopy-theory.shifts-sequential-diagrams where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.shifts-sequential-diagrams + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,26 +17,27 @@ module synthetic-homotopy-theory.shifts-sequential-diagrams where ```agda open import elementary-number-theory.natural-numbers -open import foundation.commuting-triangles-of-maps -open import foundation.contractible-types +open import foundation.commuting-triangles-of-maps funext univalence +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.homotopies +open import foundation.dependent-products-contractible-types funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.homotopies funext open import foundation.homotopy-algebra -open import foundation.identity-types -open import foundation.retractions -open import foundation.sections +open import foundation.identity-types funext +open import foundation.retractions funext +open import foundation.sections funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import foundation.whiskering-homotopies-concatenation - -open import synthetic-homotopy-theory.cocones-under-sequential-diagrams -open import synthetic-homotopy-theory.functoriality-sequential-colimits -open import synthetic-homotopy-theory.morphisms-sequential-diagrams -open import synthetic-homotopy-theory.sequential-colimits -open import synthetic-homotopy-theory.sequential-diagrams -open import synthetic-homotopy-theory.universal-property-sequential-colimits +open import foundation.whiskering-homotopies-concatenation funext + +open import synthetic-homotopy-theory.cocones-under-sequential-diagrams funext univalence truncations +open import synthetic-homotopy-theory.functoriality-sequential-colimits funext univalence truncations +open import synthetic-homotopy-theory.morphisms-sequential-diagrams funext univalence truncations +open import synthetic-homotopy-theory.sequential-colimits funext univalence truncations +open import synthetic-homotopy-theory.sequential-diagrams funext univalence +open import synthetic-homotopy-theory.universal-property-sequential-colimits funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/smash-products-of-pointed-types.lagda.md b/src/synthetic-homotopy-theory/smash-products-of-pointed-types.lagda.md index b23c3d17b8..7b06af141c 100644 --- a/src/synthetic-homotopy-theory/smash-products-of-pointed-types.lagda.md +++ b/src/synthetic-homotopy-theory/smash-products-of-pointed-types.lagda.md @@ -1,35 +1,41 @@ # Smash products of pointed types ```agda -module synthetic-homotopy-theory.smash-products-of-pointed-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.smash-products-of-pointed-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.action-on-higher-identifications-functions +open import foundation.action-on-higher-identifications-functions funext open import foundation.action-on-identifications-dependent-functions open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import foundation.whiskering-identifications-concatenation +open import foundation.whiskering-identifications-concatenation funext -open import structured-types.constant-pointed-maps -open import structured-types.pointed-cartesian-product-types -open import structured-types.pointed-homotopies -open import structured-types.pointed-maps +open import structured-types.constant-pointed-maps funext univalence truncations +open import structured-types.pointed-cartesian-product-types funext univalence truncations +open import structured-types.pointed-homotopies funext univalence truncations +open import structured-types.pointed-maps funext univalence truncations open import structured-types.pointed-types -open import structured-types.pointed-unit-type - -open import synthetic-homotopy-theory.cocones-under-pointed-span-diagrams -open import synthetic-homotopy-theory.cofibers-of-maps -open import synthetic-homotopy-theory.cofibers-of-pointed-maps -open import synthetic-homotopy-theory.pushouts -open import synthetic-homotopy-theory.pushouts-of-pointed-types -open import synthetic-homotopy-theory.wedges-of-pointed-types +open import structured-types.pointed-unit-type funext univalence truncations + +open import synthetic-homotopy-theory.cocones-under-pointed-span-diagrams funext univalence truncations +open import synthetic-homotopy-theory.cofibers-of-pointed-maps funext univalence truncations +open import synthetic-homotopy-theory.pushouts funext univalence truncations +open import synthetic-homotopy-theory.wedges-of-pointed-types funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/spectra.lagda.md b/src/synthetic-homotopy-theory/spectra.lagda.md index ba8278a8ec..3a68990532 100644 --- a/src/synthetic-homotopy-theory/spectra.lagda.md +++ b/src/synthetic-homotopy-theory/spectra.lagda.md @@ -1,7 +1,15 @@ # Spectra ```agda -module synthetic-homotopy-theory.spectra where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.spectra + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,20 +18,21 @@ module synthetic-homotopy-theory.spectra where open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.identity-types -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence open import foundation.universe-levels -open import structured-types.pointed-equivalences -open import structured-types.pointed-maps +open import structured-types.pointed-equivalences funext univalence truncations +open import structured-types.pointed-maps funext univalence truncations open import structured-types.pointed-types -open import synthetic-homotopy-theory.loop-spaces -open import synthetic-homotopy-theory.prespectra -open import synthetic-homotopy-theory.suspensions-of-pointed-types -open import synthetic-homotopy-theory.suspensions-of-types +open import synthetic-homotopy-theory.loop-spaces funext univalence truncations +open import synthetic-homotopy-theory.prespectra funext univalence truncations +open import synthetic-homotopy-theory.suspensions-of-pointed-types funext univalence truncations +open import synthetic-homotopy-theory.suspensions-of-types funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/sphere-prespectrum.lagda.md b/src/synthetic-homotopy-theory/sphere-prespectrum.lagda.md index 2a8ad9eab1..9c32fdfe3e 100644 --- a/src/synthetic-homotopy-theory/sphere-prespectrum.lagda.md +++ b/src/synthetic-homotopy-theory/sphere-prespectrum.lagda.md @@ -1,7 +1,15 @@ # The sphere prespectrum ```agda -module synthetic-homotopy-theory.sphere-prespectrum where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.sphere-prespectrum + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,10 +18,10 @@ module synthetic-homotopy-theory.sphere-prespectrum where open import foundation.dependent-pair-types open import foundation.universe-levels -open import synthetic-homotopy-theory.prespectra -open import synthetic-homotopy-theory.suspension-prespectra +open import synthetic-homotopy-theory.prespectra funext univalence truncations +open import synthetic-homotopy-theory.suspension-prespectra funext univalence truncations -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/spheres.lagda.md b/src/synthetic-homotopy-theory/spheres.lagda.md index 85490fc5db..31695fa0b6 100644 --- a/src/synthetic-homotopy-theory/spheres.lagda.md +++ b/src/synthetic-homotopy-theory/spheres.lagda.md @@ -1,7 +1,15 @@ # Spheres ```agda -module synthetic-homotopy-theory.spheres where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.spheres + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,16 +18,16 @@ module synthetic-homotopy-theory.spheres where open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.identity-types +open import foundation.function-types funext +open import foundation.identity-types funext open import foundation.universe-levels open import structured-types.pointed-types -open import synthetic-homotopy-theory.iterated-suspensions-of-pointed-types -open import synthetic-homotopy-theory.suspensions-of-types +open import synthetic-homotopy-theory.iterated-suspensions-of-pointed-types funext univalence truncations +open import synthetic-homotopy-theory.suspensions-of-types funext univalence truncations -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/suspension-prespectra.lagda.md b/src/synthetic-homotopy-theory/suspension-prespectra.lagda.md index 54a0453fb9..6852b87bb9 100644 --- a/src/synthetic-homotopy-theory/suspension-prespectra.lagda.md +++ b/src/synthetic-homotopy-theory/suspension-prespectra.lagda.md @@ -1,7 +1,15 @@ # Suspension prespectra ```agda -module synthetic-homotopy-theory.suspension-prespectra where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.suspension-prespectra + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -12,14 +20,14 @@ open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types open import foundation.universe-levels -open import structured-types.pointed-maps +open import structured-types.pointed-maps funext univalence truncations open import structured-types.pointed-types -open import synthetic-homotopy-theory.iterated-suspensions-of-pointed-types -open import synthetic-homotopy-theory.loop-spaces -open import synthetic-homotopy-theory.prespectra -open import synthetic-homotopy-theory.suspensions-of-pointed-types -open import synthetic-homotopy-theory.universal-property-suspensions-of-pointed-types +open import synthetic-homotopy-theory.iterated-suspensions-of-pointed-types funext univalence truncations +open import synthetic-homotopy-theory.loop-spaces funext univalence truncations +open import synthetic-homotopy-theory.prespectra funext univalence truncations +open import synthetic-homotopy-theory.suspensions-of-pointed-types funext univalence truncations +open import synthetic-homotopy-theory.universal-property-suspensions-of-pointed-types funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/suspension-structures.lagda.md b/src/synthetic-homotopy-theory/suspension-structures.lagda.md index 7d579d350f..a2246e9ea2 100644 --- a/src/synthetic-homotopy-theory/suspension-structures.lagda.md +++ b/src/synthetic-homotopy-theory/suspension-structures.lagda.md @@ -1,33 +1,42 @@ # Suspension Structures ```agda -module synthetic-homotopy-theory.suspension-structures where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.suspension-structures + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-identifications -open import foundation.constant-maps -open import foundation.contractible-types +open import foundation.commuting-squares-of-identifications funext +open import foundation.constant-maps funext univalence truncations +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies +open import foundation.dependent-products-contractible-types funext +open import foundation.equivalences funext +open import foundation.function-extensionality funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext open import foundation.identity-systems -open import foundation.identity-types -open import foundation.injective-maps +open import foundation.identity-types funext +open import foundation.injective-maps funext open import foundation.structure-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext univalence truncations open import foundation.unit-type -open import foundation.universal-property-unit-type +open import foundation.universal-property-unit-type funext open import foundation.universe-levels -open import foundation.whiskering-identifications-concatenation +open import foundation.whiskering-identifications-concatenation funext -open import synthetic-homotopy-theory.cocones-under-spans +open import synthetic-homotopy-theory.cocones-under-spans funext ```
diff --git a/src/synthetic-homotopy-theory/suspensions-of-pointed-types.lagda.md b/src/synthetic-homotopy-theory/suspensions-of-pointed-types.lagda.md index 3e57879259..14fa5e6dbe 100644 --- a/src/synthetic-homotopy-theory/suspensions-of-pointed-types.lagda.md +++ b/src/synthetic-homotopy-theory/suspensions-of-pointed-types.lagda.md @@ -1,22 +1,30 @@ # Suspensions of pointed types ```agda -module synthetic-homotopy-theory.suspensions-of-pointed-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.suspensions-of-pointed-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.constant-maps +open import foundation.constant-maps funext univalence truncations open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels open import structured-types.pointed-types -open import synthetic-homotopy-theory.loop-spaces -open import synthetic-homotopy-theory.suspension-structures -open import synthetic-homotopy-theory.suspensions-of-types +open import synthetic-homotopy-theory.loop-spaces funext univalence truncations +open import synthetic-homotopy-theory.suspension-structures funext univalence truncations +open import synthetic-homotopy-theory.suspensions-of-types funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/suspensions-of-propositions.lagda.md b/src/synthetic-homotopy-theory/suspensions-of-propositions.lagda.md index 95d058f84b..b89c85471f 100644 --- a/src/synthetic-homotopy-theory/suspensions-of-propositions.lagda.md +++ b/src/synthetic-homotopy-theory/suspensions-of-propositions.lagda.md @@ -1,37 +1,48 @@ # Suspensions of propositions ```agda -module synthetic-homotopy-theory.suspensions-of-propositions where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.suspensions-of-propositions + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.booleans -open import foundation.contractible-types +open import foundation.booleans funext univalence truncations +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.existential-quantification -open import foundation.function-extensionality -open import foundation.function-types +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.existential-quantification funext univalence truncations +open import foundation.function-extensionality funext +open import foundation.function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.raising-universe-levels-unit-type +open import foundation.sets funext univalence open import foundation.subsingleton-induction -open import foundation.surjective-maps -open import foundation.torsorial-type-families +open import foundation.surjective-maps funext univalence truncations +open import foundation.torsorial-type-families funext univalence truncations open import foundation.transport-along-identifications open import foundation.unit-type -open import foundation.univalence +open import foundation.univalence funext univalence open import foundation.universe-levels -open import synthetic-homotopy-theory.dependent-suspension-structures -open import synthetic-homotopy-theory.suspension-structures -open import synthetic-homotopy-theory.suspensions-of-types +open import synthetic-homotopy-theory.dependent-suspension-structures funext univalence truncations +open import synthetic-homotopy-theory.suspension-structures funext univalence truncations +open import synthetic-homotopy-theory.suspensions-of-types funext univalence truncations -open import univalent-combinatorics.kuratowski-finite-sets +open import univalent-combinatorics.kuratowski-finite-sets funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/suspensions-of-types.lagda.md b/src/synthetic-homotopy-theory/suspensions-of-types.lagda.md index b0d6084cbc..e7158cc127 100644 --- a/src/synthetic-homotopy-theory/suspensions-of-types.lagda.md +++ b/src/synthetic-homotopy-theory/suspensions-of-types.lagda.md @@ -1,7 +1,15 @@ # Suspensions of types ```agda -module synthetic-homotopy-theory.suspensions-of-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.suspensions-of-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,46 +17,49 @@ module synthetic-homotopy-theory.suspensions-of-types where ```agda open import foundation.action-on-identifications-dependent-functions open import foundation.action-on-identifications-functions -open import foundation.booleans -open import foundation.commuting-squares-of-identifications -open import foundation.connected-types -open import foundation.constant-maps -open import foundation.contractible-types -open import foundation.dependent-identifications +open import foundation.booleans funext univalence truncations +open import foundation.commuting-squares-of-identifications funext +open import foundation.connected-types funext univalence truncations +open import foundation.constant-maps funext univalence truncations +open import foundation.contractible-types funext univalence +open import foundation.dependent-identifications funext open import foundation.dependent-pair-types -open import foundation.diagonal-maps-of-types -open import foundation.equivalence-extensionality -open import foundation.equivalences -open import foundation.fibers-of-maps -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.functoriality-dependent-function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.path-algebra -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.retractions -open import foundation.sections -open import foundation.surjective-maps -open import foundation.torsorial-type-families +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.dependent-products-truncated-types funext +open import foundation.diagonal-maps-of-types funext +open import foundation.equivalence-extensionality funext +open import foundation.equivalences funext +open import foundation.fibers-of-maps funext +open import foundation.function-extensionality funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-function-types funext univalence +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.path-algebra funext +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence +open import foundation.retractions funext +open import foundation.sections funext +open import foundation.surjective-maps funext univalence truncations +open import foundation.torsorial-type-families funext univalence truncations open import foundation.transport-along-identifications -open import foundation.truncated-types +open import foundation.truncated-types funext univalence open import foundation.truncation-levels open import foundation.type-arithmetic-dependent-pair-types open import foundation.unit-type open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import synthetic-homotopy-theory.cocones-under-spans -open import synthetic-homotopy-theory.dependent-cocones-under-spans -open import synthetic-homotopy-theory.dependent-suspension-structures -open import synthetic-homotopy-theory.dependent-universal-property-suspensions -open import synthetic-homotopy-theory.pushouts -open import synthetic-homotopy-theory.suspension-structures -open import synthetic-homotopy-theory.universal-property-pushouts -open import synthetic-homotopy-theory.universal-property-suspensions +open import synthetic-homotopy-theory.cocones-under-spans funext +open import synthetic-homotopy-theory.dependent-cocones-under-spans funext univalence truncations +open import synthetic-homotopy-theory.dependent-suspension-structures funext univalence truncations +open import synthetic-homotopy-theory.dependent-universal-property-suspensions funext univalence truncations +open import synthetic-homotopy-theory.pushouts funext univalence truncations +open import synthetic-homotopy-theory.suspension-structures funext univalence truncations +open import synthetic-homotopy-theory.universal-property-pushouts funext univalence truncations +open import synthetic-homotopy-theory.universal-property-suspensions funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/tangent-spheres.lagda.md b/src/synthetic-homotopy-theory/tangent-spheres.lagda.md index ec35fb7cab..dc09348953 100644 --- a/src/synthetic-homotopy-theory/tangent-spheres.lagda.md +++ b/src/synthetic-homotopy-theory/tangent-spheres.lagda.md @@ -1,7 +1,15 @@ # Tangent spheres ```agda -module synthetic-homotopy-theory.tangent-spheres where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.tangent-spheres + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,16 +17,16 @@ module synthetic-homotopy-theory.tangent-spheres where ```agda open import elementary-number-theory.natural-numbers -open import foundation.commuting-squares-of-maps +open import foundation.commuting-squares-of-maps funext univalence open import foundation.dependent-pair-types -open import foundation.mere-equivalences +open import foundation.mere-equivalences funext univalence truncations open import foundation.unit-type open import foundation.universe-levels -open import synthetic-homotopy-theory.cocones-under-spans -open import synthetic-homotopy-theory.mere-spheres -open import synthetic-homotopy-theory.pushouts -open import synthetic-homotopy-theory.spheres +open import synthetic-homotopy-theory.cocones-under-spans funext +open import synthetic-homotopy-theory.mere-spheres funext univalence truncations +open import synthetic-homotopy-theory.pushouts funext univalence truncations +open import synthetic-homotopy-theory.spheres funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/total-cocones-families-sequential-diagrams.lagda.md b/src/synthetic-homotopy-theory/total-cocones-families-sequential-diagrams.lagda.md index 5c6d86df34..d79c316047 100644 --- a/src/synthetic-homotopy-theory/total-cocones-families-sequential-diagrams.lagda.md +++ b/src/synthetic-homotopy-theory/total-cocones-families-sequential-diagrams.lagda.md @@ -1,7 +1,15 @@ # Total cocones of type families over cocones under sequential diagrams ```agda -module synthetic-homotopy-theory.total-cocones-families-sequential-diagrams where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.total-cocones-families-sequential-diagrams + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -11,20 +19,20 @@ open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types -open import foundation.equivalences -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types +open import foundation.equality-dependent-pair-types funext +open import foundation.equivalences funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.universe-levels -open import foundation.whiskering-identifications-concatenation - -open import synthetic-homotopy-theory.cocones-under-sequential-diagrams -open import synthetic-homotopy-theory.equivalences-cocones-under-equivalences-sequential-diagrams -open import synthetic-homotopy-theory.equivalences-sequential-diagrams -open import synthetic-homotopy-theory.families-descent-data-sequential-colimits -open import synthetic-homotopy-theory.sequential-diagrams -open import synthetic-homotopy-theory.total-sequential-diagrams +open import foundation.whiskering-identifications-concatenation funext + +open import synthetic-homotopy-theory.cocones-under-sequential-diagrams funext univalence truncations +open import synthetic-homotopy-theory.equivalences-cocones-under-equivalences-sequential-diagrams funext univalence truncations +open import synthetic-homotopy-theory.equivalences-sequential-diagrams funext univalence truncations +open import synthetic-homotopy-theory.families-descent-data-sequential-colimits funext univalence truncations +open import synthetic-homotopy-theory.sequential-diagrams funext univalence +open import synthetic-homotopy-theory.total-sequential-diagrams funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/total-sequential-diagrams.lagda.md b/src/synthetic-homotopy-theory/total-sequential-diagrams.lagda.md index 22e1060a68..328b3a9af9 100644 --- a/src/synthetic-homotopy-theory/total-sequential-diagrams.lagda.md +++ b/src/synthetic-homotopy-theory/total-sequential-diagrams.lagda.md @@ -1,7 +1,15 @@ # Total sequential diagrams of dependent sequential diagrams ```agda -module synthetic-homotopy-theory.total-sequential-diagrams where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.total-sequential-diagrams + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,19 +18,19 @@ module synthetic-homotopy-theory.total-sequential-diagrams where open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext open import foundation.universe-levels -open import synthetic-homotopy-theory.cocones-under-sequential-diagrams -open import synthetic-homotopy-theory.dependent-sequential-diagrams -open import synthetic-homotopy-theory.equivalences-dependent-sequential-diagrams -open import synthetic-homotopy-theory.equivalences-sequential-diagrams -open import synthetic-homotopy-theory.functoriality-sequential-colimits -open import synthetic-homotopy-theory.morphisms-sequential-diagrams -open import synthetic-homotopy-theory.sequential-colimits -open import synthetic-homotopy-theory.sequential-diagrams -open import synthetic-homotopy-theory.universal-property-sequential-colimits +open import synthetic-homotopy-theory.cocones-under-sequential-diagrams funext univalence truncations +open import synthetic-homotopy-theory.dependent-sequential-diagrams funext univalence +open import synthetic-homotopy-theory.equivalences-dependent-sequential-diagrams funext univalence truncations +open import synthetic-homotopy-theory.equivalences-sequential-diagrams funext univalence truncations +open import synthetic-homotopy-theory.functoriality-sequential-colimits funext univalence truncations +open import synthetic-homotopy-theory.morphisms-sequential-diagrams funext univalence truncations +open import synthetic-homotopy-theory.sequential-colimits funext univalence truncations +open import synthetic-homotopy-theory.sequential-diagrams funext univalence +open import synthetic-homotopy-theory.universal-property-sequential-colimits funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/triple-loop-spaces.lagda.md b/src/synthetic-homotopy-theory/triple-loop-spaces.lagda.md index cdb70b73bf..3f1f09774d 100644 --- a/src/synthetic-homotopy-theory/triple-loop-spaces.lagda.md +++ b/src/synthetic-homotopy-theory/triple-loop-spaces.lagda.md @@ -1,7 +1,15 @@ # Triple loop spaces ```agda -module synthetic-homotopy-theory.triple-loop-spaces where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.triple-loop-spaces + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,15 +17,15 @@ module synthetic-homotopy-theory.triple-loop-spaces where ```agda open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.homotopies -open import foundation.identity-types -open import foundation.path-algebra +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.path-algebra funext open import foundation.universe-levels open import structured-types.pointed-types -open import synthetic-homotopy-theory.double-loop-spaces -open import synthetic-homotopy-theory.iterated-loop-spaces +open import synthetic-homotopy-theory.double-loop-spaces funext univalence truncations +open import synthetic-homotopy-theory.iterated-loop-spaces funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/truncated-acyclic-maps.lagda.md b/src/synthetic-homotopy-theory/truncated-acyclic-maps.lagda.md index 88c1339d10..dafc98b7b3 100644 --- a/src/synthetic-homotopy-theory/truncated-acyclic-maps.lagda.md +++ b/src/synthetic-homotopy-theory/truncated-acyclic-maps.lagda.md @@ -1,59 +1,67 @@ # `k`-acyclic maps ```agda -module synthetic-homotopy-theory.truncated-acyclic-maps where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.truncated-acyclic-maps + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types -open import foundation.cones-over-cospan-diagrams -open import foundation.connected-maps -open import foundation.connected-types -open import foundation.constant-maps -open import foundation.contractible-types -open import foundation.dependent-epimorphisms-with-respect-to-truncated-types +open import foundation.cartesian-product-types funext univalence +open import foundation.cones-over-cospan-diagrams funext +open import foundation.connected-maps funext univalence truncations +open import foundation.connected-types funext univalence truncations +open import foundation.constant-maps funext univalence truncations +open import foundation.dependent-epimorphisms-with-respect-to-truncated-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.dependent-universal-property-equivalences -open import foundation.diagonal-maps-of-types -open import foundation.embeddings -open import foundation.epimorphisms-with-respect-to-truncated-types -open import foundation.equivalences -open import foundation.fibers-of-maps -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.functoriality-dependent-function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.functoriality-fibers-of-maps -open import foundation.homotopies -open import foundation.identity-types -open import foundation.inhabited-types -open import foundation.precomposition-dependent-functions -open import foundation.precomposition-functions -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.pullbacks -open import foundation.retracts-of-maps -open import foundation.torsorial-type-families -open import foundation.truncated-types -open import foundation.truncation-equivalences +open import foundation.dependent-products-propositions funext +open import foundation.dependent-products-truncated-types funext +open import foundation.dependent-universal-property-equivalences funext +open import foundation.diagonal-maps-of-types funext +open import foundation.embeddings funext +open import foundation.epimorphisms-with-respect-to-truncated-types funext univalence truncations +open import foundation.equivalences funext +open import foundation.fibers-of-maps funext +open import foundation.function-extensionality funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-function-types funext univalence +open import foundation.functoriality-dependent-pair-types funext +open import foundation.functoriality-fibers-of-maps funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.inhabited-types funext univalence truncations +open import foundation.precomposition-dependent-functions funext +open import foundation.precomposition-functions funext +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence +open import foundation.pullbacks funext univalence truncations +open import foundation.retracts-of-maps funext univalence +open import foundation.torsorial-type-families funext univalence truncations +open import foundation.truncated-types funext univalence +open import foundation.truncation-equivalences funext univalence truncations open import foundation.truncation-levels -open import foundation.truncations +open import foundation.truncations funext univalence truncations open import foundation.type-arithmetic-dependent-pair-types -open import foundation.type-arithmetic-unit-type +open import foundation.type-arithmetic-unit-type funext open import foundation.unit-type -open import foundation.universal-property-cartesian-product-types -open import foundation.universal-property-dependent-pair-types +open import foundation.universal-property-cartesian-product-types funext +open import foundation.universal-property-dependent-pair-types funext open import foundation.universe-levels -open import synthetic-homotopy-theory.cocones-under-spans -open import synthetic-homotopy-theory.codiagonals-of-maps -open import synthetic-homotopy-theory.pushouts -open import synthetic-homotopy-theory.suspensions-of-types -open import synthetic-homotopy-theory.truncated-acyclic-types -open import synthetic-homotopy-theory.universal-property-pushouts +open import synthetic-homotopy-theory.cocones-under-spans funext +open import synthetic-homotopy-theory.codiagonals-of-maps funext univalence truncations +open import synthetic-homotopy-theory.pushouts funext univalence truncations +open import synthetic-homotopy-theory.truncated-acyclic-types funext univalence truncations +open import synthetic-homotopy-theory.universal-property-pushouts funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/truncated-acyclic-types.lagda.md b/src/synthetic-homotopy-theory/truncated-acyclic-types.lagda.md index 6324c36e58..ecdd3482e5 100644 --- a/src/synthetic-homotopy-theory/truncated-acyclic-types.lagda.md +++ b/src/synthetic-homotopy-theory/truncated-acyclic-types.lagda.md @@ -1,23 +1,33 @@ # `k`-acyclic types ```agda -module synthetic-homotopy-theory.truncated-acyclic-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.truncated-acyclic-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.connected-types -open import foundation.contractible-types -open import foundation.equivalences -open import foundation.propositions -open import foundation.retracts-of-types +open import foundation.connected-types funext univalence truncations +open import foundation.contractible-types funext univalence +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.propositions funext univalence +open import foundation.retracts-of-types funext univalence open import foundation.truncation-levels open import foundation.unit-type open import foundation.universe-levels -open import synthetic-homotopy-theory.functoriality-suspensions -open import synthetic-homotopy-theory.suspensions-of-types +open import synthetic-homotopy-theory.functoriality-suspensions funext univalence truncations +open import synthetic-homotopy-theory.suspensions-of-types funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/universal-cover-circle.lagda.md b/src/synthetic-homotopy-theory/universal-cover-circle.lagda.md index 2d69b1844c..a592e549b5 100644 --- a/src/synthetic-homotopy-theory/universal-cover-circle.lagda.md +++ b/src/synthetic-homotopy-theory/universal-cover-circle.lagda.md @@ -2,48 +2,58 @@ ```agda {-# OPTIONS --lossy-unification #-} - -module synthetic-homotopy-theory.universal-cover-circle where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.universal-cover-circle + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda +open import elementary-number-theory.equality-integers funext univalence truncations open import elementary-number-theory.integers -open import elementary-number-theory.nonzero-integers -open import elementary-number-theory.universal-property-integers +open import elementary-number-theory.nonzero-integers funext univalence truncations +open import elementary-number-theory.universal-property-integers funext univalence truncations open import foundation.action-on-identifications-dependent-functions open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-maps -open import foundation.dependent-identifications +open import foundation.commuting-squares-of-maps funext univalence +open import foundation.dependent-identifications funext open import foundation.dependent-pair-types -open import foundation.dependent-universal-property-equivalences -open import foundation.equality-dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.functoriality-dependent-function-types -open import foundation.functoriality-dependent-pair-types +open import foundation.dependent-products-truncated-types funext +open import foundation.dependent-universal-property-equivalences funext +open import foundation.equality-dependent-pair-types funext +open import foundation.equivalences funext +open import foundation.function-extensionality funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-function-types funext univalence +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.negated-equality -open import foundation.negation -open import foundation.precomposition-dependent-functions -open import foundation.raising-universe-levels -open import foundation.sets -open import foundation.torsorial-type-families +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.negated-equality funext univalence truncations +open import foundation.negation funext +open import foundation.precomposition-dependent-functions funext +open import foundation.sets funext univalence +open import foundation.torsorial-type-families funext univalence truncations open import foundation.transport-along-identifications -open import foundation.truncated-types +open import foundation.truncated-types funext univalence open import foundation.truncation-levels open import foundation.universe-levels -open import synthetic-homotopy-theory.descent-circle -open import synthetic-homotopy-theory.free-loops -open import synthetic-homotopy-theory.loop-spaces -open import synthetic-homotopy-theory.universal-property-circle +open import foundation-core.raising-universe-levels + +open import synthetic-homotopy-theory.descent-circle funext univalence truncations +open import synthetic-homotopy-theory.free-loops funext univalence truncations +open import synthetic-homotopy-theory.loop-spaces funext univalence truncations +open import synthetic-homotopy-theory.universal-property-circle funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/universal-property-circle.lagda.md b/src/synthetic-homotopy-theory/universal-property-circle.lagda.md index 9698cb554f..af3c04db35 100644 --- a/src/synthetic-homotopy-theory/universal-property-circle.lagda.md +++ b/src/synthetic-homotopy-theory/universal-property-circle.lagda.md @@ -1,7 +1,15 @@ # The universal property of the circle ```agda -module synthetic-homotopy-theory.universal-property-circle where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.universal-property-circle + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,23 +17,25 @@ module synthetic-homotopy-theory.universal-property-circle where ```agda open import foundation.action-on-identifications-dependent-functions open import foundation.action-on-identifications-functions -open import foundation.constant-type-families -open import foundation.contractible-maps -open import foundation.contractible-types +open import foundation.constant-type-families funext +open import foundation.contractible-maps funext +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.fibers-of-maps -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.propositions -open import foundation.sections +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.fibers-of-maps funext +open import foundation.function-extensionality funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.sections funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import synthetic-homotopy-theory.free-loops +open import synthetic-homotopy-theory.free-loops funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/universal-property-coequalizers.lagda.md b/src/synthetic-homotopy-theory/universal-property-coequalizers.lagda.md index 14abaccfc2..63e4e1652c 100644 --- a/src/synthetic-homotopy-theory/universal-property-coequalizers.lagda.md +++ b/src/synthetic-homotopy-theory/universal-property-coequalizers.lagda.md @@ -1,31 +1,40 @@ # The universal property of coequalizers ```agda -module synthetic-homotopy-theory.universal-property-coequalizers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.universal-property-coequalizers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.commuting-cubes-of-maps -open import foundation.commuting-squares-of-maps -open import foundation.contractible-maps -open import foundation.contractible-types -open import foundation.coproduct-types +open import foundation.commuting-cubes-of-maps funext univalence +open import foundation.commuting-squares-of-maps funext univalence +open import foundation.contractible-maps funext +open import foundation.contractible-types funext univalence +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types funext open import foundation.double-arrows -open import foundation.equivalences -open import foundation.equivalences-double-arrows -open import foundation.fibers-of-maps -open import foundation.functoriality-coproduct-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies +open import foundation.equivalences funext +open import foundation.equivalences-double-arrows funext univalence truncations +open import foundation.fibers-of-maps funext +open import foundation.functoriality-coproduct-types funext univalence truncations +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext open import foundation.universe-levels -open import synthetic-homotopy-theory.cocones-under-spans -open import synthetic-homotopy-theory.coforks -open import synthetic-homotopy-theory.equivalences-coforks-under-equivalences-double-arrows -open import synthetic-homotopy-theory.universal-property-pushouts +open import synthetic-homotopy-theory.cocones-under-spans funext +open import synthetic-homotopy-theory.coforks funext univalence truncations +open import synthetic-homotopy-theory.equivalences-coforks-under-equivalences-double-arrows funext univalence truncations +open import synthetic-homotopy-theory.universal-property-pushouts funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/universal-property-pushouts.lagda.md b/src/synthetic-homotopy-theory/universal-property-pushouts.lagda.md index 06f4082d85..bbcf9ac32f 100644 --- a/src/synthetic-homotopy-theory/universal-property-pushouts.lagda.md +++ b/src/synthetic-homotopy-theory/universal-property-pushouts.lagda.md @@ -2,39 +2,47 @@ ```agda {-# OPTIONS --lossy-unification #-} - -module synthetic-homotopy-theory.universal-property-pushouts where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.universal-property-pushouts + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-cubes-of-maps -open import foundation.commuting-squares-of-maps -open import foundation.cones-over-cospan-diagrams -open import foundation.contractible-maps -open import foundation.contractible-types +open import foundation.commuting-cubes-of-maps funext univalence +open import foundation.commuting-squares-of-maps funext univalence +open import foundation.cones-over-cospan-diagrams funext +open import foundation.contractible-maps funext +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types -open import foundation.equivalences -open import foundation.fibers-of-maps -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.precomposition-functions -open import foundation.pullbacks -open import foundation.standard-pullbacks +open import foundation.dependent-products-contractible-types funext +open import foundation.equality-dependent-pair-types funext +open import foundation.equivalences funext +open import foundation.fibers-of-maps funext +open import foundation.function-extensionality funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.precomposition-functions funext +open import foundation.pullbacks funext univalence truncations +open import foundation.standard-pullbacks funext open import foundation.subtype-identity-principle open import foundation.transport-along-identifications -open import foundation.universal-property-equivalences +open import foundation.universal-property-equivalences funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import synthetic-homotopy-theory.cocones-under-spans -open import synthetic-homotopy-theory.pullback-property-pushouts +open import synthetic-homotopy-theory.cocones-under-spans funext +open import synthetic-homotopy-theory.pullback-property-pushouts funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/universal-property-sequential-colimits.lagda.md b/src/synthetic-homotopy-theory/universal-property-sequential-colimits.lagda.md index e214baf664..4e3b28b6ff 100644 --- a/src/synthetic-homotopy-theory/universal-property-sequential-colimits.lagda.md +++ b/src/synthetic-homotopy-theory/universal-property-sequential-colimits.lagda.md @@ -1,7 +1,15 @@ # The universal property of sequential colimits ```agda -module synthetic-homotopy-theory.universal-property-sequential-colimits where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.universal-property-sequential-colimits + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,34 +18,34 @@ module synthetic-homotopy-theory.universal-property-sequential-colimits where open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-homotopies -open import foundation.commuting-triangles-of-maps -open import foundation.contractible-maps -open import foundation.contractible-types +open import foundation.commuting-squares-of-homotopies funext +open import foundation.commuting-triangles-of-maps funext univalence +open import foundation.contractible-maps funext +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.fibers-of-maps -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.precomposition-functions -open import foundation.retractions -open import foundation.sections +open import foundation.dependent-products-contractible-types funext +open import foundation.equivalences funext +open import foundation.fibers-of-maps funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.precomposition-functions funext +open import foundation.retractions funext +open import foundation.sections funext open import foundation.subtype-identity-principle -open import foundation.universal-property-equivalences +open import foundation.universal-property-equivalences funext open import foundation.universe-levels open import foundation.whiskering-higher-homotopies-composition open import foundation.whiskering-homotopies-composition -open import synthetic-homotopy-theory.cocones-under-sequential-diagrams -open import synthetic-homotopy-theory.coforks -open import synthetic-homotopy-theory.coforks-cocones-under-sequential-diagrams -open import synthetic-homotopy-theory.equivalences-cocones-under-equivalences-sequential-diagrams -open import synthetic-homotopy-theory.equivalences-sequential-diagrams -open import synthetic-homotopy-theory.sequential-diagrams -open import synthetic-homotopy-theory.universal-property-coequalizers +open import synthetic-homotopy-theory.cocones-under-sequential-diagrams funext univalence truncations +open import synthetic-homotopy-theory.coforks funext univalence truncations +open import synthetic-homotopy-theory.coforks-cocones-under-sequential-diagrams funext univalence truncations +open import synthetic-homotopy-theory.equivalences-cocones-under-equivalences-sequential-diagrams funext univalence truncations +open import synthetic-homotopy-theory.equivalences-sequential-diagrams funext univalence truncations +open import synthetic-homotopy-theory.sequential-diagrams funext univalence +open import synthetic-homotopy-theory.universal-property-coequalizers funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/universal-property-suspensions-of-pointed-types.lagda.md b/src/synthetic-homotopy-theory/universal-property-suspensions-of-pointed-types.lagda.md index a8b0a7025c..a5c0c5be76 100644 --- a/src/synthetic-homotopy-theory/universal-property-suspensions-of-pointed-types.lagda.md +++ b/src/synthetic-homotopy-theory/universal-property-suspensions-of-pointed-types.lagda.md @@ -1,30 +1,39 @@ # Universal Property of suspensions of pointed types ```agda -module synthetic-homotopy-theory.universal-property-suspensions-of-pointed-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.universal-property-suspensions-of-pointed-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.contractible-types +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.identity-types -open import foundation.torsorial-type-families +open import foundation.dependent-products-contractible-types funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.identity-types funext +open import foundation.torsorial-type-families funext univalence truncations open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels -open import structured-types.pointed-equivalences -open import structured-types.pointed-maps +open import structured-types.pointed-equivalences funext univalence truncations +open import structured-types.pointed-maps funext univalence truncations open import structured-types.pointed-types -open import synthetic-homotopy-theory.functoriality-loop-spaces -open import synthetic-homotopy-theory.loop-spaces -open import synthetic-homotopy-theory.suspensions-of-pointed-types -open import synthetic-homotopy-theory.suspensions-of-types +open import synthetic-homotopy-theory.functoriality-loop-spaces funext univalence truncations +open import synthetic-homotopy-theory.loop-spaces funext univalence truncations +open import synthetic-homotopy-theory.suspensions-of-pointed-types funext univalence truncations +open import synthetic-homotopy-theory.suspensions-of-types funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/universal-property-suspensions.lagda.md b/src/synthetic-homotopy-theory/universal-property-suspensions.lagda.md index b990b79bed..79fcaa86da 100644 --- a/src/synthetic-homotopy-theory/universal-property-suspensions.lagda.md +++ b/src/synthetic-homotopy-theory/universal-property-suspensions.lagda.md @@ -1,25 +1,33 @@ # Universal property of suspensions ```agda -module synthetic-homotopy-theory.universal-property-suspensions where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.universal-property-suspensions + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.constant-maps +open import foundation.constant-maps funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.unit-type open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import synthetic-homotopy-theory.cocones-under-spans -open import synthetic-homotopy-theory.suspension-structures -open import synthetic-homotopy-theory.universal-property-pushouts +open import synthetic-homotopy-theory.cocones-under-spans funext +open import synthetic-homotopy-theory.suspension-structures funext univalence truncations +open import synthetic-homotopy-theory.universal-property-pushouts funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/wedges-of-pointed-types.lagda.md b/src/synthetic-homotopy-theory/wedges-of-pointed-types.lagda.md index 669ca31a56..cd518ea038 100644 --- a/src/synthetic-homotopy-theory/wedges-of-pointed-types.lagda.md +++ b/src/synthetic-homotopy-theory/wedges-of-pointed-types.lagda.md @@ -1,26 +1,34 @@ # Wedges of pointed types ```agda -module synthetic-homotopy-theory.wedges-of-pointed-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.wedges-of-pointed-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.universe-levels -open import structured-types.pointed-cartesian-product-types -open import structured-types.pointed-maps +open import structured-types.pointed-cartesian-product-types funext univalence truncations +open import structured-types.pointed-maps funext univalence truncations open import structured-types.pointed-types -open import structured-types.pointed-unit-type +open import structured-types.pointed-unit-type funext univalence truncations -open import synthetic-homotopy-theory.cocones-under-pointed-span-diagrams -open import synthetic-homotopy-theory.cofibers-of-maps -open import synthetic-homotopy-theory.pushouts -open import synthetic-homotopy-theory.pushouts-of-pointed-types +open import synthetic-homotopy-theory.cocones-under-pointed-span-diagrams funext univalence truncations +open import synthetic-homotopy-theory.cofibers-of-maps funext univalence truncations +open import synthetic-homotopy-theory.pushouts funext univalence truncations +open import synthetic-homotopy-theory.pushouts-of-pointed-types funext univalence truncations ```
diff --git a/src/synthetic-homotopy-theory/zigzags-sequential-diagrams.lagda.md b/src/synthetic-homotopy-theory/zigzags-sequential-diagrams.lagda.md index 71068b80e1..2718a53063 100644 --- a/src/synthetic-homotopy-theory/zigzags-sequential-diagrams.lagda.md +++ b/src/synthetic-homotopy-theory/zigzags-sequential-diagrams.lagda.md @@ -1,7 +1,15 @@ # Zigzags between sequential diagrams ```agda -module synthetic-homotopy-theory.zigzags-sequential-diagrams where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module synthetic-homotopy-theory.zigzags-sequential-diagrams + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,24 +17,24 @@ module synthetic-homotopy-theory.zigzags-sequential-diagrams where ```agda open import elementary-number-theory.natural-numbers -open import foundation.cartesian-product-types -open import foundation.commuting-squares-of-homotopies -open import foundation.commuting-squares-of-maps -open import foundation.commuting-triangles-of-maps +open import foundation.cartesian-product-types funext univalence +open import foundation.commuting-squares-of-homotopies funext +open import foundation.commuting-squares-of-maps funext univalence +open import foundation.commuting-triangles-of-maps funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.homotopies -open import foundation.retractions +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.retractions funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import synthetic-homotopy-theory.cocones-under-sequential-diagrams -open import synthetic-homotopy-theory.functoriality-sequential-colimits -open import synthetic-homotopy-theory.morphisms-sequential-diagrams -open import synthetic-homotopy-theory.sequential-diagrams -open import synthetic-homotopy-theory.shifts-sequential-diagrams -open import synthetic-homotopy-theory.universal-property-sequential-colimits +open import synthetic-homotopy-theory.cocones-under-sequential-diagrams funext univalence truncations +open import synthetic-homotopy-theory.functoriality-sequential-colimits funext univalence truncations +open import synthetic-homotopy-theory.morphisms-sequential-diagrams funext univalence truncations +open import synthetic-homotopy-theory.sequential-diagrams funext univalence +open import synthetic-homotopy-theory.shifts-sequential-diagrams funext univalence truncations +open import synthetic-homotopy-theory.universal-property-sequential-colimits funext univalence truncations ```
diff --git a/src/trees.lagda.md b/src/trees.lagda.md index 4da5e8d445..76111aa49c 100644 --- a/src/trees.lagda.md +++ b/src/trees.lagda.md @@ -7,61 +7,69 @@ ## Files in the `trees` module ```agda -module trees where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom -open import trees.algebras-polynomial-endofunctors public -open import trees.bases-directed-trees public -open import trees.bases-enriched-directed-trees public +module trees + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where + +open import trees.algebras-polynomial-endofunctors funext univalence public +open import trees.bases-directed-trees funext univalence truncations public +open import trees.bases-enriched-directed-trees funext univalence truncations public open import trees.binary-w-types public -open import trees.bounded-multisets public -open import trees.coalgebra-of-directed-trees public -open import trees.coalgebra-of-enriched-directed-trees public -open import trees.coalgebras-polynomial-endofunctors public -open import trees.combinator-directed-trees public -open import trees.combinator-enriched-directed-trees public -open import trees.directed-trees public -open import trees.elementhood-relation-coalgebras-polynomial-endofunctors public -open import trees.elementhood-relation-w-types public -open import trees.empty-multisets public -open import trees.enriched-directed-trees public -open import trees.equivalences-directed-trees public -open import trees.equivalences-enriched-directed-trees public -open import trees.extensional-w-types public -open import trees.fibers-directed-trees public -open import trees.fibers-enriched-directed-trees public -open import trees.full-binary-trees public -open import trees.functoriality-combinator-directed-trees public -open import trees.functoriality-fiber-directed-tree public -open import trees.functoriality-w-types public -open import trees.hereditary-w-types public +open import trees.bounded-multisets funext univalence truncations public +open import trees.coalgebra-of-directed-trees funext univalence truncations public +open import trees.coalgebra-of-enriched-directed-trees funext univalence truncations public +open import trees.coalgebras-polynomial-endofunctors funext univalence public +open import trees.combinator-directed-trees funext univalence truncations public +open import trees.combinator-enriched-directed-trees funext univalence truncations public +open import trees.directed-trees funext univalence truncations public +open import trees.elementhood-relation-coalgebras-polynomial-endofunctors funext univalence truncations public +open import trees.elementhood-relation-w-types funext univalence truncations public +open import trees.empty-multisets funext univalence truncations public +open import trees.enriched-directed-trees funext univalence truncations public +open import trees.equivalences-directed-trees funext univalence truncations public +open import trees.equivalences-enriched-directed-trees funext univalence truncations public +open import trees.extensional-w-types funext univalence truncations public +open import trees.fibers-directed-trees funext univalence truncations public +open import trees.fibers-enriched-directed-trees funext univalence truncations public +open import trees.full-binary-trees funext univalence truncations public +open import trees.functoriality-combinator-directed-trees funext univalence truncations public +open import trees.functoriality-fiber-directed-tree funext univalence truncations public +open import trees.functoriality-w-types funext univalence truncations public +open import trees.hereditary-w-types funext public open import trees.indexed-w-types public -open import trees.induction-w-types public -open import trees.inequality-w-types public -open import trees.lower-types-w-types public -open import trees.morphisms-algebras-polynomial-endofunctors public -open import trees.morphisms-coalgebras-polynomial-endofunctors public -open import trees.morphisms-directed-trees public -open import trees.morphisms-enriched-directed-trees public -open import trees.multiset-indexed-dependent-products-of-types public -open import trees.multisets public -open import trees.planar-binary-trees public -open import trees.plane-trees public -open import trees.polynomial-endofunctors public -open import trees.raising-universe-levels-directed-trees public -open import trees.ranks-of-elements-w-types public -open import trees.rooted-morphisms-directed-trees public -open import trees.rooted-morphisms-enriched-directed-trees public -open import trees.rooted-quasitrees public -open import trees.rooted-undirected-trees public -open import trees.small-multisets public -open import trees.submultisets public -open import trees.transitive-multisets public -open import trees.underlying-trees-elements-coalgebras-polynomial-endofunctors public -open import trees.underlying-trees-of-elements-of-w-types public -open import trees.undirected-trees public -open import trees.universal-multiset public +open import trees.induction-w-types funext univalence truncations public +open import trees.inequality-w-types funext univalence truncations public +open import trees.lower-types-w-types funext univalence truncations public +open import trees.morphisms-algebras-polynomial-endofunctors funext univalence truncations public +open import trees.morphisms-coalgebras-polynomial-endofunctors funext univalence truncations public +open import trees.morphisms-directed-trees funext univalence truncations public +open import trees.morphisms-enriched-directed-trees funext univalence truncations public +open import trees.multiset-indexed-dependent-products-of-types funext univalence truncations public +open import trees.multisets funext univalence truncations public +open import trees.planar-binary-trees funext univalence truncations public +open import trees.plane-trees funext univalence truncations public +open import trees.polynomial-endofunctors funext univalence public +open import trees.raising-universe-levels-directed-trees funext univalence truncations public +open import trees.ranks-of-elements-w-types funext univalence truncations public +open import trees.rooted-morphisms-directed-trees funext univalence truncations public +open import trees.rooted-morphisms-enriched-directed-trees funext univalence truncations public +open import trees.rooted-quasitrees funext univalence truncations public +open import trees.rooted-undirected-trees funext univalence truncations public +open import trees.small-multisets funext univalence truncations public +open import trees.submultisets funext univalence truncations public +open import trees.transitive-multisets funext univalence truncations public +open import trees.underlying-trees-elements-coalgebras-polynomial-endofunctors funext univalence truncations public +open import trees.underlying-trees-of-elements-of-w-types funext univalence truncations public +open import trees.undirected-trees funext univalence truncations public +open import trees.universal-multiset funext univalence truncations public open import trees.universal-tree public -open import trees.w-type-of-natural-numbers public -open import trees.w-type-of-propositions public -open import trees.w-types public +open import trees.w-type-of-natural-numbers funext univalence truncations public +open import trees.w-type-of-propositions funext univalence truncations public +open import trees.w-types funext univalence truncations public ``` diff --git a/src/trees/algebras-polynomial-endofunctors.lagda.md b/src/trees/algebras-polynomial-endofunctors.lagda.md index ca1ac4e432..7d321ede8f 100644 --- a/src/trees/algebras-polynomial-endofunctors.lagda.md +++ b/src/trees/algebras-polynomial-endofunctors.lagda.md @@ -1,7 +1,13 @@ # Algebras for polynomial endofunctors ```agda -module trees.algebras-polynomial-endofunctors where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module trees.algebras-polynomial-endofunctors + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports @@ -10,7 +16,7 @@ module trees.algebras-polynomial-endofunctors where open import foundation.dependent-pair-types open import foundation.universe-levels -open import trees.polynomial-endofunctors +open import trees.polynomial-endofunctors funext univalence ```
diff --git a/src/trees/bases-directed-trees.lagda.md b/src/trees/bases-directed-trees.lagda.md index 2e96641277..3e76da1398 100644 --- a/src/trees/bases-directed-trees.lagda.md +++ b/src/trees/bases-directed-trees.lagda.md @@ -1,7 +1,15 @@ # Bases of directed trees ```agda -module trees.bases-directed-trees where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module trees.bases-directed-trees + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,26 +18,28 @@ module trees.bases-directed-trees where open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.contractible-types -open import foundation.coproduct-types +open import foundation.contractible-types funext univalence +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.equality-dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.negation -open import foundation.propositions +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.empty-types funext univalence truncations +open import foundation.equality-dependent-pair-types funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.negation funext +open import foundation.propositions funext univalence open import foundation.transport-along-identifications open import foundation.type-arithmetic-dependent-pair-types -open import foundation.type-arithmetic-empty-type +open import foundation.type-arithmetic-empty-type funext univalence truncations open import foundation.universe-levels -open import graph-theory.walks-directed-graphs +open import graph-theory.walks-directed-graphs funext univalence truncations -open import trees.directed-trees +open import trees.directed-trees funext univalence truncations ```
diff --git a/src/trees/bases-enriched-directed-trees.lagda.md b/src/trees/bases-enriched-directed-trees.lagda.md index 6d2feee2cc..9f08bb5868 100644 --- a/src/trees/bases-enriched-directed-trees.lagda.md +++ b/src/trees/bases-enriched-directed-trees.lagda.md @@ -1,26 +1,35 @@ # Bases of enriched directed trees ```agda -module trees.bases-enriched-directed-trees where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module trees.bases-enriched-directed-trees + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.contractible-types -open import foundation.coproduct-types +open import foundation.contractible-types funext univalence +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-coproduct-types -open import foundation.functoriality-dependent-pair-types -open import foundation.identity-types -open import foundation.negation -open import foundation.type-arithmetic-empty-type +open import foundation.dependent-products-contractible-types funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-coproduct-types funext univalence truncations +open import foundation.functoriality-dependent-pair-types funext +open import foundation.identity-types funext +open import foundation.negation funext +open import foundation.type-arithmetic-empty-type funext univalence truncations open import foundation.universe-levels -open import trees.bases-directed-trees -open import trees.enriched-directed-trees +open import trees.bases-directed-trees funext univalence truncations +open import trees.enriched-directed-trees funext univalence truncations ```
diff --git a/src/trees/bounded-multisets.lagda.md b/src/trees/bounded-multisets.lagda.md index ceda35ae57..5aadcca730 100644 --- a/src/trees/bounded-multisets.lagda.md +++ b/src/trees/bounded-multisets.lagda.md @@ -1,7 +1,15 @@ # Bounded multisets ```agda -module trees.bounded-multisets where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module trees.bounded-multisets + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,14 +18,15 @@ module trees.bounded-multisets where open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.existential-quantification -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.empty-types funext univalence truncations +open import foundation.existential-quantification funext univalence truncations +open import foundation.propositions funext univalence open import foundation.universe-levels -open import trees.empty-multisets -open import trees.multisets -open import trees.w-types +open import trees.empty-multisets funext univalence truncations +open import trees.multisets funext univalence truncations +open import trees.w-types funext univalence truncations ```
diff --git a/src/trees/coalgebra-of-directed-trees.lagda.md b/src/trees/coalgebra-of-directed-trees.lagda.md index e581169de0..eac7dc8589 100644 --- a/src/trees/coalgebra-of-directed-trees.lagda.md +++ b/src/trees/coalgebra-of-directed-trees.lagda.md @@ -1,7 +1,15 @@ # The coalgebra of directed trees ```agda -module trees.coalgebra-of-directed-trees where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module trees.coalgebra-of-directed-trees + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,10 +18,10 @@ module trees.coalgebra-of-directed-trees where open import foundation.dependent-pair-types open import foundation.universe-levels -open import trees.bases-directed-trees -open import trees.coalgebras-polynomial-endofunctors -open import trees.directed-trees -open import trees.fibers-directed-trees +open import trees.bases-directed-trees funext univalence truncations +open import trees.coalgebras-polynomial-endofunctors funext univalence +open import trees.directed-trees funext univalence truncations +open import trees.fibers-directed-trees funext univalence truncations ```
diff --git a/src/trees/coalgebra-of-enriched-directed-trees.lagda.md b/src/trees/coalgebra-of-enriched-directed-trees.lagda.md index 32cae5c137..d5fcd7f00f 100644 --- a/src/trees/coalgebra-of-enriched-directed-trees.lagda.md +++ b/src/trees/coalgebra-of-enriched-directed-trees.lagda.md @@ -2,8 +2,15 @@ ```agda {-# OPTIONS --lossy-unification #-} - -module trees.coalgebra-of-enriched-directed-trees where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module trees.coalgebra-of-enriched-directed-trees + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -12,10 +19,10 @@ module trees.coalgebra-of-enriched-directed-trees where open import foundation.dependent-pair-types open import foundation.universe-levels -open import trees.coalgebras-polynomial-endofunctors -open import trees.enriched-directed-trees -open import trees.fibers-enriched-directed-trees -open import trees.polynomial-endofunctors +open import trees.coalgebras-polynomial-endofunctors funext univalence +open import trees.enriched-directed-trees funext univalence truncations +open import trees.fibers-enriched-directed-trees funext univalence truncations +open import trees.polynomial-endofunctors funext univalence ```
diff --git a/src/trees/coalgebras-polynomial-endofunctors.lagda.md b/src/trees/coalgebras-polynomial-endofunctors.lagda.md index 85f9f915c3..70baf42576 100644 --- a/src/trees/coalgebras-polynomial-endofunctors.lagda.md +++ b/src/trees/coalgebras-polynomial-endofunctors.lagda.md @@ -1,7 +1,13 @@ # Coalgebras of polynomial endofunctors ```agda -module trees.coalgebras-polynomial-endofunctors where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module trees.coalgebras-polynomial-endofunctors + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports @@ -10,7 +16,7 @@ module trees.coalgebras-polynomial-endofunctors where open import foundation.dependent-pair-types open import foundation.universe-levels -open import trees.polynomial-endofunctors +open import trees.polynomial-endofunctors funext univalence ```
diff --git a/src/trees/combinator-directed-trees.lagda.md b/src/trees/combinator-directed-trees.lagda.md index 4d2862298f..b5b0ff2e72 100644 --- a/src/trees/combinator-directed-trees.lagda.md +++ b/src/trees/combinator-directed-trees.lagda.md @@ -1,39 +1,49 @@ # The combinator of directed trees ```agda -module trees.combinator-directed-trees where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module trees.combinator-directed-trees + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.contractible-types -open import foundation.coproduct-types -open import foundation.decidable-types +open import foundation.contractible-types funext univalence +open import foundation.coproduct-types funext univalence truncations +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.equality-dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.isolated-elements -open import foundation.maybe -open import foundation.negation -open import foundation.propositions +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.empty-types funext univalence truncations +open import foundation.equality-dependent-pair-types funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.isolated-elements funext univalence truncations +open import foundation.maybe funext univalence truncations +open import foundation.negation funext +open import foundation.propositions funext univalence open import foundation.universe-levels -open import graph-theory.directed-graphs -open import graph-theory.morphisms-directed-graphs -open import graph-theory.walks-directed-graphs +open import graph-theory.directed-graphs funext univalence +open import graph-theory.morphisms-directed-graphs funext univalence truncations +open import graph-theory.walks-directed-graphs funext univalence truncations -open import trees.bases-directed-trees -open import trees.directed-trees -open import trees.equivalences-directed-trees -open import trees.fibers-directed-trees -open import trees.morphisms-directed-trees +open import trees.bases-directed-trees funext univalence truncations +open import trees.directed-trees funext univalence truncations +open import trees.equivalences-directed-trees funext univalence truncations +open import trees.fibers-directed-trees funext univalence truncations +open import trees.morphisms-directed-trees funext univalence truncations ```
diff --git a/src/trees/combinator-enriched-directed-trees.lagda.md b/src/trees/combinator-enriched-directed-trees.lagda.md index 87f07372ae..03e7322497 100644 --- a/src/trees/combinator-enriched-directed-trees.lagda.md +++ b/src/trees/combinator-enriched-directed-trees.lagda.md @@ -1,29 +1,37 @@ # Combinators of enriched directed trees ```agda -module trees.combinator-enriched-directed-trees where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module trees.combinator-enriched-directed-trees + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.maybe +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.maybe funext univalence truncations open import foundation.universe-levels -open import graph-theory.directed-graphs +open import graph-theory.directed-graphs funext univalence -open import trees.combinator-directed-trees -open import trees.directed-trees -open import trees.enriched-directed-trees -open import trees.equivalences-directed-trees -open import trees.equivalences-enriched-directed-trees -open import trees.fibers-enriched-directed-trees -open import trees.morphisms-directed-trees +open import trees.combinator-directed-trees funext univalence truncations +open import trees.directed-trees funext univalence truncations +open import trees.enriched-directed-trees funext univalence truncations +open import trees.equivalences-directed-trees funext univalence truncations +open import trees.equivalences-enriched-directed-trees funext univalence truncations +open import trees.fibers-enriched-directed-trees funext univalence truncations +open import trees.morphisms-directed-trees funext univalence truncations ```
diff --git a/src/trees/directed-trees.lagda.md b/src/trees/directed-trees.lagda.md index 5c60f5b264..c3b8dc4663 100644 --- a/src/trees/directed-trees.lagda.md +++ b/src/trees/directed-trees.lagda.md @@ -1,7 +1,15 @@ # Directed trees ```agda -module trees.directed-trees where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module trees.directed-trees + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,31 +18,33 @@ module trees.directed-trees where open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types -open import foundation.contractible-types -open import foundation.coproduct-types -open import foundation.decidable-types +open import foundation.cartesian-product-types funext univalence +open import foundation.contractible-types funext univalence +open import foundation.coproduct-types funext univalence truncations +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.equality-dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-coproduct-types -open import foundation.identity-types -open import foundation.isolated-elements -open import foundation.negated-equality -open import foundation.negation -open import foundation.propositions -open import foundation.subtypes -open import foundation.torsorial-type-families +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.empty-types funext univalence truncations +open import foundation.equality-dependent-pair-types funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-coproduct-types funext univalence truncations +open import foundation.identity-types funext +open import foundation.isolated-elements funext univalence truncations +open import foundation.negated-equality funext univalence truncations +open import foundation.negation funext +open import foundation.propositions funext univalence +open import foundation.subtypes funext univalence truncations +open import foundation.torsorial-type-families funext univalence truncations open import foundation.transport-along-identifications -open import foundation.type-arithmetic-coproduct-types +open import foundation.type-arithmetic-coproduct-types funext univalence truncations open import foundation.type-arithmetic-dependent-pair-types -open import foundation.type-arithmetic-empty-type +open import foundation.type-arithmetic-empty-type funext univalence truncations open import foundation.universe-levels -open import graph-theory.directed-graphs -open import graph-theory.walks-directed-graphs +open import graph-theory.directed-graphs funext univalence +open import graph-theory.walks-directed-graphs funext univalence truncations ```
diff --git a/src/trees/elementhood-relation-coalgebras-polynomial-endofunctors.lagda.md b/src/trees/elementhood-relation-coalgebras-polynomial-endofunctors.lagda.md index 283aa1f4a3..be379334a2 100644 --- a/src/trees/elementhood-relation-coalgebras-polynomial-endofunctors.lagda.md +++ b/src/trees/elementhood-relation-coalgebras-polynomial-endofunctors.lagda.md @@ -1,20 +1,28 @@ # The elementhood relation on coalgebras of polynomial endofunctors ```agda -module trees.elementhood-relation-coalgebras-polynomial-endofunctors where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module trees.elementhood-relation-coalgebras-polynomial-endofunctors + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.fibers-of-maps +open import foundation.fibers-of-maps funext open import foundation.universe-levels -open import graph-theory.directed-graphs -open import graph-theory.walks-directed-graphs +open import graph-theory.directed-graphs funext univalence +open import graph-theory.walks-directed-graphs funext univalence truncations -open import trees.coalgebras-polynomial-endofunctors +open import trees.coalgebras-polynomial-endofunctors funext univalence ```
diff --git a/src/trees/elementhood-relation-w-types.lagda.md b/src/trees/elementhood-relation-w-types.lagda.md index df5c81a9b4..74e05ac3c1 100644 --- a/src/trees/elementhood-relation-w-types.lagda.md +++ b/src/trees/elementhood-relation-w-types.lagda.md @@ -1,20 +1,28 @@ # The elementhood relation on W-types ```agda -module trees.elementhood-relation-w-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module trees.elementhood-relation-w-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.identity-types +open import foundation.empty-types funext univalence truncations +open import foundation.identity-types funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import trees.elementhood-relation-coalgebras-polynomial-endofunctors -open import trees.w-types +open import trees.elementhood-relation-coalgebras-polynomial-endofunctors funext univalence truncations +open import trees.w-types funext univalence truncations ```
diff --git a/src/trees/empty-multisets.lagda.md b/src/trees/empty-multisets.lagda.md index d31b3e8a6b..9ddc83f1d0 100644 --- a/src/trees/empty-multisets.lagda.md +++ b/src/trees/empty-multisets.lagda.md @@ -1,21 +1,30 @@ # Empty multisets ```agda -module trees.empty-multisets where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module trees.empty-multisets + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.identity-types -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.empty-types funext univalence truncations +open import foundation.identity-types funext +open import foundation.propositions funext univalence open import foundation.universe-levels -open import trees.elementhood-relation-w-types -open import trees.multisets -open import trees.w-types +open import trees.elementhood-relation-w-types funext univalence truncations +open import trees.multisets funext univalence truncations +open import trees.w-types funext univalence truncations ```
diff --git a/src/trees/enriched-directed-trees.lagda.md b/src/trees/enriched-directed-trees.lagda.md index f17320ca15..f7b7fda2ca 100644 --- a/src/trees/enriched-directed-trees.lagda.md +++ b/src/trees/enriched-directed-trees.lagda.md @@ -1,7 +1,15 @@ # Enriched directed trees ```agda -module trees.enriched-directed-trees where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module trees.enriched-directed-trees + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,22 +18,24 @@ module trees.enriched-directed-trees where open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-maps -open import foundation.contractible-types +open import foundation.commuting-squares-of-maps funext univalence +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.isolated-elements -open import foundation.negation -open import foundation.propositions +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.isolated-elements funext univalence truncations +open import foundation.negation funext +open import foundation.propositions funext univalence open import foundation.transport-along-identifications open import foundation.universe-levels -open import graph-theory.directed-graphs +open import graph-theory.directed-graphs funext univalence -open import trees.directed-trees +open import trees.directed-trees funext univalence truncations ```
diff --git a/src/trees/equivalences-directed-trees.lagda.md b/src/trees/equivalences-directed-trees.lagda.md index 5b7a6ffa00..8115cc2751 100644 --- a/src/trees/equivalences-directed-trees.lagda.md +++ b/src/trees/equivalences-directed-trees.lagda.md @@ -1,7 +1,15 @@ # Equivalences of directed trees ```agda -module trees.equivalences-directed-trees where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module trees.equivalences-directed-trees + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,26 +17,27 @@ module trees.equivalences-directed-trees where ```agda open import foundation.action-on-identifications-functions open import foundation.binary-transport -open import foundation.contractible-types -open import foundation.coproduct-types +open import foundation.contractible-types funext univalence +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types +open import foundation.dependent-products-contractible-types funext +open import foundation.empty-types funext univalence truncations +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.subtype-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext univalence truncations open import foundation.transport-along-identifications open import foundation.universe-levels -open import graph-theory.equivalences-directed-graphs -open import graph-theory.walks-directed-graphs +open import graph-theory.equivalences-directed-graphs funext univalence truncations +open import graph-theory.walks-directed-graphs funext univalence truncations -open import trees.directed-trees -open import trees.morphisms-directed-trees -open import trees.rooted-morphisms-directed-trees +open import trees.directed-trees funext univalence truncations +open import trees.morphisms-directed-trees funext univalence truncations +open import trees.rooted-morphisms-directed-trees funext univalence truncations ```
diff --git a/src/trees/equivalences-enriched-directed-trees.lagda.md b/src/trees/equivalences-enriched-directed-trees.lagda.md index 410b7c1709..6c7d16f047 100644 --- a/src/trees/equivalences-enriched-directed-trees.lagda.md +++ b/src/trees/equivalences-enriched-directed-trees.lagda.md @@ -1,34 +1,43 @@ # Equivalences of enriched directed trees ```agda -module trees.equivalences-enriched-directed-trees where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module trees.equivalences-enriched-directed-trees + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.commuting-squares-of-maps -open import foundation.commuting-triangles-of-maps -open import foundation.contractible-types +open import foundation.commuting-squares-of-maps funext univalence +open import foundation.commuting-triangles-of-maps funext univalence +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types -open import foundation.equivalence-extensionality -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types +open import foundation.dependent-products-contractible-types funext +open import foundation.equality-dependent-function-types funext +open import foundation.equivalence-extensionality funext +open import foundation.equivalences funext +open import foundation.function-extensionality funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.structure-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext univalence truncations open import foundation.transport-along-identifications open import foundation.universe-levels -open import trees.enriched-directed-trees -open import trees.equivalences-directed-trees -open import trees.morphisms-directed-trees -open import trees.morphisms-enriched-directed-trees -open import trees.rooted-morphisms-enriched-directed-trees +open import trees.enriched-directed-trees funext univalence truncations +open import trees.equivalences-directed-trees funext univalence truncations +open import trees.morphisms-directed-trees funext univalence truncations +open import trees.morphisms-enriched-directed-trees funext univalence truncations +open import trees.rooted-morphisms-enriched-directed-trees funext univalence truncations ```
diff --git a/src/trees/extensional-w-types.lagda.md b/src/trees/extensional-w-types.lagda.md index 257d84375e..d21c84e406 100644 --- a/src/trees/extensional-w-types.lagda.md +++ b/src/trees/extensional-w-types.lagda.md @@ -1,36 +1,46 @@ # Extensional W-types ```agda -module trees.extensional-w-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module trees.extensional-w-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.contractible-types +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types -open import foundation.equivalence-extensionality -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-function-types -open import foundation.functoriality-dependent-pair-types +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.equality-dependent-function-types funext +open import foundation.equivalence-extensionality funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-function-types funext univalence +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.slice -open import foundation.torsorial-type-families +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence +open import foundation.slice funext univalence +open import foundation.torsorial-type-families funext univalence truncations open import foundation.transport-along-identifications open import foundation.type-arithmetic-dependent-pair-types -open import foundation.univalent-type-families +open import foundation.univalent-type-families funext univalence open import foundation.universe-levels -open import trees.elementhood-relation-w-types -open import trees.w-types +open import trees.elementhood-relation-w-types funext univalence truncations +open import trees.w-types funext univalence truncations ```
diff --git a/src/trees/fibers-directed-trees.lagda.md b/src/trees/fibers-directed-trees.lagda.md index b1cff222b1..b2c31a3063 100644 --- a/src/trees/fibers-directed-trees.lagda.md +++ b/src/trees/fibers-directed-trees.lagda.md @@ -1,25 +1,33 @@ # Fibers of directed trees ```agda -module trees.fibers-directed-trees where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module trees.fibers-directed-trees + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.coproduct-types +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.homotopies -open import foundation.identity-types +open import foundation.equivalences funext +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.universe-levels -open import graph-theory.directed-graphs -open import graph-theory.fibers-directed-graphs +open import graph-theory.directed-graphs funext univalence +open import graph-theory.fibers-directed-graphs funext univalence truncations -open import trees.bases-directed-trees -open import trees.directed-trees -open import trees.morphisms-directed-trees +open import trees.bases-directed-trees funext univalence truncations +open import trees.directed-trees funext univalence truncations +open import trees.morphisms-directed-trees funext univalence truncations ```
diff --git a/src/trees/fibers-enriched-directed-trees.lagda.md b/src/trees/fibers-enriched-directed-trees.lagda.md index d6c2a7b325..e067ff2914 100644 --- a/src/trees/fibers-enriched-directed-trees.lagda.md +++ b/src/trees/fibers-enriched-directed-trees.lagda.md @@ -1,26 +1,35 @@ # Fibers of enriched directed trees ```agda -module trees.fibers-enriched-directed-trees where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module trees.fibers-enriched-directed-trees + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.contractible-types +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.identity-types -open import foundation.torsorial-type-families +open import foundation.dependent-products-contractible-types funext +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.torsorial-type-families funext univalence truncations open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels -open import graph-theory.walks-directed-graphs +open import graph-theory.walks-directed-graphs funext univalence truncations -open import trees.bases-enriched-directed-trees -open import trees.directed-trees -open import trees.enriched-directed-trees -open import trees.fibers-directed-trees +open import trees.bases-enriched-directed-trees funext univalence truncations +open import trees.directed-trees funext univalence truncations +open import trees.enriched-directed-trees funext univalence truncations +open import trees.fibers-directed-trees funext univalence truncations ```
diff --git a/src/trees/full-binary-trees.lagda.md b/src/trees/full-binary-trees.lagda.md index 00ed1e42a8..e90425df72 100644 --- a/src/trees/full-binary-trees.lagda.md +++ b/src/trees/full-binary-trees.lagda.md @@ -1,7 +1,15 @@ # Full binary trees ```agda -module trees.full-binary-trees where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module trees.full-binary-trees + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,10 +17,10 @@ module trees.full-binary-trees where ```agda open import elementary-number-theory.natural-numbers -open import foundation.empty-types +open import foundation.empty-types funext univalence truncations open import foundation.universe-levels -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/trees/functoriality-combinator-directed-trees.lagda.md b/src/trees/functoriality-combinator-directed-trees.lagda.md index 62ecdf2b9c..42cf8e7d6f 100644 --- a/src/trees/functoriality-combinator-directed-trees.lagda.md +++ b/src/trees/functoriality-combinator-directed-trees.lagda.md @@ -1,7 +1,15 @@ # Functoriality of the combinator of directed trees ```agda -module trees.functoriality-combinator-directed-trees where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module trees.functoriality-combinator-directed-trees + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,19 +17,20 @@ module trees.functoriality-combinator-directed-trees where ```agda open import foundation.action-on-identifications-functions open import foundation.binary-transport -open import foundation.contractible-types +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types +open import foundation.dependent-products-contractible-types funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import trees.combinator-directed-trees -open import trees.directed-trees -open import trees.equivalences-directed-trees -open import trees.morphisms-directed-trees -open import trees.rooted-morphisms-directed-trees +open import trees.combinator-directed-trees funext univalence truncations +open import trees.directed-trees funext univalence truncations +open import trees.equivalences-directed-trees funext univalence truncations +open import trees.morphisms-directed-trees funext univalence truncations +open import trees.rooted-morphisms-directed-trees funext univalence truncations ```
diff --git a/src/trees/functoriality-fiber-directed-tree.lagda.md b/src/trees/functoriality-fiber-directed-tree.lagda.md index 2338441e60..5b4bd9057d 100644 --- a/src/trees/functoriality-fiber-directed-tree.lagda.md +++ b/src/trees/functoriality-fiber-directed-tree.lagda.md @@ -1,7 +1,15 @@ # Functoriality of the fiber operation on directed trees ```agda -module trees.functoriality-fiber-directed-tree where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module trees.functoriality-fiber-directed-tree + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,17 +17,17 @@ module trees.functoriality-fiber-directed-tree where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.functoriality-dependent-pair-types -open import foundation.identity-types +open import foundation.equivalences funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.identity-types funext open import foundation.universe-levels -open import graph-theory.walks-directed-graphs +open import graph-theory.walks-directed-graphs funext univalence truncations -open import trees.directed-trees -open import trees.equivalences-directed-trees -open import trees.fibers-directed-trees -open import trees.morphisms-directed-trees +open import trees.directed-trees funext univalence truncations +open import trees.equivalences-directed-trees funext univalence truncations +open import trees.fibers-directed-trees funext univalence truncations +open import trees.morphisms-directed-trees funext univalence truncations ```
diff --git a/src/trees/functoriality-w-types.lagda.md b/src/trees/functoriality-w-types.lagda.md index 6a32e1a93e..f8be0f9edc 100644 --- a/src/trees/functoriality-w-types.lagda.md +++ b/src/trees/functoriality-w-types.lagda.md @@ -1,33 +1,42 @@ # Functoriality of W-types ```agda -module trees.functoriality-w-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module trees.functoriality-w-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types -open import foundation.contractible-maps +open import foundation.cartesian-product-types funext univalence +open import foundation.contractible-maps funext open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalences -open import foundation.fibers-of-maps -open import foundation.function-types -open import foundation.functoriality-dependent-function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.identity-types -open import foundation.propositional-maps +open import foundation.dependent-products-truncated-types funext +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.fibers-of-maps funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-function-types funext univalence +open import foundation.functoriality-dependent-pair-types funext +open import foundation.identity-types funext +open import foundation.propositional-maps funext open import foundation.transport-along-identifications -open import foundation.truncated-maps -open import foundation.truncated-types +open import foundation.truncated-maps funext +open import foundation.truncated-types funext univalence open import foundation.truncation-levels open import foundation.type-arithmetic-dependent-pair-types -open import foundation.type-theoretic-principle-of-choice +open import foundation.type-theoretic-principle-of-choice funext open import foundation.universe-levels -open import trees.w-types +open import trees.w-types funext univalence truncations ```
diff --git a/src/trees/hereditary-w-types.lagda.md b/src/trees/hereditary-w-types.lagda.md index 3e0ff510c9..d2c30cff4f 100644 --- a/src/trees/hereditary-w-types.lagda.md +++ b/src/trees/hereditary-w-types.lagda.md @@ -1,7 +1,11 @@ # Hereditary W-types ```agda -module trees.hereditary-w-types where +open import foundation.function-extensionality-axiom + +module trees.hereditary-w-types + (funext : function-extensionality) + where ```
Imports @@ -10,12 +14,12 @@ module trees.hereditary-w-types where open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.identity-types -open import foundation.retractions -open import foundation.sections +open import foundation.equivalences funext +open import foundation.function-extensionality funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.retractions funext +open import foundation.sections funext open import foundation.universe-levels open import trees.binary-w-types diff --git a/src/trees/induction-w-types.lagda.md b/src/trees/induction-w-types.lagda.md index 1805b55311..78b3c1130f 100644 --- a/src/trees/induction-w-types.lagda.md +++ b/src/trees/induction-w-types.lagda.md @@ -1,7 +1,15 @@ # Induction principles on W-types ```agda -module trees.induction-w-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module trees.induction-w-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -11,16 +19,16 @@ open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.identity-types -open import foundation.negation +open import foundation.function-extensionality funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.negation funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import trees.elementhood-relation-w-types -open import trees.inequality-w-types -open import trees.w-types +open import trees.elementhood-relation-w-types funext univalence truncations +open import trees.inequality-w-types funext univalence truncations +open import trees.w-types funext univalence truncations ```
diff --git a/src/trees/inequality-w-types.lagda.md b/src/trees/inequality-w-types.lagda.md index e8ba671c13..ee92754336 100644 --- a/src/trees/inequality-w-types.lagda.md +++ b/src/trees/inequality-w-types.lagda.md @@ -1,7 +1,15 @@ # Inequality on W-types ```agda -module trees.inequality-w-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module trees.inequality-w-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,13 +18,13 @@ module trees.inequality-w-types where open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.identity-types -open import foundation.negation +open import foundation.empty-types funext univalence truncations +open import foundation.identity-types funext +open import foundation.negation funext open import foundation.universe-levels -open import trees.elementhood-relation-w-types -open import trees.w-types +open import trees.elementhood-relation-w-types funext univalence truncations +open import trees.w-types funext univalence truncations ```
diff --git a/src/trees/lower-types-w-types.lagda.md b/src/trees/lower-types-w-types.lagda.md index 5e283be7bb..fd81e2dbbc 100644 --- a/src/trees/lower-types-w-types.lagda.md +++ b/src/trees/lower-types-w-types.lagda.md @@ -1,17 +1,25 @@ # Lower types of elements in W-types ```agda -module trees.lower-types-w-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module trees.lower-types-w-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.existential-quantification +open import foundation.existential-quantification funext univalence truncations open import foundation.universe-levels -open import trees.ranks-of-elements-w-types -open import trees.w-types +open import trees.ranks-of-elements-w-types funext univalence truncations +open import trees.w-types funext univalence truncations ```
diff --git a/src/trees/morphisms-algebras-polynomial-endofunctors.lagda.md b/src/trees/morphisms-algebras-polynomial-endofunctors.lagda.md index 12364a1b34..acc42530fb 100644 --- a/src/trees/morphisms-algebras-polynomial-endofunctors.lagda.md +++ b/src/trees/morphisms-algebras-polynomial-endofunctors.lagda.md @@ -1,29 +1,38 @@ # Morphisms of algebras of polynomial endofunctors ```agda -module trees.morphisms-algebras-polynomial-endofunctors where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module trees.morphisms-algebras-polynomial-endofunctors + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.contractible-types +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types +open import foundation.dependent-products-contractible-types funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext open import foundation.structure-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext univalence truncations open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import trees.algebras-polynomial-endofunctors -open import trees.polynomial-endofunctors +open import trees.algebras-polynomial-endofunctors funext univalence +open import trees.polynomial-endofunctors funext univalence ```
diff --git a/src/trees/morphisms-coalgebras-polynomial-endofunctors.lagda.md b/src/trees/morphisms-coalgebras-polynomial-endofunctors.lagda.md index f6771ba67b..f257df36bc 100644 --- a/src/trees/morphisms-coalgebras-polynomial-endofunctors.lagda.md +++ b/src/trees/morphisms-coalgebras-polynomial-endofunctors.lagda.md @@ -1,29 +1,38 @@ # Morphisms of coalgebras of polynomial endofunctors ```agda -module trees.morphisms-coalgebras-polynomial-endofunctors where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module trees.morphisms-coalgebras-polynomial-endofunctors + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-maps -open import foundation.contractible-types +open import foundation.commuting-squares-of-maps funext univalence +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.functoriality-dependent-pair-types +open import foundation.dependent-products-contractible-types funext +open import foundation.equivalences funext +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext open import foundation.structure-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext univalence truncations open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import trees.coalgebras-polynomial-endofunctors -open import trees.polynomial-endofunctors +open import trees.coalgebras-polynomial-endofunctors funext univalence +open import trees.polynomial-endofunctors funext univalence ```
diff --git a/src/trees/morphisms-directed-trees.lagda.md b/src/trees/morphisms-directed-trees.lagda.md index 925111eb85..0e39cc286e 100644 --- a/src/trees/morphisms-directed-trees.lagda.md +++ b/src/trees/morphisms-directed-trees.lagda.md @@ -1,31 +1,40 @@ # Morphisms of directed trees ```agda -module trees.morphisms-directed-trees where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module trees.morphisms-directed-trees + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.binary-transport -open import foundation.contractible-types +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.negation -open import foundation.torsorial-type-families +open import foundation.dependent-products-contractible-types funext +open import foundation.equality-dependent-pair-types funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.negation funext +open import foundation.torsorial-type-families funext univalence truncations open import foundation.transport-along-identifications -open import foundation.type-arithmetic-empty-type +open import foundation.type-arithmetic-empty-type funext univalence truncations open import foundation.universe-levels -open import graph-theory.morphisms-directed-graphs -open import graph-theory.walks-directed-graphs +open import graph-theory.morphisms-directed-graphs funext univalence truncations +open import graph-theory.walks-directed-graphs funext univalence truncations -open import trees.directed-trees +open import trees.directed-trees funext univalence truncations ```
diff --git a/src/trees/morphisms-enriched-directed-trees.lagda.md b/src/trees/morphisms-enriched-directed-trees.lagda.md index 968efd173c..61a9da2e5f 100644 --- a/src/trees/morphisms-enriched-directed-trees.lagda.md +++ b/src/trees/morphisms-enriched-directed-trees.lagda.md @@ -1,25 +1,33 @@ # Morphisms of enriched directed trees ```agda -module trees.morphisms-enriched-directed-trees where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module trees.morphisms-enriched-directed-trees + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-maps -open import foundation.commuting-triangles-of-maps +open import foundation.commuting-squares-of-maps funext univalence +open import foundation.commuting-triangles-of-maps funext univalence open import foundation.dependent-pair-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.transport-along-identifications open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import trees.enriched-directed-trees -open import trees.morphisms-directed-trees +open import trees.enriched-directed-trees funext univalence truncations +open import trees.morphisms-directed-trees funext univalence truncations ```
diff --git a/src/trees/multiset-indexed-dependent-products-of-types.lagda.md b/src/trees/multiset-indexed-dependent-products-of-types.lagda.md index ed16d82c4d..d6dbd3fa69 100644 --- a/src/trees/multiset-indexed-dependent-products-of-types.lagda.md +++ b/src/trees/multiset-indexed-dependent-products-of-types.lagda.md @@ -1,7 +1,15 @@ # Multiset-indexed dependent products of types ```agda -module trees.multiset-indexed-dependent-products-of-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module trees.multiset-indexed-dependent-products-of-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -11,8 +19,8 @@ open import elementary-number-theory.natural-numbers open import foundation.universe-levels -open import trees.multisets -open import trees.w-types +open import trees.multisets funext univalence truncations +open import trees.w-types funext univalence truncations ```
diff --git a/src/trees/multisets.lagda.md b/src/trees/multisets.lagda.md index ed24b4339c..1af510c397 100644 --- a/src/trees/multisets.lagda.md +++ b/src/trees/multisets.lagda.md @@ -1,19 +1,27 @@ # Multisets ```agda -module trees.multisets where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module trees.multisets + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.function-types +open import foundation.empty-types funext univalence truncations +open import foundation.function-types funext open import foundation.universe-levels -open import trees.elementhood-relation-w-types -open import trees.w-types +open import trees.elementhood-relation-w-types funext univalence truncations +open import trees.w-types funext univalence truncations ```
diff --git a/src/trees/planar-binary-trees.lagda.md b/src/trees/planar-binary-trees.lagda.md index 3e60500e59..37acdff15e 100644 --- a/src/trees/planar-binary-trees.lagda.md +++ b/src/trees/planar-binary-trees.lagda.md @@ -1,18 +1,26 @@ # Planar binary trees ```agda -module trees.planar-binary-trees where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module trees.planar-binary-trees + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.booleans -open import foundation.empty-types -open import foundation.function-types +open import foundation.booleans funext univalence truncations +open import foundation.empty-types funext univalence truncations +open import foundation.function-types funext open import foundation.universe-levels -open import trees.w-types +open import trees.w-types funext univalence truncations ```
diff --git a/src/trees/plane-trees.lagda.md b/src/trees/plane-trees.lagda.md index 12c443c8e3..92fe349d56 100644 --- a/src/trees/plane-trees.lagda.md +++ b/src/trees/plane-trees.lagda.md @@ -1,7 +1,15 @@ # Plane trees ```agda -module trees.plane-trees where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module trees.plane-trees + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -12,20 +20,20 @@ open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.identity-types -open import foundation.maybe -open import foundation.retractions -open import foundation.sections +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.maybe funext univalence truncations +open import foundation.retractions funext +open import foundation.sections funext open import foundation.universe-levels open import lists.lists -open import trees.full-binary-trees -open import trees.w-types +open import trees.full-binary-trees funext univalence truncations +open import trees.w-types funext univalence truncations -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/trees/polynomial-endofunctors.lagda.md b/src/trees/polynomial-endofunctors.lagda.md index 793fbf9b59..043cb2bf9c 100644 --- a/src/trees/polynomial-endofunctors.lagda.md +++ b/src/trees/polynomial-endofunctors.lagda.md @@ -1,21 +1,28 @@ # Polynomial endofunctors ```agda -module trees.polynomial-endofunctors where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module trees.polynomial-endofunctors + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda -open import foundation.contractible-types +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types +open import foundation.dependent-products-contractible-types funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext open import foundation.structure-identity-principle open import foundation.transport-along-identifications open import foundation.universe-levels diff --git a/src/trees/raising-universe-levels-directed-trees.lagda.md b/src/trees/raising-universe-levels-directed-trees.lagda.md index 8f1e1ac294..9369d32b8b 100644 --- a/src/trees/raising-universe-levels-directed-trees.lagda.md +++ b/src/trees/raising-universe-levels-directed-trees.lagda.md @@ -1,24 +1,34 @@ # Raising universe levels of directed trees ```agda -module trees.raising-universe-levels-directed-trees where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module trees.raising-universe-levels-directed-trees + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.contractible-types +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.raising-universe-levels +open import foundation.dependent-products-contractible-types funext +open import foundation.equivalences funext open import foundation.universe-levels -open import graph-theory.directed-graphs -open import graph-theory.raising-universe-levels-directed-graphs -open import graph-theory.walks-directed-graphs +open import foundation-core.raising-universe-levels + +open import graph-theory.directed-graphs funext univalence +open import graph-theory.raising-universe-levels-directed-graphs funext univalence truncations +open import graph-theory.walks-directed-graphs funext univalence truncations -open import trees.directed-trees -open import trees.equivalences-directed-trees +open import trees.directed-trees funext univalence truncations +open import trees.equivalences-directed-trees funext univalence truncations ```
diff --git a/src/trees/ranks-of-elements-w-types.lagda.md b/src/trees/ranks-of-elements-w-types.lagda.md index 26e9e63740..583779ecc8 100644 --- a/src/trees/ranks-of-elements-w-types.lagda.md +++ b/src/trees/ranks-of-elements-w-types.lagda.md @@ -1,26 +1,35 @@ # Ranks of elements in W-types ```agda -module trees.ranks-of-elements-w-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module trees.ranks-of-elements-w-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.existential-quantification -open import foundation.identity-types -open import foundation.negation -open import foundation.propositional-truncations -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.empty-types funext univalence truncations +open import foundation.existential-quantification funext univalence truncations +open import foundation.identity-types funext +open import foundation.negation funext +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence open import foundation.transport-along-identifications open import foundation.universe-levels -open import trees.elementhood-relation-w-types -open import trees.inequality-w-types -open import trees.w-types +open import trees.elementhood-relation-w-types funext univalence truncations +open import trees.inequality-w-types funext univalence truncations +open import trees.w-types funext univalence truncations ```
diff --git a/src/trees/rooted-morphisms-directed-trees.lagda.md b/src/trees/rooted-morphisms-directed-trees.lagda.md index 81c9d5fc01..ae3e2aead2 100644 --- a/src/trees/rooted-morphisms-directed-trees.lagda.md +++ b/src/trees/rooted-morphisms-directed-trees.lagda.md @@ -1,7 +1,15 @@ # Rooted morphisms of directed trees ```agda -module trees.rooted-morphisms-directed-trees where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module trees.rooted-morphisms-directed-trees + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,22 +17,24 @@ module trees.rooted-morphisms-directed-trees where ```agda open import foundation.action-on-identifications-functions open import foundation.binary-transport -open import foundation.contractible-types +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.propositions +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence open import foundation.subtype-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext univalence truncations open import foundation.transport-along-identifications open import foundation.universe-levels -open import trees.bases-directed-trees -open import trees.directed-trees -open import trees.morphisms-directed-trees +open import trees.bases-directed-trees funext univalence truncations +open import trees.directed-trees funext univalence truncations +open import trees.morphisms-directed-trees funext univalence truncations ```
diff --git a/src/trees/rooted-morphisms-enriched-directed-trees.lagda.md b/src/trees/rooted-morphisms-enriched-directed-trees.lagda.md index f876ff518a..fb94697626 100644 --- a/src/trees/rooted-morphisms-enriched-directed-trees.lagda.md +++ b/src/trees/rooted-morphisms-enriched-directed-trees.lagda.md @@ -1,23 +1,32 @@ # Rooted morphisms of enriched directed trees ```agda -module trees.rooted-morphisms-enriched-directed-trees where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module trees.rooted-morphisms-enriched-directed-trees + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence open import foundation.transport-along-identifications open import foundation.universe-levels -open import trees.enriched-directed-trees -open import trees.morphisms-enriched-directed-trees -open import trees.rooted-morphisms-directed-trees +open import trees.enriched-directed-trees funext univalence truncations +open import trees.morphisms-enriched-directed-trees funext univalence truncations +open import trees.rooted-morphisms-directed-trees funext univalence truncations ```
diff --git a/src/trees/rooted-quasitrees.lagda.md b/src/trees/rooted-quasitrees.lagda.md index 596e9e1061..7aa68afca3 100644 --- a/src/trees/rooted-quasitrees.lagda.md +++ b/src/trees/rooted-quasitrees.lagda.md @@ -1,18 +1,27 @@ # Rooted quasitrees ```agda -module trees.rooted-quasitrees where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module trees.rooted-quasitrees + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.contractible-types +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types funext open import foundation.universe-levels -open import graph-theory.trails-undirected-graphs -open import graph-theory.undirected-graphs +open import graph-theory.trails-undirected-graphs funext univalence truncations +open import graph-theory.undirected-graphs funext univalence truncations ```
diff --git a/src/trees/rooted-undirected-trees.lagda.md b/src/trees/rooted-undirected-trees.lagda.md index 52cf306b9b..b3d5547965 100644 --- a/src/trees/rooted-undirected-trees.lagda.md +++ b/src/trees/rooted-undirected-trees.lagda.md @@ -1,7 +1,15 @@ # Rooted undirected trees ```agda -module trees.rooted-undirected-trees where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module trees.rooted-undirected-trees + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,16 +17,16 @@ module trees.rooted-undirected-trees where ```agda open import elementary-number-theory.natural-numbers -open import foundation.coproduct-types +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types open import foundation.unit-type open import foundation.universe-levels -open import foundation.unordered-pairs +open import foundation.unordered-pairs funext univalence truncations -open import graph-theory.trails-undirected-graphs -open import graph-theory.undirected-graphs +open import graph-theory.trails-undirected-graphs funext univalence truncations +open import graph-theory.undirected-graphs funext univalence truncations -open import trees.undirected-trees +open import trees.undirected-trees funext univalence truncations ```
diff --git a/src/trees/small-multisets.lagda.md b/src/trees/small-multisets.lagda.md index 6a8bc2b79f..f388021bb9 100644 --- a/src/trees/small-multisets.lagda.md +++ b/src/trees/small-multisets.lagda.md @@ -1,7 +1,15 @@ # Small multisets ```agda -module trees.small-multisets where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module trees.small-multisets + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,22 +17,24 @@ module trees.small-multisets where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.propositions -open import foundation.raising-universe-levels -open import foundation.small-types -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.empty-types funext univalence truncations +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.small-types funext univalence truncations +open import foundation.subtypes funext univalence truncations open import foundation.transport-along-identifications -open import foundation.univalence +open import foundation.univalence funext univalence open import foundation.universe-levels -open import trees.multisets -open import trees.w-types +open import foundation-core.raising-universe-levels + +open import trees.multisets funext univalence truncations +open import trees.w-types funext univalence truncations ```
diff --git a/src/trees/submultisets.lagda.md b/src/trees/submultisets.lagda.md index f04365fa46..7d456d119f 100644 --- a/src/trees/submultisets.lagda.md +++ b/src/trees/submultisets.lagda.md @@ -1,17 +1,25 @@ # Submultisets ```agda -module trees.submultisets where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module trees.submultisets + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.embeddings -open import foundation.equivalences +open import foundation.embeddings funext +open import foundation.equivalences funext open import foundation.universe-levels -open import trees.multisets +open import trees.multisets funext univalence truncations ```
diff --git a/src/trees/transitive-multisets.lagda.md b/src/trees/transitive-multisets.lagda.md index e09627c816..bed1d8b5a5 100644 --- a/src/trees/transitive-multisets.lagda.md +++ b/src/trees/transitive-multisets.lagda.md @@ -1,7 +1,15 @@ # Transitive multisets ```agda -module trees.transitive-multisets where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module trees.transitive-multisets + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,8 +17,8 @@ module trees.transitive-multisets where ```agda open import foundation.universe-levels -open import trees.multisets -open import trees.submultisets +open import trees.multisets funext univalence truncations +open import trees.submultisets funext univalence truncations ```
diff --git a/src/trees/underlying-trees-elements-coalgebras-polynomial-endofunctors.lagda.md b/src/trees/underlying-trees-elements-coalgebras-polynomial-endofunctors.lagda.md index 9184f6da42..512b0e170e 100644 --- a/src/trees/underlying-trees-elements-coalgebras-polynomial-endofunctors.lagda.md +++ b/src/trees/underlying-trees-elements-coalgebras-polynomial-endofunctors.lagda.md @@ -1,7 +1,15 @@ # The underlying trees of elements of coalgebras of polynomial endofunctors ```agda -module trees.underlying-trees-elements-coalgebras-polynomial-endofunctors where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module trees.underlying-trees-elements-coalgebras-polynomial-endofunctors + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,37 +17,39 @@ module trees.underlying-trees-elements-coalgebras-polynomial-endofunctors where ```agda open import foundation.action-on-identifications-functions open import foundation.binary-transport -open import foundation.contractible-types -open import foundation.coproduct-types +open import foundation.contractible-types funext univalence +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.equivalence-extensionality -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.empty-types funext univalence truncations +open import foundation.equivalence-extensionality funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.isolated-elements -open import foundation.negated-equality -open import foundation.propositions -open import foundation.torsorial-type-families +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.isolated-elements funext univalence truncations +open import foundation.negated-equality funext univalence truncations +open import foundation.propositions funext univalence +open import foundation.torsorial-type-families funext univalence truncations open import foundation.transport-along-identifications -open import foundation.type-arithmetic-empty-type +open import foundation.type-arithmetic-empty-type funext univalence truncations open import foundation.universe-levels -open import graph-theory.directed-graphs -open import graph-theory.morphisms-directed-graphs -open import graph-theory.walks-directed-graphs - -open import trees.coalgebras-polynomial-endofunctors -open import trees.combinator-directed-trees -open import trees.combinator-enriched-directed-trees -open import trees.directed-trees -open import trees.elementhood-relation-coalgebras-polynomial-endofunctors -open import trees.enriched-directed-trees -open import trees.equivalences-directed-trees -open import trees.equivalences-enriched-directed-trees +open import graph-theory.directed-graphs funext univalence +open import graph-theory.morphisms-directed-graphs funext univalence truncations +open import graph-theory.walks-directed-graphs funext univalence truncations + +open import trees.coalgebras-polynomial-endofunctors funext univalence +open import trees.combinator-directed-trees funext univalence truncations +open import trees.combinator-enriched-directed-trees funext univalence truncations +open import trees.directed-trees funext univalence truncations +open import trees.elementhood-relation-coalgebras-polynomial-endofunctors funext univalence truncations +open import trees.enriched-directed-trees funext univalence truncations +open import trees.equivalences-directed-trees funext univalence truncations +open import trees.equivalences-enriched-directed-trees funext univalence truncations ```
diff --git a/src/trees/underlying-trees-of-elements-of-w-types.lagda.md b/src/trees/underlying-trees-of-elements-of-w-types.lagda.md index bd9f754279..bca4dd83b3 100644 --- a/src/trees/underlying-trees-of-elements-of-w-types.lagda.md +++ b/src/trees/underlying-trees-of-elements-of-w-types.lagda.md @@ -1,41 +1,51 @@ # The underlying trees of elements of W-types ```agda -module trees.underlying-trees-of-elements-of-w-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module trees.underlying-trees-of-elements-of-w-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.contractible-types -open import foundation.coproduct-types +open import foundation.contractible-types funext univalence +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.equivalence-extensionality -open import foundation.equivalences -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.isolated-elements -open import foundation.negated-equality -open import foundation.propositions -open import foundation.torsorial-type-families +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.empty-types funext univalence truncations +open import foundation.equivalence-extensionality funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.isolated-elements funext univalence truncations +open import foundation.negated-equality funext univalence truncations +open import foundation.propositions funext univalence +open import foundation.torsorial-type-families funext univalence truncations open import foundation.transport-along-identifications open import foundation.universe-levels -open import graph-theory.directed-graphs -open import graph-theory.morphisms-directed-graphs -open import graph-theory.walks-directed-graphs - -open import trees.combinator-directed-trees -open import trees.combinator-enriched-directed-trees -open import trees.directed-trees -open import trees.elementhood-relation-w-types -open import trees.enriched-directed-trees -open import trees.equivalences-directed-trees -open import trees.equivalences-enriched-directed-trees -open import trees.underlying-trees-elements-coalgebras-polynomial-endofunctors -open import trees.w-types +open import graph-theory.directed-graphs funext univalence +open import graph-theory.morphisms-directed-graphs funext univalence truncations +open import graph-theory.walks-directed-graphs funext univalence truncations + +open import trees.combinator-directed-trees funext univalence truncations +open import trees.combinator-enriched-directed-trees funext univalence truncations +open import trees.directed-trees funext univalence truncations +open import trees.elementhood-relation-w-types funext univalence truncations +open import trees.enriched-directed-trees funext univalence truncations +open import trees.equivalences-directed-trees funext univalence truncations +open import trees.equivalences-enriched-directed-trees funext univalence truncations +open import trees.underlying-trees-elements-coalgebras-polynomial-endofunctors funext univalence truncations +open import trees.w-types funext univalence truncations ```
diff --git a/src/trees/undirected-trees.lagda.md b/src/trees/undirected-trees.lagda.md index f60cce11cf..e02585083e 100644 --- a/src/trees/undirected-trees.lagda.md +++ b/src/trees/undirected-trees.lagda.md @@ -1,7 +1,15 @@ # Undirected trees ```agda -module trees.undirected-trees where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module trees.undirected-trees + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,23 +18,25 @@ module trees.undirected-trees where open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.contractible-types -open import foundation.decidable-equality -open import foundation.decidable-types +open import foundation.contractible-types funext univalence +open import foundation.decidable-equality funext univalence truncations +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.identity-types -open import foundation.mere-equality -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.sets +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.empty-types funext univalence truncations +open import foundation.identity-types funext +open import foundation.mere-equality funext univalence truncations +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence +open import foundation.sets funext univalence open import foundation.transport-along-identifications open import foundation.universe-levels -open import graph-theory.paths-undirected-graphs -open import graph-theory.trails-undirected-graphs -open import graph-theory.undirected-graphs -open import graph-theory.walks-undirected-graphs +open import graph-theory.paths-undirected-graphs funext univalence truncations +open import graph-theory.trails-undirected-graphs funext univalence truncations +open import graph-theory.undirected-graphs funext univalence truncations +open import graph-theory.walks-undirected-graphs funext univalence truncations ```
diff --git a/src/trees/universal-multiset.lagda.md b/src/trees/universal-multiset.lagda.md index 954321d15a..061afcec5a 100644 --- a/src/trees/universal-multiset.lagda.md +++ b/src/trees/universal-multiset.lagda.md @@ -1,25 +1,34 @@ # The universal multiset ```agda -module trees.universal-multiset where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module trees.universal-multiset + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.identity-types -open import foundation.raising-universe-levels -open import foundation.small-types -open import foundation.small-universes +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.small-types funext univalence truncations +open import foundation.small-universes funext univalence truncations open import foundation.transport-along-identifications open import foundation.universe-levels -open import trees.functoriality-w-types -open import trees.multisets -open import trees.small-multisets -open import trees.w-types +open import foundation-core.raising-universe-levels + +open import trees.functoriality-w-types funext univalence truncations +open import trees.multisets funext univalence truncations +open import trees.small-multisets funext univalence truncations +open import trees.w-types funext univalence truncations ```
diff --git a/src/trees/w-type-of-natural-numbers.lagda.md b/src/trees/w-type-of-natural-numbers.lagda.md index 0d61f98e88..5255816f0b 100644 --- a/src/trees/w-type-of-natural-numbers.lagda.md +++ b/src/trees/w-type-of-natural-numbers.lagda.md @@ -1,7 +1,15 @@ # The W-type of natural numbers ```agda -module trees.w-type-of-natural-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module trees.w-type-of-natural-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,19 +18,20 @@ module trees.w-type-of-natural-numbers where open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.booleans -open import foundation.contractible-types +open import foundation.booleans funext univalence truncations +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types +open import foundation.dependent-products-contractible-types funext +open import foundation.equivalences funext +open import foundation.function-extensionality funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.unit-type -open import foundation.universal-property-empty-type +open import foundation.universal-property-empty-type funext open import foundation.universe-levels -open import trees.w-types +open import trees.w-types funext univalence truncations ```
diff --git a/src/trees/w-type-of-propositions.lagda.md b/src/trees/w-type-of-propositions.lagda.md index 0b9f78bdb3..678a91a1f3 100644 --- a/src/trees/w-type-of-propositions.lagda.md +++ b/src/trees/w-type-of-propositions.lagda.md @@ -1,23 +1,33 @@ # The W-type of the type of propositions ```agda -module trees.w-type-of-propositions where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module trees.w-type-of-propositions + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.coproduct-types +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.propositional-extensionality -open import foundation.propositions -open import foundation.sets +open import foundation.dependent-products-propositions funext +open import foundation.empty-types funext univalence truncations +open import foundation.propositional-extensionality funext univalence truncations +open import foundation.propositions funext univalence +open import foundation.raising-universe-levels-unit-type +open import foundation.sets funext univalence open import foundation.unit-type open import foundation.universe-levels -open import trees.extensional-w-types -open import trees.w-types +open import trees.extensional-w-types funext univalence truncations +open import trees.w-types funext univalence truncations ```
diff --git a/src/trees/w-types.lagda.md b/src/trees/w-types.lagda.md index cf2df81dea..5efffeb8d2 100644 --- a/src/trees/w-types.lagda.md +++ b/src/trees/w-types.lagda.md @@ -1,38 +1,48 @@ # W-types ```agda -module trees.w-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module trees.w-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.contractible-types +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-types +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-truncated-types funext +open import foundation.empty-types funext univalence truncations +open import foundation.equivalences funext +open import foundation.function-extensionality funext +open import foundation.function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types -open import foundation.postcomposition-functions -open import foundation.propositional-truncations -open import foundation.sets -open import foundation.torsorial-type-families +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext +open import foundation.postcomposition-functions funext +open import foundation.propositional-truncations funext univalence +open import foundation.sets funext univalence +open import foundation.torsorial-type-families funext univalence truncations open import foundation.transport-along-identifications -open import foundation.truncated-types +open import foundation.truncated-types funext univalence open import foundation.truncation-levels -open import foundation.type-theoretic-principle-of-choice +open import foundation.type-theoretic-principle-of-choice funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import trees.algebras-polynomial-endofunctors -open import trees.coalgebras-polynomial-endofunctors -open import trees.morphisms-algebras-polynomial-endofunctors -open import trees.polynomial-endofunctors +open import trees.algebras-polynomial-endofunctors funext univalence +open import trees.coalgebras-polynomial-endofunctors funext univalence +open import trees.morphisms-algebras-polynomial-endofunctors funext univalence truncations +open import trees.polynomial-endofunctors funext univalence ```
diff --git a/src/type-theories.lagda.md b/src/type-theories.lagda.md index 1255733d03..3d96683c91 100644 --- a/src/type-theories.lagda.md +++ b/src/type-theories.lagda.md @@ -7,16 +7,24 @@ ## Modules in the type theories namespace ```agda -module type-theories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module type-theories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where open import type-theories.comprehension-type-theories public -open import type-theories.dependent-type-theories public -open import type-theories.fibered-dependent-type-theories public -open import type-theories.pi-types-precategories-with-attributes public -open import type-theories.pi-types-precategories-with-families public -open import type-theories.precategories-with-attributes public -open import type-theories.precategories-with-families public -open import type-theories.sections-dependent-type-theories public -open import type-theories.simple-type-theories public -open import type-theories.unityped-type-theories public +open import type-theories.dependent-type-theories funext univalence public +open import type-theories.fibered-dependent-type-theories funext univalence public +open import type-theories.pi-types-precategories-with-attributes funext univalence truncations public +open import type-theories.pi-types-precategories-with-families funext univalence truncations public +open import type-theories.precategories-with-attributes funext univalence truncations public +open import type-theories.precategories-with-families funext univalence truncations public +open import type-theories.sections-dependent-type-theories funext univalence public +open import type-theories.simple-type-theories funext univalence public +open import type-theories.unityped-type-theories funext univalence public ``` diff --git a/src/type-theories/dependent-type-theories.lagda.md b/src/type-theories/dependent-type-theories.lagda.md index 6f40eba0bc..68fdfc601c 100644 --- a/src/type-theories/dependent-type-theories.lagda.md +++ b/src/type-theories/dependent-type-theories.lagda.md @@ -2,8 +2,13 @@ ```agda {-# OPTIONS --guardedness #-} +open import foundation-core.univalence +open import foundation.function-extensionality-axiom -module type-theories.dependent-type-theories where +module type-theories.dependent-type-theories + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports @@ -12,14 +17,15 @@ module type-theories.dependent-type-theories where open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence open import foundation.transport-along-identifications open import foundation.universe-levels -open import foundation.whiskering-identifications-concatenation +open import foundation.whiskering-identifications-concatenation funext ```
diff --git a/src/type-theories/fibered-dependent-type-theories.lagda.md b/src/type-theories/fibered-dependent-type-theories.lagda.md index a5da36d53a..34358b2fbd 100644 --- a/src/type-theories/fibered-dependent-type-theories.lagda.md +++ b/src/type-theories/fibered-dependent-type-theories.lagda.md @@ -2,8 +2,13 @@ ```agda {-# OPTIONS --guardedness #-} +open import foundation-core.univalence +open import foundation.function-extensionality-axiom -module type-theories.fibered-dependent-type-theories where +module type-theories.fibered-dependent-type-theories + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports @@ -11,12 +16,12 @@ module type-theories.fibered-dependent-type-theories where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.identity-types +open import foundation.function-types funext +open import foundation.identity-types funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import type-theories.dependent-type-theories +open import type-theories.dependent-type-theories funext univalence ```
diff --git a/src/type-theories/pi-types-precategories-with-attributes.lagda.md b/src/type-theories/pi-types-precategories-with-attributes.lagda.md index bb36bc9fc8..c3ed3e09e2 100644 --- a/src/type-theories/pi-types-precategories-with-attributes.lagda.md +++ b/src/type-theories/pi-types-precategories-with-attributes.lagda.md @@ -1,18 +1,26 @@ # `Π`-types in precategories with attributes ```agda -module type-theories.pi-types-precategories-with-attributes where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module type-theories.pi-types-precategories-with-attributes + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.equivalences -open import foundation.identity-types +open import foundation.equivalences funext +open import foundation.identity-types funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import type-theories.precategories-with-attributes +open import type-theories.precategories-with-attributes funext univalence truncations ```
diff --git a/src/type-theories/pi-types-precategories-with-families.lagda.md b/src/type-theories/pi-types-precategories-with-families.lagda.md index 95f6a2b8e2..73cc163d48 100644 --- a/src/type-theories/pi-types-precategories-with-families.lagda.md +++ b/src/type-theories/pi-types-precategories-with-families.lagda.md @@ -1,18 +1,26 @@ # Π-types in precategories with families ```agda -module type-theories.pi-types-precategories-with-families where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module type-theories.pi-types-precategories-with-families + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.equivalences -open import foundation.identity-types +open import foundation.equivalences funext +open import foundation.identity-types funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import type-theories.precategories-with-families +open import type-theories.precategories-with-families funext univalence truncations ```
diff --git a/src/type-theories/precategories-with-attributes.lagda.md b/src/type-theories/precategories-with-attributes.lagda.md index 2531279eac..a143d50e38 100644 --- a/src/type-theories/precategories-with-attributes.lagda.md +++ b/src/type-theories/precategories-with-attributes.lagda.md @@ -1,32 +1,34 @@ # Precategories with attributes ```agda -module type-theories.precategories-with-attributes where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module type-theories.precategories-with-attributes + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.commuting-squares-of-morphisms-in-precategories -open import category-theory.functors-precategories -open import category-theory.natural-transformations-functors-precategories -open import category-theory.opposite-precategories -open import category-theory.precategories -open import category-theory.precategory-of-elements-of-a-presheaf -open import category-theory.presheaf-categories -open import category-theory.pullbacks-in-precategories +open import category-theory.commuting-squares-of-morphisms-in-precategories funext univalence truncations +open import category-theory.functors-precategories funext univalence truncations +open import category-theory.natural-transformations-functors-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations +open import category-theory.precategory-of-elements-of-a-presheaf funext univalence truncations +open import category-theory.presheaf-categories funext univalence truncations +open import category-theory.pullbacks-in-precategories funext univalence truncations open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types -open import foundation.category-of-sets +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.identity-types -open import foundation.sections -open import foundation.sets -open import foundation.subtypes -open import foundation.transport-along-identifications +open import foundation.identity-types funext +open import foundation.sets funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels ``` diff --git a/src/type-theories/precategories-with-families.lagda.md b/src/type-theories/precategories-with-families.lagda.md index 386c313d65..a8fc8a4890 100644 --- a/src/type-theories/precategories-with-families.lagda.md +++ b/src/type-theories/precategories-with-families.lagda.md @@ -1,29 +1,28 @@ # Precategories with families ```agda -module type-theories.precategories-with-families where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module type-theories.precategories-with-families + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.functors-precategories -open import category-theory.natural-transformations-functors-precategories -open import category-theory.opposite-precategories -open import category-theory.precategories -open import category-theory.precategory-of-elements-of-a-presheaf -open import category-theory.presheaf-categories -open import category-theory.pullbacks-in-precategories - -open import foundation.cartesian-product-types -open import foundation.category-of-sets +open import category-theory.functors-precategories funext univalence truncations +open import category-theory.precategories funext univalence truncations +open import category-theory.precategory-of-elements-of-a-presheaf funext univalence truncations +open import category-theory.presheaf-categories funext univalence truncations + open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.identity-types -open import foundation.sections -open import foundation.sets -open import foundation.subtypes +open import foundation.equivalences funext +open import foundation.identity-types funext open import foundation.transport-along-identifications open import foundation.universe-levels ``` diff --git a/src/type-theories/sections-dependent-type-theories.lagda.md b/src/type-theories/sections-dependent-type-theories.lagda.md index 339dc4c6e7..a660278332 100644 --- a/src/type-theories/sections-dependent-type-theories.lagda.md +++ b/src/type-theories/sections-dependent-type-theories.lagda.md @@ -2,19 +2,24 @@ ```agda {-# OPTIONS --guardedness #-} +open import foundation-core.univalence +open import foundation.function-extensionality-axiom -module type-theories.sections-dependent-type-theories where +module type-theories.sections-dependent-type-theories + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import type-theories.dependent-type-theories -open import type-theories.fibered-dependent-type-theories +open import type-theories.dependent-type-theories funext univalence +open import type-theories.fibered-dependent-type-theories funext univalence ```
diff --git a/src/type-theories/simple-type-theories.lagda.md b/src/type-theories/simple-type-theories.lagda.md index b8e45f3112..95a1677635 100644 --- a/src/type-theories/simple-type-theories.lagda.md +++ b/src/type-theories/simple-type-theories.lagda.md @@ -2,17 +2,22 @@ ```agda {-# OPTIONS --guardedness --allow-unsolved-metas #-} +open import foundation-core.univalence +open import foundation.function-extensionality-axiom -module type-theories.simple-type-theories where +module type-theories.simple-type-theories + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.transport-along-identifications open import foundation.universe-levels ``` diff --git a/src/type-theories/unityped-type-theories.lagda.md b/src/type-theories/unityped-type-theories.lagda.md index 99c7fb918f..ca1a7eddf3 100644 --- a/src/type-theories/unityped-type-theories.lagda.md +++ b/src/type-theories/unityped-type-theories.lagda.md @@ -2,8 +2,13 @@ ```agda {-# OPTIONS --guardedness --allow-unsolved-metas #-} +open import foundation-core.univalence +open import foundation.function-extensionality-axiom -module type-theories.unityped-type-theories where +module type-theories.unityped-type-theories + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports @@ -12,10 +17,10 @@ module type-theories.unityped-type-theories where open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.natural-numbers -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.sets +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.sets funext univalence open import foundation.universe-levels ``` diff --git a/src/univalent-combinatorics.lagda.md b/src/univalent-combinatorics.lagda.md index 96025ac714..cd2b574f66 100644 --- a/src/univalent-combinatorics.lagda.md +++ b/src/univalent-combinatorics.lagda.md @@ -23,101 +23,109 @@ and closedness under Π under a mild condition {{#cite Anel24}}. ## Modules in the univalent combinatorics namespace ```agda -module univalent-combinatorics where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom -open import univalent-combinatorics.2-element-decidable-subtypes public -open import univalent-combinatorics.2-element-subtypes public -open import univalent-combinatorics.2-element-types public -open import univalent-combinatorics.binomial-types public -open import univalent-combinatorics.bracelets public -open import univalent-combinatorics.cartesian-product-types public -open import univalent-combinatorics.classical-finite-types public -open import univalent-combinatorics.complements-isolated-elements public -open import univalent-combinatorics.coproduct-types public -open import univalent-combinatorics.counting public -open import univalent-combinatorics.counting-decidable-subtypes public -open import univalent-combinatorics.counting-dependent-pair-types public +module univalent-combinatorics + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where + +open import univalent-combinatorics.2-element-decidable-subtypes funext univalence truncations public +open import univalent-combinatorics.2-element-subtypes funext univalence truncations public +open import univalent-combinatorics.2-element-types funext univalence truncations public +open import univalent-combinatorics.binomial-types funext univalence truncations public +open import univalent-combinatorics.bracelets funext univalence truncations public +open import univalent-combinatorics.cartesian-product-types funext univalence truncations public +open import univalent-combinatorics.classical-finite-types funext univalence truncations public +open import univalent-combinatorics.complements-isolated-elements funext univalence truncations public +open import univalent-combinatorics.coproduct-types funext univalence truncations public +open import univalent-combinatorics.counting funext univalence truncations public +open import univalent-combinatorics.counting-decidable-subtypes funext univalence truncations public +open import univalent-combinatorics.counting-dependent-pair-types funext univalence truncations public open import univalent-combinatorics.counting-fibers-of-maps public -open import univalent-combinatorics.counting-maybe public -open import univalent-combinatorics.cubes public -open import univalent-combinatorics.cycle-partitions public -open import univalent-combinatorics.cycle-prime-decomposition-natural-numbers public -open import univalent-combinatorics.cyclic-finite-types public -open import univalent-combinatorics.de-morgans-law public -open import univalent-combinatorics.decidable-dependent-function-types public -open import univalent-combinatorics.decidable-dependent-pair-types public -open import univalent-combinatorics.decidable-equivalence-relations public -open import univalent-combinatorics.decidable-propositions public -open import univalent-combinatorics.decidable-subtypes public -open import univalent-combinatorics.dedekind-finite-sets public -open import univalent-combinatorics.dependent-function-types public -open import univalent-combinatorics.dependent-pair-types public -open import univalent-combinatorics.discrete-sigma-decompositions public -open import univalent-combinatorics.distributivity-of-set-truncation-over-finite-products public -open import univalent-combinatorics.double-counting public -open import univalent-combinatorics.embeddings public -open import univalent-combinatorics.embeddings-standard-finite-types public -open import univalent-combinatorics.equality-finite-types public -open import univalent-combinatorics.equality-standard-finite-types public -open import univalent-combinatorics.equivalences public -open import univalent-combinatorics.equivalences-cubes public -open import univalent-combinatorics.equivalences-standard-finite-types public -open import univalent-combinatorics.ferrers-diagrams public -open import univalent-combinatorics.fibers-of-maps public -open import univalent-combinatorics.finite-choice public +open import univalent-combinatorics.counting-maybe funext univalence truncations public +open import univalent-combinatorics.cubes funext univalence truncations public +open import univalent-combinatorics.cycle-partitions funext univalence truncations public +open import univalent-combinatorics.cycle-prime-decomposition-natural-numbers funext univalence truncations public +open import univalent-combinatorics.cyclic-finite-types funext univalence truncations public +open import univalent-combinatorics.de-morgans-law funext univalence truncations public +open import univalent-combinatorics.decidable-dependent-function-types funext univalence truncations public +open import univalent-combinatorics.decidable-dependent-pair-types funext univalence truncations public +open import univalent-combinatorics.decidable-equivalence-relations funext univalence truncations public +open import univalent-combinatorics.decidable-propositions funext univalence truncations public +open import univalent-combinatorics.decidable-subtypes funext univalence truncations public +open import univalent-combinatorics.dedekind-finite-sets funext univalence public +open import univalent-combinatorics.dependent-function-types funext univalence truncations public +open import univalent-combinatorics.dependent-pair-types funext univalence truncations public +open import univalent-combinatorics.discrete-sigma-decompositions funext univalence truncations public +open import univalent-combinatorics.distributivity-of-set-truncation-over-finite-products funext univalence truncations public +open import univalent-combinatorics.double-counting funext univalence truncations public +open import univalent-combinatorics.embeddings funext univalence truncations public +open import univalent-combinatorics.embeddings-standard-finite-types funext univalence truncations public +open import univalent-combinatorics.equality-finite-types funext univalence truncations public +open import univalent-combinatorics.equality-standard-finite-types funext univalence truncations public +open import univalent-combinatorics.equivalences funext univalence truncations public +open import univalent-combinatorics.equivalences-cubes funext univalence truncations public +open import univalent-combinatorics.equivalences-standard-finite-types funext univalence truncations public +open import univalent-combinatorics.ferrers-diagrams funext univalence truncations public +open import univalent-combinatorics.fibers-of-maps funext univalence truncations public +open import univalent-combinatorics.finite-choice funext univalence truncations public open import univalent-combinatorics.finite-presentations public -open import univalent-combinatorics.finite-types public -open import univalent-combinatorics.finitely-many-connected-components public -open import univalent-combinatorics.finitely-presented-types public -open import univalent-combinatorics.function-types public -open import univalent-combinatorics.image-of-maps public -open import univalent-combinatorics.inequality-types-with-counting public -open import univalent-combinatorics.inhabited-finite-types public -open import univalent-combinatorics.injective-maps public -open import univalent-combinatorics.involution-standard-finite-types public -open import univalent-combinatorics.isotopies-latin-squares public -open import univalent-combinatorics.kuratowski-finite-sets public -open import univalent-combinatorics.latin-squares public -open import univalent-combinatorics.locally-finite-types public -open import univalent-combinatorics.main-classes-of-latin-hypercubes public -open import univalent-combinatorics.main-classes-of-latin-squares public -open import univalent-combinatorics.maybe public -open import univalent-combinatorics.necklaces public -open import univalent-combinatorics.orientations-complete-undirected-graph public -open import univalent-combinatorics.orientations-cubes public -open import univalent-combinatorics.partitions public -open import univalent-combinatorics.petri-nets public -open import univalent-combinatorics.pi-finite-types public -open import univalent-combinatorics.pigeonhole-principle public +open import univalent-combinatorics.finite-types funext univalence truncations public +open import univalent-combinatorics.finitely-many-connected-components funext univalence truncations public +open import univalent-combinatorics.finitely-presented-types funext univalence truncations public +open import univalent-combinatorics.function-types funext univalence truncations public +open import univalent-combinatorics.image-of-maps funext univalence truncations public +open import univalent-combinatorics.inequality-types-with-counting funext univalence truncations public +open import univalent-combinatorics.inhabited-finite-types funext univalence truncations public +open import univalent-combinatorics.injective-maps funext univalence truncations public +open import univalent-combinatorics.involution-standard-finite-types funext univalence truncations public +open import univalent-combinatorics.isotopies-latin-squares funext univalence truncations public +open import univalent-combinatorics.kuratowski-finite-sets funext univalence truncations public +open import univalent-combinatorics.latin-squares funext univalence truncations public +open import univalent-combinatorics.locally-finite-types funext univalence truncations public +open import univalent-combinatorics.main-classes-of-latin-hypercubes funext univalence truncations public +open import univalent-combinatorics.main-classes-of-latin-squares funext univalence truncations public +open import univalent-combinatorics.maybe funext univalence truncations public +open import univalent-combinatorics.necklaces funext univalence truncations public +open import univalent-combinatorics.orientations-complete-undirected-graph funext univalence truncations public +open import univalent-combinatorics.orientations-cubes funext univalence truncations public +open import univalent-combinatorics.partitions funext univalence truncations public +open import univalent-combinatorics.petri-nets funext univalence truncations public +open import univalent-combinatorics.pi-finite-types funext univalence truncations public +open import univalent-combinatorics.pigeonhole-principle funext univalence truncations public open import univalent-combinatorics.presented-pi-finite-types public -open import univalent-combinatorics.quotients-finite-types public -open import univalent-combinatorics.ramsey-theory public -open import univalent-combinatorics.repetitions-of-values public +open import univalent-combinatorics.quotients-finite-types funext univalence truncations public +open import univalent-combinatorics.ramsey-theory funext univalence truncations public +open import univalent-combinatorics.repetitions-of-values funext univalence truncations public open import univalent-combinatorics.repetitions-of-values-sequences public -open import univalent-combinatorics.retracts-of-finite-types public -open import univalent-combinatorics.riffle-shuffles public -open import univalent-combinatorics.sequences-finite-types public -open import univalent-combinatorics.set-quotients-of-index-two public -open import univalent-combinatorics.sigma-decompositions public -open import univalent-combinatorics.skipping-element-standard-finite-types public -open import univalent-combinatorics.small-types public -open import univalent-combinatorics.standard-finite-pruned-trees public -open import univalent-combinatorics.standard-finite-trees public -open import univalent-combinatorics.standard-finite-types public -open import univalent-combinatorics.steiner-systems public -open import univalent-combinatorics.steiner-triple-systems public -open import univalent-combinatorics.sums-of-natural-numbers public -open import univalent-combinatorics.surjective-maps public -open import univalent-combinatorics.symmetric-difference public -open import univalent-combinatorics.trivial-sigma-decompositions public -open import univalent-combinatorics.type-duality public -open import univalent-combinatorics.unbounded-pi-finite-types public -open import univalent-combinatorics.unions-subtypes public -open import univalent-combinatorics.universal-property-standard-finite-types public +open import univalent-combinatorics.retracts-of-finite-types funext univalence truncations public +open import univalent-combinatorics.riffle-shuffles funext univalence truncations public +open import univalent-combinatorics.sequences-finite-types funext univalence truncations public +open import univalent-combinatorics.set-quotients-of-index-two funext univalence truncations public +open import univalent-combinatorics.sigma-decompositions funext univalence truncations public +open import univalent-combinatorics.skipping-element-standard-finite-types funext univalence truncations public +open import univalent-combinatorics.small-types funext univalence truncations public +open import univalent-combinatorics.standard-finite-pruned-trees funext univalence truncations public +open import univalent-combinatorics.standard-finite-trees funext univalence truncations public +open import univalent-combinatorics.standard-finite-types funext univalence truncations public +open import univalent-combinatorics.steiner-systems funext univalence truncations public +open import univalent-combinatorics.steiner-triple-systems funext univalence truncations public +open import univalent-combinatorics.sums-of-natural-numbers funext univalence truncations public +open import univalent-combinatorics.surjective-maps funext univalence truncations public +open import univalent-combinatorics.symmetric-difference funext univalence truncations public +open import univalent-combinatorics.trivial-sigma-decompositions funext univalence truncations public +open import univalent-combinatorics.type-duality funext univalence truncations public +open import univalent-combinatorics.unbounded-pi-finite-types funext univalence truncations public +open import univalent-combinatorics.unions-subtypes funext univalence truncations public +open import univalent-combinatorics.universal-property-standard-finite-types funext univalence truncations public open import univalent-combinatorics.unlabeled-partitions public open import univalent-combinatorics.unlabeled-rooted-trees public open import univalent-combinatorics.unlabeled-trees public -open import univalent-combinatorics.untruncated-pi-finite-types public +open import univalent-combinatorics.untruncated-pi-finite-types funext univalence truncations public ``` ## References diff --git a/src/univalent-combinatorics/2-element-decidable-subtypes.lagda.md b/src/univalent-combinatorics/2-element-decidable-subtypes.lagda.md index f223fc9b23..f49cfa9c5b 100644 --- a/src/univalent-combinatorics/2-element-decidable-subtypes.lagda.md +++ b/src/univalent-combinatorics/2-element-decidable-subtypes.lagda.md @@ -1,52 +1,59 @@ # `2`-element decidable subtypes ```agda -module univalent-combinatorics.2-element-decidable-subtypes where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module univalent-combinatorics.2-element-decidable-subtypes + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.equality-natural-numbers +open import elementary-number-theory.equality-natural-numbers funext univalence truncations open import elementary-number-theory.natural-numbers -open import elementary-number-theory.well-ordering-principle-standard-finite-types - -open import foundation.automorphisms -open import foundation.booleans -open import foundation.coproduct-types -open import foundation.decidable-equality -open import foundation.decidable-propositions -open import foundation.decidable-types +open import elementary-number-theory.well-ordering-principle-standard-finite-types funext univalence truncations + +open import foundation.automorphisms funext univalence +open import foundation.booleans funext univalence truncations +open import foundation.decidable-equality funext univalence truncations +open import foundation.decidable-propositions funext univalence truncations +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equality-dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.functoriality-coproduct-types -open import foundation.functoriality-dependent-pair-types -open import foundation.functoriality-propositional-truncation -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.logical-equivalences -open import foundation.mere-equivalences -open import foundation.negated-equality -open import foundation.negation -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.sets -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.embeddings funext +open import foundation.equality-dependent-pair-types funext +open import foundation.equivalences funext +open import foundation.function-extensionality funext +open import foundation.function-types funext +open import foundation.functoriality-coproduct-types funext univalence truncations +open import foundation.functoriality-dependent-pair-types funext +open import foundation.functoriality-propositional-truncation funext univalence truncations +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.logical-equivalences funext +open import foundation.mere-equivalences funext univalence truncations +open import foundation.negated-equality funext univalence truncations +open import foundation.negation funext +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.transport-along-identifications -open import foundation.type-arithmetic-coproduct-types -open import foundation.univalence +open import foundation.type-arithmetic-coproduct-types funext univalence truncations +open import foundation.univalence funext univalence open import foundation.universe-levels -open import univalent-combinatorics.2-element-subtypes -open import univalent-combinatorics.2-element-types -open import univalent-combinatorics.decidable-subtypes -open import univalent-combinatorics.dependent-function-types -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.2-element-subtypes funext univalence truncations +open import univalent-combinatorics.2-element-types funext univalence truncations +open import univalent-combinatorics.decidable-subtypes funext univalence truncations +open import univalent-combinatorics.dependent-function-types funext univalence truncations +open import univalent-combinatorics.finite-types funext univalence truncations +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/univalent-combinatorics/2-element-subtypes.lagda.md b/src/univalent-combinatorics/2-element-subtypes.lagda.md index 9c1bd2707d..6a8606470e 100644 --- a/src/univalent-combinatorics/2-element-subtypes.lagda.md +++ b/src/univalent-combinatorics/2-element-subtypes.lagda.md @@ -1,37 +1,47 @@ # `2`-element subtypes ```agda -module univalent-combinatorics.2-element-subtypes where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module univalent-combinatorics.2-element-subtypes + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.automorphisms -open import foundation.contractible-types -open import foundation.coproduct-types +open import foundation.automorphisms funext univalence +open import foundation.contractible-types funext univalence +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-coproduct-types -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.logical-equivalences -open import foundation.mere-equivalences -open import foundation.negated-equality -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.sets -open import foundation.subtypes -open import foundation.torsorial-type-families +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-coproduct-types funext univalence truncations +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.logical-equivalences funext +open import foundation.mere-equivalences funext univalence truncations +open import foundation.negated-equality funext univalence truncations +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.subtypes funext univalence truncations +open import foundation.torsorial-type-families funext univalence truncations open import foundation.transport-along-identifications -open import foundation.type-arithmetic-coproduct-types +open import foundation.type-arithmetic-coproduct-types funext univalence truncations open import foundation.unit-type open import foundation.universe-levels -open import univalent-combinatorics.2-element-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.2-element-types funext univalence truncations +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/univalent-combinatorics/2-element-types.lagda.md b/src/univalent-combinatorics/2-element-types.lagda.md index b44650d1ca..92e6911df3 100644 --- a/src/univalent-combinatorics/2-element-types.lagda.md +++ b/src/univalent-combinatorics/2-element-types.lagda.md @@ -1,58 +1,69 @@ # `2`-element types ```agda -module univalent-combinatorics.2-element-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module univalent-combinatorics.2-element-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.equality-natural-numbers -open import elementary-number-theory.modular-arithmetic-standard-finite-types +open import elementary-number-theory.equality-natural-numbers funext univalence truncations +open import elementary-number-theory.modular-arithmetic-standard-finite-types funext univalence truncations open import foundation.action-on-identifications-functions -open import foundation.automorphisms -open import foundation.connected-components-universes -open import foundation.contractible-maps -open import foundation.contractible-types -open import foundation.coproduct-types -open import foundation.decidable-types +open import foundation.automorphisms funext univalence +open import foundation.connected-components-universes funext univalence truncations +open import foundation.contractible-maps funext +open import foundation.contractible-types funext univalence +open import foundation.coproduct-types funext univalence truncations +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.double-negation -open import foundation.empty-types -open import foundation.equivalence-extensionality -open import foundation.fibers-of-maps -open import foundation.function-types -open import foundation.functoriality-coproduct-types -open import foundation.functoriality-dependent-pair-types +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.double-negation funext univalence truncations +open import foundation.empty-types funext univalence truncations +open import foundation.equivalence-extensionality funext +open import foundation.fibers-of-maps funext +open import foundation.function-types funext +open import foundation.functoriality-coproduct-types funext univalence truncations +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies +open import foundation.homotopies funext open import foundation.identity-systems -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.involutions -open import foundation.mere-equivalences -open import foundation.negated-equality -open import foundation.negation -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.raising-universe-levels -open import foundation.sets -open import foundation.subuniverses -open import foundation.torsorial-type-families +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.involutions funext univalence +open import foundation.mere-equivalences funext univalence truncations +open import foundation.negated-equality funext univalence truncations +open import foundation.negation funext +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.subuniverses funext univalence +open import foundation.torsorial-type-families funext univalence truncations open import foundation.transport-along-identifications -open import foundation.type-arithmetic-coproduct-types +open import foundation.type-arithmetic-coproduct-types funext univalence truncations open import foundation.type-arithmetic-dependent-pair-types -open import foundation.type-arithmetic-empty-type -open import foundation.type-arithmetic-unit-type +open import foundation.type-arithmetic-empty-type funext univalence truncations +open import foundation.type-arithmetic-unit-type funext open import foundation.unit-type -open import foundation.universal-property-identity-systems +open import foundation.universal-property-identity-systems funext open import foundation.universe-levels -open import univalent-combinatorics.equality-standard-finite-types -open import univalent-combinatorics.equivalences -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.standard-finite-types +open import foundation-core.raising-universe-levels + +open import univalent-combinatorics.equality-standard-finite-types funext univalence truncations +open import univalent-combinatorics.equivalences funext univalence truncations +open import univalent-combinatorics.finite-types funext univalence truncations +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/univalent-combinatorics/binomial-types.lagda.md b/src/univalent-combinatorics/binomial-types.lagda.md index f815dbd237..b35abfda0b 100644 --- a/src/univalent-combinatorics/binomial-types.lagda.md +++ b/src/univalent-combinatorics/binomial-types.lagda.md @@ -1,57 +1,68 @@ # The binomial types ```agda -module univalent-combinatorics.binomial-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module univalent-combinatorics.binomial-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.binomial-coefficients +open import elementary-number-theory.binomial-coefficients funext univalence truncations open import elementary-number-theory.natural-numbers -open import foundation.booleans -open import foundation.connected-components-universes -open import foundation.contractible-maps -open import foundation.contractible-types -open import foundation.coproduct-types -open import foundation.decidable-embeddings -open import foundation.decidable-propositions -open import foundation.decidable-subtypes +open import foundation.booleans funext univalence truncations +open import foundation.connected-components-universes funext univalence truncations +open import foundation.contractible-maps funext +open import foundation.contractible-types funext univalence +open import foundation.coproduct-types funext univalence truncations +open import foundation.decidable-embeddings funext univalence truncations +open import foundation.decidable-propositions funext univalence truncations +open import foundation.decidable-subtypes funext univalence truncations open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.empty-types -open import foundation.equivalences -open import foundation.equivalences-maybe -open import foundation.fibers-of-maps -open import foundation.function-types -open import foundation.functoriality-coproduct-types -open import foundation.functoriality-dependent-pair-types -open import foundation.functoriality-function-types -open import foundation.functoriality-propositional-truncation -open import foundation.logical-equivalences -open import foundation.maybe -open import foundation.mere-equivalences -open import foundation.negation -open import foundation.postcomposition-functions -open import foundation.propositional-extensionality -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.raising-universe-levels +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.embeddings funext +open import foundation.empty-types funext univalence truncations +open import foundation.equivalences funext +open import foundation.equivalences-maybe funext univalence truncations +open import foundation.fibers-of-maps funext +open import foundation.function-types funext +open import foundation.functoriality-coproduct-types funext univalence truncations +open import foundation.functoriality-dependent-pair-types funext +open import foundation.functoriality-propositional-truncation funext univalence truncations +open import foundation.logical-equivalences funext +open import foundation.maybe funext univalence truncations +open import foundation.mere-equivalences funext univalence truncations +open import foundation.negation funext +open import foundation.postcomposition-functions funext +open import foundation.propositional-extensionality funext univalence truncations +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence +open import foundation.raising-universe-levels-unit-type open import foundation.type-arithmetic-cartesian-product-types -open import foundation.type-arithmetic-coproduct-types +open import foundation.type-arithmetic-coproduct-types funext univalence truncations open import foundation.type-arithmetic-dependent-pair-types -open import foundation.type-arithmetic-empty-type -open import foundation.type-arithmetic-unit-type +open import foundation.type-arithmetic-empty-type funext univalence truncations +open import foundation.type-arithmetic-unit-type funext open import foundation.unit-type -open import foundation.universal-property-empty-type -open import foundation.universal-property-equivalences -open import foundation.universal-property-maybe +open import foundation.universal-property-empty-type funext +open import foundation.universal-property-equivalences funext +open import foundation.universal-property-maybe funext open import foundation.universe-levels -open import univalent-combinatorics.coproduct-types -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.standard-finite-types +open import foundation-core.raising-universe-levels + +open import univalent-combinatorics.coproduct-types funext univalence truncations +open import univalent-combinatorics.finite-types funext univalence truncations +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/univalent-combinatorics/bracelets.lagda.md b/src/univalent-combinatorics/bracelets.lagda.md index f2e65151d7..fe1b12467e 100644 --- a/src/univalent-combinatorics/bracelets.lagda.md +++ b/src/univalent-combinatorics/bracelets.lagda.md @@ -1,7 +1,15 @@ # Bracelets ```agda -module univalent-combinatorics.bracelets where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module univalent-combinatorics.bracelets + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -12,9 +20,9 @@ open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types open import foundation.universe-levels -open import graph-theory.polygons +open import graph-theory.polygons funext univalence truncations -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/univalent-combinatorics/cartesian-product-types.lagda.md b/src/univalent-combinatorics/cartesian-product-types.lagda.md index 43dee54458..e223febe11 100644 --- a/src/univalent-combinatorics/cartesian-product-types.lagda.md +++ b/src/univalent-combinatorics/cartesian-product-types.lagda.md @@ -1,7 +1,15 @@ # Cartesian products of finite types ```agda -module univalent-combinatorics.cartesian-product-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module univalent-combinatorics.cartesian-product-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,35 +18,36 @@ module univalent-combinatorics.cartesian-product-types where open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import foundation.cartesian-product-types -open import foundation.contractible-types -open import foundation.decidable-equality +open import foundation.cartesian-product-types funext univalence +open import foundation.contractible-types funext univalence +open import foundation.decidable-equality funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-cartesian-product-types -open import foundation.functoriality-coproduct-types -open import foundation.functoriality-dependent-pair-types -open import foundation.functoriality-propositional-truncation -open import foundation.identity-types -open import foundation.mere-equivalences -open import foundation.propositional-truncations -open import foundation.torsorial-type-families +open import foundation.dependent-products-contractible-types funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.functoriality-coproduct-types funext univalence truncations +open import foundation.functoriality-dependent-pair-types funext +open import foundation.functoriality-propositional-truncation funext univalence truncations +open import foundation.identity-types funext +open import foundation.mere-equivalences funext univalence truncations +open import foundation.propositional-truncations funext univalence +open import foundation.torsorial-type-families funext univalence truncations open import foundation.type-arithmetic-cartesian-product-types -open import foundation.type-arithmetic-coproduct-types +open import foundation.type-arithmetic-coproduct-types funext univalence truncations open import foundation.type-arithmetic-dependent-pair-types -open import foundation.type-arithmetic-empty-type -open import foundation.type-arithmetic-unit-type +open import foundation.type-arithmetic-empty-type funext univalence truncations +open import foundation.type-arithmetic-unit-type funext open import foundation.unit-type open import foundation.universe-levels -open import univalent-combinatorics.coproduct-types -open import univalent-combinatorics.counting -open import univalent-combinatorics.counting-dependent-pair-types -open import univalent-combinatorics.decidable-propositions -open import univalent-combinatorics.double-counting -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.coproduct-types funext univalence truncations +open import univalent-combinatorics.counting funext univalence truncations +open import univalent-combinatorics.counting-dependent-pair-types funext univalence truncations +open import univalent-combinatorics.decidable-propositions funext univalence truncations +open import univalent-combinatorics.double-counting funext univalence truncations +open import univalent-combinatorics.finite-types funext univalence truncations +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/univalent-combinatorics/classical-finite-types.lagda.md b/src/univalent-combinatorics/classical-finite-types.lagda.md index 95091e94ec..cb377d3f86 100644 --- a/src/univalent-combinatorics/classical-finite-types.lagda.md +++ b/src/univalent-combinatorics/classical-finite-types.lagda.md @@ -1,22 +1,30 @@ # The classical definition of the standard finite types ```agda -module univalent-combinatorics.classical-finite-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module univalent-combinatorics.classical-finite-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.congruence-natural-numbers -open import elementary-number-theory.modular-arithmetic-standard-finite-types +open import elementary-number-theory.congruence-natural-numbers funext univalence truncations +open import elementary-number-theory.modular-arithmetic-standard-finite-types funext univalence truncations open import elementary-number-theory.natural-numbers -open import elementary-number-theory.strict-inequality-natural-numbers +open import elementary-number-theory.strict-inequality-natural-numbers funext univalence truncations open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/univalent-combinatorics/complements-isolated-elements.lagda.md b/src/univalent-combinatorics/complements-isolated-elements.lagda.md index add3d8ff3f..ac44f5ec7b 100644 --- a/src/univalent-combinatorics/complements-isolated-elements.lagda.md +++ b/src/univalent-combinatorics/complements-isolated-elements.lagda.md @@ -1,7 +1,15 @@ # Complements of isolated elements of finite types ```agda -module univalent-combinatorics.complements-isolated-elements where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module univalent-combinatorics.complements-isolated-elements + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,16 +18,16 @@ module univalent-combinatorics.complements-isolated-elements where open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.equivalences-maybe -open import foundation.identity-types -open import foundation.isolated-elements -open import foundation.maybe -open import foundation.propositional-truncations +open import foundation.equivalences funext +open import foundation.equivalences-maybe funext univalence truncations +open import foundation.identity-types funext +open import foundation.isolated-elements funext univalence truncations +open import foundation.maybe funext univalence truncations +open import foundation.propositional-truncations funext univalence open import foundation.universe-levels -open import univalent-combinatorics.equality-finite-types -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.equality-finite-types funext univalence truncations +open import univalent-combinatorics.finite-types funext univalence truncations ```
diff --git a/src/univalent-combinatorics/coproduct-types.lagda.md b/src/univalent-combinatorics/coproduct-types.lagda.md index 87603eab3b..a6c98b93e8 100644 --- a/src/univalent-combinatorics/coproduct-types.lagda.md +++ b/src/univalent-combinatorics/coproduct-types.lagda.md @@ -1,7 +1,15 @@ # Coproducts of finite types ```agda -module univalent-combinatorics.coproduct-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module univalent-combinatorics.coproduct-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -11,28 +19,26 @@ open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.coproduct-types +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalence-extensionality -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.functoriality-coproduct-types -open import foundation.functoriality-propositional-truncation -open import foundation.homotopies -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.mere-equivalences -open import foundation.propositional-truncations -open import foundation.type-arithmetic-coproduct-types -open import foundation.type-arithmetic-empty-type +open import foundation.equivalence-extensionality funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-coproduct-types funext univalence truncations +open import foundation.functoriality-propositional-truncation funext univalence truncations +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.mere-equivalences funext univalence truncations +open import foundation.propositional-truncations funext univalence +open import foundation.type-arithmetic-coproduct-types funext univalence truncations +open import foundation.type-arithmetic-empty-type funext univalence truncations open import foundation.universe-levels -open import univalent-combinatorics.counting -open import univalent-combinatorics.counting-decidable-subtypes -open import univalent-combinatorics.double-counting -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.counting funext univalence truncations +open import univalent-combinatorics.counting-decidable-subtypes funext univalence truncations +open import univalent-combinatorics.double-counting funext univalence truncations +open import univalent-combinatorics.finite-types funext univalence truncations +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/univalent-combinatorics/counting-decidable-subtypes.lagda.md b/src/univalent-combinatorics/counting-decidable-subtypes.lagda.md index 2dc4eea133..b15d8e134d 100644 --- a/src/univalent-combinatorics/counting-decidable-subtypes.lagda.md +++ b/src/univalent-combinatorics/counting-decidable-subtypes.lagda.md @@ -1,9 +1,17 @@ # Counting the elements of decidable subtypes ```agda -module univalent-combinatorics.counting-decidable-subtypes where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module univalent-combinatorics.counting-decidable-subtypes + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where -open import foundation.decidable-subtypes public +open import foundation.decidable-subtypes funext univalence truncations public ```
Imports @@ -11,31 +19,33 @@ open import foundation.decidable-subtypes public ```agda open import elementary-number-theory.natural-numbers -open import foundation.contractible-types -open import foundation.coproduct-types -open import foundation.decidable-embeddings -open import foundation.decidable-types +open import foundation.contractible-types funext univalence +open import foundation.coproduct-types funext univalence truncations +open import foundation.decidable-embeddings funext univalence truncations +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalences -open import foundation.fibers-of-maps -open import foundation.function-types -open import foundation.functoriality-coproduct-types -open import foundation.functoriality-dependent-pair-types -open import foundation.identity-types -open import foundation.propositional-maps -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.subtypes -open import foundation.type-arithmetic-coproduct-types -open import foundation.type-arithmetic-empty-type +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.fibers-of-maps funext +open import foundation.function-types funext +open import foundation.functoriality-coproduct-types funext univalence truncations +open import foundation.functoriality-dependent-pair-types funext +open import foundation.identity-types funext +open import foundation.propositional-maps funext +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence +open import foundation.subtypes funext univalence truncations +open import foundation.type-arithmetic-coproduct-types funext univalence truncations +open import foundation.type-arithmetic-empty-type funext univalence truncations open import foundation.unit-type open import foundation.universe-levels -open import univalent-combinatorics.counting -open import univalent-combinatorics.decidable-propositions -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.counting funext univalence truncations +open import univalent-combinatorics.decidable-propositions funext univalence truncations +open import univalent-combinatorics.finite-types funext univalence truncations +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/univalent-combinatorics/counting-dependent-pair-types.lagda.md b/src/univalent-combinatorics/counting-dependent-pair-types.lagda.md index ce45d38d86..dc2e7c05c6 100644 --- a/src/univalent-combinatorics/counting-dependent-pair-types.lagda.md +++ b/src/univalent-combinatorics/counting-dependent-pair-types.lagda.md @@ -1,44 +1,53 @@ # Counting the elements of dependent pair types ```agda -module univalent-combinatorics.counting-dependent-pair-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module univalent-combinatorics.counting-dependent-pair-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.equality-natural-numbers +open import elementary-number-theory.equality-natural-numbers funext univalence truncations open import elementary-number-theory.natural-numbers -open import elementary-number-theory.sums-of-natural-numbers +open import elementary-number-theory.sums-of-natural-numbers funext univalence truncations open import foundation.action-on-identifications-functions -open import foundation.contractible-types -open import foundation.coproduct-types -open import foundation.decidable-equality -open import foundation.decidable-types +open import foundation.contractible-types funext univalence +open import foundation.coproduct-types funext univalence truncations +open import foundation.decidable-equality funext univalence truncations +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types -open import foundation.equivalences -open import foundation.fibers-of-maps -open import foundation.function-types -open import foundation.functoriality-coproduct-types -open import foundation.functoriality-dependent-pair-types -open import foundation.identity-types -open import foundation.sections -open import foundation.torsorial-type-families +open import foundation.dependent-products-contractible-types funext +open import foundation.equality-dependent-pair-types funext +open import foundation.equivalences funext +open import foundation.fibers-of-maps funext +open import foundation.function-types funext +open import foundation.functoriality-coproduct-types funext univalence truncations +open import foundation.functoriality-dependent-pair-types funext +open import foundation.identity-types funext +open import foundation.sections funext +open import foundation.torsorial-type-families funext univalence truncations open import foundation.transport-along-identifications -open import foundation.type-arithmetic-coproduct-types +open import foundation.type-arithmetic-coproduct-types funext univalence truncations open import foundation.type-arithmetic-dependent-pair-types -open import foundation.type-arithmetic-unit-type +open import foundation.type-arithmetic-unit-type funext open import foundation.unit-type open import foundation.universe-levels -open import univalent-combinatorics.coproduct-types -open import univalent-combinatorics.counting -open import univalent-combinatorics.decidable-propositions -open import univalent-combinatorics.double-counting -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.coproduct-types funext univalence truncations +open import univalent-combinatorics.counting funext univalence truncations +open import univalent-combinatorics.decidable-propositions funext univalence truncations +open import univalent-combinatorics.double-counting funext univalence truncations +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/univalent-combinatorics/counting-maybe.lagda.md b/src/univalent-combinatorics/counting-maybe.lagda.md index a77a6a7cfb..3a4ecedb2f 100644 --- a/src/univalent-combinatorics/counting-maybe.lagda.md +++ b/src/univalent-combinatorics/counting-maybe.lagda.md @@ -1,7 +1,15 @@ # Counting the elements in Maybe ```agda -module univalent-combinatorics.counting-maybe where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module univalent-combinatorics.counting-maybe + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,13 +18,14 @@ module univalent-combinatorics.counting-maybe where open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.equivalences-maybe -open import foundation.identity-types -open import foundation.maybe +open import foundation.equivalences-maybe funext univalence truncations open import foundation.universe-levels -open import univalent-combinatorics.coproduct-types -open import univalent-combinatorics.counting +open import foundation-core.identity-types +open import foundation-core.maybe + +open import univalent-combinatorics.coproduct-types funext univalence truncations +open import univalent-combinatorics.counting funext univalence truncations ```
diff --git a/src/univalent-combinatorics/counting.lagda.md b/src/univalent-combinatorics/counting.lagda.md index b9c4fa6d19..04d5a89194 100644 --- a/src/univalent-combinatorics/counting.lagda.md +++ b/src/univalent-combinatorics/counting.lagda.md @@ -1,7 +1,15 @@ # Counting in type theory ```agda -module univalent-combinatorics.counting where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module univalent-combinatorics.counting + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,25 +17,27 @@ module univalent-combinatorics.counting where ```agda open import elementary-number-theory.natural-numbers -open import foundation.contractible-types -open import foundation.coproduct-types -open import foundation.decidable-equality -open import foundation.decidable-types +open import foundation.contractible-types funext univalence +open import foundation.coproduct-types funext univalence truncations +open import foundation.decidable-equality funext univalence truncations +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.sets +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.empty-types funext univalence truncations +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence +open import foundation.sets funext univalence open import foundation.unit-type open import foundation.universe-levels -open import univalent-combinatorics.equality-standard-finite-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.equality-standard-finite-types funext univalence truncations +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/univalent-combinatorics/cubes.lagda.md b/src/univalent-combinatorics/cubes.lagda.md index 658ef99b5f..d4f6204dc5 100644 --- a/src/univalent-combinatorics/cubes.lagda.md +++ b/src/univalent-combinatorics/cubes.lagda.md @@ -1,7 +1,15 @@ # Cubes ```agda -module univalent-combinatorics.cubes where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module univalent-combinatorics.cubes + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -12,8 +20,8 @@ open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types open import foundation.universe-levels -open import univalent-combinatorics.complements-isolated-elements -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.complements-isolated-elements funext univalence truncations +open import univalent-combinatorics.finite-types funext univalence truncations ```
diff --git a/src/univalent-combinatorics/cycle-partitions.lagda.md b/src/univalent-combinatorics/cycle-partitions.lagda.md index 2b24b1903a..c974540131 100644 --- a/src/univalent-combinatorics/cycle-partitions.lagda.md +++ b/src/univalent-combinatorics/cycle-partitions.lagda.md @@ -1,7 +1,15 @@ # Cycle partitions of finite types ```agda -module univalent-combinatorics.cycle-partitions where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module univalent-combinatorics.cycle-partitions + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,11 +18,11 @@ module univalent-combinatorics.cycle-partitions where open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.equivalences +open import foundation.equivalences funext open import foundation.universe-levels -open import univalent-combinatorics.cyclic-finite-types -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.cyclic-finite-types funext univalence truncations +open import univalent-combinatorics.finite-types funext univalence truncations ```
diff --git a/src/univalent-combinatorics/cycle-prime-decomposition-natural-numbers.lagda.md b/src/univalent-combinatorics/cycle-prime-decomposition-natural-numbers.lagda.md index f1c5ab49c3..fcbd9e011e 100644 --- a/src/univalent-combinatorics/cycle-prime-decomposition-natural-numbers.lagda.md +++ b/src/univalent-combinatorics/cycle-prime-decomposition-natural-numbers.lagda.md @@ -1,41 +1,50 @@ # Cycle prime decompositions of natural numbers ```agda -module univalent-combinatorics.cycle-prime-decomposition-natural-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module univalent-combinatorics.cycle-prime-decomposition-natural-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.decidable-total-order-natural-numbers -open import elementary-number-theory.fundamental-theorem-of-arithmetic -open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.decidable-total-order-natural-numbers funext univalence truncations +open import elementary-number-theory.fundamental-theorem-of-arithmetic funext univalence truncations +open import elementary-number-theory.inequality-natural-numbers funext univalence truncations open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import finite-group-theory.permutations-standard-finite-types +open import finite-group-theory.permutations-standard-finite-types funext univalence truncations open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types -open import foundation.contractible-types +open import foundation.cartesian-product-types funext univalence +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.identity-types -open import foundation.iterated-cartesian-product-types +open import foundation.dependent-products-contractible-types funext +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.iterated-cartesian-product-types funext univalence truncations open import foundation.transport-along-identifications -open import foundation.univalence +open import foundation.univalence funext univalence open import foundation.universe-levels -open import group-theory.concrete-groups -open import group-theory.iterated-cartesian-products-concrete-groups +open import group-theory.concrete-groups funext univalence truncations +open import group-theory.iterated-cartesian-products-concrete-groups funext univalence truncations -open import lists.arrays -open import lists.concatenation-lists -open import lists.functoriality-lists -open import lists.permutation-lists -open import lists.sort-by-insertion-lists +open import lists.arrays funext univalence truncations +open import lists.concatenation-lists funext univalence truncations +open import lists.functoriality-lists funext univalence truncations +open import lists.permutation-lists funext univalence truncations +open import lists.sort-by-insertion-lists funext univalence truncations -open import univalent-combinatorics.cyclic-finite-types +open import univalent-combinatorics.cyclic-finite-types funext univalence truncations ```
diff --git a/src/univalent-combinatorics/cyclic-finite-types.lagda.md b/src/univalent-combinatorics/cyclic-finite-types.lagda.md index da2741d64a..c4d8dcb0dd 100644 --- a/src/univalent-combinatorics/cyclic-finite-types.lagda.md +++ b/src/univalent-combinatorics/cyclic-finite-types.lagda.md @@ -1,52 +1,61 @@ # Cyclic finite types ```agda -module univalent-combinatorics.cyclic-finite-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module univalent-combinatorics.cyclic-finite-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.addition-integers +open import elementary-number-theory.addition-integers funext univalence truncations open import elementary-number-theory.integers -open import elementary-number-theory.modular-arithmetic -open import elementary-number-theory.modular-arithmetic-standard-finite-types +open import elementary-number-theory.modular-arithmetic funext univalence truncations +open import elementary-number-theory.modular-arithmetic-standard-finite-types funext univalence truncations open import elementary-number-theory.natural-numbers -open import elementary-number-theory.standard-cyclic-groups +open import elementary-number-theory.standard-cyclic-groups funext univalence truncations -open import foundation.0-connected-types +open import foundation.0-connected-types funext univalence truncations open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-maps -open import foundation.contractible-types -open import foundation.coproduct-types +open import foundation.commuting-squares-of-maps funext univalence +open import foundation.contractible-types funext univalence +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types +open import foundation.dependent-products-contractible-types funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.mere-equality -open import foundation.propositional-truncations -open import foundation.sets +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.mere-equality funext univalence truncations +open import foundation.propositional-truncations funext univalence +open import foundation.sets funext univalence open import foundation.subtype-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext univalence truncations open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels -open import group-theory.concrete-groups -open import group-theory.groups -open import group-theory.isomorphisms-groups +open import group-theory.concrete-groups funext univalence truncations +open import group-theory.groups funext univalence truncations +open import group-theory.isomorphisms-groups funext univalence truncations -open import higher-group-theory.higher-groups +open import higher-group-theory.higher-groups funext univalence truncations -open import structured-types.equivalences-types-equipped-with-endomorphisms -open import structured-types.mere-equivalences-types-equipped-with-endomorphisms +open import structured-types.equivalences-types-equipped-with-endomorphisms funext univalence truncations +open import structured-types.mere-equivalences-types-equipped-with-endomorphisms funext univalence truncations open import structured-types.pointed-types -open import structured-types.types-equipped-with-endomorphisms +open import structured-types.types-equipped-with-endomorphisms funext univalence -open import synthetic-homotopy-theory.groups-of-loops-in-1-types -open import synthetic-homotopy-theory.loop-spaces +open import synthetic-homotopy-theory.groups-of-loops-in-1-types funext univalence truncations +open import synthetic-homotopy-theory.loop-spaces funext univalence truncations ```
diff --git a/src/univalent-combinatorics/de-morgans-law.lagda.md b/src/univalent-combinatorics/de-morgans-law.lagda.md index bca666f108..d1983e2d73 100644 --- a/src/univalent-combinatorics/de-morgans-law.lagda.md +++ b/src/univalent-combinatorics/de-morgans-law.lagda.md @@ -1,7 +1,15 @@ # De Morgan's law for finite families of propositions ```agda -module univalent-combinatorics.de-morgans-law where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module univalent-combinatorics.de-morgans-law + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,24 +17,24 @@ module univalent-combinatorics.de-morgans-law where ```agda open import elementary-number-theory.natural-numbers -open import foundation.coproduct-types -open import foundation.decidable-dependent-pair-types -open import foundation.decidable-types +open import foundation.coproduct-types funext univalence truncations +open import foundation.decidable-dependent-pair-types funext univalence truncations +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.equivalences -open import foundation.existential-quantification -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.negation +open import foundation.empty-types funext univalence truncations +open import foundation.equivalences funext +open import foundation.existential-quantification funext univalence truncations +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.negation funext open import foundation.unit-type open import foundation.universe-levels -open import logic.de-morgan-propositions -open import logic.de-morgan-types +open import logic.de-morgan-propositions funext univalence truncations +open import logic.de-morgan-types funext univalence truncations -open import univalent-combinatorics.counting -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.counting funext univalence truncations +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/univalent-combinatorics/decidable-dependent-function-types.lagda.md b/src/univalent-combinatorics/decidable-dependent-function-types.lagda.md index 5f6cfff00c..dac473c9d3 100644 --- a/src/univalent-combinatorics/decidable-dependent-function-types.lagda.md +++ b/src/univalent-combinatorics/decidable-dependent-function-types.lagda.md @@ -1,9 +1,17 @@ # Decidable dependent function types ```agda -module univalent-combinatorics.decidable-dependent-function-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom -open import elementary-number-theory.decidable-dependent-function-types public +module univalent-combinatorics.decidable-dependent-function-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where + +open import elementary-number-theory.decidable-dependent-function-types funext univalence truncations public ```
Imports @@ -11,21 +19,22 @@ open import elementary-number-theory.decidable-dependent-function-types public ```agda open import elementary-number-theory.natural-numbers -open import foundation.coproduct-types -open import foundation.decidable-propositions -open import foundation.decidable-types -open import foundation.empty-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.propositional-truncations -open import foundation.propositions +open import foundation.coproduct-types funext univalence truncations +open import foundation.decidable-propositions funext univalence truncations +open import foundation.decidable-types funext univalence truncations +open import foundation.dependent-products-propositions funext +open import foundation.empty-types funext univalence truncations +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence open import foundation.unit-type open import foundation.universe-levels -open import univalent-combinatorics.counting -open import univalent-combinatorics.finite-choice -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.counting funext univalence truncations +open import univalent-combinatorics.finite-choice funext univalence truncations +open import univalent-combinatorics.finite-types funext univalence truncations +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/univalent-combinatorics/decidable-dependent-pair-types.lagda.md b/src/univalent-combinatorics/decidable-dependent-pair-types.lagda.md index 9e48dbc5b3..1544d1ea42 100644 --- a/src/univalent-combinatorics/decidable-dependent-pair-types.lagda.md +++ b/src/univalent-combinatorics/decidable-dependent-pair-types.lagda.md @@ -1,7 +1,15 @@ # Decidability of dependent pair types ```agda -module univalent-combinatorics.decidable-dependent-pair-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module univalent-combinatorics.decidable-dependent-pair-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,18 +17,18 @@ module univalent-combinatorics.decidable-dependent-pair-types where ```agda open import elementary-number-theory.natural-numbers -open import foundation.coproduct-types -open import foundation.decidable-dependent-pair-types -open import foundation.decidable-types +open import foundation.coproduct-types funext univalence truncations +open import foundation.decidable-dependent-pair-types funext univalence truncations +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.equivalences -open import foundation.function-types +open import foundation.empty-types funext univalence truncations +open import foundation.equivalences funext +open import foundation.function-types funext open import foundation.unit-type open import foundation.universe-levels -open import univalent-combinatorics.counting -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.counting funext univalence truncations +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/univalent-combinatorics/decidable-equivalence-relations.lagda.md b/src/univalent-combinatorics/decidable-equivalence-relations.lagda.md index 46f0521430..5964c54d1f 100644 --- a/src/univalent-combinatorics/decidable-equivalence-relations.lagda.md +++ b/src/univalent-combinatorics/decidable-equivalence-relations.lagda.md @@ -1,7 +1,15 @@ # Decidable equivalence relations on finite types ```agda -module univalent-combinatorics.decidable-equivalence-relations where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module univalent-combinatorics.decidable-equivalence-relations + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,32 +17,33 @@ module univalent-combinatorics.decidable-equivalence-relations where ```agda open import elementary-number-theory.natural-numbers -open import foundation.binary-relations -open import foundation.cartesian-product-types -open import foundation.decidable-equality -open import foundation.decidable-equivalence-relations -open import foundation.decidable-relations -open import foundation.decidable-types -open import foundation.equivalence-relations -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-cartesian-product-types -open import foundation.functoriality-dependent-pair-types -open import foundation.propositional-truncations -open import foundation.propositions +open import foundation.binary-relations funext univalence truncations +open import foundation.cartesian-product-types funext univalence +open import foundation.decidable-equality funext univalence truncations +open import foundation.decidable-equivalence-relations funext univalence truncations +open import foundation.decidable-relations funext univalence truncations +open import foundation.decidable-types funext univalence truncations +open import foundation.dependent-products-propositions funext +open import foundation.equivalence-relations funext univalence truncations +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence open import foundation.type-arithmetic-cartesian-product-types open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels -open import univalent-combinatorics.cartesian-product-types -open import univalent-combinatorics.counting -open import univalent-combinatorics.decidable-propositions -open import univalent-combinatorics.dependent-function-types -open import univalent-combinatorics.dependent-pair-types -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.function-types -open import univalent-combinatorics.standard-finite-types -open import univalent-combinatorics.surjective-maps +open import univalent-combinatorics.cartesian-product-types funext univalence truncations +open import univalent-combinatorics.counting funext univalence truncations +open import univalent-combinatorics.decidable-propositions funext univalence truncations +open import univalent-combinatorics.dependent-function-types funext univalence truncations +open import univalent-combinatorics.dependent-pair-types funext univalence truncations +open import univalent-combinatorics.finite-types funext univalence truncations +open import univalent-combinatorics.function-types funext univalence truncations +open import univalent-combinatorics.standard-finite-types funext univalence truncations +open import univalent-combinatorics.surjective-maps funext univalence truncations ```
diff --git a/src/univalent-combinatorics/decidable-propositions.lagda.md b/src/univalent-combinatorics/decidable-propositions.lagda.md index c825d693f8..9f9263cf6d 100644 --- a/src/univalent-combinatorics/decidable-propositions.lagda.md +++ b/src/univalent-combinatorics/decidable-propositions.lagda.md @@ -1,9 +1,17 @@ # Decidable propositions ```agda -module univalent-combinatorics.decidable-propositions where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom -open import foundation.decidable-propositions public +module univalent-combinatorics.decidable-propositions + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where + +open import foundation.decidable-propositions funext univalence truncations public ```
Imports @@ -11,17 +19,18 @@ open import foundation.decidable-propositions public ```agda open import elementary-number-theory.natural-numbers -open import foundation.coproduct-types -open import foundation.decidable-equality -open import foundation.decidable-types +open import foundation.coproduct-types funext univalence truncations +open import foundation.decidable-equality funext univalence truncations +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.identity-types -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence open import foundation.universe-levels -open import univalent-combinatorics.counting -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.counting funext univalence truncations +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/univalent-combinatorics/decidable-subtypes.lagda.md b/src/univalent-combinatorics/decidable-subtypes.lagda.md index d7b83a688c..ebaf3350f0 100644 --- a/src/univalent-combinatorics/decidable-subtypes.lagda.md +++ b/src/univalent-combinatorics/decidable-subtypes.lagda.md @@ -1,37 +1,46 @@ # Decidable subtypes of finite types ```agda -module univalent-combinatorics.decidable-subtypes where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module univalent-combinatorics.decidable-subtypes + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where -open import foundation.decidable-subtypes public +open import foundation.decidable-subtypes funext univalence truncations public ```
Imports ```agda -open import elementary-number-theory.exponentiation-natural-numbers +open import elementary-number-theory.exponentiation-natural-numbers funext univalence truncations open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.coproduct-types -open import foundation.decidable-equality -open import foundation.decidable-propositions -open import foundation.embeddings -open import foundation.function-types -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.sets -open import foundation.subtypes +open import foundation.coproduct-types funext univalence truncations +open import foundation.decidable-equality funext univalence truncations +open import foundation.decidable-propositions funext univalence truncations +open import foundation.dependent-products-propositions funext +open import foundation.embeddings funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.transport-along-identifications open import foundation.universe-levels -open import univalent-combinatorics.decidable-dependent-pair-types -open import univalent-combinatorics.dependent-pair-types -open import univalent-combinatorics.equality-finite-types -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.function-types +open import univalent-combinatorics.decidable-dependent-pair-types funext univalence truncations +open import univalent-combinatorics.dependent-pair-types funext univalence truncations +open import univalent-combinatorics.equality-finite-types funext univalence truncations +open import univalent-combinatorics.finite-types funext univalence truncations +open import univalent-combinatorics.function-types funext univalence truncations ```
diff --git a/src/univalent-combinatorics/dedekind-finite-sets.lagda.md b/src/univalent-combinatorics/dedekind-finite-sets.lagda.md index f3d73ff2db..f128eb5e22 100644 --- a/src/univalent-combinatorics/dedekind-finite-sets.lagda.md +++ b/src/univalent-combinatorics/dedekind-finite-sets.lagda.md @@ -1,17 +1,24 @@ # Dedekind finite sets ```agda -module univalent-combinatorics.dedekind-finite-sets where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module univalent-combinatorics.dedekind-finite-sets + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalences -open import foundation.propositions -open import foundation.sets +open import foundation.dependent-products-propositions funext +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence open import foundation.universe-levels ``` diff --git a/src/univalent-combinatorics/dependent-function-types.lagda.md b/src/univalent-combinatorics/dependent-function-types.lagda.md index f8354b654c..31417afed9 100644 --- a/src/univalent-combinatorics/dependent-function-types.lagda.md +++ b/src/univalent-combinatorics/dependent-function-types.lagda.md @@ -1,7 +1,15 @@ # Counting the elements of dependent function types ```agda -module univalent-combinatorics.dependent-function-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module univalent-combinatorics.dependent-function-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,28 +17,28 @@ module univalent-combinatorics.dependent-function-types where ```agda open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.products-of-natural-numbers +open import elementary-number-theory.products-of-natural-numbers funext univalence truncations open import foundation.action-on-identifications-functions -open import foundation.coproduct-types +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.dependent-universal-property-equivalences -open import foundation.equivalences -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.propositional-truncations +open import foundation.dependent-universal-property-equivalences funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.propositional-truncations funext univalence open import foundation.unit-type -open import foundation.universal-property-coproduct-types -open import foundation.universal-property-empty-type -open import foundation.universal-property-unit-type +open import foundation.universal-property-coproduct-types funext +open import foundation.universal-property-empty-type funext +open import foundation.universal-property-unit-type funext open import foundation.universe-levels -open import univalent-combinatorics.cartesian-product-types -open import univalent-combinatorics.counting -open import univalent-combinatorics.finite-choice -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.cartesian-product-types funext univalence truncations +open import univalent-combinatorics.counting funext univalence truncations +open import univalent-combinatorics.finite-choice funext univalence truncations +open import univalent-combinatorics.finite-types funext univalence truncations +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/univalent-combinatorics/dependent-pair-types.lagda.md b/src/univalent-combinatorics/dependent-pair-types.lagda.md index 491d05e318..b0832e22a4 100644 --- a/src/univalent-combinatorics/dependent-pair-types.lagda.md +++ b/src/univalent-combinatorics/dependent-pair-types.lagda.md @@ -1,7 +1,15 @@ # Dependent pair types of finite types ```agda -module univalent-combinatorics.dependent-pair-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module univalent-combinatorics.dependent-pair-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where open import foundation.dependent-pair-types public ``` @@ -10,34 +18,34 @@ open import foundation.dependent-pair-types public ```agda open import foundation.complements -open import foundation.contractible-types -open import foundation.decidable-types -open import foundation.empty-types -open import foundation.equality-dependent-pair-types -open import foundation.equivalences -open import foundation.fibers-of-maps -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.functoriality-propositional-truncation -open import foundation.identity-types -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.sections -open import foundation.sets -open import foundation.subtypes -open import foundation.torsorial-type-families +open import foundation.decidable-types funext univalence truncations +open import foundation.dependent-products-propositions funext +open import foundation.empty-types funext univalence truncations +open import foundation.equality-dependent-pair-types funext +open import foundation.equivalences funext +open import foundation.fibers-of-maps funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.functoriality-propositional-truncation funext univalence truncations +open import foundation.identity-types funext +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence +open import foundation.sections funext +open import foundation.sets funext univalence +open import foundation.subtypes funext univalence truncations +open import foundation.torsorial-type-families funext univalence truncations open import foundation.transport-along-identifications -open import foundation.type-arithmetic-coproduct-types +open import foundation.type-arithmetic-coproduct-types funext univalence truncations open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels -open import univalent-combinatorics.coproduct-types -open import univalent-combinatorics.counting -open import univalent-combinatorics.counting-dependent-pair-types -open import univalent-combinatorics.decidable-propositions -open import univalent-combinatorics.equality-finite-types -open import univalent-combinatorics.finite-choice -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.coproduct-types funext univalence truncations +open import univalent-combinatorics.counting funext univalence truncations +open import univalent-combinatorics.counting-dependent-pair-types funext univalence truncations +open import univalent-combinatorics.decidable-propositions funext univalence truncations +open import univalent-combinatorics.equality-finite-types funext univalence truncations +open import univalent-combinatorics.finite-choice funext univalence truncations +open import univalent-combinatorics.finite-types funext univalence truncations ```
diff --git a/src/univalent-combinatorics/discrete-sigma-decompositions.lagda.md b/src/univalent-combinatorics/discrete-sigma-decompositions.lagda.md index cb68b48e7d..823b4c6f23 100644 --- a/src/univalent-combinatorics/discrete-sigma-decompositions.lagda.md +++ b/src/univalent-combinatorics/discrete-sigma-decompositions.lagda.md @@ -1,23 +1,34 @@ # Finite discrete Σ-decompositions ```agda -module univalent-combinatorics.discrete-sigma-decompositions where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module univalent-combinatorics.discrete-sigma-decompositions + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where -open import foundation.discrete-sigma-decompositions public +open import foundation.discrete-sigma-decompositions funext univalence truncations public ```
Imports ```agda -open import foundation.contractible-types +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.subtypes +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.raising-universe-levels-unit-type +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.sigma-decompositions +open import univalent-combinatorics.finite-types funext univalence truncations +open import univalent-combinatorics.sigma-decompositions funext univalence truncations ```
diff --git a/src/univalent-combinatorics/distributivity-of-set-truncation-over-finite-products.lagda.md b/src/univalent-combinatorics/distributivity-of-set-truncation-over-finite-products.lagda.md index 64609a61a2..c361776d2e 100644 --- a/src/univalent-combinatorics/distributivity-of-set-truncation-over-finite-products.lagda.md +++ b/src/univalent-combinatorics/distributivity-of-set-truncation-over-finite-products.lagda.md @@ -1,7 +1,15 @@ # Distributivity of set truncation over finite products ```agda -module univalent-combinatorics.distributivity-of-set-truncation-over-finite-products where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module univalent-combinatorics.distributivity-of-set-truncation-over-finite-products + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,37 +18,38 @@ module univalent-combinatorics.distributivity-of-set-truncation-over-finite-prod open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.contractible-types -open import foundation.coproduct-types +open import foundation.contractible-types funext univalence +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.dependent-universal-property-equivalences -open import foundation.empty-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.functoriality-cartesian-product-types -open import foundation.functoriality-dependent-function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.functoriality-function-types -open import foundation.functoriality-set-truncation -open import foundation.homotopies -open import foundation.identity-types -open import foundation.postcomposition-functions -open import foundation.precomposition-dependent-functions -open import foundation.precomposition-functions -open import foundation.propositional-truncations -open import foundation.set-truncations -open import foundation.sets +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-universal-property-equivalences funext +open import foundation.empty-types funext univalence truncations +open import foundation.equivalences funext +open import foundation.function-extensionality funext +open import foundation.function-types funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.functoriality-dependent-function-types funext univalence +open import foundation.functoriality-dependent-pair-types funext +open import foundation.functoriality-function-types funext univalence +open import foundation.functoriality-set-truncation funext univalence truncations +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.postcomposition-functions funext +open import foundation.precomposition-dependent-functions funext +open import foundation.precomposition-functions funext +open import foundation.propositional-truncations funext univalence +open import foundation.set-truncations funext univalence +open import foundation.sets funext univalence open import foundation.unit-type -open import foundation.universal-property-dependent-pair-types -open import foundation.universal-property-empty-type -open import foundation.universal-property-equivalences -open import foundation.universal-property-maybe +open import foundation.universal-property-dependent-pair-types funext +open import foundation.universal-property-empty-type funext +open import foundation.universal-property-equivalences funext +open import foundation.universal-property-maybe funext open import foundation.universe-levels -open import univalent-combinatorics.counting -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.counting funext univalence truncations +open import univalent-combinatorics.finite-types funext univalence truncations +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/univalent-combinatorics/double-counting.lagda.md b/src/univalent-combinatorics/double-counting.lagda.md index a6a55dcc85..5f4139e0fc 100644 --- a/src/univalent-combinatorics/double-counting.lagda.md +++ b/src/univalent-combinatorics/double-counting.lagda.md @@ -1,19 +1,27 @@ # Double counting ```agda -module univalent-combinatorics.double-counting where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module univalent-combinatorics.double-counting + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.identity-types +open import foundation.equivalences funext +open import foundation.identity-types funext open import foundation.universe-levels -open import univalent-combinatorics.counting -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.counting funext univalence truncations +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/univalent-combinatorics/embeddings-standard-finite-types.lagda.md b/src/univalent-combinatorics/embeddings-standard-finite-types.lagda.md index 458ec1b433..63caa1c649 100644 --- a/src/univalent-combinatorics/embeddings-standard-finite-types.lagda.md +++ b/src/univalent-combinatorics/embeddings-standard-finite-types.lagda.md @@ -1,29 +1,37 @@ # Embeddings between standard finite types ```agda -module univalent-combinatorics.embeddings-standard-finite-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module univalent-combinatorics.embeddings-standard-finite-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import elementary-number-theory.natural-numbers -open import elementary-number-theory.repeating-element-standard-finite-type +open import elementary-number-theory.repeating-element-standard-finite-type funext univalence truncations open import foundation.action-on-identifications-functions -open import foundation.coproduct-types -open import foundation.decidable-types +open import foundation.coproduct-types funext univalence truncations +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.empty-types -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.sets +open import foundation.embeddings funext +open import foundation.empty-types funext univalence truncations +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.sets funext univalence open import foundation.unit-type open import foundation.universe-levels -open import univalent-combinatorics.equality-standard-finite-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.equality-standard-finite-types funext univalence truncations +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/univalent-combinatorics/embeddings.lagda.md b/src/univalent-combinatorics/embeddings.lagda.md index e9776b2416..9cb4a2dc9a 100644 --- a/src/univalent-combinatorics/embeddings.lagda.md +++ b/src/univalent-combinatorics/embeddings.lagda.md @@ -1,9 +1,17 @@ # Embeddings ```agda -module univalent-combinatorics.embeddings where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module univalent-combinatorics.embeddings + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where -open import foundation.embeddings public +open import foundation.embeddings funext public ```
Imports @@ -11,22 +19,23 @@ open import foundation.embeddings public ```agda open import elementary-number-theory.natural-numbers -open import foundation.coproduct-types -open import foundation.decidable-embeddings -open import foundation.decidable-types +open import foundation.coproduct-types funext univalence truncations +open import foundation.decidable-embeddings funext univalence truncations +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.equivalences -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.sets +open import foundation.dependent-products-propositions funext +open import foundation.empty-types funext univalence truncations +open import foundation.equivalences funext +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence +open import foundation.sets funext univalence open import foundation.unit-type open import foundation.universe-levels -open import univalent-combinatorics.counting -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.injective-maps -open import univalent-combinatorics.retracts-of-finite-types +open import univalent-combinatorics.counting funext univalence truncations +open import univalent-combinatorics.finite-types funext univalence truncations +open import univalent-combinatorics.injective-maps funext univalence truncations +open import univalent-combinatorics.retracts-of-finite-types funext univalence truncations ```
diff --git a/src/univalent-combinatorics/equality-finite-types.lagda.md b/src/univalent-combinatorics/equality-finite-types.lagda.md index 220051d0d8..4709bfcdc5 100644 --- a/src/univalent-combinatorics/equality-finite-types.lagda.md +++ b/src/univalent-combinatorics/equality-finite-types.lagda.md @@ -1,7 +1,15 @@ # Equality in finite types ```agda -module univalent-combinatorics.equality-finite-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module univalent-combinatorics.equality-finite-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,16 +17,16 @@ module univalent-combinatorics.equality-finite-types where ```agda open import elementary-number-theory.natural-numbers -open import foundation.decidable-equality +open import foundation.decidable-equality funext univalence truncations open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.propositional-truncations +open import foundation.identity-types funext +open import foundation.propositional-truncations funext univalence open import foundation.universe-levels -open import univalent-combinatorics.counting -open import univalent-combinatorics.decidable-propositions -open import univalent-combinatorics.equality-standard-finite-types -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.counting funext univalence truncations +open import univalent-combinatorics.decidable-propositions funext univalence truncations +open import univalent-combinatorics.equality-standard-finite-types funext univalence truncations +open import univalent-combinatorics.finite-types funext univalence truncations ```
diff --git a/src/univalent-combinatorics/equality-standard-finite-types.lagda.md b/src/univalent-combinatorics/equality-standard-finite-types.lagda.md index 637b3cf66a..64c4d2a0ac 100644 --- a/src/univalent-combinatorics/equality-standard-finite-types.lagda.md +++ b/src/univalent-combinatorics/equality-standard-finite-types.lagda.md @@ -1,38 +1,48 @@ # Equality in the standard finite types ```agda -module univalent-combinatorics.equality-standard-finite-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module univalent-combinatorics.equality-standard-finite-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.inequality-natural-numbers funext univalence truncations open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.apartness-relations -open import foundation.contractible-types -open import foundation.coproduct-types -open import foundation.decidable-types +open import foundation.apartness-relations funext univalence truncations +open import foundation.contractible-types funext univalence +open import foundation.coproduct-types funext univalence truncations +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.discrete-types -open import foundation.empty-types -open import foundation.equivalences -open import foundation.functoriality-coproduct-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.negated-equality -open import foundation.negation -open import foundation.propositions -open import foundation.set-truncations -open import foundation.tight-apartness-relations +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.discrete-types funext univalence truncations +open import foundation.empty-types funext univalence truncations +open import foundation.equivalences funext +open import foundation.functoriality-coproduct-types funext univalence truncations +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.negated-equality funext univalence truncations +open import foundation.negation funext +open import foundation.propositions funext univalence +open import foundation.set-truncations funext univalence +open import foundation.tight-apartness-relations funext univalence truncations open import foundation.unit-type open import foundation.universe-levels -open import foundation-core.decidable-propositions +open import foundation-core.decidable-propositions funext univalence truncations -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/univalent-combinatorics/equivalences-cubes.lagda.md b/src/univalent-combinatorics/equivalences-cubes.lagda.md index c4971042e6..7f9734a0b9 100644 --- a/src/univalent-combinatorics/equivalences-cubes.lagda.md +++ b/src/univalent-combinatorics/equivalences-cubes.lagda.md @@ -1,7 +1,15 @@ # Equivalences of cubes ```agda -module univalent-combinatorics.equivalences-cubes where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module univalent-combinatorics.equivalences-cubes + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,20 +18,20 @@ module univalent-combinatorics.equivalences-cubes where open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types -open import foundation.equivalence-extensionality -open import foundation.equivalences -open import foundation.function-types +open import foundation.equality-dependent-function-types funext +open import foundation.equivalence-extensionality funext +open import foundation.equivalences funext +open import foundation.function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.identity-types +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.structure-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext univalence truncations open import foundation.transport-along-identifications open import foundation.universe-levels -open import univalent-combinatorics.cubes -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.cubes funext univalence truncations +open import univalent-combinatorics.finite-types funext univalence truncations ```
diff --git a/src/univalent-combinatorics/equivalences-standard-finite-types.lagda.md b/src/univalent-combinatorics/equivalences-standard-finite-types.lagda.md index b7044ed428..c2130db3dc 100644 --- a/src/univalent-combinatorics/equivalences-standard-finite-types.lagda.md +++ b/src/univalent-combinatorics/equivalences-standard-finite-types.lagda.md @@ -1,26 +1,35 @@ # Equivalences between standard finite types ```agda -module univalent-combinatorics.equivalences-standard-finite-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module univalent-combinatorics.equivalences-standard-finite-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.exponentiation-natural-numbers +open import elementary-number-theory.exponentiation-natural-numbers funext univalence truncations open import elementary-number-theory.natural-numbers -open import foundation.contractible-types -open import foundation.equivalences -open import foundation.functoriality-cartesian-product-types -open import foundation.type-arithmetic-empty-type +open import foundation.contractible-types funext univalence +open import foundation.dependent-products-contractible-types funext +open import foundation.equivalences funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.type-arithmetic-empty-type funext univalence truncations open import foundation.unit-type -open import foundation.universal-property-coproduct-types -open import foundation.universal-property-empty-type -open import foundation.universal-property-unit-type +open import foundation.universal-property-coproduct-types funext +open import foundation.universal-property-empty-type funext +open import foundation.universal-property-unit-type funext -open import univalent-combinatorics.cartesian-product-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.cartesian-product-types funext univalence truncations +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/univalent-combinatorics/equivalences.lagda.md b/src/univalent-combinatorics/equivalences.lagda.md index 6b439ee5a4..6c74b527ea 100644 --- a/src/univalent-combinatorics/equivalences.lagda.md +++ b/src/univalent-combinatorics/equivalences.lagda.md @@ -1,21 +1,29 @@ # Equivalences between finite types ```agda -module univalent-combinatorics.equivalences where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom -open import foundation.equivalences public +module univalent-combinatorics.equivalences + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where + +open import foundation.equivalences funext public ```
Imports ```agda -open import foundation.decidable-types +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types open import foundation.universe-levels -open import univalent-combinatorics.embeddings -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.surjective-maps +open import univalent-combinatorics.embeddings funext univalence truncations +open import univalent-combinatorics.finite-types funext univalence truncations +open import univalent-combinatorics.surjective-maps funext univalence truncations ```
diff --git a/src/univalent-combinatorics/ferrers-diagrams.lagda.md b/src/univalent-combinatorics/ferrers-diagrams.lagda.md index 034b26e3ad..1fb13902ff 100644 --- a/src/univalent-combinatorics/ferrers-diagrams.lagda.md +++ b/src/univalent-combinatorics/ferrers-diagrams.lagda.md @@ -1,28 +1,37 @@ # Ferrers diagrams (unlabeled partitions) ```agda -module univalent-combinatorics.ferrers-diagrams where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module univalent-combinatorics.ferrers-diagrams + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types -open import foundation.equivalences +open import foundation.dependent-products-propositions funext +open import foundation.equality-dependent-function-types funext +open import foundation.equivalences funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types -open import foundation.mere-equivalences -open import foundation.propositional-truncations -open import foundation.propositions +open import foundation.identity-types funext +open import foundation.mere-equivalences funext univalence truncations +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence open import foundation.structure-identity-principle open import foundation.subtype-identity-principle -open import foundation.torsorial-type-families -open import foundation.univalence +open import foundation.torsorial-type-families funext univalence truncations +open import foundation.univalence funext univalence open import foundation.universe-levels -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.finite-types funext univalence truncations ```
diff --git a/src/univalent-combinatorics/fibers-of-maps.lagda.md b/src/univalent-combinatorics/fibers-of-maps.lagda.md index 2d9e458ea5..0a15749c96 100644 --- a/src/univalent-combinatorics/fibers-of-maps.lagda.md +++ b/src/univalent-combinatorics/fibers-of-maps.lagda.md @@ -1,40 +1,48 @@ # Fibers of maps between finite types ```agda -module univalent-combinatorics.fibers-of-maps where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom -open import foundation.fibers-of-maps public +module univalent-combinatorics.fibers-of-maps + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where + +open import foundation.fibers-of-maps funext public ```
Imports ```agda open import elementary-number-theory.natural-numbers -open import elementary-number-theory.sums-of-natural-numbers - -open import foundation.contractible-types -open import foundation.decidable-types -open import foundation.equality-dependent-pair-types -open import foundation.equivalences -open import foundation.functoriality-dependent-pair-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.sections -open import foundation.torsorial-type-families +open import elementary-number-theory.sums-of-natural-numbers funext univalence truncations + +open import foundation.decidable-types funext univalence truncations +open import foundation.dependent-products-propositions funext +open import foundation.equality-dependent-pair-types funext +open import foundation.equivalences funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence +open import foundation.sections funext +open import foundation.torsorial-type-families funext univalence truncations open import foundation.transport-along-identifications open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels -open import univalent-combinatorics.counting -open import univalent-combinatorics.counting-dependent-pair-types -open import univalent-combinatorics.decidable-propositions -open import univalent-combinatorics.dependent-pair-types -open import univalent-combinatorics.double-counting -open import univalent-combinatorics.equality-finite-types -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.counting funext univalence truncations +open import univalent-combinatorics.counting-dependent-pair-types funext univalence truncations +open import univalent-combinatorics.decidable-propositions funext univalence truncations +open import univalent-combinatorics.dependent-pair-types funext univalence truncations +open import univalent-combinatorics.double-counting funext univalence truncations +open import univalent-combinatorics.equality-finite-types funext univalence truncations +open import univalent-combinatorics.finite-types funext univalence truncations +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/univalent-combinatorics/finite-choice.lagda.md b/src/univalent-combinatorics/finite-choice.lagda.md index 9446a425cb..7946ae57c2 100644 --- a/src/univalent-combinatorics/finite-choice.lagda.md +++ b/src/univalent-combinatorics/finite-choice.lagda.md @@ -1,39 +1,47 @@ # Finite choice ```agda -module univalent-combinatorics.finite-choice where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module univalent-combinatorics.finite-choice + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import elementary-number-theory.natural-numbers -open import elementary-number-theory.well-ordering-principle-standard-finite-types +open import elementary-number-theory.well-ordering-principle-standard-finite-types funext univalence truncations -open import foundation.coproduct-types -open import foundation.decidable-embeddings +open import foundation.coproduct-types funext univalence truncations +open import foundation.decidable-embeddings funext univalence truncations open import foundation.dependent-pair-types -open import foundation.dependent-universal-property-equivalences -open import foundation.empty-types -open import foundation.equivalences -open import foundation.fiber-inclusions -open import foundation.fibers-of-maps -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.functoriality-propositional-truncation -open import foundation.hilberts-epsilon-operators -open import foundation.identity-types -open import foundation.propositional-truncations -open import foundation.sets +open import foundation.dependent-universal-property-equivalences funext +open import foundation.empty-types funext univalence truncations +open import foundation.equivalences funext +open import foundation.fiber-inclusions funext univalence +open import foundation.fibers-of-maps funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.functoriality-propositional-truncation funext univalence truncations +open import foundation.hilberts-epsilon-operators funext univalence truncations +open import foundation.identity-types funext +open import foundation.propositional-truncations funext univalence +open import foundation.sets funext univalence open import foundation.unit-type -open import foundation.universal-property-coproduct-types -open import foundation.universal-property-unit-type +open import foundation.universal-property-coproduct-types funext +open import foundation.universal-property-unit-type funext open import foundation.universe-levels -open import univalent-combinatorics.counting -open import univalent-combinatorics.counting-decidable-subtypes -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.counting funext univalence truncations +open import univalent-combinatorics.counting-decidable-subtypes funext univalence truncations +open import univalent-combinatorics.finite-types funext univalence truncations +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/univalent-combinatorics/finite-types.lagda.md b/src/univalent-combinatorics/finite-types.lagda.md index 0ddff4cb5a..c7d8e233bf 100644 --- a/src/univalent-combinatorics/finite-types.lagda.md +++ b/src/univalent-combinatorics/finite-types.lagda.md @@ -1,50 +1,60 @@ # Finite types ```agda -module univalent-combinatorics.finite-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module univalent-combinatorics.finite-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.equality-natural-numbers +open import elementary-number-theory.equality-natural-numbers funext univalence truncations open import elementary-number-theory.natural-numbers -open import foundation.0-connected-types -open import foundation.1-types +open import foundation.0-connected-types funext univalence truncations +open import foundation.1-types funext univalence open import foundation.action-on-identifications-functions -open import foundation.connected-components-universes -open import foundation.contractible-types -open import foundation.decidable-types +open import foundation.connected-components-universes funext univalence truncations +open import foundation.contractible-types funext univalence +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-coproduct-types -open import foundation.functoriality-dependent-pair-types -open import foundation.functoriality-propositional-truncation -open import foundation.identity-types -open import foundation.inhabited-types -open import foundation.logical-equivalences -open import foundation.mere-equivalences -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.raising-universe-levels -open import foundation.sets -open import foundation.subtypes -open import foundation.subuniverses +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.empty-types funext univalence truncations +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-coproduct-types funext univalence truncations +open import foundation.functoriality-dependent-pair-types funext +open import foundation.functoriality-propositional-truncation funext univalence truncations +open import foundation.identity-types funext +open import foundation.inhabited-types funext univalence truncations +open import foundation.logical-equivalences funext +open import foundation.mere-equivalences funext univalence truncations +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence +open import foundation.raising-universe-levels-unit-type +open import foundation.sets funext univalence +open import foundation.subtypes funext univalence truncations +open import foundation.subuniverses funext univalence open import foundation.transport-along-identifications open import foundation.type-arithmetic-dependent-pair-types -open import foundation.type-arithmetic-empty-type +open import foundation.type-arithmetic-empty-type funext univalence truncations open import foundation.unit-type -open import foundation.univalence +open import foundation.univalence funext univalence open import foundation.universe-levels +open import foundation-core.raising-universe-levels open import foundation-core.torsorial-type-families -open import univalent-combinatorics.counting -open import univalent-combinatorics.double-counting -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.counting funext univalence truncations +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/univalent-combinatorics/finitely-many-connected-components.lagda.md b/src/univalent-combinatorics/finitely-many-connected-components.lagda.md index b2d49dc3a5..5d821bd47e 100644 --- a/src/univalent-combinatorics/finitely-many-connected-components.lagda.md +++ b/src/univalent-combinatorics/finitely-many-connected-components.lagda.md @@ -1,7 +1,15 @@ # Finiteness of the type of connected components ```agda -module univalent-combinatorics.finitely-many-connected-components where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module univalent-combinatorics.finitely-many-connected-components + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,28 +17,30 @@ module univalent-combinatorics.finitely-many-connected-components where ```agda open import elementary-number-theory.natural-numbers -open import foundation.0-connected-types -open import foundation.contractible-types -open import foundation.coproduct-types +open import foundation.0-connected-types funext univalence truncations +open import foundation.contractible-types funext univalence +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-set-truncation -open import foundation.mere-equivalences -open import foundation.propositions -open import foundation.retracts-of-types -open import foundation.set-truncations -open import foundation.sets +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.empty-types funext univalence truncations +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-set-truncation funext univalence truncations +open import foundation.mere-equivalences funext univalence truncations +open import foundation.propositions funext univalence +open import foundation.retracts-of-types funext univalence +open import foundation.set-truncations funext univalence +open import foundation.sets funext univalence open import foundation.unit-type open import foundation.universe-levels -open import univalent-combinatorics.coproduct-types -open import univalent-combinatorics.dependent-function-types -open import univalent-combinatorics.distributivity-of-set-truncation-over-finite-products -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.retracts-of-finite-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.coproduct-types funext univalence truncations +open import univalent-combinatorics.dependent-function-types funext univalence truncations +open import univalent-combinatorics.distributivity-of-set-truncation-over-finite-products funext univalence truncations +open import univalent-combinatorics.finite-types funext univalence truncations +open import univalent-combinatorics.retracts-of-finite-types funext univalence truncations +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/univalent-combinatorics/finitely-presented-types.lagda.md b/src/univalent-combinatorics/finitely-presented-types.lagda.md index 6cc22a250a..eb5205e78d 100644 --- a/src/univalent-combinatorics/finitely-presented-types.lagda.md +++ b/src/univalent-combinatorics/finitely-presented-types.lagda.md @@ -1,7 +1,15 @@ # Finitely presented types ```agda -module univalent-combinatorics.finitely-presented-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module univalent-combinatorics.finitely-presented-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,20 +18,21 @@ module univalent-combinatorics.finitely-presented-types where open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.fibers-of-maps -open import foundation.function-types -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.set-presented-types -open import foundation.set-truncations -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.fibers-of-maps funext +open import foundation.function-types funext +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence +open import foundation.set-presented-types funext univalence truncations +open import foundation.set-truncations funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels -open import univalent-combinatorics.finite-choice -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.finitely-many-connected-components -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.finite-choice funext univalence truncations +open import univalent-combinatorics.finite-types funext univalence truncations +open import univalent-combinatorics.finitely-many-connected-components funext univalence truncations +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/univalent-combinatorics/function-types.lagda.md b/src/univalent-combinatorics/function-types.lagda.md index 9929152a41..890202831a 100644 --- a/src/univalent-combinatorics/function-types.lagda.md +++ b/src/univalent-combinatorics/function-types.lagda.md @@ -1,29 +1,36 @@ # Finite function types ```agda -module univalent-combinatorics.function-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module univalent-combinatorics.function-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.equality-natural-numbers -open import elementary-number-theory.exponentiation-natural-numbers -open import elementary-number-theory.natural-numbers +open import elementary-number-theory.equality-natural-numbers funext univalence truncations +open import elementary-number-theory.exponentiation-natural-numbers funext univalence truncations open import foundation.action-on-identifications-binary-functions -open import foundation.equivalences -open import foundation.identity-types -open import foundation.propositional-truncations -open import foundation.sets +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.propositional-truncations funext univalence +open import foundation.sets funext univalence open import foundation.universe-levels -open import univalent-combinatorics.cartesian-product-types -open import univalent-combinatorics.counting -open import univalent-combinatorics.dependent-function-types -open import univalent-combinatorics.dependent-pair-types -open import univalent-combinatorics.equality-finite-types -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.cartesian-product-types funext univalence truncations +open import univalent-combinatorics.counting funext univalence truncations +open import univalent-combinatorics.dependent-function-types funext univalence truncations +open import univalent-combinatorics.dependent-pair-types funext univalence truncations +open import univalent-combinatorics.equality-finite-types funext univalence truncations +open import univalent-combinatorics.finite-types funext univalence truncations ```
diff --git a/src/univalent-combinatorics/image-of-maps.lagda.md b/src/univalent-combinatorics/image-of-maps.lagda.md index db8cf058d7..c0dd74e341 100644 --- a/src/univalent-combinatorics/image-of-maps.lagda.md +++ b/src/univalent-combinatorics/image-of-maps.lagda.md @@ -1,25 +1,33 @@ # The image of a map ```agda -module univalent-combinatorics.image-of-maps where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module univalent-combinatorics.image-of-maps + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where -open import foundation.images public +open import foundation.images funext univalence truncations public ```
Imports ```agda -open import foundation.decidable-equality -open import foundation.decidable-types -open import foundation.fibers-of-maps -open import foundation.propositional-truncations -open import foundation.subtypes -open import foundation.surjective-maps +open import foundation.decidable-equality funext univalence truncations +open import foundation.decidable-types funext univalence truncations +open import foundation.fibers-of-maps funext +open import foundation.propositional-truncations funext univalence +open import foundation.subtypes funext univalence truncations +open import foundation.surjective-maps funext univalence truncations open import foundation.universe-levels -open import univalent-combinatorics.dependent-pair-types -open import univalent-combinatorics.equality-finite-types -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.dependent-pair-types funext univalence truncations +open import univalent-combinatorics.equality-finite-types funext univalence truncations +open import univalent-combinatorics.finite-types funext univalence truncations ```
diff --git a/src/univalent-combinatorics/inequality-types-with-counting.lagda.md b/src/univalent-combinatorics/inequality-types-with-counting.lagda.md index 137bb6bd70..50ed02a172 100644 --- a/src/univalent-combinatorics/inequality-types-with-counting.lagda.md +++ b/src/univalent-combinatorics/inequality-types-with-counting.lagda.md @@ -1,23 +1,31 @@ # Inequality on types equipped with a counting ```agda -module univalent-combinatorics.inequality-types-with-counting where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module univalent-combinatorics.inequality-types-with-counting + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.inequality-standard-finite-types +open import elementary-number-theory.inequality-standard-finite-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.sets +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.sets funext univalence open import foundation.universe-levels -open import univalent-combinatorics.counting -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.counting funext univalence truncations +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/univalent-combinatorics/inhabited-finite-types.lagda.md b/src/univalent-combinatorics/inhabited-finite-types.lagda.md index f6ad56cab3..2e3dca1e58 100644 --- a/src/univalent-combinatorics/inhabited-finite-types.lagda.md +++ b/src/univalent-combinatorics/inhabited-finite-types.lagda.md @@ -1,7 +1,15 @@ # Inhabited finite types ```agda -module univalent-combinatorics.inhabited-finite-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module univalent-combinatorics.inhabited-finite-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,20 +17,21 @@ module univalent-combinatorics.inhabited-finite-types where ```agda open import elementary-number-theory.natural-numbers -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-function-types -open import foundation.identity-types -open import foundation.inhabited-types -open import foundation.propositions -open import foundation.subtypes -open import foundation.subuniverses +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-function-types funext univalence +open import foundation.identity-types funext +open import foundation.inhabited-types funext univalence truncations +open import foundation.propositions funext univalence +open import foundation.subtypes funext univalence truncations +open import foundation.subuniverses funext univalence open import foundation.type-arithmetic-dependent-pair-types -open import foundation.type-theoretic-principle-of-choice +open import foundation.type-theoretic-principle-of-choice funext open import foundation.universe-levels -open import univalent-combinatorics.dependent-pair-types -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.dependent-pair-types funext univalence truncations +open import univalent-combinatorics.finite-types funext univalence truncations ```
diff --git a/src/univalent-combinatorics/injective-maps.lagda.md b/src/univalent-combinatorics/injective-maps.lagda.md index b848851cf0..9da445e271 100644 --- a/src/univalent-combinatorics/injective-maps.lagda.md +++ b/src/univalent-combinatorics/injective-maps.lagda.md @@ -1,21 +1,29 @@ # Injective maps between finite types ```agda -module univalent-combinatorics.injective-maps where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom -open import foundation.injective-maps public +module univalent-combinatorics.injective-maps + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where + +open import foundation.injective-maps funext public ```
Imports ```agda -open import foundation.decidable-types -open import foundation.identity-types +open import foundation.decidable-types funext univalence truncations +open import foundation.identity-types funext open import foundation.universe-levels -open import univalent-combinatorics.decidable-dependent-function-types -open import univalent-combinatorics.equality-finite-types -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.decidable-dependent-function-types funext univalence truncations +open import univalent-combinatorics.equality-finite-types funext univalence truncations +open import univalent-combinatorics.finite-types funext univalence truncations ```
diff --git a/src/univalent-combinatorics/involution-standard-finite-types.lagda.md b/src/univalent-combinatorics/involution-standard-finite-types.lagda.md index 72c2a01a68..e44e1bad94 100644 --- a/src/univalent-combinatorics/involution-standard-finite-types.lagda.md +++ b/src/univalent-combinatorics/involution-standard-finite-types.lagda.md @@ -1,20 +1,28 @@ # An involution on the standard finite types ```agda -module univalent-combinatorics.involution-standard-finite-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module univalent-combinatorics.involution-standard-finite-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.modular-arithmetic-standard-finite-types +open import elementary-number-theory.modular-arithmetic-standard-finite-types funext univalence truncations open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.identity-types -open import foundation.involutions +open import foundation.identity-types funext +open import foundation.involutions funext univalence -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/univalent-combinatorics/isotopies-latin-squares.lagda.md b/src/univalent-combinatorics/isotopies-latin-squares.lagda.md index 58d4aa23c2..3308e37d6e 100644 --- a/src/univalent-combinatorics/isotopies-latin-squares.lagda.md +++ b/src/univalent-combinatorics/isotopies-latin-squares.lagda.md @@ -1,18 +1,26 @@ # Isotopies of Latin squares ```agda -module univalent-combinatorics.isotopies-latin-squares where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module univalent-combinatorics.isotopies-latin-squares + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.identity-types +open import foundation.equivalences funext +open import foundation.identity-types funext open import foundation.universe-levels -open import univalent-combinatorics.latin-squares +open import univalent-combinatorics.latin-squares funext univalence truncations ```
diff --git a/src/univalent-combinatorics/kuratowski-finite-sets.lagda.md b/src/univalent-combinatorics/kuratowski-finite-sets.lagda.md index 7de999ba15..c792eb0120 100644 --- a/src/univalent-combinatorics/kuratowski-finite-sets.lagda.md +++ b/src/univalent-combinatorics/kuratowski-finite-sets.lagda.md @@ -1,7 +1,15 @@ # Kuratowski finite sets ```agda -module univalent-combinatorics.kuratowski-finite-sets where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module univalent-combinatorics.kuratowski-finite-sets + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,19 +17,20 @@ module univalent-combinatorics.kuratowski-finite-sets where ```agda open import elementary-number-theory.natural-numbers -open import foundation.decidable-equality +open import foundation.decidable-equality funext univalence truncations open import foundation.dependent-pair-types -open import foundation.existential-quantification -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.sets -open import foundation.surjective-maps +open import foundation.dependent-products-propositions funext +open import foundation.existential-quantification funext univalence truncations +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence +open import foundation.sets funext univalence +open import foundation.surjective-maps funext univalence truncations open import foundation.universe-levels -open import univalent-combinatorics.equality-finite-types -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.image-of-maps -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.equality-finite-types funext univalence truncations +open import univalent-combinatorics.finite-types funext univalence truncations +open import univalent-combinatorics.image-of-maps funext univalence truncations +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/univalent-combinatorics/latin-squares.lagda.md b/src/univalent-combinatorics/latin-squares.lagda.md index 228092c29d..24e7b14fdd 100644 --- a/src/univalent-combinatorics/latin-squares.lagda.md +++ b/src/univalent-combinatorics/latin-squares.lagda.md @@ -1,7 +1,15 @@ # Latin squares ```agda -module univalent-combinatorics.latin-squares where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module univalent-combinatorics.latin-squares + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,7 +17,7 @@ module univalent-combinatorics.latin-squares where ```agda open import foundation.binary-equivalences open import foundation.dependent-pair-types -open import foundation.inhabited-types +open import foundation.inhabited-types funext univalence truncations open import foundation.universe-levels ``` diff --git a/src/univalent-combinatorics/locally-finite-types.lagda.md b/src/univalent-combinatorics/locally-finite-types.lagda.md index 04f398816f..67b9328339 100644 --- a/src/univalent-combinatorics/locally-finite-types.lagda.md +++ b/src/univalent-combinatorics/locally-finite-types.lagda.md @@ -1,7 +1,15 @@ # Locally finite types ```agda -module univalent-combinatorics.locally-finite-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module univalent-combinatorics.locally-finite-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,68 +17,35 @@ module univalent-combinatorics.locally-finite-types where ```agda open import elementary-number-theory.natural-numbers -open import foundation.0-connected-types -open import foundation.1-types -open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types -open import foundation.constant-maps -open import foundation.contractible-types -open import foundation.coproduct-types -open import foundation.decidable-equality -open import foundation.decidable-propositions -open import foundation.decidable-types -open import foundation.dependent-universal-property-equivalences -open import foundation.embeddings -open import foundation.empty-types +open import foundation.1-types funext univalence +open import foundation.cartesian-product-types funext univalence +open import foundation.contractible-types funext univalence +open import foundation.coproduct-types funext univalence truncations +open import foundation.decidable-equality funext univalence truncations +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.dependent-universal-property-equivalences funext +open import foundation.empty-types funext univalence truncations open import foundation.equality-cartesian-product-types -open import foundation.equality-coproduct-types -open import foundation.equality-dependent-pair-types -open import foundation.equivalences -open import foundation.fiber-inclusions -open import foundation.fibers-of-maps -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.functoriality-coproduct-types -open import foundation.functoriality-dependent-pair-types -open import foundation.functoriality-set-truncation -open import foundation.homotopies -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.logical-equivalences -open import foundation.maybe -open import foundation.mere-equality -open import foundation.mere-equivalences -open import foundation.propositional-extensionality -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.set-truncations -open import foundation.sets -open import foundation.subtypes -open import foundation.surjective-maps +open import foundation.equality-dependent-pair-types funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence open import foundation.transport-along-identifications -open import foundation.truncated-types -open import foundation.truncation-levels -open import foundation.type-arithmetic-coproduct-types open import foundation.unit-type -open import foundation.univalence -open import foundation.universal-property-coproduct-types -open import foundation.universal-property-empty-type -open import foundation.universal-property-unit-type +open import foundation.universal-property-coproduct-types funext +open import foundation.universal-property-empty-type funext +open import foundation.universal-property-unit-type funext open import foundation.universe-levels -open import foundation.whiskering-homotopies-composition - -open import univalent-combinatorics.cartesian-product-types -open import univalent-combinatorics.coproduct-types -open import univalent-combinatorics.counting -open import univalent-combinatorics.dependent-function-types -open import univalent-combinatorics.dependent-pair-types -open import univalent-combinatorics.distributivity-of-set-truncation-over-finite-products -open import univalent-combinatorics.equality-finite-types -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.finitely-presented-types -open import univalent-combinatorics.function-types -open import univalent-combinatorics.image-of-maps -open import univalent-combinatorics.standard-finite-types + +open import univalent-combinatorics.cartesian-product-types funext univalence truncations +open import univalent-combinatorics.counting funext univalence truncations +open import univalent-combinatorics.dependent-pair-types funext univalence truncations +open import univalent-combinatorics.equality-finite-types funext univalence truncations +open import univalent-combinatorics.finite-types funext univalence truncations +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/univalent-combinatorics/main-classes-of-latin-hypercubes.lagda.md b/src/univalent-combinatorics/main-classes-of-latin-hypercubes.lagda.md index f88ff5969a..83bccef6ca 100644 --- a/src/univalent-combinatorics/main-classes-of-latin-hypercubes.lagda.md +++ b/src/univalent-combinatorics/main-classes-of-latin-hypercubes.lagda.md @@ -1,7 +1,15 @@ # The groupoid of main classes of Latin hypercubes ```agda -module univalent-combinatorics.main-classes-of-latin-hypercubes where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module univalent-combinatorics.main-classes-of-latin-hypercubes + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,24 +17,25 @@ module univalent-combinatorics.main-classes-of-latin-hypercubes where ```agda open import elementary-number-theory.natural-numbers -open import foundation.1-types -open import foundation.contractible-types -open import foundation.decidable-propositions +open import foundation.1-types funext univalence +open import foundation.contractible-types funext univalence +open import foundation.decidable-propositions funext univalence truncations open import foundation.dependent-pair-types -open import foundation.inhabited-types -open import foundation.mere-equivalences -open import foundation.products-unordered-tuples-of-types -open import foundation.set-truncations +open import foundation.dependent-products-contractible-types funext +open import foundation.inhabited-types funext univalence truncations +open import foundation.mere-equivalences funext univalence truncations +open import foundation.products-unordered-tuples-of-types funext univalence truncations +open import foundation.set-truncations funext univalence open import foundation.universe-levels -open import foundation.unordered-tuples - -open import univalent-combinatorics.complements-isolated-elements -open import univalent-combinatorics.decidable-subtypes -open import univalent-combinatorics.dependent-function-types -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.pi-finite-types -open import univalent-combinatorics.standard-finite-types -open import univalent-combinatorics.untruncated-pi-finite-types +open import foundation.unordered-tuples funext univalence truncations + +open import univalent-combinatorics.complements-isolated-elements funext univalence truncations +open import univalent-combinatorics.decidable-subtypes funext univalence truncations +open import univalent-combinatorics.dependent-function-types funext univalence truncations +open import univalent-combinatorics.finite-types funext univalence truncations +open import univalent-combinatorics.pi-finite-types funext univalence truncations +open import univalent-combinatorics.standard-finite-types funext univalence truncations +open import univalent-combinatorics.untruncated-pi-finite-types funext univalence truncations ```
diff --git a/src/univalent-combinatorics/main-classes-of-latin-squares.lagda.md b/src/univalent-combinatorics/main-classes-of-latin-squares.lagda.md index 0f3d9410e3..b8b843fbfb 100644 --- a/src/univalent-combinatorics/main-classes-of-latin-squares.lagda.md +++ b/src/univalent-combinatorics/main-classes-of-latin-squares.lagda.md @@ -1,7 +1,15 @@ # The groupoid of main classes of Latin squares ```agda -module univalent-combinatorics.main-classes-of-latin-squares where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module univalent-combinatorics.main-classes-of-latin-squares + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,15 +17,15 @@ module univalent-combinatorics.main-classes-of-latin-squares where ```agda open import elementary-number-theory.natural-numbers -open import foundation.1-types -open import foundation.mere-equivalences -open import foundation.set-truncations +open import foundation.1-types funext univalence +open import foundation.mere-equivalences funext univalence truncations +open import foundation.set-truncations funext univalence open import foundation.universe-levels -open import univalent-combinatorics.main-classes-of-latin-hypercubes -open import univalent-combinatorics.pi-finite-types -open import univalent-combinatorics.standard-finite-types -open import univalent-combinatorics.untruncated-pi-finite-types +open import univalent-combinatorics.main-classes-of-latin-hypercubes funext univalence truncations +open import univalent-combinatorics.pi-finite-types funext univalence truncations +open import univalent-combinatorics.standard-finite-types funext univalence truncations +open import univalent-combinatorics.untruncated-pi-finite-types funext univalence truncations ```
diff --git a/src/univalent-combinatorics/maybe.lagda.md b/src/univalent-combinatorics/maybe.lagda.md index 9a9c68812f..6d239d40c0 100644 --- a/src/univalent-combinatorics/maybe.lagda.md +++ b/src/univalent-combinatorics/maybe.lagda.md @@ -1,9 +1,17 @@ # The maybe monad on finite types ```agda -module univalent-combinatorics.maybe where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom -open import foundation.maybe public +module univalent-combinatorics.maybe + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where + +open import foundation-core.maybe public ```
Imports @@ -13,8 +21,8 @@ open import elementary-number-theory.natural-numbers open import foundation.universe-levels -open import univalent-combinatorics.coproduct-types -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.coproduct-types funext univalence truncations +open import univalent-combinatorics.finite-types funext univalence truncations ```
diff --git a/src/univalent-combinatorics/necklaces.lagda.md b/src/univalent-combinatorics/necklaces.lagda.md index 49abdc1f29..0194433cd2 100644 --- a/src/univalent-combinatorics/necklaces.lagda.md +++ b/src/univalent-combinatorics/necklaces.lagda.md @@ -1,7 +1,15 @@ # Necklaces ```agda -module univalent-combinatorics.necklaces where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module univalent-combinatorics.necklaces + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,19 +18,19 @@ module univalent-combinatorics.necklaces where open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types +open import foundation.equivalences funext +open import foundation.function-extensionality funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.structure-identity-principle open import foundation.universe-levels -open import structured-types.types-equipped-with-endomorphisms +open import structured-types.types-equipped-with-endomorphisms funext univalence -open import univalent-combinatorics.cyclic-finite-types -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.cyclic-finite-types funext univalence truncations +open import univalent-combinatorics.finite-types funext univalence truncations +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/univalent-combinatorics/orientations-complete-undirected-graph.lagda.md b/src/univalent-combinatorics/orientations-complete-undirected-graph.lagda.md index 6dd93e951d..b9fc11dcd6 100644 --- a/src/univalent-combinatorics/orientations-complete-undirected-graph.lagda.md +++ b/src/univalent-combinatorics/orientations-complete-undirected-graph.lagda.md @@ -2,66 +2,74 @@ ```agda {-# OPTIONS --lossy-unification #-} +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom -module univalent-combinatorics.orientations-complete-undirected-graph where +module univalent-combinatorics.orientations-complete-undirected-graph + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.congruence-natural-numbers -open import elementary-number-theory.distance-natural-numbers -open import elementary-number-theory.inequality-natural-numbers -open import elementary-number-theory.modular-arithmetic-standard-finite-types +open import elementary-number-theory.congruence-natural-numbers funext univalence truncations +open import elementary-number-theory.distance-natural-numbers funext univalence truncations +open import elementary-number-theory.inequality-natural-numbers funext univalence truncations +open import elementary-number-theory.modular-arithmetic-standard-finite-types funext univalence truncations open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import finite-group-theory.transpositions +open import finite-group-theory.transpositions funext univalence truncations open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types -open import foundation.coproduct-types -open import foundation.decidable-equivalence-relations -open import foundation.decidable-propositions -open import foundation.decidable-types +open import foundation.cartesian-product-types funext univalence +open import foundation.coproduct-types funext univalence truncations +open import foundation.decidable-equivalence-relations funext univalence truncations +open import foundation.decidable-propositions funext univalence truncations +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.equality-dependent-pair-types -open import foundation.equivalence-classes -open import foundation.equivalence-extensionality -open import foundation.equivalence-relations -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.functoriality-propositional-truncation -open import foundation.homotopies -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.intersections-subtypes -open import foundation.involutions -open import foundation.logical-equivalences -open import foundation.mere-equivalences -open import foundation.negated-equality -open import foundation.negation -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.sets +open import foundation.dependent-products-propositions funext +open import foundation.empty-types funext univalence truncations +open import foundation.equality-dependent-pair-types funext +open import foundation.equivalence-classes funext univalence truncations +open import foundation.equivalence-extensionality funext +open import foundation.equivalence-relations funext univalence truncations +open import foundation.equivalences funext +open import foundation.function-extensionality funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.functoriality-propositional-truncation funext univalence truncations +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.intersections-subtypes funext univalence truncations +open import foundation.involutions funext univalence +open import foundation.logical-equivalences funext +open import foundation.mere-equivalences funext univalence truncations +open import foundation.negated-equality funext univalence truncations +open import foundation.negation funext +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence +open import foundation.sets funext univalence open import foundation.transport-along-identifications open import foundation.unit-type open import foundation.universe-levels -open import univalent-combinatorics.2-element-decidable-subtypes -open import univalent-combinatorics.2-element-types -open import univalent-combinatorics.counting -open import univalent-combinatorics.decidable-subtypes -open import univalent-combinatorics.equality-finite-types -open import univalent-combinatorics.equality-standard-finite-types -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.standard-finite-types -open import univalent-combinatorics.symmetric-difference +open import univalent-combinatorics.2-element-decidable-subtypes funext univalence truncations +open import univalent-combinatorics.2-element-types funext univalence truncations +open import univalent-combinatorics.counting funext univalence truncations +open import univalent-combinatorics.decidable-subtypes funext univalence truncations +open import univalent-combinatorics.equality-finite-types funext univalence truncations +open import univalent-combinatorics.equality-standard-finite-types funext univalence truncations +open import univalent-combinatorics.finite-types funext univalence truncations +open import univalent-combinatorics.standard-finite-types funext univalence truncations +open import univalent-combinatorics.symmetric-difference funext univalence truncations ```
diff --git a/src/univalent-combinatorics/orientations-cubes.lagda.md b/src/univalent-combinatorics/orientations-cubes.lagda.md index 9d6c029313..d9d90a35e2 100644 --- a/src/univalent-combinatorics/orientations-cubes.lagda.md +++ b/src/univalent-combinatorics/orientations-cubes.lagda.md @@ -1,7 +1,15 @@ # Orientations of cubes ```agda -module univalent-combinatorics.orientations-cubes where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module univalent-combinatorics.orientations-cubes + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,16 +17,16 @@ module univalent-combinatorics.orientations-cubes where ```agda open import elementary-number-theory.natural-numbers -open import foundation.identity-types -open import foundation.iterating-functions +open import foundation.identity-types funext +open import foundation.iterating-functions funext univalence truncations open import foundation.universe-levels -open import univalent-combinatorics.cubes -open import univalent-combinatorics.dependent-pair-types -open import univalent-combinatorics.equality-finite-types -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.function-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.cubes funext univalence truncations +open import univalent-combinatorics.dependent-pair-types funext univalence truncations +open import univalent-combinatorics.equality-finite-types funext univalence truncations +open import univalent-combinatorics.finite-types funext univalence truncations +open import univalent-combinatorics.function-types funext univalence truncations +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/univalent-combinatorics/partitions.lagda.md b/src/univalent-combinatorics/partitions.lagda.md index 1d697a9f42..33f6d480c6 100644 --- a/src/univalent-combinatorics/partitions.lagda.md +++ b/src/univalent-combinatorics/partitions.lagda.md @@ -1,7 +1,15 @@ # Partitions of finite types ```agda -module univalent-combinatorics.partitions where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module univalent-combinatorics.partitions + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,25 +17,26 @@ module univalent-combinatorics.partitions where ```agda open import elementary-number-theory.natural-numbers -open import foundation.binary-relations -open import foundation.cartesian-product-types +open import foundation.binary-relations funext univalence truncations +open import foundation.cartesian-product-types funext univalence +open import foundation.dependent-products-propositions funext open import foundation.equality-cartesian-product-types -open import foundation.equivalence-extensionality -open import foundation.equivalence-relations -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.sets +open import foundation.equivalence-extensionality funext +open import foundation.equivalence-relations funext univalence truncations +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence +open import foundation.sets funext univalence open import foundation.structure-identity-principle open import foundation.type-arithmetic-cartesian-product-types open import foundation.universe-levels -open import univalent-combinatorics.dependent-pair-types -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.dependent-pair-types funext univalence truncations +open import univalent-combinatorics.finite-types funext univalence truncations ```
diff --git a/src/univalent-combinatorics/petri-nets.lagda.md b/src/univalent-combinatorics/petri-nets.lagda.md index 0c3f656649..57464504e3 100644 --- a/src/univalent-combinatorics/petri-nets.lagda.md +++ b/src/univalent-combinatorics/petri-nets.lagda.md @@ -1,17 +1,25 @@ # Petri-nets ```agda -module univalent-combinatorics.petri-nets where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module univalent-combinatorics.petri-nets + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types open import foundation.universe-levels -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.finite-types funext univalence truncations ```
diff --git a/src/univalent-combinatorics/pi-finite-types.lagda.md b/src/univalent-combinatorics/pi-finite-types.lagda.md index 5632fede24..048eefc565 100644 --- a/src/univalent-combinatorics/pi-finite-types.lagda.md +++ b/src/univalent-combinatorics/pi-finite-types.lagda.md @@ -1,7 +1,15 @@ # π-finite types ```agda -module univalent-combinatorics.pi-finite-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module univalent-combinatorics.pi-finite-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,16 +18,18 @@ module univalent-combinatorics.pi-finite-types where open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.set-truncations -open import foundation.truncated-types +open import foundation.dependent-products-propositions funext +open import foundation.dependent-products-truncated-types funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.set-truncations funext univalence +open import foundation.truncated-types funext univalence open import foundation.truncation-levels open import foundation.universe-levels -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.finitely-many-connected-components -open import univalent-combinatorics.untruncated-pi-finite-types +open import univalent-combinatorics.finite-types funext univalence truncations +open import univalent-combinatorics.finitely-many-connected-components funext univalence truncations +open import univalent-combinatorics.untruncated-pi-finite-types funext univalence truncations ```
diff --git a/src/univalent-combinatorics/pigeonhole-principle.lagda.md b/src/univalent-combinatorics/pigeonhole-principle.lagda.md index 8c52386070..1401369bd4 100644 --- a/src/univalent-combinatorics/pigeonhole-principle.lagda.md +++ b/src/univalent-combinatorics/pigeonhole-principle.lagda.md @@ -1,39 +1,48 @@ # The pigeonhole principle ```agda -module univalent-combinatorics.pigeonhole-principle where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module univalent-combinatorics.pigeonhole-principle + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.inequality-natural-numbers funext univalence truncations open import elementary-number-theory.natural-numbers -open import elementary-number-theory.strict-inequality-natural-numbers +open import elementary-number-theory.strict-inequality-natural-numbers funext univalence truncations -open import foundation.coproduct-types +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.empty-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.negated-equality -open import foundation.negation -open import foundation.pairs-of-distinct-elements -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.sets +open import foundation.dependent-products-propositions funext +open import foundation.embeddings funext +open import foundation.empty-types funext univalence truncations +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.negated-equality funext univalence truncations +open import foundation.negation funext +open import foundation.pairs-of-distinct-elements funext univalence truncations +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence +open import foundation.sets funext univalence open import foundation.unit-type open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import univalent-combinatorics.counting -open import univalent-combinatorics.embeddings-standard-finite-types -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.repetitions-of-values -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.counting funext univalence truncations +open import univalent-combinatorics.embeddings-standard-finite-types funext univalence truncations +open import univalent-combinatorics.finite-types funext univalence truncations +open import univalent-combinatorics.repetitions-of-values funext univalence truncations +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/univalent-combinatorics/quotients-finite-types.lagda.md b/src/univalent-combinatorics/quotients-finite-types.lagda.md index 0566bd152d..3d691254a5 100644 --- a/src/univalent-combinatorics/quotients-finite-types.lagda.md +++ b/src/univalent-combinatorics/quotients-finite-types.lagda.md @@ -1,7 +1,15 @@ # Quotients of finite types ```agda -module univalent-combinatorics.quotients-finite-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module univalent-combinatorics.quotients-finite-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,10 +18,10 @@ module univalent-combinatorics.quotients-finite-types where open import foundation.dependent-pair-types open import foundation.universe-levels -open import univalent-combinatorics.decidable-equivalence-relations -open import univalent-combinatorics.decidable-subtypes -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.image-of-maps +open import univalent-combinatorics.decidable-equivalence-relations funext univalence truncations +open import univalent-combinatorics.decidable-subtypes funext univalence truncations +open import univalent-combinatorics.finite-types funext univalence truncations +open import univalent-combinatorics.image-of-maps funext univalence truncations ```
diff --git a/src/univalent-combinatorics/ramsey-theory.lagda.md b/src/univalent-combinatorics/ramsey-theory.lagda.md index c5e0cc22ff..6c559993f9 100644 --- a/src/univalent-combinatorics/ramsey-theory.lagda.md +++ b/src/univalent-combinatorics/ramsey-theory.lagda.md @@ -1,7 +1,15 @@ # Ramsey theory ```agda -module univalent-combinatorics.ramsey-theory where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module univalent-combinatorics.ramsey-theory + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,14 +18,15 @@ module univalent-combinatorics.ramsey-theory where open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.identity-types -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence open import foundation.unit-type open import foundation.universe-levels -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.finite-types funext univalence truncations +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/univalent-combinatorics/repetitions-of-values.lagda.md b/src/univalent-combinatorics/repetitions-of-values.lagda.md index f051b846bd..e0863c214d 100644 --- a/src/univalent-combinatorics/repetitions-of-values.lagda.md +++ b/src/univalent-combinatorics/repetitions-of-values.lagda.md @@ -1,30 +1,37 @@ # Repetitions of values ```agda -module univalent-combinatorics.repetitions-of-values where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module univalent-combinatorics.repetitions-of-values + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where -open import foundation.repetitions-of-values public +open import foundation.repetitions-of-values funext univalence truncations public ```
Imports ```agda open import elementary-number-theory.natural-numbers -open import elementary-number-theory.well-ordering-principle-standard-finite-types - -open import foundation.cartesian-product-types -open import foundation.decidable-types -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.negated-equality -open import foundation.negation -open import foundation.sets - -open import univalent-combinatorics.decidable-dependent-function-types -open import univalent-combinatorics.decidable-propositions -open import univalent-combinatorics.dependent-pair-types -open import univalent-combinatorics.equality-standard-finite-types -open import univalent-combinatorics.standard-finite-types +open import elementary-number-theory.well-ordering-principle-standard-finite-types funext univalence truncations + +open import foundation.cartesian-product-types funext univalence +open import foundation.decidable-types funext univalence truncations +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.negated-equality funext univalence truncations +open import foundation.negation funext + +open import univalent-combinatorics.decidable-dependent-function-types funext univalence truncations +open import univalent-combinatorics.decidable-propositions funext univalence truncations +open import univalent-combinatorics.dependent-pair-types funext univalence truncations +open import univalent-combinatorics.equality-standard-finite-types funext univalence truncations +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/univalent-combinatorics/retracts-of-finite-types.lagda.md b/src/univalent-combinatorics/retracts-of-finite-types.lagda.md index d7b3d888e4..6043bb4720 100644 --- a/src/univalent-combinatorics/retracts-of-finite-types.lagda.md +++ b/src/univalent-combinatorics/retracts-of-finite-types.lagda.md @@ -1,7 +1,15 @@ # Retracts of finite types ```agda -module univalent-combinatorics.retracts-of-finite-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module univalent-combinatorics.retracts-of-finite-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,23 +17,23 @@ module univalent-combinatorics.retracts-of-finite-types where ```agda open import elementary-number-theory.natural-numbers -open import foundation.decidable-embeddings -open import foundation.decidable-maps +open import foundation.decidable-embeddings funext univalence truncations +open import foundation.decidable-maps funext univalence truncations open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.fibers-of-maps -open import foundation.functoriality-propositional-truncation -open import foundation.injective-maps -open import foundation.retractions -open import foundation.retracts-of-types +open import foundation.embeddings funext +open import foundation.fibers-of-maps funext +open import foundation.functoriality-propositional-truncation funext univalence truncations +open import foundation.injective-maps funext +open import foundation.retractions funext +open import foundation.retracts-of-types funext univalence open import foundation.universe-levels -open import univalent-combinatorics.counting -open import univalent-combinatorics.counting-decidable-subtypes -open import univalent-combinatorics.equality-finite-types -open import univalent-combinatorics.equality-standard-finite-types -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.counting funext univalence truncations +open import univalent-combinatorics.counting-decidable-subtypes funext univalence truncations +open import univalent-combinatorics.equality-finite-types funext univalence truncations +open import univalent-combinatorics.equality-standard-finite-types funext univalence truncations +open import univalent-combinatorics.finite-types funext univalence truncations +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/univalent-combinatorics/riffle-shuffles.lagda.md b/src/univalent-combinatorics/riffle-shuffles.lagda.md index f4c76c4499..608d4630dd 100644 --- a/src/univalent-combinatorics/riffle-shuffles.lagda.md +++ b/src/univalent-combinatorics/riffle-shuffles.lagda.md @@ -1,30 +1,38 @@ # Riffle shuffles ```agda -module univalent-combinatorics.riffle-shuffles where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module univalent-combinatorics.riffle-shuffles + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.inequality-standard-finite-types +open import elementary-number-theory.inequality-standard-finite-types funext univalence truncations open import elementary-number-theory.natural-numbers -open import foundation.automorphisms -open import foundation.conjunction +open import foundation.automorphisms funext univalence +open import foundation.conjunction funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types +open import foundation.equivalences funext +open import foundation.function-types funext open import foundation.universe-levels open import foundation-core.coproduct-types open import foundation-core.propositions -open import order-theory.order-preserving-maps-posets -open import order-theory.posets +open import order-theory.order-preserving-maps-posets funext univalence truncations +open import order-theory.posets funext univalence truncations -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/univalent-combinatorics/sequences-finite-types.lagda.md b/src/univalent-combinatorics/sequences-finite-types.lagda.md index e9cd8106af..d7abfa276d 100644 --- a/src/univalent-combinatorics/sequences-finite-types.lagda.md +++ b/src/univalent-combinatorics/sequences-finite-types.lagda.md @@ -1,36 +1,44 @@ # Sequences of elements in finite types ```agda -module univalent-combinatorics.sequences-finite-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module univalent-combinatorics.sequences-finite-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.decidable-types +open import elementary-number-theory.decidable-types funext univalence truncations open import elementary-number-theory.natural-numbers -open import elementary-number-theory.strict-inequality-natural-numbers -open import elementary-number-theory.well-ordering-principle-natural-numbers +open import elementary-number-theory.strict-inequality-natural-numbers funext univalence truncations +open import elementary-number-theory.well-ordering-principle-natural-numbers funext univalence truncations open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.negated-equality -open import foundation.pairs-of-distinct-elements -open import foundation.repetitions-of-values -open import foundation.repetitions-sequences +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.negated-equality funext univalence truncations +open import foundation.pairs-of-distinct-elements funext univalence truncations +open import foundation.repetitions-of-values funext univalence truncations +open import foundation.repetitions-sequences funext univalence truncations open import foundation.sequences -open import foundation.sets +open import foundation.sets funext univalence open import foundation.universe-levels -open import univalent-combinatorics.counting -open import univalent-combinatorics.equality-standard-finite-types -open import univalent-combinatorics.pigeonhole-principle -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.counting funext univalence truncations +open import univalent-combinatorics.equality-standard-finite-types funext univalence truncations +open import univalent-combinatorics.pigeonhole-principle funext univalence truncations +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/univalent-combinatorics/set-quotients-of-index-two.lagda.md b/src/univalent-combinatorics/set-quotients-of-index-two.lagda.md index afd05cac1d..eafa3d357b 100644 --- a/src/univalent-combinatorics/set-quotients-of-index-two.lagda.md +++ b/src/univalent-combinatorics/set-quotients-of-index-two.lagda.md @@ -2,33 +2,41 @@ ```agda {-# OPTIONS --lossy-unification #-} +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom -module univalent-combinatorics.set-quotients-of-index-two where +module univalent-combinatorics.set-quotients-of-index-two + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-maps -open import foundation.contractible-types -open import foundation.coproduct-types +open import foundation.commuting-squares-of-maps funext univalence +open import foundation.contractible-types funext univalence +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.empty-types -open import foundation.equivalence-relations -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-set-quotients -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.logical-equivalences -open import foundation.reflecting-maps-equivalence-relations -open import foundation.sets -open import foundation.universal-property-set-quotients +open import foundation.dependent-products-contractible-types funext +open import foundation.embeddings funext +open import foundation.empty-types funext univalence truncations +open import foundation.equivalence-relations funext univalence truncations +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-set-quotients funext univalence truncations +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.logical-equivalences funext +open import foundation.reflecting-maps-equivalence-relations funext univalence truncations +open import foundation.sets funext univalence +open import foundation.universal-property-set-quotients funext univalence truncations open import foundation.universe-levels -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/univalent-combinatorics/sigma-decompositions.lagda.md b/src/univalent-combinatorics/sigma-decompositions.lagda.md index 1a8c3c1436..2073c06c1b 100644 --- a/src/univalent-combinatorics/sigma-decompositions.lagda.md +++ b/src/univalent-combinatorics/sigma-decompositions.lagda.md @@ -1,38 +1,46 @@ # Finite Σ-decompositions of finite types ```agda -module univalent-combinatorics.sigma-decompositions where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module univalent-combinatorics.sigma-decompositions + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where -open import foundation.sigma-decompositions public +open import foundation.sigma-decompositions funext univalence truncations public ```
Imports ```agda -open import foundation.cartesian-product-types -open import foundation.dependent-universal-property-equivalences -open import foundation.embeddings -open import foundation.equivalences -open import foundation.functoriality-dependent-function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.inhabited-types -open import foundation.logical-equivalences -open import foundation.precomposition-functions -open import foundation.propositions -open import foundation.relaxed-sigma-decompositions -open import foundation.subtypes -open import foundation.surjective-maps +open import foundation.cartesian-product-types funext univalence +open import foundation.dependent-products-propositions funext +open import foundation.dependent-universal-property-equivalences funext +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.functoriality-dependent-function-types funext univalence +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.inhabited-types funext univalence truncations +open import foundation.logical-equivalences funext +open import foundation.propositions funext univalence +open import foundation.relaxed-sigma-decompositions funext univalence +open import foundation.subtypes funext univalence truncations +open import foundation.surjective-maps funext univalence truncations open import foundation.type-arithmetic-dependent-pair-types -open import foundation.type-theoretic-principle-of-choice +open import foundation.type-theoretic-principle-of-choice funext open import foundation.universe-levels -open import univalent-combinatorics.decidable-equivalence-relations -open import univalent-combinatorics.dependent-pair-types -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.inhabited-finite-types -open import univalent-combinatorics.type-duality +open import univalent-combinatorics.decidable-equivalence-relations funext univalence truncations +open import univalent-combinatorics.dependent-pair-types funext univalence truncations +open import univalent-combinatorics.finite-types funext univalence truncations +open import univalent-combinatorics.inhabited-finite-types funext univalence truncations +open import univalent-combinatorics.type-duality funext univalence truncations ```
diff --git a/src/univalent-combinatorics/skipping-element-standard-finite-types.lagda.md b/src/univalent-combinatorics/skipping-element-standard-finite-types.lagda.md index 9cadf867c1..27c68310d8 100644 --- a/src/univalent-combinatorics/skipping-element-standard-finite-types.lagda.md +++ b/src/univalent-combinatorics/skipping-element-standard-finite-types.lagda.md @@ -1,7 +1,15 @@ # Skipping elements in standard finite types ```agda -module univalent-combinatorics.skipping-element-standard-finite-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module univalent-combinatorics.skipping-element-standard-finite-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,16 +18,16 @@ module univalent-combinatorics.skipping-element-standard-finite-types where open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.coproduct-types +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equality-coproduct-types -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.sets +open import foundation.embeddings funext +open import foundation.equality-coproduct-types funext univalence truncations +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.sets funext univalence open import foundation.unit-type -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/univalent-combinatorics/small-types.lagda.md b/src/univalent-combinatorics/small-types.lagda.md index 3a8347ad4a..8f099287e9 100644 --- a/src/univalent-combinatorics/small-types.lagda.md +++ b/src/univalent-combinatorics/small-types.lagda.md @@ -1,9 +1,17 @@ # Small types ```agda -module univalent-combinatorics.small-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom -open import foundation.small-types public +module univalent-combinatorics.small-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where + +open import foundation.small-types funext univalence truncations public ```
Imports @@ -12,11 +20,11 @@ open import foundation.small-types public open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.propositional-truncations +open import foundation.propositional-truncations funext univalence open import foundation.universe-levels -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.finite-types funext univalence truncations +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/univalent-combinatorics/standard-finite-pruned-trees.lagda.md b/src/univalent-combinatorics/standard-finite-pruned-trees.lagda.md index b310a181ee..299e8a141a 100644 --- a/src/univalent-combinatorics/standard-finite-pruned-trees.lagda.md +++ b/src/univalent-combinatorics/standard-finite-pruned-trees.lagda.md @@ -1,7 +1,15 @@ # Standard finite pruned trees ```agda -module univalent-combinatorics.standard-finite-pruned-trees where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module univalent-combinatorics.standard-finite-pruned-trees + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -11,7 +19,7 @@ open import elementary-number-theory.natural-numbers open import foundation.universe-levels -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/univalent-combinatorics/standard-finite-trees.lagda.md b/src/univalent-combinatorics/standard-finite-trees.lagda.md index 9ef39e079f..7618b4c5a2 100644 --- a/src/univalent-combinatorics/standard-finite-trees.lagda.md +++ b/src/univalent-combinatorics/standard-finite-trees.lagda.md @@ -1,23 +1,31 @@ # Standard finite trees ```agda -module univalent-combinatorics.standard-finite-trees where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module univalent-combinatorics.standard-finite-trees + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.maximum-natural-numbers +open import elementary-number-theory.maximum-natural-numbers funext univalence truncations open import elementary-number-theory.natural-numbers -open import elementary-number-theory.sums-of-natural-numbers +open import elementary-number-theory.sums-of-natural-numbers funext univalence truncations -open import foundation.cartesian-product-types -open import foundation.empty-types -open import foundation.identity-types +open import foundation.cartesian-product-types funext univalence +open import foundation.empty-types funext univalence truncations +open import foundation.identity-types funext open import foundation.unit-type open import foundation.universe-levels -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/univalent-combinatorics/standard-finite-types.lagda.md b/src/univalent-combinatorics/standard-finite-types.lagda.md index 31d90d106c..4293e14d94 100644 --- a/src/univalent-combinatorics/standard-finite-types.lagda.md +++ b/src/univalent-combinatorics/standard-finite-types.lagda.md @@ -1,45 +1,55 @@ # The standard finite types ```agda -module univalent-combinatorics.standard-finite-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module univalent-combinatorics.standard-finite-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.equality-natural-numbers -open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.equality-natural-numbers funext univalence truncations +open import elementary-number-theory.inequality-natural-numbers funext univalence truncations open import elementary-number-theory.natural-numbers -open import elementary-number-theory.strict-inequality-natural-numbers +open import elementary-number-theory.strict-inequality-natural-numbers funext univalence truncations -open import foundation.action-on-higher-identifications-functions +open import foundation.action-on-higher-identifications-functions funext open import foundation.action-on-identifications-functions -open import foundation.contractible-types -open import foundation.coproduct-types -open import foundation.decidable-types +open import foundation.contractible-types funext univalence +open import foundation.coproduct-types funext univalence truncations +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.empty-types -open import foundation.equality-coproduct-types -open import foundation.equivalence-injective-type-families -open import foundation.equivalences -open import foundation.equivalences-maybe -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.negated-equality -open import foundation.negation -open import foundation.noncontractible-types -open import foundation.preunivalent-type-families -open import foundation.raising-universe-levels -open import foundation.retractions -open import foundation.sets +open import foundation.dependent-products-contractible-types funext +open import foundation.embeddings funext +open import foundation.empty-types funext univalence truncations +open import foundation.equality-coproduct-types funext univalence truncations +open import foundation.equivalence-injective-type-families funext univalence +open import foundation.equivalences funext +open import foundation.equivalences-maybe funext univalence truncations +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.negated-equality funext univalence truncations +open import foundation.negation funext +open import foundation.noncontractible-types funext univalence truncations +open import foundation.preunivalent-type-families funext univalence +open import foundation.retractions funext +open import foundation.sets funext univalence open import foundation.transport-along-identifications open import foundation.unit-type open import foundation.universe-levels -open import structured-types.types-equipped-with-endomorphisms +open import foundation-core.raising-universe-levels + +open import structured-types.types-equipped-with-endomorphisms funext univalence ```
diff --git a/src/univalent-combinatorics/steiner-systems.lagda.md b/src/univalent-combinatorics/steiner-systems.lagda.md index 5c3a9d87d2..9afbd720ac 100644 --- a/src/univalent-combinatorics/steiner-systems.lagda.md +++ b/src/univalent-combinatorics/steiner-systems.lagda.md @@ -1,7 +1,15 @@ # Steiner systems ```agda -module univalent-combinatorics.steiner-systems where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module univalent-combinatorics.steiner-systems + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,12 +17,13 @@ module univalent-combinatorics.steiner-systems where ```agda open import elementary-number-theory.natural-numbers -open import foundation.contractible-types -open import foundation.decidable-subtypes +open import foundation.contractible-types funext univalence +open import foundation.decidable-subtypes funext univalence truncations open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types funext open import foundation.universe-levels -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.finite-types funext univalence truncations ```
diff --git a/src/univalent-combinatorics/steiner-triple-systems.lagda.md b/src/univalent-combinatorics/steiner-triple-systems.lagda.md index 2ac3dd0658..6056f33480 100644 --- a/src/univalent-combinatorics/steiner-triple-systems.lagda.md +++ b/src/univalent-combinatorics/steiner-triple-systems.lagda.md @@ -1,7 +1,15 @@ # Steiner triple systems ```agda -module univalent-combinatorics.steiner-triple-systems where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module univalent-combinatorics.steiner-triple-systems + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -11,7 +19,7 @@ open import elementary-number-theory.natural-numbers open import foundation.universe-levels -open import univalent-combinatorics.steiner-systems +open import univalent-combinatorics.steiner-systems funext univalence truncations ```
diff --git a/src/univalent-combinatorics/sums-of-natural-numbers.lagda.md b/src/univalent-combinatorics/sums-of-natural-numbers.lagda.md index 6fff4532d6..464bc2a655 100644 --- a/src/univalent-combinatorics/sums-of-natural-numbers.lagda.md +++ b/src/univalent-combinatorics/sums-of-natural-numbers.lagda.md @@ -1,9 +1,17 @@ # Combinatorial identities of sums of natural numbers ```agda -module univalent-combinatorics.sums-of-natural-numbers where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom -open import elementary-number-theory.sums-of-natural-numbers public +module univalent-combinatorics.sums-of-natural-numbers + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where + +open import elementary-number-theory.sums-of-natural-numbers funext univalence truncations public ```
Imports @@ -12,14 +20,14 @@ open import elementary-number-theory.sums-of-natural-numbers public open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels -open import univalent-combinatorics.counting -open import univalent-combinatorics.counting-dependent-pair-types -open import univalent-combinatorics.double-counting -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.counting funext univalence truncations +open import univalent-combinatorics.counting-dependent-pair-types funext univalence truncations +open import univalent-combinatorics.double-counting funext univalence truncations +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/univalent-combinatorics/surjective-maps.lagda.md b/src/univalent-combinatorics/surjective-maps.lagda.md index 2ebd5851c5..ff41bfae6c 100644 --- a/src/univalent-combinatorics/surjective-maps.lagda.md +++ b/src/univalent-combinatorics/surjective-maps.lagda.md @@ -1,9 +1,17 @@ # Surjective maps between finite types ```agda -module univalent-combinatorics.surjective-maps where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module univalent-combinatorics.surjective-maps + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where -open import foundation.surjective-maps public +open import foundation.surjective-maps funext univalence truncations public ```
Imports @@ -11,26 +19,27 @@ open import foundation.surjective-maps public ```agda open import elementary-number-theory.natural-numbers -open import foundation.cartesian-product-types -open import foundation.decidable-embeddings -open import foundation.decidable-equality -open import foundation.decidable-types +open import foundation.cartesian-product-types funext univalence +open import foundation.decidable-embeddings funext univalence truncations +open import foundation.decidable-equality funext univalence truncations +open import foundation.decidable-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.logical-equivalences -open import foundation.propositional-truncations -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.logical-equivalences funext +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels -open import univalent-combinatorics.counting -open import univalent-combinatorics.counting-decidable-subtypes -open import univalent-combinatorics.counting-dependent-pair-types -open import univalent-combinatorics.decidable-dependent-function-types -open import univalent-combinatorics.embeddings -open import univalent-combinatorics.fibers-of-maps -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.counting funext univalence truncations +open import univalent-combinatorics.counting-decidable-subtypes funext univalence truncations +open import univalent-combinatorics.counting-dependent-pair-types funext univalence truncations +open import univalent-combinatorics.decidable-dependent-function-types funext univalence truncations +open import univalent-combinatorics.embeddings funext univalence truncations +open import univalent-combinatorics.fibers-of-maps funext univalence truncations +open import univalent-combinatorics.finite-types funext univalence truncations +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/univalent-combinatorics/symmetric-difference.lagda.md b/src/univalent-combinatorics/symmetric-difference.lagda.md index 1a75f29a9a..739b629ed5 100644 --- a/src/univalent-combinatorics/symmetric-difference.lagda.md +++ b/src/univalent-combinatorics/symmetric-difference.lagda.md @@ -1,9 +1,17 @@ # Symmetric difference of finite subtypes ```agda -module univalent-combinatorics.symmetric-difference where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom -open import foundation.symmetric-difference public +module univalent-combinatorics.symmetric-difference + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where + +open import foundation.symmetric-difference funext univalence truncations public ```
Imports @@ -14,18 +22,18 @@ open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.coproduct-types +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.identity-types -open import foundation.intersections-subtypes -open import foundation.mere-equivalences -open import foundation.propositional-truncations +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.intersections-subtypes funext univalence truncations +open import foundation.mere-equivalences funext univalence truncations +open import foundation.propositional-truncations funext univalence open import foundation.universe-levels -open import univalent-combinatorics.coproduct-types -open import univalent-combinatorics.decidable-subtypes -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.coproduct-types funext univalence truncations +open import univalent-combinatorics.decidable-subtypes funext univalence truncations +open import univalent-combinatorics.finite-types funext univalence truncations ```
diff --git a/src/univalent-combinatorics/trivial-sigma-decompositions.lagda.md b/src/univalent-combinatorics/trivial-sigma-decompositions.lagda.md index 4bace31233..30b75e8a73 100644 --- a/src/univalent-combinatorics/trivial-sigma-decompositions.lagda.md +++ b/src/univalent-combinatorics/trivial-sigma-decompositions.lagda.md @@ -1,24 +1,35 @@ # Finite trivial Σ-decompositions ```agda -module univalent-combinatorics.trivial-sigma-decompositions where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module univalent-combinatorics.trivial-sigma-decompositions + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where -open import foundation.trivial-sigma-decompositions public +open import foundation.trivial-sigma-decompositions funext univalence truncations public ```
Imports ```agda -open import foundation.contractible-types +open import foundation.contractible-types funext univalence open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.inhabited-types -open import foundation.propositions -open import foundation.subtypes +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.identity-types funext +open import foundation.inhabited-types funext univalence truncations +open import foundation.propositions funext univalence +open import foundation.raising-universe-levels-unit-type +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.sigma-decompositions +open import univalent-combinatorics.finite-types funext univalence truncations +open import univalent-combinatorics.sigma-decompositions funext univalence truncations ```
diff --git a/src/univalent-combinatorics/type-duality.lagda.md b/src/univalent-combinatorics/type-duality.lagda.md index bdfc816854..7767085b87 100644 --- a/src/univalent-combinatorics/type-duality.lagda.md +++ b/src/univalent-combinatorics/type-duality.lagda.md @@ -1,35 +1,43 @@ # Type duality of finite types ```agda -module univalent-combinatorics.type-duality where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom -open import foundation.type-duality public +module univalent-combinatorics.type-duality + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where + +open import foundation.type-duality funext univalence truncations public ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.full-subtypes -open import foundation.functoriality-dependent-function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.functoriality-function-types -open import foundation.inhabited-types -open import foundation.postcomposition-functions -open import foundation.propositions -open import foundation.structure -open import foundation.structured-type-duality -open import foundation.surjective-maps +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.full-subtypes funext univalence truncations +open import foundation.functoriality-dependent-function-types funext univalence +open import foundation.functoriality-dependent-pair-types funext +open import foundation.inhabited-types funext univalence truncations +open import foundation.postcomposition-functions funext +open import foundation.propositions funext univalence +open import foundation.structure funext univalence +open import foundation.structured-type-duality funext univalence truncations +open import foundation.surjective-maps funext univalence truncations open import foundation.type-arithmetic-cartesian-product-types open import foundation.type-arithmetic-dependent-pair-types -open import foundation.type-theoretic-principle-of-choice +open import foundation.type-theoretic-principle-of-choice funext open import foundation.universe-levels -open import univalent-combinatorics.fibers-of-maps -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.inhabited-finite-types +open import univalent-combinatorics.fibers-of-maps funext univalence truncations +open import univalent-combinatorics.finite-types funext univalence truncations +open import univalent-combinatorics.inhabited-finite-types funext univalence truncations ```
diff --git a/src/univalent-combinatorics/unbounded-pi-finite-types.lagda.md b/src/univalent-combinatorics/unbounded-pi-finite-types.lagda.md index f4335a963a..aeb87a9f11 100644 --- a/src/univalent-combinatorics/unbounded-pi-finite-types.lagda.md +++ b/src/univalent-combinatorics/unbounded-pi-finite-types.lagda.md @@ -2,8 +2,15 @@ ```agda {-# OPTIONS --guardedness #-} - -module univalent-combinatorics.unbounded-pi-finite-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module univalent-combinatorics.unbounded-pi-finite-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -11,30 +18,31 @@ module univalent-combinatorics.unbounded-pi-finite-types where ```agda open import elementary-number-theory.natural-numbers -open import foundation.cartesian-product-types -open import foundation.contractible-types -open import foundation.coproduct-types +open import foundation.cartesian-product-types funext univalence +open import foundation.contractible-types funext univalence +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.equality-coproduct-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.identity-types -open import foundation.maybe -open import foundation.retracts-of-types -open import foundation.set-truncations -open import foundation.sets +open import foundation.dependent-products-contractible-types funext +open import foundation.empty-types funext univalence truncations +open import foundation.equality-coproduct-types funext univalence truncations +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.maybe funext univalence truncations +open import foundation.retracts-of-types funext univalence +open import foundation.set-truncations funext univalence +open import foundation.sets funext univalence open import foundation.unit-type open import foundation.universe-levels -open import univalent-combinatorics.counting -open import univalent-combinatorics.equality-finite-types -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.finitely-many-connected-components -open import univalent-combinatorics.function-types -open import univalent-combinatorics.pi-finite-types -open import univalent-combinatorics.standard-finite-types -open import univalent-combinatorics.untruncated-pi-finite-types +open import univalent-combinatorics.counting funext univalence truncations +open import univalent-combinatorics.equality-finite-types funext univalence truncations +open import univalent-combinatorics.finite-types funext univalence truncations +open import univalent-combinatorics.finitely-many-connected-components funext univalence truncations +open import univalent-combinatorics.function-types funext univalence truncations +open import univalent-combinatorics.pi-finite-types funext univalence truncations +open import univalent-combinatorics.standard-finite-types funext univalence truncations +open import univalent-combinatorics.untruncated-pi-finite-types funext univalence truncations ```
diff --git a/src/univalent-combinatorics/unions-subtypes.lagda.md b/src/univalent-combinatorics/unions-subtypes.lagda.md index 9649925534..7df5b3887c 100644 --- a/src/univalent-combinatorics/unions-subtypes.lagda.md +++ b/src/univalent-combinatorics/unions-subtypes.lagda.md @@ -1,25 +1,33 @@ # Unions of finite subtypes ```agda -module univalent-combinatorics.unions-subtypes where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom -open import foundation.unions-subtypes public +module univalent-combinatorics.unions-subtypes + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where + +open import foundation.unions-subtypes funext univalence truncations public ```
Imports ```agda -open import foundation.decidable-equality -open import foundation.propositional-truncations -open import foundation.subtypes +open import foundation.decidable-equality funext univalence truncations +open import foundation.propositional-truncations funext univalence +open import foundation.subtypes funext univalence truncations open import foundation.universe-levels -open import univalent-combinatorics.coproduct-types -open import univalent-combinatorics.counting -open import univalent-combinatorics.counting-decidable-subtypes -open import univalent-combinatorics.counting-dependent-pair-types -open import univalent-combinatorics.embeddings -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.coproduct-types funext univalence truncations +open import univalent-combinatorics.counting funext univalence truncations +open import univalent-combinatorics.counting-decidable-subtypes funext univalence truncations +open import univalent-combinatorics.counting-dependent-pair-types funext univalence truncations +open import univalent-combinatorics.embeddings funext univalence truncations +open import univalent-combinatorics.finite-types funext univalence truncations ```
diff --git a/src/univalent-combinatorics/universal-property-standard-finite-types.lagda.md b/src/univalent-combinatorics/universal-property-standard-finite-types.lagda.md index 087aa5e436..07f282c303 100644 --- a/src/univalent-combinatorics/universal-property-standard-finite-types.lagda.md +++ b/src/univalent-combinatorics/universal-property-standard-finite-types.lagda.md @@ -1,7 +1,15 @@ # The universal property of the standard finite types ```agda -module univalent-combinatorics.universal-property-standard-finite-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module univalent-combinatorics.universal-property-standard-finite-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,23 +17,25 @@ module univalent-combinatorics.universal-property-standard-finite-types where ```agda open import elementary-number-theory.natural-numbers -open import foundation.cartesian-product-types -open import foundation.contractible-types -open import foundation.coproduct-types +open import foundation.cartesian-product-types funext univalence +open import foundation.contractible-types funext univalence +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.functoriality-cartesian-product-types -open import foundation.homotopies -open import foundation.identity-types +open import foundation.dependent-products-contractible-types funext +open import foundation.equivalences funext +open import foundation.function-extensionality funext +open import foundation.function-types funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.raising-universe-levels-unit-type open import foundation.unit-type -open import foundation.universal-property-contractible-types -open import foundation.universal-property-empty-type -open import foundation.universal-property-maybe +open import foundation.universal-property-contractible-types funext +open import foundation.universal-property-empty-type funext +open import foundation.universal-property-maybe funext open import foundation.universe-levels -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/univalent-combinatorics/untruncated-pi-finite-types.lagda.md b/src/univalent-combinatorics/untruncated-pi-finite-types.lagda.md index 63f9ba773a..c4e6a70b49 100644 --- a/src/univalent-combinatorics/untruncated-pi-finite-types.lagda.md +++ b/src/univalent-combinatorics/untruncated-pi-finite-types.lagda.md @@ -1,7 +1,15 @@ # Untruncated π-finite types ```agda -module univalent-combinatorics.untruncated-pi-finite-types where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module univalent-combinatorics.untruncated-pi-finite-types + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,54 +17,56 @@ module univalent-combinatorics.untruncated-pi-finite-types where ```agda open import elementary-number-theory.natural-numbers -open import foundation.0-connected-types +open import foundation.0-connected-types funext univalence truncations open import foundation.action-on-identifications-functions -open import foundation.contractible-types -open import foundation.coproduct-types -open import foundation.decidable-propositions -open import foundation.decidable-types -open import foundation.dependent-identifications -open import foundation.embeddings -open import foundation.empty-types -open import foundation.equality-coproduct-types -open import foundation.equality-dependent-pair-types -open import foundation.equivalences -open import foundation.fiber-inclusions -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.functoriality-set-truncation -open import foundation.homotopies -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.maybe -open import foundation.mere-equality -open import foundation.propositional-extensionality -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.retracts-of-types -open import foundation.set-presented-types -open import foundation.set-truncations -open import foundation.sets -open import foundation.subtypes -open import foundation.surjective-maps +open import foundation.contractible-types funext univalence +open import foundation.coproduct-types funext univalence truncations +open import foundation.decidable-propositions funext univalence truncations +open import foundation.decidable-types funext univalence truncations +open import foundation.dependent-identifications funext +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.embeddings funext +open import foundation.empty-types funext univalence truncations +open import foundation.equality-coproduct-types funext univalence truncations +open import foundation.equality-dependent-pair-types funext +open import foundation.equivalences funext +open import foundation.fiber-inclusions funext univalence +open import foundation.function-extensionality funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.functoriality-set-truncation funext univalence truncations +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.maybe funext univalence truncations +open import foundation.mere-equality funext univalence truncations +open import foundation.propositional-extensionality funext univalence truncations +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence +open import foundation.retracts-of-types funext univalence +open import foundation.set-presented-types funext univalence truncations +open import foundation.set-truncations funext univalence +open import foundation.sets funext univalence +open import foundation.subtypes funext univalence truncations +open import foundation.surjective-maps funext univalence truncations open import foundation.transport-along-identifications -open import foundation.type-arithmetic-coproduct-types +open import foundation.type-arithmetic-coproduct-types funext univalence truncations open import foundation.unit-type -open import foundation.univalence +open import foundation.univalence funext univalence open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import univalent-combinatorics.coproduct-types -open import univalent-combinatorics.counting -open import univalent-combinatorics.dependent-pair-types -open import univalent-combinatorics.equality-finite-types -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.finitely-many-connected-components -open import univalent-combinatorics.finitely-presented-types -open import univalent-combinatorics.function-types -open import univalent-combinatorics.image-of-maps -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.coproduct-types funext univalence truncations +open import univalent-combinatorics.counting funext univalence truncations +open import univalent-combinatorics.dependent-pair-types funext univalence truncations +open import univalent-combinatorics.equality-finite-types funext univalence truncations +open import univalent-combinatorics.finite-types funext univalence truncations +open import univalent-combinatorics.finitely-many-connected-components funext univalence truncations +open import univalent-combinatorics.finitely-presented-types funext univalence truncations +open import univalent-combinatorics.function-types funext univalence truncations +open import univalent-combinatorics.image-of-maps funext univalence truncations +open import univalent-combinatorics.standard-finite-types funext univalence truncations ```
diff --git a/src/universal-algebra.lagda.md b/src/universal-algebra.lagda.md index 183927520e..4a04cfadb9 100644 --- a/src/universal-algebra.lagda.md +++ b/src/universal-algebra.lagda.md @@ -3,17 +3,25 @@ ## Modules in the universal algebra namespace ```agda -module universal-algebra where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom -open import universal-algebra.abstract-equations-over-signatures public -open import universal-algebra.algebraic-theories public -open import universal-algebra.algebraic-theory-of-groups public -open import universal-algebra.algebras-of-theories public -open import universal-algebra.congruences public -open import universal-algebra.homomorphisms-of-algebras public -open import universal-algebra.kernels public -open import universal-algebra.models-of-signatures public -open import universal-algebra.quotient-algebras public -open import universal-algebra.signatures public -open import universal-algebra.terms-over-signatures public +module universal-algebra + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where + +open import universal-algebra.abstract-equations-over-signatures funext univalence truncations public +open import universal-algebra.algebraic-theories funext univalence truncations public +open import universal-algebra.algebraic-theory-of-groups funext univalence truncations public +open import universal-algebra.algebras-of-theories funext univalence truncations public +open import universal-algebra.congruences funext univalence truncations public +open import universal-algebra.homomorphisms-of-algebras funext univalence truncations public +open import universal-algebra.kernels funext univalence truncations public +open import universal-algebra.models-of-signatures funext univalence truncations public +open import universal-algebra.quotient-algebras funext univalence truncations public +open import universal-algebra.signatures funext univalence public +open import universal-algebra.terms-over-signatures funext univalence truncations public ``` diff --git a/src/universal-algebra/abstract-equations-over-signatures.lagda.md b/src/universal-algebra/abstract-equations-over-signatures.lagda.md index 836403a525..355c90ce7b 100644 --- a/src/universal-algebra/abstract-equations-over-signatures.lagda.md +++ b/src/universal-algebra/abstract-equations-over-signatures.lagda.md @@ -1,18 +1,26 @@ # Abstract equations over signatures ```agda -module universal-algebra.abstract-equations-over-signatures where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module universal-algebra.abstract-equations-over-signatures + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types open import foundation.universe-levels -open import universal-algebra.signatures -open import universal-algebra.terms-over-signatures +open import universal-algebra.signatures funext univalence +open import universal-algebra.terms-over-signatures funext univalence truncations ```
diff --git a/src/universal-algebra/algebraic-theories.lagda.md b/src/universal-algebra/algebraic-theories.lagda.md index bff4ee1bee..96f4696dbd 100644 --- a/src/universal-algebra/algebraic-theories.lagda.md +++ b/src/universal-algebra/algebraic-theories.lagda.md @@ -1,7 +1,15 @@ # Algebraic theories ```agda -module universal-algebra.algebraic-theories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module universal-algebra.algebraic-theories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,8 +18,8 @@ module universal-algebra.algebraic-theories where open import foundation.dependent-pair-types open import foundation.universe-levels -open import universal-algebra.abstract-equations-over-signatures -open import universal-algebra.signatures +open import universal-algebra.abstract-equations-over-signatures funext univalence truncations +open import universal-algebra.signatures funext univalence ```
diff --git a/src/universal-algebra/algebraic-theory-of-groups.lagda.md b/src/universal-algebra/algebraic-theory-of-groups.lagda.md index 719d008255..0f0dfe4ebb 100644 --- a/src/universal-algebra/algebraic-theory-of-groups.lagda.md +++ b/src/universal-algebra/algebraic-theory-of-groups.lagda.md @@ -1,7 +1,15 @@ # Algebraic theory of groups ```agda -module universal-algebra.algebraic-theory-of-groups where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module universal-algebra.algebraic-theory-of-groups + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,21 +18,22 @@ module universal-algebra.algebraic-theory-of-groups where open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.identity-types -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.equality-dependent-pair-types funext +open import foundation.equivalences funext +open import foundation.function-extensionality funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence open import foundation.universe-levels -open import group-theory.groups +open import group-theory.groups funext univalence truncations -open import linear-algebra.vectors +open import linear-algebra.vectors funext univalence truncations -open import universal-algebra.algebraic-theories -open import universal-algebra.algebras-of-theories -open import universal-algebra.signatures -open import universal-algebra.terms-over-signatures +open import universal-algebra.algebraic-theories funext univalence truncations +open import universal-algebra.algebras-of-theories funext univalence truncations +open import universal-algebra.signatures funext univalence +open import universal-algebra.terms-over-signatures funext univalence truncations ```
diff --git a/src/universal-algebra/algebras-of-theories.lagda.md b/src/universal-algebra/algebras-of-theories.lagda.md index 3ae5fa65d3..5be4c36332 100644 --- a/src/universal-algebra/algebras-of-theories.lagda.md +++ b/src/universal-algebra/algebras-of-theories.lagda.md @@ -1,23 +1,32 @@ # Algebras ```agda -module universal-algebra.algebras-of-theories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module universal-algebra.algebras-of-theories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets +open import foundation.dependent-products-propositions funext +open import foundation.identity-types funext +open import foundation.propositions funext univalence +open import foundation.sets funext univalence open import foundation.universe-levels -open import universal-algebra.abstract-equations-over-signatures -open import universal-algebra.algebraic-theories -open import universal-algebra.models-of-signatures -open import universal-algebra.signatures -open import universal-algebra.terms-over-signatures +open import universal-algebra.abstract-equations-over-signatures funext univalence truncations +open import universal-algebra.algebraic-theories funext univalence truncations +open import universal-algebra.models-of-signatures funext univalence truncations +open import universal-algebra.signatures funext univalence +open import universal-algebra.terms-over-signatures funext univalence truncations ```
diff --git a/src/universal-algebra/congruences.lagda.md b/src/universal-algebra/congruences.lagda.md index 811e9e865c..2331f8ba47 100644 --- a/src/universal-algebra/congruences.lagda.md +++ b/src/universal-algebra/congruences.lagda.md @@ -1,7 +1,15 @@ # Congruences ```agda -module universal-algebra.congruences where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module universal-algebra.congruences + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -9,18 +17,20 @@ module universal-algebra.congruences where ```agda open import elementary-number-theory.natural-numbers -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.equivalence-relations -open import foundation.propositions +open import foundation.dependent-products-propositions funext +open import foundation.equivalence-relations funext univalence truncations +open import foundation.propositions funext univalence +open import foundation.raising-universe-levels-unit-type open import foundation.unit-type open import foundation.universe-levels -open import linear-algebra.vectors +open import linear-algebra.vectors funext univalence truncations -open import universal-algebra.algebraic-theories -open import universal-algebra.algebras-of-theories -open import universal-algebra.signatures +open import universal-algebra.algebraic-theories funext univalence truncations +open import universal-algebra.algebras-of-theories funext univalence truncations +open import universal-algebra.signatures funext univalence ```
diff --git a/src/universal-algebra/homomorphisms-of-algebras.lagda.md b/src/universal-algebra/homomorphisms-of-algebras.lagda.md index f8c7ad948a..dcc186edba 100644 --- a/src/universal-algebra/homomorphisms-of-algebras.lagda.md +++ b/src/universal-algebra/homomorphisms-of-algebras.lagda.md @@ -1,22 +1,30 @@ # Homomorphisms of algebras ```agda -module universal-algebra.homomorphisms-of-algebras where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module universal-algebra.homomorphisms-of-algebras + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import linear-algebra.functoriality-vectors -open import linear-algebra.vectors +open import linear-algebra.functoriality-vectors funext univalence truncations +open import linear-algebra.vectors funext univalence truncations -open import universal-algebra.algebraic-theories -open import universal-algebra.algebras-of-theories -open import universal-algebra.signatures +open import universal-algebra.algebraic-theories funext univalence truncations +open import universal-algebra.algebras-of-theories funext univalence truncations +open import universal-algebra.signatures funext univalence ```
diff --git a/src/universal-algebra/kernels.lagda.md b/src/universal-algebra/kernels.lagda.md index e8c0fe6128..7707c91271 100644 --- a/src/universal-algebra/kernels.lagda.md +++ b/src/universal-algebra/kernels.lagda.md @@ -1,7 +1,15 @@ # Kernels of homomorphisms of algebras ```agda -module universal-algebra.kernels where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module universal-algebra.kernels + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -11,20 +19,20 @@ open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.binary-relations +open import foundation.binary-relations funext univalence truncations open import foundation.dependent-pair-types -open import foundation.equivalence-relations -open import foundation.identity-types +open import foundation.equivalence-relations funext univalence truncations +open import foundation.identity-types funext open import foundation.universe-levels -open import linear-algebra.functoriality-vectors -open import linear-algebra.vectors +open import linear-algebra.functoriality-vectors funext univalence truncations +open import linear-algebra.vectors funext univalence truncations -open import universal-algebra.algebraic-theories -open import universal-algebra.algebras-of-theories -open import universal-algebra.congruences -open import universal-algebra.homomorphisms-of-algebras -open import universal-algebra.signatures +open import universal-algebra.algebraic-theories funext univalence truncations +open import universal-algebra.algebras-of-theories funext univalence truncations +open import universal-algebra.congruences funext univalence truncations +open import universal-algebra.homomorphisms-of-algebras funext univalence truncations +open import universal-algebra.signatures funext univalence ```
diff --git a/src/universal-algebra/models-of-signatures.lagda.md b/src/universal-algebra/models-of-signatures.lagda.md index 18b796de52..00b2434eb0 100644 --- a/src/universal-algebra/models-of-signatures.lagda.md +++ b/src/universal-algebra/models-of-signatures.lagda.md @@ -1,19 +1,27 @@ # Models of signatures ```agda -module universal-algebra.models-of-signatures where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module universal-algebra.models-of-signatures + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.sets +open import foundation.sets funext univalence open import foundation.universe-levels -open import linear-algebra.vectors +open import linear-algebra.vectors funext univalence truncations -open import universal-algebra.signatures +open import universal-algebra.signatures funext univalence ```
diff --git a/src/universal-algebra/quotient-algebras.lagda.md b/src/universal-algebra/quotient-algebras.lagda.md index 6a031ee6f2..ca17cc4ea2 100644 --- a/src/universal-algebra/quotient-algebras.lagda.md +++ b/src/universal-algebra/quotient-algebras.lagda.md @@ -1,7 +1,15 @@ # Quotient algebras ```agda -module universal-algebra.quotient-algebras where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module universal-algebra.quotient-algebras + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -10,27 +18,29 @@ module universal-algebra.quotient-algebras where open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.equivalence-classes -open import foundation.equivalence-relations -open import foundation.equivalences -open import foundation.functoriality-propositional-truncation -open import foundation.multivariable-functoriality-set-quotients -open import foundation.multivariable-operations -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.set-quotients -open import foundation.sets +open import foundation.dependent-products-propositions funext +open import foundation.equivalence-classes funext univalence truncations +open import foundation.equivalence-relations funext univalence truncations +open import foundation.equivalences funext +open import foundation.functoriality-propositional-truncation funext univalence truncations +open import foundation.multivariable-functoriality-set-quotients funext univalence truncations +open import foundation.multivariable-operations funext univalence truncations +open import foundation.propositional-truncations funext univalence +open import foundation.propositions funext univalence +open import foundation.raising-universe-levels-unit-type +open import foundation.set-quotients funext univalence truncations +open import foundation.sets funext univalence open import foundation.unit-type open import foundation.universe-levels -open import foundation.vectors-set-quotients +open import foundation.vectors-set-quotients funext univalence truncations -open import linear-algebra.vectors +open import linear-algebra.vectors funext univalence truncations -open import universal-algebra.algebraic-theories -open import universal-algebra.algebras-of-theories -open import universal-algebra.congruences -open import universal-algebra.models-of-signatures -open import universal-algebra.signatures +open import universal-algebra.algebraic-theories funext univalence truncations +open import universal-algebra.algebras-of-theories funext univalence truncations +open import universal-algebra.congruences funext univalence truncations +open import universal-algebra.models-of-signatures funext univalence truncations +open import universal-algebra.signatures funext univalence ```
diff --git a/src/universal-algebra/signatures.lagda.md b/src/universal-algebra/signatures.lagda.md index e5b118ac6b..9897d029d4 100644 --- a/src/universal-algebra/signatures.lagda.md +++ b/src/universal-algebra/signatures.lagda.md @@ -1,7 +1,13 @@ # Signatures ```agda -module universal-algebra.signatures where +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module universal-algebra.signatures + (funext : function-extensionality) + (univalence : univalence-axiom) + where ```
Imports @@ -9,10 +15,10 @@ module universal-algebra.signatures where ```agda open import elementary-number-theory.natural-numbers -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.identity-types +open import foundation.embeddings funext +open import foundation.identity-types funext open import foundation.universe-levels ``` diff --git a/src/universal-algebra/terms-over-signatures.lagda.md b/src/universal-algebra/terms-over-signatures.lagda.md index 8a5cf6febf..a52ed36130 100644 --- a/src/universal-algebra/terms-over-signatures.lagda.md +++ b/src/universal-algebra/terms-over-signatures.lagda.md @@ -1,31 +1,40 @@ # Terms over signatures ```agda -module universal-algebra.terms-over-signatures where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module universal-algebra.terms-over-signatures + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import elementary-number-theory.equality-natural-numbers +open import elementary-number-theory.equality-natural-numbers funext univalence truncations open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.coproduct-types +open import foundation.coproduct-types funext univalence truncations open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext +open import foundation.raising-universe-levels-unit-type open import foundation.transport-along-identifications open import foundation.unit-type open import foundation.universe-levels -open import linear-algebra.functoriality-vectors -open import linear-algebra.vectors +open import linear-algebra.functoriality-vectors funext univalence truncations +open import linear-algebra.vectors funext univalence truncations open import lists.lists -open import lists.lists-discrete-types +open import lists.lists-discrete-types funext univalence truncations -open import universal-algebra.models-of-signatures -open import universal-algebra.signatures +open import universal-algebra.models-of-signatures funext univalence truncations +open import universal-algebra.signatures funext univalence ```
diff --git a/src/wild-category-theory.lagda.md b/src/wild-category-theory.lagda.md index 72cf1254d2..90c58bc67d 100644 --- a/src/wild-category-theory.lagda.md +++ b/src/wild-category-theory.lagda.md @@ -11,14 +11,22 @@ ## Modules in the wild category theory namespace ```agda -module wild-category-theory where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom -open import wild-category-theory.coinductive-isomorphisms-in-noncoherent-large-omega-precategories public -open import wild-category-theory.coinductive-isomorphisms-in-noncoherent-omega-precategories public -open import wild-category-theory.colax-functors-noncoherent-large-omega-precategories public -open import wild-category-theory.colax-functors-noncoherent-omega-precategories public -open import wild-category-theory.maps-noncoherent-large-omega-precategories public -open import wild-category-theory.maps-noncoherent-omega-precategories public -open import wild-category-theory.noncoherent-large-omega-precategories public -open import wild-category-theory.noncoherent-omega-precategories public +module wild-category-theory + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where + +open import wild-category-theory.coinductive-isomorphisms-in-noncoherent-large-omega-precategories funext univalence truncations public +open import wild-category-theory.coinductive-isomorphisms-in-noncoherent-omega-precategories funext univalence truncations public +open import wild-category-theory.colax-functors-noncoherent-large-omega-precategories funext univalence truncations public +open import wild-category-theory.colax-functors-noncoherent-omega-precategories funext univalence truncations public +open import wild-category-theory.maps-noncoherent-large-omega-precategories funext univalence truncations public +open import wild-category-theory.maps-noncoherent-omega-precategories funext univalence truncations public +open import wild-category-theory.noncoherent-large-omega-precategories funext univalence truncations public +open import wild-category-theory.noncoherent-omega-precategories funext univalence truncations public ``` diff --git a/src/wild-category-theory/coinductive-isomorphisms-in-noncoherent-large-omega-precategories.lagda.md b/src/wild-category-theory/coinductive-isomorphisms-in-noncoherent-large-omega-precategories.lagda.md index 303c5653ac..ab8469c8c7 100644 --- a/src/wild-category-theory/coinductive-isomorphisms-in-noncoherent-large-omega-precategories.lagda.md +++ b/src/wild-category-theory/coinductive-isomorphisms-in-noncoherent-large-omega-precategories.lagda.md @@ -2,8 +2,15 @@ ```agda {-# OPTIONS --guardedness #-} - -module wild-category-theory.coinductive-isomorphisms-in-noncoherent-large-omega-precategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module wild-category-theory.coinductive-isomorphisms-in-noncoherent-large-omega-precategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -12,8 +19,8 @@ module wild-category-theory.coinductive-isomorphisms-in-noncoherent-large-omega- open import foundation.dependent-pair-types open import foundation.universe-levels -open import wild-category-theory.coinductive-isomorphisms-in-noncoherent-omega-precategories -open import wild-category-theory.noncoherent-large-omega-precategories +open import wild-category-theory.coinductive-isomorphisms-in-noncoherent-omega-precategories funext univalence truncations +open import wild-category-theory.noncoherent-large-omega-precategories funext univalence truncations ```
diff --git a/src/wild-category-theory/coinductive-isomorphisms-in-noncoherent-omega-precategories.lagda.md b/src/wild-category-theory/coinductive-isomorphisms-in-noncoherent-omega-precategories.lagda.md index c2494822ea..464e8a9bcb 100644 --- a/src/wild-category-theory/coinductive-isomorphisms-in-noncoherent-omega-precategories.lagda.md +++ b/src/wild-category-theory/coinductive-isomorphisms-in-noncoherent-omega-precategories.lagda.md @@ -2,8 +2,15 @@ ```agda {-# OPTIONS --guardedness #-} - -module wild-category-theory.coinductive-isomorphisms-in-noncoherent-omega-precategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module wild-category-theory.coinductive-isomorphisms-in-noncoherent-omega-precategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports @@ -12,7 +19,7 @@ module wild-category-theory.coinductive-isomorphisms-in-noncoherent-omega-precat open import foundation.dependent-pair-types open import foundation.universe-levels -open import wild-category-theory.noncoherent-omega-precategories +open import wild-category-theory.noncoherent-omega-precategories funext univalence truncations ```
diff --git a/src/wild-category-theory/colax-functors-noncoherent-large-omega-precategories.lagda.md b/src/wild-category-theory/colax-functors-noncoherent-large-omega-precategories.lagda.md index 714375f4a2..ac6573c32d 100644 --- a/src/wild-category-theory/colax-functors-noncoherent-large-omega-precategories.lagda.md +++ b/src/wild-category-theory/colax-functors-noncoherent-large-omega-precategories.lagda.md @@ -2,29 +2,36 @@ ```agda {-# OPTIONS --guardedness #-} - -module wild-category-theory.colax-functors-noncoherent-large-omega-precategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module wild-category-theory.colax-functors-noncoherent-large-omega-precategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.identity-types +open import foundation.function-types funext +open import foundation.identity-types funext open import foundation.universe-levels -open import globular-types.globular-maps +open import globular-types.globular-maps funext open import globular-types.globular-types -open import globular-types.large-colax-reflexive-globular-maps -open import globular-types.large-colax-transitive-globular-maps -open import globular-types.large-globular-maps - -open import wild-category-theory.colax-functors-noncoherent-omega-precategories -open import wild-category-theory.maps-noncoherent-large-omega-precategories -open import wild-category-theory.maps-noncoherent-omega-precategories -open import wild-category-theory.noncoherent-large-omega-precategories -open import wild-category-theory.noncoherent-omega-precategories +open import globular-types.large-colax-reflexive-globular-maps funext univalence truncations +open import globular-types.large-colax-transitive-globular-maps funext univalence truncations +open import globular-types.large-globular-maps funext + +open import wild-category-theory.colax-functors-noncoherent-omega-precategories funext univalence truncations +open import wild-category-theory.maps-noncoherent-large-omega-precategories funext univalence truncations +open import wild-category-theory.maps-noncoherent-omega-precategories funext univalence truncations +open import wild-category-theory.noncoherent-large-omega-precategories funext univalence truncations +open import wild-category-theory.noncoherent-omega-precategories funext univalence truncations ```
diff --git a/src/wild-category-theory/colax-functors-noncoherent-omega-precategories.lagda.md b/src/wild-category-theory/colax-functors-noncoherent-omega-precategories.lagda.md index 8bb9dc1251..fadc3dfaa4 100644 --- a/src/wild-category-theory/colax-functors-noncoherent-omega-precategories.lagda.md +++ b/src/wild-category-theory/colax-functors-noncoherent-omega-precategories.lagda.md @@ -2,26 +2,33 @@ ```agda {-# OPTIONS --guardedness #-} - -module wild-category-theory.colax-functors-noncoherent-omega-precategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module wild-category-theory.colax-functors-noncoherent-omega-precategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.identity-types +open import foundation.function-types funext +open import foundation.identity-types funext open import foundation.universe-levels -open import globular-types.colax-reflexive-globular-maps -open import globular-types.colax-transitive-globular-maps -open import globular-types.globular-maps +open import globular-types.colax-reflexive-globular-maps funext univalence truncations +open import globular-types.colax-transitive-globular-maps funext univalence truncations +open import globular-types.globular-maps funext open import globular-types.globular-types -open import globular-types.reflexive-globular-types +open import globular-types.reflexive-globular-types funext univalence truncations -open import wild-category-theory.maps-noncoherent-omega-precategories -open import wild-category-theory.noncoherent-omega-precategories +open import wild-category-theory.maps-noncoherent-omega-precategories funext univalence truncations +open import wild-category-theory.noncoherent-omega-precategories funext univalence truncations ```
diff --git a/src/wild-category-theory/maps-noncoherent-large-omega-precategories.lagda.md b/src/wild-category-theory/maps-noncoherent-large-omega-precategories.lagda.md index e7adea0a47..c309106711 100644 --- a/src/wild-category-theory/maps-noncoherent-large-omega-precategories.lagda.md +++ b/src/wild-category-theory/maps-noncoherent-large-omega-precategories.lagda.md @@ -2,26 +2,33 @@ ```agda {-# OPTIONS --guardedness #-} - -module wild-category-theory.maps-noncoherent-large-omega-precategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module wild-category-theory.maps-noncoherent-large-omega-precategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.identity-types +open import foundation.function-types funext +open import foundation.identity-types funext open import foundation.universe-levels -open import globular-types.globular-maps +open import globular-types.globular-maps funext open import globular-types.globular-types -open import globular-types.large-globular-maps +open import globular-types.large-globular-maps funext open import globular-types.large-globular-types -open import wild-category-theory.maps-noncoherent-omega-precategories -open import wild-category-theory.noncoherent-large-omega-precategories -open import wild-category-theory.noncoherent-omega-precategories +open import wild-category-theory.maps-noncoherent-omega-precategories funext univalence truncations +open import wild-category-theory.noncoherent-large-omega-precategories funext univalence truncations +open import wild-category-theory.noncoherent-omega-precategories funext univalence truncations ```
diff --git a/src/wild-category-theory/maps-noncoherent-omega-precategories.lagda.md b/src/wild-category-theory/maps-noncoherent-omega-precategories.lagda.md index 2573be3c1a..614974b827 100644 --- a/src/wild-category-theory/maps-noncoherent-omega-precategories.lagda.md +++ b/src/wild-category-theory/maps-noncoherent-omega-precategories.lagda.md @@ -2,22 +2,29 @@ ```agda {-# OPTIONS --guardedness #-} - -module wild-category-theory.maps-noncoherent-omega-precategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module wild-category-theory.maps-noncoherent-omega-precategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.identity-types +open import foundation.function-types funext +open import foundation.identity-types funext open import foundation.universe-levels -open import globular-types.globular-maps +open import globular-types.globular-maps funext open import globular-types.globular-types -open import wild-category-theory.noncoherent-omega-precategories +open import wild-category-theory.noncoherent-omega-precategories funext univalence truncations ```
diff --git a/src/wild-category-theory/noncoherent-large-omega-precategories.lagda.md b/src/wild-category-theory/noncoherent-large-omega-precategories.lagda.md index d40fa26fd8..579edc7afc 100644 --- a/src/wild-category-theory/noncoherent-large-omega-precategories.lagda.md +++ b/src/wild-category-theory/noncoherent-large-omega-precategories.lagda.md @@ -2,32 +2,39 @@ ```agda {-# OPTIONS --guardedness #-} - -module wild-category-theory.noncoherent-large-omega-precategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module wild-category-theory.noncoherent-large-omega-precategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.precategories +open import category-theory.precategories funext univalence truncations open import foundation.action-on-identifications-binary-functions open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.sets -open import foundation.strictly-involutive-identity-types +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.sets funext univalence +open import foundation.strictly-involutive-identity-types funext univalence open import foundation.universe-levels open import globular-types.globular-types open import globular-types.large-globular-types -open import globular-types.large-reflexive-globular-types -open import globular-types.large-transitive-globular-types -open import globular-types.reflexive-globular-types -open import globular-types.transitive-globular-types +open import globular-types.large-reflexive-globular-types funext univalence truncations +open import globular-types.large-transitive-globular-types funext univalence truncations +open import globular-types.reflexive-globular-types funext univalence truncations +open import globular-types.transitive-globular-types funext univalence truncations -open import wild-category-theory.noncoherent-omega-precategories +open import wild-category-theory.noncoherent-omega-precategories funext univalence truncations ```
diff --git a/src/wild-category-theory/noncoherent-omega-precategories.lagda.md b/src/wild-category-theory/noncoherent-omega-precategories.lagda.md index 648d1f464f..9e9c9563e2 100644 --- a/src/wild-category-theory/noncoherent-omega-precategories.lagda.md +++ b/src/wild-category-theory/noncoherent-omega-precategories.lagda.md @@ -2,28 +2,35 @@ ```agda {-# OPTIONS --guardedness #-} - -module wild-category-theory.noncoherent-omega-precategories where +open import foundation.truncations-exist +open import foundation-core.univalence +open import foundation.function-extensionality-axiom + +module wild-category-theory.noncoherent-omega-precategories + (funext : function-extensionality) + (univalence : univalence-axiom) + (truncations : truncations-exist) + where ```
Imports ```agda -open import category-theory.precategories +open import category-theory.precategories funext univalence truncations open import foundation.action-on-identifications-binary-functions -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext univalence open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.sets -open import foundation.strictly-involutive-identity-types +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.sets funext univalence +open import foundation.strictly-involutive-identity-types funext univalence open import foundation.universe-levels open import globular-types.globular-types -open import globular-types.reflexive-globular-types -open import globular-types.transitive-globular-types +open import globular-types.reflexive-globular-types funext univalence truncations +open import globular-types.transitive-globular-types funext univalence truncations ```