Dualize limits, right Kan extensions, and monads #1442
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I've made your suggested changes for both left and right (Kan) extensions. |
src/category-theory/copointed-endofunctors-precategories.lagda.md
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src/category-theory/right-kan-extensions-precategories.lagda.md
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src/category-theory/coalgebras-comonads-on-precategories.lagda.md
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I forgot that I also needed pushouts, so I dualized them from pullbacks as well. I made some changes to pullbacks since a couple of the names didn't match conventions; these weren't used anywhere else in the library. I dualized pushouts using pullbacks in the opposite category: same as for coproducts/products dualizing the definition explicitly gives something judgementally equal to the concept in the opposite category, and this way there's only one definition/proof in the library. |
src/category-theory/pointed-endofunctors-precategories.lagda.md
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src/category-theory/precategory-of-coalgebras-comonads-on-precategories.lagda.md
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I removed the pushout and pullback business, they're in #1448. |
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Sorry for being so slow to review this one. I'll try and finish my review today, so hang tight! |
Co-authored-by: Fredrik Bakke <fredrbak@gmail.com>
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This explicitly dualizes limits, right Kan extensions, and monads. The definitions and proofs are exactly dual, save for certain parts of cocones where re-use of
coherence-triangle-hom-Precategorymeant a rotation was needed.This also fixes a minor indendation problem in monads.