[Merged by Bors] - feat(Order/Category): partial orders with order embeddings as morphisms

[joelriou]

This category will be relevant in the study of accessible categories. I am making Johan Commelin a co-author as the new file PartOrdEmb.lean is essentially a copy-paste of PartOrd.Lean.

Co-authored-by: Johan Commelin johan@commelin.net

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[github-actions]

PR summary 2c2d756603

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference
Mathlib.Order.Category.PartOrdEmb (new file)	462

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Declarations diff

+ Hom
+ Hom.Simps.hom
+ Hom.hom
+ Hom.injective
+ Iso.mk
+ PartOrdEmb
+ coe_comp
+ coe_id
+ coe_of
+ comp_apply
+ dual
+ dualEquiv
+ ext
+ forget_map
+ hasForgetToPartOrd
+ hom_comp
+ hom_ext
+ hom_id
+ hom_inv_apply
+ hom_ofHom
+ id_apply
+ instance : Category PartOrdEmb.{u}
+ instance : CoeSort PartOrdEmb (Type _)
+ instance : ConcreteCategory PartOrdEmb (· ↪o ·)
+ inv_hom_apply
+ of
+ ofHom
+ ofHom_apply
+ ofHom_comp
+ ofHom_hom
+ ofHom_id
+ partOrdEmb_dual_comp_forget_to_pardOrd

You can run this locally as follows

## summary with just the declaration names:
./scripts/declarations_diff.sh <optional_commit>

## more verbose report:
./scripts/declarations_diff.sh long <optional_commit>

The doc-module for script/declarations_diff.sh contains some details about this script.

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No changes to technical debt.

You can run this locally as

./scripts/technical-debt-metrics.sh pr_summary

• The relative value is the weighted sum of the differences with weight given by the inverse of the current value of the statistic.
• The absolute value is the relative value divided by the total sum of the inverses of the current values (i.e. the weighted average of the differences).

[kim-em]

Do we have the subcategory of monomorphisms somewhere? Can we identify this with that?

I'm happy for you to proceed if that either is too big a detour, or there's a reason you think it wouldn't be helpful.

bors d+

[joelriou]

Actually, monomorphisms correspond to injective maps, but there are some injective monotone maps between partial orders that are not order embeddings (consider the identity of Fin 2 where there is the usual order on the target but in the source 0 and 1 are not comparable).

[mathlib-bors]

✌️ joelriou can now approve this pull request. To approve and merge a pull request, simply reply with bors r+. More detailed instructions are available here.

[joelriou]

Thanks!

bors merge

[mathlib-bors]

Pull request successfully merged into master.

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