feat(Order/Category): PardOrdEmb has filtered colimits

[joelriou]

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• depends on: feat(Order/Category): partial orders with order embeddings as morphisms #30693

[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)	639

---

Declarations diff

+ CoconePt
+ CoconePt.desc
+ CoconePt.fac_apply
+ Hom
+ Hom.Simps.hom
+ Hom.hom
+ Hom.injective
+ Hom.le_iff_le
+ Iso.mk
+ PartOrdEmb
+ cocone
+ 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 ·)
+ instance : HasColimit F
+ instance : HasColimitsOfShape J PartOrdEmb.{u}
+ instance : HasFilteredColimitsOfSize.{u, u} PartOrdEmb.{u}
+ instance : PartialOrder (CoconePt hc)
+ instance : PreservesColimit F (forget _)
+ instance : PreservesColimitsOfShape J (forget PartOrdEmb.{u})
+ instance : PreservesFilteredColimitsOfSize.{u, u} (forget PartOrdEmb.{u})
+ inv_hom_apply
+ isColimitCocone
+ jointly_surjective_of_isColimit₂
+ 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.

---

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).

[mathlib4-dependent-issues-bot]

This PR/issue depends on:

• feat(Order/Category): partial orders with order embeddings as morphisms #30693
  By Dependent Issues (🤖). Happy coding!