feat(CategoryTheory): κ-filtered categories

[joelriou]

---

• depends on: feat(CategoryTheory): Arrow A is finite iff A is a finite category #19945
• depends on: feat(SetTheory): the predicate HasCardinalLT #19959
• depends on: feat(CategoryTheory): the category with two objects zero and one, and an arbitrary type of morphisms from zero to one #20006

[github-actions]

PR summary c506a03c82

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference
Mathlib.SetTheory.Cardinal.HasCardinalLT (new file)	771
Mathlib.CategoryTheory.Presentable.ParallelMaps (new file)	799
Mathlib.CategoryTheory.Comma.CardinalArrow (new file)	820
Mathlib.CategoryTheory.Presentable.IsCardinalFiltered (new file)	852

---

Declarations diff

+ Arrow.discreteEquiv
+ Arrow.equivSigma
+ Arrow.ext
+ Arrow.finite
+ Arrow.finite_iff
+ Arrow.opEquiv
+ Arrow.shrinkEquiv
+ Arrow.shrinkHomsEquiv
+ HasCardinalLT
+ Hom
+ Hom.comp
+ IsCardinalFiltered
+ ParallelMaps
+ arrowEquiv
+ cocone
+ coeq
+ coeqHom
+ coeq_condition
+ hasCardinalLT
+ hasCardinalLT_aleph0_iff
+ hasCardinalLT_arrow_discrete_iff
+ hasCardinalLT_arrow_shrinkHoms_iff
+ hasCardinalLT_arrow_shrink_iff
+ hasCardinalLT_iff_cardinal_mk_lt
+ hasCardinalLT_iff_of_equiv
+ hasCardinalLT_of_hasCardinalLT_arrow
+ hasCardinalLT_option_iff
+ hasCardinal_arrow_op_iff
+ instance (C : Type u) [Category.{v} C] [Small.{w'} C] [LocallySmall.{w} C] :
+ instance : Category (ParallelMaps T)
+ instance : Fact Cardinal.aleph0.IsRegular
+ isCardinalFiltered_aleph0_iff
+ isCardinalFiltered_preorder
+ isFiltered_of_isCardinalDirected
+ locallySmall_of_small_arrow
+ max
+ mkFunctor
+ of_injective
+ of_surjective
+ small
+ small_of_small_arrow
+ toCoeq
+ toMax
++ of_le

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.

---

Increase in tech debt: (relative, absolute) = (2.00, 0.00)

Current number	Change	Type
1491	2	erw

Current commit c506a03c82
Reference commit 468b507def

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(CategoryTheory): Arrow A is finite iff A is a finite category #19945
• feat(SetTheory): the predicate HasCardinalLT #19959
• feat(CategoryTheory): the category with two objects zero and one, and an arbitrary type of morphisms from zero to one #20006
  By Dependent Issues (🤖). Happy coding!