feat(CategoryTheory): expand the API for AB axioms

[dagurtomas]

---

•  depends on: feat(CategoryTheory): add some API for countable products and countable filtered colimits #19192
• depends on: feat(CategoryTheory): weaken assumptions and dualize file Limits/Constructions/Filtered.lean #19196

[github-actions]

PR summary b9fa6a81f4

Import changes exceeding 2%

%	File
+46.01%	Mathlib.CategoryTheory.Abelian.GrothendieckAxioms

Import changes for modified files

Dependency changes

File	Base Count	Head Count	Change
Mathlib.CategoryTheory.Abelian.GrothendieckAxioms	626	914	+288 (+46.01%)
Mathlib.Algebra.Category.Grp.AB5	1302	1305	+3 (+0.23%)
Mathlib.CategoryTheory.Limits.Shapes.Countable	566	567	+1 (+0.18%)
Mathlib.Topology.Category.LightProfinite.Basic	1468	1469	+1 (+0.07%)

Import changes for all files

Files	Import difference
5 files Mathlib.Topology.Category.LightProfinite.Extend Mathlib.Topology.Category.LightProfinite.AsLimit Mathlib.CategoryTheory.Limits.Shapes.Countable Mathlib.Topology.Category.LightProfinite.Basic Mathlib.Topology.Category.LightProfinite.Sequence	1
Mathlib.Algebra.Category.Grp.AB5	3
Mathlib.CategoryTheory.Abelian.GrothendieckAxioms	288

---

Declarations diff

+ AB4Star.ofAB5Star
+ ABOfShape
+ ABOfShapeDiscreteFinite
+ ABOfShapeDiscreteOfABOfShapeFinsetDiscrete
+ ABOfShapeOfFinal
+ ABOfShapeOfPreservesMono
+ ABStarOfShape
+ ABStarOfShapeDiscreteFinite
+ ABStarOfShapeDiscreteOfABStarOfShapeFinsetDiscreteOp
+ ABStarOfShapeOfInitial
+ ABStarOfShapeOfPreservesEpi
+ CountableAB4
+ CountableAB4.ofABOfShapeNat
+ CountableAB4.ofABOfShapeNatAndFinite
+ CountableAB4.ofCountableAB5
+ CountableAB4Star
+ CountableAB4Star.ofABStarOfShapeNat
+ CountableAB4Star.ofABStarOfShapeNatAndFinite
+ CountableAB4Star.ofCountableAB5Star
+ HasCountableCoproducts
+ HasCountableProducts
+ instance (priority := 100) hasCountableCoproducts_of_hasCoproducts [HasCoproducts C] :
+ instance (priority := 100) hasCountableCoproducts_of_hasCountableColimits [HasCountableColimits C] :
+ instance (priority := 100) hasCountableProducts_of_hasCountableLimits [HasCountableLimits C] :
+ instance (priority := 100) hasCountableProducts_of_hasProducts [HasProducts C] :
+ instance (priority := 100) hasFiniteCoproducts_of_hasCountableCoproducts
+ instance (priority := 100) hasFiniteProducts_of_hasCountableProducts [HasCountableProducts C] :
+ instance [HasCoproducts C] [AB4 C] (J : Type v) : ABOfShape (Discrete J) C := inferInstance
+ instance [HasCountableCoproducts C] : HasCoproductsOfShape J C
+ instance [HasCountableProducts C] : HasProductsOfShape J C
+ liftToFinset
+ liftToFinsetEvaluationIso
+ liftToFinsetLimIso
+ liftToFinsetLimitCone
+ liftToFinsetObj
+ preservesFiniteColimitsLiftToFinset
+ sequentialFunctor_final
+ sequentialFunctor_final_aux
+ sequentialFunctor_initial
+ sequentialFunctor_initial_aux
++ sequentialFunctor
++ sequentialFunctor_map
++ sequentialFunctor_obj

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) = (1.00, 0.00)

Current number	Change	Type
1554	1	erw

Current commit b9fa6a81f4
Reference commit bcef7c52e8

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).

[dagurtomas]

PR summary 2df551d9ea

Import changes exceeding 2%

% File
+46.01% Mathlib.CategoryTheory.Abelian.GrothendieckAxioms

Import changes for modified files

Declarations diff

Increase in tech debt: (relative, absolute) = (1.00, 0.00)

Since the GrothendieckAxioms file isn't much used, I think this is fine

[mathlib4-dependent-issues-bot]

This PR/issue depends on:

• feat(CategoryTheory): add some API for countable products and countable filtered colimits #19192
• feat(CategoryTheory): weaken assumptions and dualize file Limits/Constructions/Filtered.lean #19196
  By Dependent Issues (🤖). Happy coding!