feat(Condensed): light condensed modules satisfy countable AB4*

[dagurtomas]

---

•  depends on: [Merged by Bors] - feat(Condensed): a sequential limit of epimorphisms in light condensed modules is epimorphic #18336
• depends on: [Merged by Bors] - feat(CategoryTheory): a biproduct of epimorphisms is an epimorphism, etc #19190
• depends on: feat(CategoryTheory): add some API for countable products and countable filtered colimits #19192
• depends on: feat(CategoryTheory): add Pi.map_isIso and hasProductsOfShape_of_hasProducts + duals #19195
• depends on: feat(CategoryTheory): weaken assumptions and dualize file Limits/Constructions/Filtered.lean #19196
• depends on: feat(CategoryTheory): split up a product into a binary product #19199

[github-actions]

PR summary a865b21b2b

Import changes exceeding 2%

%	File
+46.08%	Mathlib.CategoryTheory.Abelian.GrothendieckAxioms

Import changes for modified files

Dependency changes

File	Base Count	Head Count	Change
Mathlib.CategoryTheory.Abelian.GrothendieckAxioms	625	913	+288 (+46.08%)
Mathlib.Algebra.Category.Grp.AB5	1301	1304	+3 (+0.23%)

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.Condensed.Light.Epi	2
Mathlib.Algebra.Category.Grp.AB5	3
Mathlib.CategoryTheory.Abelian.GrothendieckAxioms	288
Mathlib.CategoryTheory.Limits.Shapes.PiProd	404
Mathlib.Condensed.Light.AB	1780

---

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
+ Pi.binaryFanOfProp
+ Pi.binaryFanOfPropIsLimit
+ Pi.map_epi
+ Pi.map_eq_prod_map
+ Pi.map_isIso
+ Sigma.map_mono
+ biprod.map_epi
+ biprod.map_mono
+ biproduct.map_epi
+ biproduct.map_mono
+ cone_π_app_comp_Pi_π_neg
+ cone_π_app_comp_Pi_π_pos
+ coprod.map_mono
+ 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 (priority := 100) hasProductsOfShape_of_hasProducts [h : HasProducts.{w} C] (J : Type w) :
+ instance : (lim (J := Discrete ℕ) (C := LightCondMod R)).PreservesEpimorphisms
+ instance : AB5 (AddCommGrp.{u}) := fun _ ↦ ⟨inferInstance⟩
+ instance : CountableAB4Star (LightCondMod.{u} R)
+ instance : Epi (Limits.Pi.map f) := by
+ instance : HasLimitsOfSize.{0, 0} (LightCondMod.{u} R)
+ instance : HasLimitsOfSize.{u, u} (LightCondMod.{u} R)
+ 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
+ prod.map_epi
+ sequentialFunctor_final
+ sequentialFunctor_final_aux
+ sequentialFunctor_initial
+ sequentialFunctor_initial_aux
++ sequentialFunctor
++ sequentialFunctor_map
++ sequentialFunctor_obj
- instance : AB5 (AddCommGrp.{u})
- instance : HasLimitsOfSize.{u, u} (LightCondMod.{u} R) := by

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) = (4.00, 0.00)

Current number	Change	Type
1564	4	erw

Current commit a865b21b2b
Reference commit 0b70c3228f

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:

• [Merged by Bors] - feat(Condensed): a sequential limit of epimorphisms in light condensed modules is epimorphic #18336
• [Merged by Bors] - feat(CategoryTheory): a biproduct of epimorphisms is an epimorphism, etc #19190
• feat(CategoryTheory): add some API for countable products and countable filtered colimits #19192
• feat(CategoryTheory): add Pi.map_isIso and hasProductsOfShape_of_hasProducts + duals #19195
• feat(CategoryTheory): weaken assumptions and dualize file Limits/Constructions/Filtered.lean #19196
• feat(CategoryTheory): split up a product into a binary product #19199
  By Dependent Issues (🤖). Happy coding!