feat(Algebra/Category/ModuleCat): the category of sheaves of modules is Grothendieck abelian

[joelriou]

---

[github-actions]

PR summary cd2b62f025

Import changes for modified files

Dependency changes

File	Base Count	Head Count	Change
Mathlib.AlgebraicGeometry.Modules.Sheaf	2384	2331	-53 (-2.22%)
Mathlib.AlgebraicGeometry.Modules.Tilde	2410	2426	+16 (+0.66%)

Import changes for all files

Files	Import difference
Mathlib.AlgebraicGeometry.Modules.Sheaf	-53
Mathlib.AlgebraicGeometry.Modules.Tilde	16
Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.PresheafOfModules (new file)	1435
Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.SheafOfModules (new file)	1651

---

Declarations diff (regex)

+ HasCoseparator.of_adjunction
+ HasSeparator.of_adjunction
+ IsCoseparating.strictMap_rightAdjoint
+ IsCoseparator.rightAdjoint_obj
+ IsSeparating.strictMap_leftAdjoint
+ IsSeparator.leftAdjoint_obj
+ hasSeparator
+ instance : IsGrothendieckAbelian.{u} X.Modules
+ instance {C : Type u} [SmallCategory C] (R : Cᵒᵖ ⥤ RingCat.{u}) :
+ instance {C : Type u} [SmallCategory C] {J : GrothendieckTopology C}

You can run this locally as follows

## from your `mathlib4` directory:
git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci

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

## more verbose report:
../mathlib-ci/scripts/pr_summary/declarations_diff.sh long <optional_commit>

The doc-module for scripts/pr_summary/declarations_diff.sh in the mathlib-ci repository contains some details about this script.

Declarations diff (Lean)

✅ Lean-aware diff — post-build, computed from the Lean environment (commit cd2b62f).

• +10 new declarations
• −0 removed declarations

+AlgebraicGeometry.Scheme.Modules.instIsGrothendieckAbelian
+CategoryTheory.HasCoseparator.of_adjunction
+CategoryTheory.HasSeparator.of_adjunction
+CategoryTheory.IsCoseparator.rightAdjoint_obj
+CategoryTheory.IsSeparator.leftAdjoint_obj
+CategoryTheory.ObjectProperty.IsCoseparating.strictMap_rightAdjoint
+CategoryTheory.ObjectProperty.IsSeparating.strictMap_leftAdjoint
+PresheafOfModules.hasSeparator
+PresheafOfModules.instIsGrothendieckAbelian
+SheafOfModules.instIsGrothendieckAbelian

---

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

Current number	Change	Type (strong)
5659	1	backward.isDefEq.respectTransparency

No changes to weak technical debt.

Current commit cd2b62f025
Reference commit bb577fa4a1

This script lives in the mathlib-ci repository. To run it locally, from your mathlib4 directory:

git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci
../mathlib-ci/scripts/reporting/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).