[Merged by Bors] - feat(CategoryTheory): ContAction FintypeCat G is a Galois category

[joelriou]

---

• depends on: [Merged by Bors] - feat(CategoryTheory): properties of objects that are closed under finite limits #42396
• depends on: [Merged by Bors] - feat(CategoryTheory/Galois): full subcategories #42320

[github-actions]

PR summary 29f0f3e212

Import changes exceeding 2%

%	File
+2.96%	Mathlib.CategoryTheory.Galois.FullSubcategory
+38.78%	Mathlib.CategoryTheory.ObjectProperty.FiniteLimits

Import changes for modified files

Dependency changes

File	Base Count	Head Count	Change
Mathlib.CategoryTheory.ObjectProperty.FiniteLimits	673	934	+261 (+38.78%)
Mathlib.CategoryTheory.Galois.FullSubcategory	1048	1079	+31 (+2.96%)

Import changes for all files

Files	Import difference
Mathlib.CategoryTheory.Galois.FullSubcategory	31
Mathlib.CategoryTheory.ObjectProperty.FiniteLimits	261
Mathlib.CategoryTheory.Galois.ContAction (new file)	1425

---

Declarations diff (regex)

+ Action.isContinuous
+ exists_openSubgroup_of_isContinuous_of_finite
+ iInfOfFinite
+ iInfOfFinite_le
+ instance (J : Type*) [Category* J] [HasColimitsOfShape J V] (S : Set G) :
+ instance (J : Type*) [Category* J] [HasLimitsOfShape J V] (S : Set G) :
+ instance (P : ObjectProperty C) [P.IsClosedUnderFiniteColimits]
+ instance (S : Set G) : (trivialOnSet FintypeCat.{w} S).IsGaloisSubcategory
+ instance (S : Set G) [HasPullbacks V] :
+ instance : (isContinuous FintypeCat.{w} G).IsClosedUnderFiniteColimits
+ instance : (isContinuous FintypeCat.{w} G).IsClosedUnderFiniteLimits
+ instance : (isContinuous FintypeCat.{w} G).IsClosedUnderSubobjects := by
+ instance : (isContinuous FintypeCat.{w} G).IsGaloisSubcategory
+ instance : P.IsClosedUnderFiniteCoproducts
+ instance : P.IsClosedUnderFiniteProducts
+ instance [HasFiniteColimits V] (S : Set G) :
+ instance [HasFiniteLimits V] (S : Set G) :
+ instance {ι : Type*} (P : ι → ObjectProperty C) [∀ i, (P i).IsClosedUnderQuotients] :
+ instance {ι : Type*} (P : ι → ObjectProperty C) [∀ i, (P i).IsClosedUnderSubobjects] :
+ isContinuous_eq_iSup
+ trivialOnSet
+ trivialOnSet_antitone
+ trivialOnSet_le_isContinuous
+ ρ_apply_eq_smul

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 29f0f3e).

• +26 new declarations
• −0 removed declarations

+Action.exists_openSubgroup_of_isContinuous_of_finite
+Action.instIsClosedUnderColimitsOfShapeTrivialOnSetOfHasColimitsOfShape
+Action.instIsClosedUnderFiniteColimitsFintypeCatIsContinuousFunObjFinite
+Action.instIsClosedUnderFiniteColimitsTrivialOnSetOfHasFiniteColimits
+Action.instIsClosedUnderFiniteLimitsFintypeCatIsContinuousFunObjFinite
+Action.instIsClosedUnderFiniteLimitsTrivialOnSetOfHasFiniteLimits
+Action.instIsClosedUnderLimitsOfShapeTrivialOnSetOfHasLimitsOfShape
+Action.instIsClosedUnderSubobjectsFintypeCatIsContinuousFunObjFinite
+Action.instIsClosedUnderSubobjectsTrivialOnSetOfHasPullbacks
+Action.instIsGaloisSubcategoryFintypeCatIsContinuousFunObjFinite
+Action.instIsGaloisSubcategoryFintypeCatTrivialOnSet
+Action.isContinuous
+Action.isContinuous_eq_iSup
+Action.trivialOnSet
+Action.trivialOnSet_antitone
+Action.trivialOnSet_le_isContinuous
+Action.ρ_apply_eq_smul
+CategoryTheory.ObjectProperty.IsClosedUnderFiniteColimits.instIsClosedUnderFiniteCoproducts
+CategoryTheory.ObjectProperty.IsClosedUnderFiniteLimits.instIsClosedUnderFiniteProducts
+CategoryTheory.ObjectProperty.instIsClosedUnderColimitsOfShapeSingleObjOfIsClosedUnderFiniteColimitsOfFinite
+CategoryTheory.ObjectProperty.instIsClosedUnderQuotientsISup
+CategoryTheory.ObjectProperty.instIsClosedUnderSubobjectsISup
+OpenAddSubgroup.iInfOfFinite
+OpenAddSubgroup.iInfOfFinite_le
+OpenSubgroup.iInfOfFinite
+OpenSubgroup.iInfOfFinite_le

---

No changes to strong technical debt.

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

Current number	Change	Type (weak)
exposed public sections	5048	1

Current commit 29f0f3e212
Reference commit 69fe4f49ff

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.py 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).

[mathlib-dependent-issues]

This PR/issue depends on:

• [Merged by Bors] - feat(CategoryTheory): properties of objects that are closed under finite limits #42396
• [Merged by Bors] - feat(CategoryTheory/Galois): full subcategories #42320
  By Dependent Issues (🤖). Happy coding!

[robin-carlier]

LGTM, my only nitpick concerns the addition of some docstrings

[robin-carlier]

Thanks!

maintainer delegate

[github-actions]

🚀 Pull request has been placed on the maintainer queue by robin-carlier.

[jcommelin]

Thanks 🎉

bors merge

[mathlib-bors]

Pull request successfully merged into master.

Build succeeded:

• ci (staging) / Lint style
• ci (staging) / Build
• ci (staging) / Post-Build Step
• ci (staging) / Test and lint
• ci (staging) / Post-CI job