feat(CategoryTheory): triangulated derived functors using derivability structures

[joelriou]

---

• depends on: feat(CategoryTheory): pointwise left derived functors using derivability structures #43237
• depends on: [Merged by Bors] - feat(CategoryTheory): right Kan extensions and Guitart exact squares #43063
• depends on: [Merged by Bors] - feat(CategoryTheory/Functor/Derived): derived functors are triangulated #39126
• depends on: [Merged by Bors] - feat(CategoryTheory): the right derived functor commutes with the shift #39117

[github-actions]

PR summary c0440e0493

Import changes for modified files

Dependency changes

File	Base Count	Head Count	Change
Mathlib.CategoryTheory.Localization.DerivabilityStructure.Derives	692	695	+3 (+0.43%)

Import changes for all files

Files	Import difference
3 files Mathlib.Algebra.Homology.DerivedCategory.DerivabilityStructureInjectives Mathlib.Algebra.Homology.DerivedCategory.RightDerivedFunctorPlus Mathlib.CategoryTheory.Localization.DerivabilityStructure.Derives	3
Mathlib.CategoryTheory.Localization.DerivabilityStructure.PointwiseLeftDerived (new file)	691
Mathlib.CategoryTheory.Localization.DerivabilityStructure.DerivesTriangulated (new file)	1196

---

Declarations diff (regex)

+ hasPointwiseLeftDerivedFunctor
+ hasPointwiseLeftDerivedFunctorAt_iff_of_isLeftDerivabilityStructure
+ hasPointwiseLeftDerivedFunctor_iff_of_isLeftDerivabilityStructure
+ instance : IsIso (Φ.leftDerivedFunctorComparison L₁ L₂ F F₁ α₁ F₂ α₂) := by
+ isIso'
+ isIso_iff_of_isLeftDerivabilityStructure
+ isLeftDerivedFunctor_iff_isIso
+ isLeftDerivedFunctor_of_isIso
+ isTriangulated_of_isLeftDerivedFunctor
+ isTriangulated_of_isRightDerivedFunctor
+ leftDerivedFunctorComparison
+ leftDerivedFunctorComparison_fac
+ leftDerivedFunctorComparison_fac_app

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 c0440e0).

• +17 new declarations
• −0 removed declarations

+CategoryTheory.Functor.totalLeftDerived.congr_simp
+CategoryTheory.LocalizerMorphism.Derives.hasPointwiseLeftDerivedFunctor
+CategoryTheory.LocalizerMorphism.Derives.isIso'
+CategoryTheory.LocalizerMorphism.Derives.isLeftDerivedFunctor_iff_isIso
+CategoryTheory.LocalizerMorphism.Derives.isLeftDerivedFunctor_of_isIso
+CategoryTheory.LocalizerMorphism.Derives.isTriangulated_of_isLeftDerivedFunctor
+CategoryTheory.LocalizerMorphism.Derives.isTriangulated_of_isRightDerivedFunctor
+CategoryTheory.LocalizerMorphism.hasPointwiseLeftDerivedFunctorAt_iff_of_isLeftDerivabilityStructure
+CategoryTheory.LocalizerMorphism.hasPointwiseLeftDerivedFunctor_iff_of_isLeftDerivabilityStructure
+CategoryTheory.LocalizerMorphism.instIsIsoFunctorLeftDerivedFunctorComparison
+CategoryTheory.LocalizerMorphism.isIso_iff_of_isLeftDerivabilityStructure
+CategoryTheory.LocalizerMorphism.leftDerivedFunctorComparison
+CategoryTheory.LocalizerMorphism.leftDerivedFunctorComparison.congr_simp
+CategoryTheory.LocalizerMorphism.leftDerivedFunctorComparison_fac
+CategoryTheory.LocalizerMorphism.leftDerivedFunctorComparison_fac_app
+CategoryTheory.LocalizerMorphism.leftDerivedFunctorComparison_fac_app_assoc
+CategoryTheory.LocalizerMorphism.leftDerivedFunctorComparison_fac_assoc

---

Increase in strong tech debt: (relative, absolute) = (2.23, 0.00)

Current number	Change	Type (strong)
backward.defeqAttrib.useBackward	4297	2
backward.isDefEq.respectTransparency	4856	1
backward.isDefEq.respectTransparency.types	2509	3

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

Current number	Change	Type (weak)
exposed public sections	5032	2

Current commit c0440e0493
Reference commit 2ca39e6298

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-merge-conflicts]

This pull request has conflicts, please merge master and resolve them.

[mathlib-dependent-issues]

This PR/issue depends on:

• feat(CategoryTheory): pointwise left derived functors using derivability structures #43237
• [Merged by Bors] - feat(CategoryTheory): right Kan extensions and Guitart exact squares #43063
• [Merged by Bors] - feat(CategoryTheory/Functor/Derived): derived functors are triangulated #39126
• [Merged by Bors] - feat(CategoryTheory): the right derived functor commutes with the shift #39117
  By Dependent Issues (🤖). Happy coding!

[mathlib-merge-conflicts]

This pull request has conflicts, please merge master and resolve them.