feat(Algebra/Homology): existence of injective resolutions for cochain complexes

[joelriou]

---

• depends on: [Merged by Bors] - feat(Algebra/Homology/Embedding): various results about truncations #40885

[github-actions]

PR summary f843dcd493

Import changes for modified files

Dependency changes

File	Base Count	Head Count	Change
Mathlib.Algebra.Homology.Factorizations.CM5a	1396	1403	+7 (+0.50%)

Import changes for all files

Files	Import difference
Mathlib.Algebra.Homology.ModelCategory.Injective	5
Mathlib.Algebra.Homology.Factorizations.CM5a	7

---

Declarations diff (regex)

+ exists_injective_resolution
+ exists_injective_resolution'

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 f843dcd).

• +2 new declarations
• −0 removed declarations

+CochainComplex.Plus.modelCategoryQuillen.exists_injective_resolution
+CochainComplex.Plus.modelCategoryQuillen.exists_injective_resolution'

---

No changes to strong technical debt.

No changes to weak technical debt.

Current commit f843dcd493
Reference commit 096aa7bdd1

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).

[mathlib-dependent-issues]

This PR/issue depends on:

• [Merged by Bors] - feat(Algebra/Homology/Embedding): various results about truncations #40885
  By Dependent Issues (🤖). Happy coding!

[smorel394]

The math looks good. It would be nice to maybe have some explanations about what is going on, in particular how the first result exists_injective_resolution' is used to deduce the second result exists_injective_resolution.

[joelriou]

The math looks good. It would be nice to maybe have some explanations about what is going on, in particular how the first result exists_injective_resolution' is used to deduce the second result exists_injective_resolution.

Thanks for the reviews! I have added some comments about the proof.