feat(CategoryTheory/Abelian): projective dimension

[joelriou]

We introduce a typeclass HasProjectiveDimensionLT X n expressing that Ext X Y i all vanish when n ≤ i. We study how it behaves with respect to short exact sequences.
When #19591 will be merged, it will possible to show HasProjectiveDimensionLT X 1 ↔ Projective X.

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• depends on: [Merged by Bors] - feat(CategoryTheory/Abelian): Ext.{w} does not depend on the universe w #19602

[github-actions]

PR summary cdc230ebe4

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference
Mathlib.CategoryTheory.Abelian.ProjectiveDimension (new file)	1422

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Declarations diff

+ Abelian.Ext.eq_zero_of_hasProjectiveDimensionLT
+ HasExt.standard
+ HasProjectiveDimensionLT
+ Limits.IsZero.hasProjectiveDimensionLT_zero
+ Retract.hasProjectiveDimensionLT
+ hasProjectiveDimensionLT_X₁
+ hasProjectiveDimensionLT_X₂
+ hasProjectiveDimensionLT_X₃
+ hasProjectiveDimensionLT_X₃_iff
+ hasProjectiveDimensionLT_iff
+ hasProjectiveDimensionLT_of_ge
+ hasProjectiveDimensionLT_of_iso
+ instance (X Y : C) (n : ℕ) [HasProjectiveDimensionLT X n]
+ instance : HasProjectiveDimensionLT (0 : C) 0
+ instance [HasProjectiveDimensionLT X n] :
+ mk
+ refl
+ retract
+ subsingleton
+ trans
++ instance [HasProjectiveDimensionLT X n] (k : ℕ) :

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.

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No changes to technical debt.

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(CategoryTheory/Abelian): Ext.{w} does not depend on the universe w #19602
  By Dependent Issues (🤖). Happy coding!