[Merged by Bors] - feat(CategoryTheory/Abelian): exactness of colimits (short complex version)#21990
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[Merged by Bors] - feat(CategoryTheory/Abelian): exactness of colimits (short complex version)#21990
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…map-short-complex
PR summary 88d0941b5bImport changes exceeding 2%
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| File | Base Count | Head Count | Change |
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| Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Colim | 601 | 945 | +344 (+57.24%) |
Import changes for all files
| Files | Import difference |
|---|---|
Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Colim |
344 |
Declarations diff
+ colim.exact_mapShortComplex
+ colim.mapShortComplex
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.
No changes to technical debt.
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./scripts/technical-debt-metrics.sh pr_summary
- The
relativevalue is the weighted sum of the differences with weight given by the inverse of the current value of the statistic. - The
absolutevalue is therelativevalue divided by the total sum of the inverses of the current values (i.e. the weighted average of the differences).
TwoFX
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Feb 17, 2025
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| namespace CategoryTheory.Limits | ||
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| variable {C : Type u} [Category.{v} C] [Abelian C] |
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I think the entire file isn't really about abelian categories at all, the Abelian C can be replaced by HasZeroMorphisms C. So I think it makes sense to move the file to GrothendieckAxioms instead of GrothendieckCategory and generalize the typeclass assumption.
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Thanks for the suggestion, I have moved the code into GrothendieckAxioms.Colim with a HasZeroMorphisms assumption.
Co-authored-by: Markus Himmel <markus@himmel-villmar.de>
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…rsion) (#21990) Assuming `HasExactColimitsOfShape J C`, we rephrase the exactness of `colim : (J ⥤ C) ⥤ C` by saying that if `S : ShortComplex (J ⥤ C)` is exact, and we have colimit cocones `c₁`, `c₂`, `c₃` for `S.X₁`, `S.X₂` and `S.X₃`, then the induced short complex `c₁.pt ⟶ c₂.pt ⟶ c₃.pt` is exact. Co-authored-by: Joël Riou <37772949+joelriou@users.noreply.github.com>
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Assuming
HasExactColimitsOfShape J C, we rephrase the exactness ofcolim : (J ⥤ C) ⥤ Cby saying that ifS : ShortComplex (J ⥤ C)is exact, and we have colimit coconesc₁,c₂,c₃forS.X₁,S.X₂andS.X₃, then the induced short complexc₁.pt ⟶ c₂.pt ⟶ c₃.ptis exact.