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[Merged by Bors] - feat: the homological functor on the homotopy category of cochain complexes in an abelian category #11760

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@joelriou joelriou commented Mar 29, 2024

In this PR, it is shown that the homology functors on the homotopy category of cochain complexes in an abelian category are homological functors (in the sense that they send distinguished triangles to exact sequences). This PR also shows that the category of homological complexes in an abelian category is an abelian category.


Note: the two new definitions like Abelian.isColimitMapCoconeOfCokernelCoforkOfπKernelConditionOfEpi are also used in order to show that the category of presheaves of modules is abelian #12721.

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@joelriou joelriou added the t-category-theory Category theory label Mar 29, 2024
@leanprover-community-mathlib4-bot leanprover-community-mathlib4-bot added the blocked-by-other-PR This PR depends on another PR to Mathlib (this label is automatically managed by a bot) label Mar 29, 2024
@leanprover-community-mathlib4-bot leanprover-community-mathlib4-bot removed the blocked-by-other-PR This PR depends on another PR to Mathlib (this label is automatically managed by a bot) label Apr 29, 2024
@leanprover-community-mathlib4-bot leanprover-community-mathlib4-bot added the merge-conflict The PR has a merge conflict with master, and needs manual merging. (this label is managed by a bot) label Apr 29, 2024
@leanprover-community-mathlib4-bot leanprover-community-mathlib4-bot removed the merge-conflict The PR has a merge conflict with master, and needs manual merging. (this label is managed by a bot) label Apr 30, 2024
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LGTM, but one question about names.

Mathlib/CategoryTheory/Abelian/Basic.lean Outdated Show resolved Hide resolved
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Thanks 🎉

bors merge

@github-actions github-actions bot added ready-to-merge This PR has been sent to bors. and removed awaiting-review labels May 11, 2024
mathlib-bors bot pushed a commit that referenced this pull request May 11, 2024
…plexes in an abelian category (#11760)

In this PR, it is shown that the homology functors on the homotopy category of cochain complexes in an abelian category are homological functors (in the sense that they send distinguished triangles to exact sequences). This PR also shows that the category of homological complexes in an abelian category is an abelian category.
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mathlib-bors bot commented May 11, 2024

Pull request successfully merged into master.

Build succeeded:

@mathlib-bors mathlib-bors bot changed the title feat: the homological functor on the homotopy category of cochain complexes in an abelian category [Merged by Bors] - feat: the homological functor on the homotopy category of cochain complexes in an abelian category May 11, 2024
@mathlib-bors mathlib-bors bot closed this May 11, 2024
@mathlib-bors mathlib-bors bot deleted the homotopy-category-homological-functor branch May 11, 2024 08:45
apnelson1 pushed a commit that referenced this pull request May 12, 2024
…plexes in an abelian category (#11760)

In this PR, it is shown that the homology functors on the homotopy category of cochain complexes in an abelian category are homological functors (in the sense that they send distinguished triangles to exact sequences). This PR also shows that the category of homological complexes in an abelian category is an abelian category.
callesonne pushed a commit that referenced this pull request May 16, 2024
…plexes in an abelian category (#11760)

In this PR, it is shown that the homology functors on the homotopy category of cochain complexes in an abelian category are homological functors (in the sense that they send distinguished triangles to exact sequences). This PR also shows that the category of homological complexes in an abelian category is an abelian category.
grunweg pushed a commit that referenced this pull request May 17, 2024
…plexes in an abelian category (#11760)

In this PR, it is shown that the homology functors on the homotopy category of cochain complexes in an abelian category are homological functors (in the sense that they send distinguished triangles to exact sequences). This PR also shows that the category of homological complexes in an abelian category is an abelian category.
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