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[Merged by Bors] - feat(CategoryTheory): exact sequences#8152

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joelriou wants to merge 17 commits intomasterfrom
exact-sequence
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[Merged by Bors] - feat(CategoryTheory): exact sequences#8152
joelriou wants to merge 17 commits intomasterfrom
exact-sequence

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@joelriou joelriou commented Nov 3, 2023

This PR defines the predicate ComposableArrows.Exact.


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@joelriou joelriou added WIP Work in progress t-category-theory Category theory labels Nov 3, 2023
@ghost ghost added the blocked-by-other-PR This PR depends on another PR (this label is automatically managed by a bot) label Nov 3, 2023
@ghost ghost removed the blocked-by-other-PR This PR depends on another PR (this label is automatically managed by a bot) label Nov 3, 2023
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ghost commented Nov 3, 2023

@joelriou joelriou removed the WIP Work in progress label Nov 4, 2023
lemma exact_iff_of_iso {S₁ S₂ : ComposableArrows C n} (e : S₁ ≅ S₂) :
S₁.Exact ↔ S₂.Exact :=
⟨exact_of_iso e, exact_of_iso e.symm⟩

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Could you please add a statement that if you start with a ShortComplex and turn it into a ComposableArrows _ 2, then one is exact iff the other is exact?

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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 Nov 10, 2023
mathlib-bors bot pushed a commit that referenced this pull request Nov 10, 2023
This PR defines the predicate `ComposableArrows.Exact`.
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mathlib-bors bot commented Nov 10, 2023

Pull request successfully merged into master.

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@mathlib-bors mathlib-bors bot changed the title feat(CategoryTheory): exact sequences [Merged by Bors] - feat(CategoryTheory): exact sequences Nov 10, 2023
@mathlib-bors mathlib-bors bot closed this Nov 10, 2023
@mathlib-bors mathlib-bors bot deleted the exact-sequence branch November 10, 2023 13:09
grunweg pushed a commit that referenced this pull request Dec 15, 2023
This PR defines the predicate `ComposableArrows.Exact`.
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