[Merged by Bors] - feat(CategoryTheory/Triangulated): the long exact sequence of a homological functor#11805
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[Merged by Bors] - feat(CategoryTheory/Triangulated): the long exact sequence of a homological functor#11805
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…triangulated subcategory
…riangulated-subcategory-w
…riangulated-subcategory-w
…omological-functor
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Thanks! |
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🚀 Pull request has been placed on the maintainer queue by erdOne. |
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Thanks! I left a suggestion about comments depicting commutative diagrams.
bors d+
| F.shiftMap (f ≫ g) a a' ha' = (F.shift a).map f ≫ F.shiftMap g a a' ha' := by | ||
| simp [shiftMap] | ||
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| lemma shiftIso_hom_app_comp_shiftMap {X Y : C} {m : M} (f : X ⟶ Y⟦m⟧) (n mn : M) (hnm : m + n = mn) |
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I'll leave this as optional but personally I think it might be nice to have some kind of ASCII art for this lemma and the next one just showing what they actually say, because it's very hard to read the statements, even within VS Code.
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Thanks for the suggestion. I have added docstrings with how I understand what these lemmas say.
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✌️ joelriou can now approve this pull request. To approve and merge a pull request, simply reply with |
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Thanks! bors merge |
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…ogical functor (#11805) Assuming `F : C ⥤ A` is a homological functor (from a pretriangulated category to an abelian category), we show that any distinguished triangle leads to a long exact sequence (assuming `n₀ + 1 = n₁`): `... ⟶ (F.shift n₀).obj T.obj₁ ⟶ (F.shift n₀).obj T.obj₂ ⟶ (F.shift n₀).obj T.obj₃ ⟶ (F.shift n₁).obj T.obj₁ ⟶ ...`
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Pull request successfully merged into master. Build succeeded: |
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…ogical functor (#11805) Assuming `F : C ⥤ A` is a homological functor (from a pretriangulated category to an abelian category), we show that any distinguished triangle leads to a long exact sequence (assuming `n₀ + 1 = n₁`): `... ⟶ (F.shift n₀).obj T.obj₁ ⟶ (F.shift n₀).obj T.obj₂ ⟶ (F.shift n₀).obj T.obj₃ ⟶ (F.shift n₁).obj T.obj₁ ⟶ ...`
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…ogical functor (#11805) Assuming `F : C ⥤ A` is a homological functor (from a pretriangulated category to an abelian category), we show that any distinguished triangle leads to a long exact sequence (assuming `n₀ + 1 = n₁`): `... ⟶ (F.shift n₀).obj T.obj₁ ⟶ (F.shift n₀).obj T.obj₂ ⟶ (F.shift n₀).obj T.obj₃ ⟶ (F.shift n₁).obj T.obj₁ ⟶ ...`
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Assuming
F : C ⥤ Ais a homological functor (from a pretriangulated category to an abelian category), we show that any distinguished triangle leads to a long exact sequence (assumingn₀ + 1 = n₁):... ⟶ (F.shift n₀).obj T.obj₁ ⟶ (F.shift n₀).obj T.obj₂ ⟶ (F.shift n₀).obj T.obj₃ ⟶ (F.shift n₁).obj T.obj₁ ⟶ ...