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[Merged by Bors] - feat(CategoryTheory/Shift): sequences of functors from a category with a shift #9001
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jcommelin
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Thanks 🎉
bors merge
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…h a shift (#9001) Let `F : C ⥤ A` be a functor from a category `C` that is equipped with a shift by an additive monoid `M`. In this PR, we define a typeclass `F.ShiftSequence M` which includes the data of a sequence of functors `F.shift a : C ⥤ A` for all `a : A`. For each `a : A`, we have an isomorphism `F.isoShift a : shiftFunctor C a ⋙ F ≅ F.shift a` which satisfies some coherence relations. This will allow a better formulation of the long exact sequence attached to homological functors from a triangulated category to an abelian category.
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…h a shift (#9001) Let `F : C ⥤ A` be a functor from a category `C` that is equipped with a shift by an additive monoid `M`. In this PR, we define a typeclass `F.ShiftSequence M` which includes the data of a sequence of functors `F.shift a : C ⥤ A` for all `a : A`. For each `a : A`, we have an isomorphism `F.isoShift a : shiftFunctor C a ⋙ F ≅ F.shift a` which satisfies some coherence relations. This will allow a better formulation of the long exact sequence attached to homological functors from a triangulated category to an abelian category.
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feat(CategoryTheory/Shift): sequences of functors from a category with a shift
[Merged by Bors] - feat(CategoryTheory/Shift): sequences of functors from a category with a shift
Dec 27, 2023
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Let
F : C ⥤ A
be a functor from a categoryC
that is equipped with a shift by an additive monoidM
. In this PR, we define a typeclassF.ShiftSequence M
which includes the data of a sequence of functorsF.shift a : C ⥤ A
for alla : A
. For eacha : A
, we have an isomorphismF.isoShift a : shiftFunctor C a ⋙ F ≅ F.shift a
which satisfies some coherence relations. This will allow a better formulation of the long exact sequence attached to homological functors from a triangulated category to an abelian category.