Structures · Category theory
CategoryTheory.Functor.ShiftSequence
A shift sequence for a functor F : C ⥤ A when C is equipped with a shift
by a monoid M involves a sequence of functor sequence n : C ⥤ A for all n : M
which behave like shiftFunctor C n ⋙ F.
- Shape
- 2 explicit arguments · adds sequence, isoZero, shiftIso, shiftIso_zero, shiftIso_add
Extends0
Extends nothing: this is a root of the hierarchy.
Extended by0
Nothing extends this class yet.
Concrete types that are instances5
- HomologicalComplex
- HomotopyCategory
- DerivedCategory
- DerivedCategory.Plus
- Opposite
How is a type an instance?
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Assumed by78
- CategoryTheory.Functor.shift
- CategoryTheory.Functor.shiftIso
- CategoryTheory.Functor.shiftMap
- CategoryTheory.Functor.homologySequenceδ
- CategoryTheory.Functor.homologySequence_exact₂
- CategoryTheory.Functor.homologySequence_comp
- CategoryTheory.Functor.homologySequence_exact₃
- CategoryTheory.Functor.isoShift
- CategoryTheory.Functor.ShiftSequence.induced
- CategoryTheory.Functor.comp_homologySequenceδ
- CategoryTheory.Functor.homologySequenceδ_comp
- CategoryTheory.Functor.homologySequence_exact₁
- CategoryTheory.Functor.shiftMap_comp'
- CategoryTheory.Functor.shiftMap_comp
- CategoryTheory.Functor.isoShiftZero
- CategoryTheory.Functor.shiftIso_add
- CategoryTheory.Functor.ShiftSequence.leftComp
- CategoryTheory.Functor.ShiftSequence.sequence
- CategoryTheory.Functor.ShiftSequence.induced_shiftMap
- CategoryTheory.Functor.ShiftSequence.induced_shiftIso_hom_app_obj
- CategoryTheory.Functor.ShiftSequence.shiftIso
- CategoryTheory.Functor.ShiftSequence.induced.shiftIso
- CategoryTheory.Functor.isoShift_hom_naturality
- CategoryTheory.Functor.homologySequence_mono_shift_map_mor₁_iff
- CategoryTheory.Functor.homologySequenceComposableArrows₅
- CategoryTheory.Functor.shiftMap_zero
- CategoryTheory.Functor.homologySequence_epi_shift_map_mor₁_iff
- CategoryTheory.Functor.shiftIso_add'
- CategoryTheory.Functor.shiftIso_add'_hom_app
- CategoryTheory.Functor.shiftIso_zero
- CategoryTheory.Functor.shiftIso_hom_naturality
- CategoryTheory.Functor.shiftIso_hom_app_comp_shiftMap_of_add_eq_zero
- CategoryTheory.Functor.shiftIso_hom_naturality_assoc
- CategoryTheory.Functor.shiftIso_hom_app_comp_shiftMap
- CategoryTheory.Functor.homologySequence_mono_shift_map_mor₂_iff
- CategoryTheory.Functor.shiftIso_zero_hom_app
- CategoryTheory.Functor.ShiftSequence.shiftIso_add
- CategoryTheory.Functor.shiftIso_hom_app_comp
- CategoryTheory.Functor.ShiftSequence.shiftIso_zero
- CategoryTheory.Functor.ShiftSequence.induced_isoShiftZero_hom_app_obj
- CategoryTheory.Functor.mem_homologicalKernel_trW_iff
- CategoryTheory.Functor.homologySequence_epi_shift_map_mor₂_iff
- CategoryTheory.Functor.homologySequenceδ_naturality
- CategoryTheory.Functor.ShiftSequence.induced.shiftIso_hom_app_obj
- CategoryTheory.Functor.ShiftSequence.induced.isoZero
- CategoryTheory.Functor.shiftIso_inv_naturality
- CategoryTheory.Functor.ShiftSequence.isoZero
- CategoryTheory.Functor.mem_homologicalKernel_iff
- CategoryTheory.Functor.isoShift_inv_naturality
- CategoryTheory.Functor.homologySequenceComposableArrows₅_exact
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