Structures · Category theory
CategoryTheory.Functor.IsHomological
A functor from a pretriangulated category to an abelian category is a homological functor if it sends distinguished triangles to exact sequences.
- Shape
- One type argument · adds exact
Extends1
Extended by0
Nothing extends this class yet.
Concrete types that are instances4
- HomotopyCategory
- DerivedCategory
- DerivedCategory.Plus
- Opposite
How is a type an instance?
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Assumed by25
- CategoryTheory.Functor.homologySequence_exact₂
- CategoryTheory.Functor.homologySequence_comp
- CategoryTheory.Functor.homologySequence_exact₃
- CategoryTheory.Functor.comp_homologySequenceδ
- CategoryTheory.Functor.homologySequenceδ_comp
- CategoryTheory.Functor.homologySequence_exact₁
- CategoryTheory.Functor.map_distinguished_exact
- CategoryTheory.Functor.homologySequence_mono_shift_map_mor₁_iff
- CategoryTheory.Functor.homologySequence_epi_shift_map_mor₁_iff
- CategoryTheory.Functor.homologySequence_mono_shift_map_mor₂_iff
- CategoryTheory.Functor.IsHomological.of_iso
- CategoryTheory.Functor.mem_homologicalKernel_trW_iff
- CategoryTheory.Functor.homologySequence_epi_shift_map_mor₂_iff
- CategoryTheory.Functor.map_distinguished_op_exact
- CategoryTheory.Functor.IsHomological.exact
- CategoryTheory.Functor.homologySequenceComposableArrows₅_exact
- CategoryTheory.Functor.homologySequence_comp_assoc
- CategoryTheory.Functor.IsHomological.toPreservesZeroMorphisms
- CategoryTheory.Functor.comp_homologySequenceδ_assoc
- CategoryTheory.Functor.instIsHomologicalCompOfIsTriangulated
- CategoryTheory.Functor.instAdditiveOfIsHomological
- CategoryTheory.Functor.isHomological_of_localization
- CategoryTheory.Functor.instIsTriangulatedHomologicalKernel
- CategoryTheory.Functor.instPreservesLimitsOfShapeDiscreteWalkingPairOfIsHomological
- CategoryTheory.Functor.homologySequenceδ_comp_assoc