Structures · Category theory
CategoryTheory.Functor.IsTriangulated
A functor which commutes with the shift by ℤ is triangulated if
it sends distinguished triangles to distinguished triangles.
- Shape
- One type argument · adds map_distinguished
Extends0
Extends nothing: this is a root of the hierarchy.
Extended by1
Forgetful instances
Provided automatically by
Concrete types that are instances5
- CategoryTheory.ObjectProperty.FullSubcategory
- HomotopyCategory
- DerivedCategory
- HomotopyCategory.Plus
- Opposite
How is a type an instance?
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Assumed by40
- CategoryTheory.Functor.map_distinguished
- CategoryTheory.Adjunction.isTriangulated_rightAdjoint
- CategoryTheory.Functor.map_distinguished_iff
- CategoryTheory.Triangulated.SpectralObject.mapTriangulatedFunctor
- CategoryTheory.Triangulated.Octahedron.map
- CategoryTheory.Functor.isTriangulated_of_op
- CategoryTheory.Functor.isTriangulated_of_iso
- CategoryTheory.Functor.mem_mapTriangle_essImage_of_distinguished
- CategoryTheory.Functor.isTriangulated_of_precomp
- CategoryTheory.Functor.IsTriangulated.map_distinguished
- CategoryTheory.isTriangulated_of_essSurj_mapComposableArrows_two
- CategoryTheory.Adjunction.isTriangulated_leftAdjoint
- CategoryTheory.Functor.distTriang_iff
- CategoryTheory.ObjectProperty.inverseImage_trW_isInverted
- CategoryTheory.Adjunction.IsTriangulated.mk''
- CategoryTheory.ObjectProperty.inverseImage_trW_iff
- CategoryTheory.Triangulated.Localization.isTriangulated
- CategoryTheory.IsTriangulated.of_fully_faithful_triangulated_functor
- CategoryTheory.Equivalence.IsTriangulated.instIsTriangulatedInverseSymmOfFunctor
- CategoryTheory.Functor.isTriangulated_iff_comp_right
- CategoryTheory.Functor.IsTriangulated.instPreservesZeroMorphisms
- CategoryTheory.Functor.IsTriangulated.instComp
- CategoryTheory.Functor.isTriangulated_of_precomp_iso
- CategoryTheory.Triangulated.Octahedron.map_m₃
- CategoryTheory.Functor.instIsHomologicalCompOfIsTriangulated
- CategoryTheory.Pretriangulated.Opposite.functor_isTriangulated_op
- CategoryTheory.Functor.mapTriangulatedSpectralObject
- CategoryTheory.ObjectProperty.isTriangulated_lift
- CategoryTheory.Functor.IsTriangulated.instAdditive
- CategoryTheory.ObjectProperty.instIsTriangulatedInverseImage
- CategoryTheory.Triangulated.SpectralObject.mapTriangulatedFunctor_δ
- CategoryTheory.Adjunction.IsTriangulated.mk'
- CategoryTheory.Functor.isHomological_of_localization
- CategoryTheory.Equivalence.IsTriangulated.instIsTriangulatedFunctorSymmOfInverse
- CategoryTheory.Triangulated.SpectralObject.mapTriangulatedFunctor_ω₁
- CategoryTheory.Triangulated.SpectralObject.mapTriangulatedFunctor_δ'
- CategoryTheory.Functor.IsTriangulated.instPreservesLimitsOfShapeDiscreteWalkingPair
- CategoryTheory.ObjectProperty.instIsTriangulatedMapOfIsTriangulatedOfFull
- CategoryTheory.ObjectProperty.instIsTriangulatedEssImageOfIsTriangulatedOfFull
- CategoryTheory.Triangulated.Octahedron.map_m₁
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