Structures · Category theory
CategoryTheory.IsTriangulated
A triangulated category is a pretriangulated category which satisfies the octahedron axiom (TR 4).
- Shape
- One type argument · adds octahedron_axiom
Extends0
Extends nothing: this is a root of the hierarchy.
Extended by0
Nothing extends this class yet.
Concrete types that are instances5
- CategoryTheory.ObjectProperty.FullSubcategory
- HomotopyCategory
- CategoryTheory.MorphismProperty.Localization
- DerivedCategory
- CategoryTheory.MorphismProperty.Localization'
How is a type an instance?
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Assumed by132
- CategoryTheory.Triangulated.TStructure.eTruncLTGEIsoGELT
- CategoryTheory.Triangulated.TStructure.triangleω₁δ
- CategoryTheory.Triangulated.TStructure.eTruncLTLTIsoLT
- CategoryTheory.Triangulated.TStructure.ω₁δ
- CategoryTheory.Triangulated.someOctahedron
- CategoryTheory.Triangulated.TStructure.truncGELTToLTGE
- CategoryTheory.Triangulated.TStructure.eTruncGEIsoGEGE
- CategoryTheory.Triangulated.TStructure.spectralObject
- CategoryTheory.ObjectProperty.extensionProduct_assoc
- CategoryTheory.Triangulated.TStructure.isIso_truncLT_map_truncLTι_app
- CategoryTheory.Triangulated.TStructure.truncGELTToLTGE_app_pentagon
- CategoryTheory.Triangulated.TStructure.eTruncGEIsoGEGE_hom
- CategoryTheory.Triangulated.TStructure.isIso_truncGE_map_truncGEπ_app
- CategoryTheory.Triangulated.TStructure.isIso₂_truncGE_map_of_isLE
- CategoryTheory.Triangulated.TStructure.eTruncLTGEIsoGELT_hom_naturality
- CategoryTheory.Triangulated.TStructure.eTruncLTLTIsoLT_inv_hom_id_app
- CategoryTheory.Triangulated.TStructure.ω₁δ_app
- CategoryTheory.Triangulated.TStructure.isIso₁_truncLT_map_of_isGE
- CategoryTheory.Triangulated.TStructure.spectralObjectFunctor
- CategoryTheory.ObjectProperty.extensionProductIter_succ'
- CategoryTheory.Triangulated.TStructure.eTruncLTGEIsoGELT_hom_app_fac
- CategoryTheory.Triangulated.TStructure.eTruncLTGEIsoGELT_naturality_app
- CategoryTheory.Triangulated.TStructure.eTruncLTLTIsoLT_inv_hom_id_app_eTruncLT_obj
- CategoryTheory.Triangulated.TStructure.eTruncGEIsoGEGE_hom_inv_id_app
- CategoryTheory.Triangulated.TStructure.eTruncLTLTIsoLT_hom
- CategoryTheory.Triangulated.TStructure.truncGELTToLTGE_app_pentagon_uniqueness
- CategoryTheory.Triangulated.TStructure.eTruncLTGEIsoGELT_hom_app_fac_assoc
- CategoryTheory.Triangulated.TStructure.ω₁δ_naturality
- CategoryTheory.Triangulated.TStructure.eTruncGEIsoGEGE_inv_hom_id_app
- CategoryTheory.Triangulated.TStructure.eTruncLTGEIsoGELT_hom_app_fac'
- CategoryTheory.Triangulated.TStructure.isIso_eTruncLT_obj_map_truncLTπ_app
- CategoryTheory.isTriangulated_of_essSurj_mapComposableArrows_two
- CategoryTheory.Triangulated.TStructure.isIso_eTruncGE_obj_map_truncGEπ_app
- CategoryTheory.ObjectProperty.leftOrthogonal.map_bijective_of_isTriangulated
- CategoryTheory.Triangulated.TStructure.truncLT_map_truncGE_map_truncLTι_app_fac
- CategoryTheory.ObjectProperty.extensionProductIter_add
- CategoryTheory.ObjectProperty.extensionProductIter_add'
- CategoryTheory.Triangulated.TStructure.eTruncLTLTIsoLT_hom_inv_id_app
- CategoryTheory.ObjectProperty.rightOrthogonal.map_bijective_of_isTriangulated
- CategoryTheory.Triangulated.someOctahedron'
- CategoryTheory.Triangulated.TStructure.triangleω₁δObjIso
- CategoryTheory.ObjectProperty.instFullLocalizedFunctorFullSubcategoryTrWInverseImageιTriangulatedLocalizerMorphism
- CategoryTheory.Triangulated.Localization.instIsTriangulatedLocalization'
- CategoryTheory.Triangulated.TStructure.eTruncLTGEIsoGELT_hom_app_fac'_assoc
- CategoryTheory.Triangulated.TStructure.eTruncLTGEIsoGELT_naturality_app_assoc
- CategoryTheory.Triangulated.someOctahedron.congr_simp
- CategoryTheory.ObjectProperty.instAdditiveLocalizedFunctorFullSubcategoryTrWInverseImageιTriangulatedLocalizerMorphism_1
- CategoryTheory.Triangulated.TStructure.triangleω₁δ_obj_obj₁
- CategoryTheory.Triangulated.TStructure.instIsGEObjTruncLTGE
- CategoryTheory.Triangulated.TStructure.triangleω₁δ_obj_mor₁
Ancestors0
No ancestors.