Structures · Algebra
TotalComplexShapeSymmetry
A total complex shape symmetry contains the data and properties which allow the
identification of the two total complex functors
HomologicalComplex₂ C c₁ c₂ ⥤ HomologicalComplex C c₁₂
and HomologicalComplex₂ C c₂ c₁ ⥤ HomologicalComplex C c₁₂ via the flip.
- Shape
- 3 explicit arguments · adds symm, σ, σ_ε₁, σ_ε₂
Extends0
Extends nothing: this is a root of the hierarchy.
Extended by0
Nothing extends this class yet.
Concrete types that are instances1
- Int
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Assumed by40
- ComplexShape.σ
- HomologicalComplex₂.totalFlipIso
- HomologicalComplex.mapBifunctorFlipIso
- HomologicalComplex₂.totalFlipIsoX
- TotalComplexShapeSymmetry.σ
- HomologicalComplex₂.ιTotal_totalFlipIso_f_hom
- HomologicalComplex₂.ιTotal_totalFlipIso_f_inv
- ComplexShape.π_symm
- HomologicalComplex₂.totalFlipIsoX_hom_D₁
- HomologicalComplex.ι_mapBifunctorFlipIso_hom
- HomologicalComplex₂.totalFlipIsoX_hom_D₂
- ComplexShape.symmetryEquiv
- HomologicalComplex.ι_mapBifunctorFlipIso_hom_assoc
- HomologicalComplex₂.flip_totalFlipIso
- TotalComplexShapeSymmetry.symmetry
- HomologicalComplex.mapBifunctorFlipIso_hom_naturality
- ComplexShape.σ_symm
- TotalComplexShapeSymmetry.σ_ε₂
- TotalComplexShapeSymmetry.σ_ε₁
- HomologicalComplex₂.totalFlipIso_hom_f_D₁
- HomologicalComplex.ι_mapBifunctorFlipIso_inv
- ComplexShape.σ_ε₁
- ComplexShape.σ_ε₂
- HomologicalComplex₂.totalFlipIso_hom_f_D₂
- HomologicalComplex₂.flip_hasTotal_iff
- TotalComplexShapeSymmetry.symm
- HomologicalComplex.instHasMapBifunctorFlip
- ComplexShape.symmetryEquiv_symm_apply_coe
- HomologicalComplex₂.ιTotal_totalFlipIso_f_hom_assoc
- HomologicalComplex₂.totalFlipIsoX_hom_D₁_assoc
- HomologicalComplex₂.totalFlipIso_hom_f_D₁_assoc
- HomologicalComplex₂.totalFlipIso_hom_f_D₂_assoc
- HomologicalComplex₂.ιTotal_totalFlipIso_f_inv_assoc
- HomologicalComplex₂.instHasTotalFlip
- HomologicalComplex₂.totalFlipIsoX_hom_D₂_assoc
- HomologicalComplex.mapBifunctorFlipIso_flip
- HomologicalComplex.hasMapBifunctor_flip_iff
- ComplexShape.symmetryEquiv_apply_coe
- HomologicalComplex.mapBifunctorFlipIso_hom_naturality_assoc
- HomologicalComplex.ι_mapBifunctorFlipIso_inv_assoc
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