Theorems · Theorem · category theory

HomologicalComplex.mapBifunctorFlipIso_flip

∀ {C₁ : Type u_1} {C₂ : Type u_2} {D : Type u_3} [inst : CategoryTheory.Category.{v_1, u_1} C₁]
  [inst_1 : CategoryTheory.Category.{v_2, u_2} C₂] [inst_2 : CategoryTheory.Category.{v_3, u_3} D] {I₁ : Type u_4}
  {I₂ : Type u_5} {J : Type u_6} {c₁ : ComplexShape I₁} {c₂ : ComplexShape I₂}
  [inst_3 : CategoryTheory.Limits.HasZeroMorphisms C₁] [inst_4 : CategoryTheory.Limits.HasZeroMorphisms C₂]
  [inst_5 : CategoryTheory.Preadditive D] (K₁ : HomologicalComplex C₁ c₁) (K₂ : HomologicalComplex C₂ c₂)
  (F : CategoryTheory.Functor C₁ (CategoryTheory.Functor C₂ D)) [inst_6 : F.PreservesZeroMorphisms]
  [inst_7 : ∀ (X₁ : C₁), (F.obj X₁).PreservesZeroMorphisms] (c : ComplexShape J) [inst_8 : TotalComplexShape c₁ c₂ c]
  [inst_9 : TotalComplexShape c₂ c₁ c] [inst_10 : TotalComplexShapeSymmetry c₁ c₂ c] [inst_11 : DecidableEq J]
  [inst_12 : K₁.HasMapBifunctor K₂ F c] [inst_13 : TotalComplexShapeSymmetry c₂ c₁ c]
  [TotalComplexShapeSymmetrySymmetry c₁ c₂ c], K₂.mapBifunctorFlipIso K₁ F.flip c = (K₁.mapBifunctorFlipIso K₂ F c).symm

Defined in

Mathlib.Algebra.Homology.BifunctorFlip

Cited by

0 results in Mathlib

Foundations

Depth 55 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.PreadditiveCategoryTheory.Functor.PreservesZeroMorphismsCategoryTheory.Functor.PreservesZeroMorphismsTotalComplexShapeTotalComplexShapeTotalComplexShapeSymmetryDecidableEqHomologicalComplex.HasMapBifunctorTotalComplexShapeSymmetryTotalComplexShapeSymmetrySymmetry