Theorems · Theorem · category theory

HomologicalComplex.mapBifunctorFlipIso_hom_naturality

∀ {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 L₁ : HomologicalComplex C₁ c₁} (φ₁ : K₁ ⟶ L₁)
  {K₂ L₂ : HomologicalComplex C₂ c₂} (φ₂ : K₂ ⟶ L₂) (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 : L₁.HasMapBifunctor L₂ F c],
  CategoryTheory.CategoryStruct.comp (HomologicalComplex.mapBifunctorMap φ₂ φ₁ F.flip c)
      (L₁.mapBifunctorFlipIso L₂ F c).hom =
    CategoryTheory.CategoryStruct.comp (K₁.mapBifunctorFlipIso K₂ F c).hom
      (HomologicalComplex.mapBifunctorMap φ₁ φ₂ F c)

Defined in

Mathlib.Algebra.Homology.BifunctorFlip

Cited by

1 results in Mathlib

Foundations

Depth 56 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.PreadditiveCategoryTheory.Functor.PreservesZeroMorphismsCategoryTheory.Functor.PreservesZeroMorphismsTotalComplexShapeTotalComplexShapeTotalComplexShapeSymmetryDecidableEqHomologicalComplex.HasMapBifunctorHomologicalComplex.HasMapBifunctor