Theorems · Theorem · category theory

CategoryTheory.NatTrans.mapHomologicalComplex_naturality_assoc

∀ {ι : Type u_1} {W₁ : Type u_3} {W₂ : Type u_4} [inst : CategoryTheory.Category.{v_2, u_3} W₁]
  [inst_1 : CategoryTheory.Category.{v_3, u_4} W₂] [inst_2 : CategoryTheory.Limits.HasZeroMorphisms W₁]
  [inst_3 : CategoryTheory.Limits.HasZeroMorphisms W₂] {c : ComplexShape ι} {F G : CategoryTheory.Functor W₁ W₂}
  [inst_4 : F.PreservesZeroMorphisms] [inst_5 : G.PreservesZeroMorphisms] (α : F ⟶ G) {C D : HomologicalComplex W₁ c}
  (f : C ⟶ D) {Z : HomologicalComplex W₂ c} (h : (G.mapHomologicalComplex c).obj D ⟶ Z),
  CategoryTheory.CategoryStruct.comp ((F.mapHomologicalComplex c).map f)
      (CategoryTheory.CategoryStruct.comp ((CategoryTheory.NatTrans.mapHomologicalComplex α c).app D) h) =
    CategoryTheory.CategoryStruct.comp ((CategoryTheory.NatTrans.mapHomologicalComplex α c).app C)
      (CategoryTheory.CategoryStruct.comp ((G.mapHomologicalComplex c).map f) h)

Defined in

Mathlib.Algebra.Homology.Additive

Cited by

0 results in Mathlib

Foundations

Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Functor.PreservesZeroMorphismsCategoryTheory.Functor.PreservesZeroMorphisms