Theorems · Theorem · category theory

CategoryTheory.Abelian.LeftResolution.chainComplexMap_comp_assoc

∀ {A : Type u_1} {C : Type u_2} [inst : CategoryTheory.Category.{v_1, u_2} C]
  [inst_1 : CategoryTheory.Category.{v_2, u_1} A] {ι : CategoryTheory.Functor C A}
  (Λ : CategoryTheory.Abelian.LeftResolution ι) {X Y Z : A} (f : X ⟶ Y) (g : Y ⟶ Z) [inst_2 : ι.Full]
  [inst_3 : ι.Faithful] [inst_4 : CategoryTheory.Limits.HasZeroMorphisms C] [inst_5 : CategoryTheory.Abelian A]
  {Z_1 : ChainComplex C ℕ} (h : Λ.chainComplex Z ⟶ Z_1),
  CategoryTheory.CategoryStruct.comp (Λ.chainComplexMap (CategoryTheory.CategoryStruct.comp f g)) h =
    CategoryTheory.CategoryStruct.comp (Λ.chainComplexMap f)
      (CategoryTheory.CategoryStruct.comp (Λ.chainComplexMap g) h)

Defined in

Mathlib.Algebra.Homology.LeftResolution.Basic

Cited by

0 results in Mathlib

Foundations

Depth 41 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.FullCategoryTheory.Functor.FaithfulCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Abelian