Theorems · Theorem · category theory

HomologicalComplex.Hom.comm_assoc

∀ {ι : Type u_1} {V : Type u} [inst : CategoryTheory.Category.{v, u} V]
  [inst_1 : CategoryTheory.Limits.HasZeroMorphisms V] {c : ComplexShape ι} {A B : HomologicalComplex V c} (f : A.Hom B)
  (i j : ι) {Z : V} (h : B.X j ⟶ Z),
  CategoryTheory.CategoryStruct.comp (f.f i) (CategoryTheory.CategoryStruct.comp (B.d i j) h) =
    CategoryTheory.CategoryStruct.comp (A.d i j) (CategoryTheory.CategoryStruct.comp (f.f j) h)

Defined in

Mathlib.Algebra.Homology.HomologicalComplex

Cited by

10 results in Mathlib

Foundations

Depth 13 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphisms