Theorems · Theorem · category theory

CategoryTheory.ShortComplex.HomologyMapData.comm_assoc

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
  {S₁ S₂ : CategoryTheory.ShortComplex C} {φ : S₁ ⟶ S₂} {h₁ : S₁.HomologyData} {h₂ : S₂.HomologyData}
  (h : CategoryTheory.ShortComplex.HomologyMapData φ h₁ h₂) {Z : C} (h_1 : h₂.right.H ⟶ Z),
  CategoryTheory.CategoryStruct.comp h.left.φH (CategoryTheory.CategoryStruct.comp h₂.iso.hom h_1) =
    CategoryTheory.CategoryStruct.comp h₁.iso.hom (CategoryTheory.CategoryStruct.comp h.right.φH h_1)

Defined in

Mathlib.Algebra.Homology.ShortComplex.Homology

Cited by

2 results in Mathlib

Foundations

Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphisms