Theorems · Theorem · category theory

CategoryTheory.ShortComplex.LeftHomologyMapData.homologyMap_eq

∀ {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.LeftHomologyData} {h₂ : S₂.LeftHomologyData}
  (γ : CategoryTheory.ShortComplex.LeftHomologyMapData φ h₁ h₂) [inst_2 : S₁.HasHomology] [inst_3 : S₂.HasHomology],
  CategoryTheory.ShortComplex.homologyMap φ =
    CategoryTheory.CategoryStruct.comp h₁.homologyIso.hom (CategoryTheory.CategoryStruct.comp γ.φH h₂.homologyIso.inv)

Defined in

Mathlib.Algebra.Homology.ShortComplex.Homology

Cited by

3 results in Mathlib

Foundations

Depth 40 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.ShortComplex.HasHomologyCategoryTheory.ShortComplex.HasHomology