Theorems · Theorem · category theory

CategoryTheory.ShortComplex.rightHomologyIso_hom_naturality_assoc

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
  {S₁ S₂ : CategoryTheory.ShortComplex C} [inst_2 : S₁.HasHomology] [inst_3 : S₂.HasHomology] (φ : S₁ ⟶ S₂) {Z : C}
  (h : S₂.homology ⟶ Z),
  CategoryTheory.CategoryStruct.comp S₁.rightHomologyIso.hom
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.ShortComplex.homologyMap φ) h) =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.ShortComplex.rightHomologyMap φ)
      (CategoryTheory.CategoryStruct.comp S₂.rightHomologyIso.hom h)

Defined in

Mathlib.Algebra.Homology.ShortComplex.Homology

Cited by

1 results in Mathlib

Foundations

Depth 46 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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