Theorems · Definition · category theory

CategoryTheory.InjectiveResolution.descHomotopy

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.Abelian C] →
      {Y Z : C} →
        (f : Y ⟶ Z) →
          {I : CategoryTheory.InjectiveResolution Y} →
            {J : CategoryTheory.InjectiveResolution Z} →
              (g h : I.cocomplex ⟶ J.cocomplex) →
                CategoryTheory.CategoryStruct.comp I.ι g =
                    CategoryTheory.CategoryStruct.comp ((CochainComplex.single₀ C).map f) J.ι →
                  CategoryTheory.CategoryStruct.comp I.ι h =
                      CategoryTheory.CategoryStruct.comp ((CochainComplex.single₀ C).map f) J.ι →
                    Homotopy g h

Two descents of the same morphism are homotopic.

Defined in

Mathlib.CategoryTheory.Abelian.Injective.Resolution

Cited by

1 results in Mathlib

Foundations

Depth 105 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Abelian