Theorems · Theorem · category theory

CategoryTheory.InjectiveResolution.desc_commutes

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

The resolution maps intertwine the descent of a morphism and that morphism.

Defined in

Mathlib.CategoryTheory.Abelian.Injective.Resolution

Cited by

4 results in Mathlib

Foundations

Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Abelian