Theorems · Theorem · category theory

CategoryTheory.InjectiveResolution.comp_descHomotopyZeroOne

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Abelian C] {Y Z : C}
  {I : CategoryTheory.InjectiveResolution Y} {J : CategoryTheory.InjectiveResolution Z} (f : I.cocomplex ⟶ J.cocomplex)
  (comm : CategoryTheory.CategoryStruct.comp I.ι f = 0),
  CategoryTheory.CategoryStruct.comp (I.cocomplex.d 1 2)
      (CategoryTheory.InjectiveResolution.descHomotopyZeroOne f comm) =
    f.f 1 -
      CategoryTheory.CategoryStruct.comp (CategoryTheory.InjectiveResolution.descHomotopyZeroZero f comm)
        (J.cocomplex.d 0 1)

Defined in

Mathlib.CategoryTheory.Abelian.Injective.Resolution

Cited by

1 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.Abelian