Theorems · Definition · category theory

CategoryTheory.InjectiveResolution.descHomotopyZeroSucc

{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) →
              (n : ℕ) →
                (g : I.cocomplex.X (n + 1) ⟶ J.cocomplex.X n) →
                  (g' : I.cocomplex.X (n + 2) ⟶ J.cocomplex.X (n + 1)) →
                    f.f (n + 1) =
                        CategoryTheory.CategoryStruct.comp (I.cocomplex.d (n + 1) (n + 2)) g' +
                          CategoryTheory.CategoryStruct.comp g (J.cocomplex.d n (n + 1)) →
                      (I.cocomplex.X (n + 3) ⟶ J.cocomplex.X (n + 2))

An auxiliary definition for descHomotopyZero.

Defined in

Mathlib.CategoryTheory.Abelian.Injective.Resolution

Cited by

3 results in Mathlib

Foundations

Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Abelian