Theorems · Theorem · category theory

CategoryTheory.InjectiveResolution.descHomotopyZeroSucc.congr_simp

∀ {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 f_1 : I.cocomplex ⟶ J.cocomplex) (e_f : f = f_1) (n : ℕ) (g g_1 : I.cocomplex.X (n + 1) ⟶ J.cocomplex.X n)
  (e_g : g = g_1) (g' g'_1 : I.cocomplex.X (n + 2) ⟶ J.cocomplex.X (n + 1)) (e_g' : g' = g'_1)
  (w :
    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))),
  CategoryTheory.InjectiveResolution.descHomotopyZeroSucc f n g g' w =
    CategoryTheory.InjectiveResolution.descHomotopyZeroSucc f_1 n g_1 g'_1 ⋯

Defined in

Mathlib.CategoryTheory.Abelian.Injective.Resolution

Cited by

0 results in Mathlib

Foundations

Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Abelian