Theorems · Theorem · category theory

CategoryTheory.InjectiveResolution.cochainComplex_d_assoc

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Limits.HasZeroObject C]
  [inst_2 : CategoryTheory.Preadditive C] {X : C} (R : CategoryTheory.InjectiveResolution X) (n₁ n₂ : ℤ) (k₁ k₂ : ℕ)
  (h₁ : ↑k₁ = n₁) (h₂ : ↑k₂ = n₂) {Z : C} (h : R.cochainComplex.X n₂ ⟶ Z),
  CategoryTheory.CategoryStruct.comp (R.cochainComplex.d n₁ n₂) h =
    CategoryTheory.CategoryStruct.comp (R.cochainComplexXIso n₁ k₁ h₁).hom
      (CategoryTheory.CategoryStruct.comp (R.cocomplex.d k₁ k₂)
        (CategoryTheory.CategoryStruct.comp (R.cochainComplexXIso n₂ k₂ h₂).inv h))

Defined in

Mathlib.CategoryTheory.Abelian.Injective.Extend

Cited by

0 results in Mathlib

Foundations

Depth 56 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroObjectCategoryTheory.Preadditive