Theorems · Theorem · category theory

CategoryTheory.ProjectiveResolution.cochainComplex_d

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Limits.HasZeroObject C]
  [inst_2 : CategoryTheory.Preadditive C] {X : C} (R : CategoryTheory.ProjectiveResolution X) (n₁ n₂ : ℤ) (k₁ k₂ : ℕ)
  (h₁ : autoParam (-↑k₁ = n₁) CategoryTheory.ProjectiveResolution.cochainComplex_d._auto_1)
  (h₂ : autoParam (-↑k₂ = n₂) CategoryTheory.ProjectiveResolution.cochainComplex_d._auto_3),
  R.cochainComplex.d n₁ n₂ =
    CategoryTheory.CategoryStruct.comp (R.cochainComplexXIso n₁ k₁ ⋯).hom
      (CategoryTheory.CategoryStruct.comp (R.complex.d k₁ k₂) (R.cochainComplexXIso n₂ k₂ ⋯).inv)

Defined in

Mathlib.CategoryTheory.Abelian.Projective.Extend

Cited by

8 results in Mathlib

Foundations

Depth 55 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroObjectCategoryTheory.Preadditive