Theorems · Definition · category theory

CategoryTheory.ProjectiveResolution.cochainComplex

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.Limits.HasZeroObject C] →
      [inst_2 : CategoryTheory.Preadditive C] → {X : C} → CategoryTheory.ProjectiveResolution X → CochainComplex C ℤ

If R : ProjectiveResolution X, this is the cochain complex indexed by ℤ obtained by extending by zero the chain complex R.complex indexed by ℕ.

Defined in

Mathlib.CategoryTheory.Abelian.Projective.Extend

Cited by

30 results in Mathlib

Foundations

Depth 53 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroObjectCategoryTheory.Preadditive