Theorems · Definition · category theory

CategoryTheory.projectiveResolutions

(C : Type u) →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.Abelian C] →
      [CategoryTheory.HasProjectiveResolutions C] → CategoryTheory.Functor C (HomotopyCategory C (ComplexShape.down ℕ))

Taking projective resolutions is functorial, if considered with target the homotopy category (ℕ-indexed chain complexes and chain maps up to homotopy).

Defined in

Mathlib.CategoryTheory.Abelian.Projective.Resolution

Cited by

7 results in Mathlib

Foundations

Depth 107 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.AbelianCategoryTheory.HasProjectiveResolutions