Theorems · Definition · category theory

CategoryTheory.InjectiveResolution.iso

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.Abelian C] →
      [inst_2 : CategoryTheory.HasInjectiveResolutions C] →
        {X : C} →
          (I : CategoryTheory.InjectiveResolution X) →
            (CategoryTheory.injectiveResolutions C).obj X ≅
              (HomotopyCategory.quotient C (ComplexShape.up ℕ)).obj I.cocomplex

If I : InjectiveResolution X, then the chosen (injectiveResolutions C).obj X is isomorphic (in the homotopy category) to I.cocomplex.

Defined in

Mathlib.CategoryTheory.Abelian.Injective.Resolution

Cited by

7 results in Mathlib

Foundations

Depth 109 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.AbelianCategoryTheory.HasInjectiveResolutions