Theorems · Definition · category theory

CategoryTheory.ProjectiveResolution.cochainComplexXIso

{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) →
            (n : ℤ) →
              (k : ℕ) →
                autoParam (-↑k = n) CategoryTheory.ProjectiveResolution.cochainComplexXIso._auto_1 →
                  (R.cochainComplex.X n ≅ R.complex.X k)

If R : ProjectiveResolution X, then R.cochainComplex.X n (with n : ℕ) is isomorphic to R.complex.X k (with k : ℕ) when k = n.

Defined in

Mathlib.CategoryTheory.Abelian.Projective.Extend

Cited by

18 results in Mathlib

Foundations

Depth 54 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroObjectCategoryTheory.Preadditive