Theorems · Definition · category theory

CategoryTheory.ProjectiveResolution.extAddEquivCohomologyClass

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.Abelian C] →
      [inst_2 : CategoryTheory.HasExt C] →
        {X Y : C} →
          (R : CategoryTheory.ProjectiveResolution X) →
            {n : ℕ} →
              CategoryTheory.Abelian.Ext X Y n ≃+
                CochainComplex.HomComplex.CohomologyClass R.cochainComplex ((CochainComplex.singleFunctor C 0).obj Y) ↑n

If R is a projective resolution of X, then Ext X Y n identifies to the type of cohomology classes of degree n from R.cochainComplex to (singleFunctor C 0).obj Y.

Defined in

Mathlib.CategoryTheory.Abelian.Projective.Ext

Cited by

9 results in Mathlib

Foundations

Depth 128 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.AbelianCategoryTheory.HasExt