Theorems · Definition · category theory

CochainComplex.HomComplex.CohomologyClass.toSmallShiftedHom

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.Abelian C] →
      {K L : CochainComplex C ℤ} →
        {n : ℤ} →
          [inst_2 :
              CategoryTheory.Localization.HasSmallLocalizedShiftedHom
                (HomologicalComplex.quasiIso C (ComplexShape.up ℤ)) ℤ K L] →
            CochainComplex.HomComplex.CohomologyClass K L n →
              CategoryTheory.Localization.SmallShiftedHom (HomologicalComplex.quasiIso C (ComplexShape.up ℤ)) K L n

Given x : CohomologyClass K L n, this is the element in the type SmallShiftedHom relatively to quasi-isomorphisms that is associated to the x.

Defined in

Mathlib.Algebra.Homology.DerivedCategory.SmallShiftedHom

Cited by

10 results in Mathlib

Foundations

Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.AbelianCategoryTheory.Localization.HasSmallLocalizedShiftedHom