∀ {C : Type u_3} [inst : CategoryTheory.Category.{u_2, u_3} C] [inst_1 : CategoryTheory.Abelian C]
  [CategoryTheory.HasExt C] {Y : C} (R : CategoryTheory.InjectiveResolution Y) (a b : ℤ),
  CategoryTheory.Localization.HasSmallLocalizedHom (HomologicalComplex.quasiIso C (ComplexShape.up ℤ))
    ((CategoryTheory.shiftFunctor (HomologicalComplex C (ComplexShape.up ℤ)) a).obj
      ((CochainComplex.singleFunctor C 0).obj Y))
    ((CategoryTheory.shiftFunctor (HomologicalComplex C (ComplexShape.up ℤ)) b).obj R.cochainComplex)