Theorems · Theorem · category theory

CochainComplex.HomComplex.CohomologyClass.toSmallShiftedHom_mk

∀ {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]
  (x : CochainComplex.HomComplex.Cocycle K L n),
  (CochainComplex.HomComplex.CohomologyClass.mk x).toSmallShiftedHom =
    CategoryTheory.Localization.SmallShiftedHom.mk (HomologicalComplex.quasiIso C (ComplexShape.up ℤ))
      (CochainComplex.HomComplex.Cocycle.equivHomShift.symm x)

Defined in: Mathlib.Algebra.Homology.DerivedCategory.SmallShiftedHom
Cited by: 0 results in Mathlib
Foundations: Depth 107 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Abelian CategoryTheory.Localization.HasSmallLocalizedShiftedHom

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DFunLike.coestatement · cited by 62,936
CategoryTheory.Categorystatement and proof · cited by 32,673
Quiver.Homstatement · cited by 32,603
CategoryTheory.Functor.objstatement · cited by 19,642
CategoryTheory.Abelianstatement and proof · cited by 1,753
HomologicalComplexstatement · cited by 1,691
CategoryTheory.shiftFunctorstatement · cited by 1,553
ComplexShape.upstatement and proof · cited by 1,123
AddEquivstatement · cited by 1,087
CochainComplexstatement and proof · cited by 1,016
AddEquiv.symmstatement · cited by 530
CochainComplex.HomComplex.Cocyclestatement and proof · cited by 130

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