Theorems · Theorem · category theory

CochainComplex.HomComplex.CohomologyClass.equivOfIsKInjective_symm_apply

∀ {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]
  [inst_3 : L.IsKInjective]
  (b : CategoryTheory.Localization.SmallShiftedHom (HomologicalComplex.quasiIso C (ComplexShape.up ℤ)) K L n),
  CochainComplex.HomComplex.CohomologyClass.equivOfIsKInjective.symm b = Function.surjInv ⋯ b

Defined in: Mathlib.Algebra.Homology.DerivedCategory.KInjective
Cited by: 0 results in Mathlib
Foundations: Depth 110 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Abelian CategoryTheory.Localization.HasSmallLocalizedShiftedHom CochainComplex.IsKInjective

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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coestatement and proof · cited by 62,936
CategoryTheory.Categorystatement and proof · cited by 32,673
Equivstatement · cited by 8,337
Equiv.symmstatement and proof · cited by 3,681
CategoryTheory.Abelianstatement and proof · cited by 1,753
HomologicalComplexstatement · cited by 1,691
ComplexShape.upstatement and proof · cited by 1,123
CochainComplexstatement and proof · cited by 1,016
Function.Bijective.surjectivestatement · cited by 114
Function.surjInvstatement · cited by 63
CochainComplex.HomComplex.CohomologyClassstatement · cited by 49
HomologicalComplex.quasiIsostatement and proof · cited by 42

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