Theorems · Theorem · category theory

CochainComplex.IsKProjective.Qh_map_bijective

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Abelian C]
  [inst_2 : HasDerivedCategory C] (K : CochainComplex C ℤ) (L : HomotopyCategory C (ComplexShape.up ℤ))
  [K.IsKProjective], Function.Bijective DerivedCategory.Qh.map

Defined in: Mathlib.Algebra.Homology.DerivedCategory.KProjective
Cited by: 2 results in Mathlib
Foundations: Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Abelian HasDerivedCategory CochainComplex.IsKProjective

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Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites17

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

CategoryTheory.Categorystatement and proof · cited by 32,673
Quiver.Homstatement · cited by 32,603
CategoryTheory.Functor.objstatement · cited by 19,642
CategoryTheory.Functor.mapstatement · cited by 8,698
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.Bijectivestatement · cited by 863
HasDerivedCategorystatement and proof · cited by 190
DerivedCategorystatement · cited by 165
HomotopyCategorystatement and proof · cited by 132

Cited by2

Results whose statement or proof uses this declaration.

CochainComplex.IsKProjective.quasiIso_iffproof · cited by 1
CochainComplex.HomComplex.CohomologyClass.bijective_toSmallShiftedHom_of_isKProjectiveproof · cited by 1