Theorems · Theorem · category theory
CochainComplex.IsKInjective.quasiIso_iff
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Abelian C] {K L : CochainComplex C ℤ}
[K.IsKInjective] [L.IsKInjective] (f : K ⟶ L),
QuasiIso f ↔ HomologicalComplex.homotopyEquivalences C (ComplexShape.up ℤ) f- Cited by
- 2 results in Mathlib
- Foundations
- Depth 103 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites39
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 and proof · cited by 32,603
- CategoryTheory.Functor.objproof · cited by 19,642
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- CategoryTheory.Functor.mapproof · cited by 8,698
- CategoryTheory.Iso.homproof · cited by 7,684
- CategoryTheory.NatTrans.appproof · cited by 7,406
- CategoryTheory.Iso.invproof · cited by 6,514
- CategoryTheory.Category.assocproof · cited by 6,433
- CategoryTheory.CategoryStruct.idproof · cited by 6,235
- CategoryTheory.MorphismPropertyproof · cited by 2,179
- CategoryTheory.Abelianstatement and proof · cited by 1,753
Cited by2
Results whose statement or proof uses this declaration.
- HomotopyCategory.Plus.isIso_quotient_map_iffproof · cited by 0
- CochainComplex.quasiIso_iff_of_injectiveproof · cited by 0