Theorems · Theorem · category theory
quasiIsoAt_iff
∀ {ι : Type u_1} {C : Type u} [inst : CategoryTheory.Category.{v, u} C]
[inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] {c : ComplexShape ι} {K L : HomologicalComplex C c} (f : K ⟶ L)
(i : ι) [inst_2 : K.HasHomology i] [inst_3 : L.HasHomology i],
QuasiIsoAt f i ↔ CategoryTheory.ShortComplex.QuasiIso ((HomologicalComplex.shortComplexFunctor C c i).map f)- Defined in
- Mathlib.Algebra.Homology.QuasiIso
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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.objstatement · cited by 19,642
- CategoryTheory.Functor.mapstatement and proof · cited by 8,698
- CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
- CategoryTheory.ShortComplexstatement · cited by 1,850
- HomologicalComplexstatement and proof · cited by 1,691
- ComplexShapestatement and proof · cited by 1,684
- HomologicalComplex.HasHomologystatement and proof · cited by 342
- HomologicalComplex.shortComplexFunctorstatement and proof · cited by 72
- QuasiIsoAtstatement and proof · cited by 55
- CategoryTheory.ShortComplex.QuasiIsostatement and proof · cited by 35
Cited by5
Results whose statement or proof uses this declaration.
- quasiIsoAt_iff_isIso_homologyMapproof · cited by 6
- quasiIsoAt_iff'proof · cited by 4
- HomologicalComplex.quasiIsoAt_πTruncGEproof · cited by 2
- HomologicalComplex.truncGE'.quasiIsoAt_restrictionToTruncGE'proof · cited by 1
- quasiIsoAt_of_retractproof · cited by 1