Theorems · Theorem · category theory
quasiIsoAt_iff_isIso_homologyMap
∀ {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.IsIso (HomologicalComplex.homologyMap f i)- Defined in
- Mathlib.Algebra.Homology.QuasiIso
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 39 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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.mapproof · cited by 8,698
- CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
- HomologicalComplexstatement and proof · cited by 1,691
- ComplexShapestatement and proof · cited by 1,684
- CategoryTheory.IsIsostatement and proof · cited by 1,156
- HomologicalComplex.HasHomologystatement and proof · cited by 342
- HomologicalComplex.homologystatement · cited by 209
- HomologicalComplex.homologyMapstatement and proof · cited by 102
- HomologicalComplex.shortComplexFunctorproof · cited by 72
- QuasiIsoAtstatement · cited by 55
Cited by6
Results whose statement or proof uses this declaration.
- HomologicalComplexUpToQuasiIso.isIso_Q_map_iff_mem_quasiIsoproof · cited by 2
- quasiIsoAt_of_comp_leftproof · cited by 1
- CochainComplex.mappingCone.quasiIso_descShortComplexproof · cited by 1
- quasiIsoAt_of_comp_rightproof · cited by 1
- HomologicalComplex.HomologySequence.quasiIso_τ₃proof · cited by 0
- HomologicalComplex.quasiIsoAt_shortComplexTruncLE_gproof · cited by 0