Theorems · Theorem · category theory
quasiIsoAt_iff_exactAt
∀ {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], K.ExactAt i → (QuasiIsoAt f i ↔ L.ExactAt i)- Defined in
- Mathlib.Algebra.Homology.QuasiIso
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 42 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites23
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.CategoryStruct.idproof · cited by 6,235
- CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
- HomologicalComplexstatement and proof · cited by 1,691
- ComplexShapestatement and proof · cited by 1,684
- CategoryTheory.IsIsoproof · cited by 1,156
- CategoryTheory.Iso.symmproof · cited by 993
- HomologicalComplex.HasHomologystatement and proof · cited by 342
Cited by5
Results whose statement or proof uses this declaration.
- exactAt_iff_of_quasiIsoAtproof · cited by 4
- HomologicalComplex.quasiIso_truncGEMap_iffproof · cited by 2
- HomologicalComplex.quasiIso_πTruncGE_iff_isSupportedproof · cited by 2
- HomologicalComplex.quasiIso_extendMap_iffproof · cited by 2
- CategoryTheory.InjectiveResolution.cocomplex_exactAt_succproof · cited by 1