Theorems · Theorem · category theory
exactAt_iff_of_quasiIsoAt
∀ {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], K.ExactAt i ↔ L.ExactAt i- Defined in
- Mathlib.Algebra.Homology.QuasiIso
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 43 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
- HomologicalComplexstatement and proof · cited by 1,691
- ComplexShapestatement and proof · cited by 1,684
- HomologicalComplex.HasHomologystatement and proof · cited by 342
- QuasiIsoAtstatement and proof · cited by 55
- HomologicalComplex.ExactAtstatement and proof · cited by 44
- quasiIsoAt_iff_exactAtproof · cited by 5
- quasiIsoAt_iff_exactAt'proof · cited by 3
Cited by4
Results whose statement or proof uses this declaration.
- HomologicalComplex.acyclic_truncGE_iff_isSupportedOutsideproof · cited by 3
- HomologicalComplex.quasiIso_πTruncGE_iff_isSupportedproof · cited by 2
- SSet.exactAt_chainComplex_of_hasDimensionLTproof · cited by 1
- HomologicalComplex.isSupported_iff_of_quasiIsoproof · cited by 0