Theorems · Definition · category theory
CochainComplex.Plus.quasiIso
(C : Type u_1) →
[inst : CategoryTheory.Category.{v_1, u_1} C] →
[inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] →
[CategoryTheory.CategoryWithHomology C] → CategoryTheory.MorphismProperty (CochainComplex.Plus C)The class of quasi-isomorphisms in the category of bounded below cochain complexes.
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 57 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
- CategoryTheory.MorphismPropertystatement · cited by 2,179
- ComplexShape.upstatement and proof · cited by 1,123
- CochainComplexstatement · cited by 1,016
- CategoryTheory.CategoryWithHomologystatement and proof · cited by 116
- CategoryTheory.MorphismProperty.inverseImageproof · cited by 83
- HomologicalComplex.quasiIsoproof · cited by 42
- CochainComplex.plusstatement · cited by 24
- CochainComplex.Plusstatement · cited by 20
- CochainComplex.Plus.ιproof · cited by 8
Cited by8
Results whose statement or proof uses this declaration.
- CochainComplex.Plus.localizerMorphismstatement · cited by 1
- CochainComplex.Plus.exists_quasiIso_injectivestatement · cited by 1
- CochainComplex.Plus.localizerMorphism_functorstatement · cited by 0
- DerivedCategory.Plus.exists_injective_nonempty_isoproof · cited by 0
- CochainComplex.Plus.quasiIso.congr_simpstatement and proof · cited by 0
- CochainComplex.Plus.fibrantObjectLocalizerMorphismstatement · cited by 0
- HomotopyCategory.Plus.inverseImage_quasiIso_mapCochainComplexPlus_injectiveObjectιstatement and proof · cited by 0
- HomotopyCategory.Plus.isIso_quotient_map_iffstatement and proof · cited by 0