Theorems · Definition · category theory
HomologicalComplex.quasiIso
{ι : Type u_1} →
(C : Type u) →
[inst : CategoryTheory.Category.{v, u} C] →
[inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] →
(c : ComplexShape ι) →
[CategoryTheory.CategoryWithHomology C] → CategoryTheory.MorphismProperty (HomologicalComplex C c)The morphism property on HomologicalComplex C c given by quasi-isomorphisms.
- Defined in
- Mathlib.Algebra.Homology.QuasiIso
- Cited by
- 42 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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.Homproof · cited by 32,603
- CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
- CategoryTheory.MorphismPropertystatement · cited by 2,179
- HomologicalComplexstatement and proof · cited by 1,691
- ComplexShapestatement and proof · cited by 1,684
- CategoryTheory.CategoryWithHomologystatement and proof · cited by 116
- QuasiIsoproof · cited by 52
Cited by66
Results whose statement or proof uses this declaration.
- CategoryTheory.HasExtproof · cited by 218
- CategoryTheory.Abelian.Extproof · cited by 191
- HasDerivedCategoryproof · cited by 190
- CategoryTheory.Abelian.Ext.mk₀proof · cited by 94
- HasDerivedCategory.standardproof · cited by 42
- CategoryTheory.ShortComplex.ShortExact.extClassproof · cited by 36
- CategoryTheory.Abelian.Ext.comp_homproof · cited by 27
- CategoryTheory.Abelian.Ext.mk₀_homproof · cited by 20
- HomologicalComplexUpToQuasiIsostatement and proof · cited by 12
- HomologicalComplexUpToQuasiIso.Qstatement and proof · cited by 11
- CochainComplex.HomComplex.CohomologyClass.toSmallShiftedHomstatement and proof · cited by 10
- CategoryTheory.Abelian.Ext.homEquivproof · cited by 8