Theorems · Definition · category theory
HomotopyCategory.quasiIso
(C : Type u_1) →
[inst : CategoryTheory.Category.{v_1, u_1} C] →
{ι : Type u_2} →
(c : ComplexShape ι) →
[inst_1 : CategoryTheory.Preadditive C] →
[CategoryTheory.CategoryWithHomology C] → CategoryTheory.MorphismProperty (HomotopyCategory C c)The class of quasi-isomorphisms in the homotopy category.
- Defined in
- Mathlib.Algebra.Homology.Localization
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 44 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.Homproof · cited by 32,603
- CategoryTheory.Functor.mapproof · cited by 8,698
- CategoryTheory.Preadditivestatement and proof · cited by 3,309
- CategoryTheory.MorphismPropertystatement · cited by 2,179
- ComplexShapestatement and proof · cited by 1,684
- CategoryTheory.IsIsoproof · cited by 1,156
- HomotopyCategorystatement and proof · cited by 132
- CategoryTheory.CategoryWithHomologystatement and proof · cited by 116
- HomotopyCategory.homologyFunctorproof · cited by 36
Cited by13
Results whose statement or proof uses this declaration.
- HomotopyCategory.Plus.quasiIsoproof · cited by 3
- DerivedCategory.isIso_Qh_map_iffstatement and proof · cited by 3
- HomotopyCategory.mem_quasiIso_iffstatement · cited by 2
- HomotopyCategory.quasiIso_eq_trW_subcategoryAcyclicstatement and proof · cited by 2
- HomotopyCategory.quotient_map_mem_quasiIso_iffstatement · cited by 2
- DerivedCategory.right_facproof · cited by 1
- DerivedCategory.left_facproof · cited by 1
- HomotopyCategory.Plus.quasiIso_iffstatement · cited by 0
- HomotopyCategory.quasiIso.congr_simpstatement and proof · cited by 0
- HomotopyCategory.quasiIso_eq_quasiIso_map_quotientstatement and proof · cited by 0
- HomotopyCategory.quasiIso_eq_subcategoryAcyclic_Wstatement · cited by 0
- HomotopyCategory.homologyFunctor_inverts_quasiIsostatement and proof · cited by 0