Theorems · Theorem · category theory
HomologicalComplexUpToQuasiIso.Q_map_eq_of_homotopy
∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] {ι : Type u_2} {c : ComplexShape ι}
[inst_1 : CategoryTheory.Preadditive C] [inst_2 : CategoryTheory.CategoryWithHomology C]
[inst_3 : (HomologicalComplex.quasiIso C c).HasLocalization] [c.QFactorsThroughHomotopy C]
{K L : HomologicalComplex C c} {f g : K ⟶ L} (h : Homotopy f g),
HomologicalComplexUpToQuasiIso.Q.map f = HomologicalComplexUpToQuasiIso.Q.map g- Defined in
- Mathlib.Algebra.Homology.Localization
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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.objstatement · cited by 19,642
- CategoryTheory.Functor.mapstatement · cited by 8,698
- CategoryTheory.Preadditivestatement and proof · cited by 3,309
- HomologicalComplexstatement and proof · cited by 1,691
- ComplexShapestatement and proof · cited by 1,684
- CategoryTheory.CategoryWithHomologystatement and proof · cited by 116
- Homotopystatement and proof · cited by 106
- HomologicalComplex.quasiIsostatement and proof · cited by 42
- CategoryTheory.MorphismProperty.HasLocalizationstatement and proof · cited by 15
- HomologicalComplexUpToQuasiIsostatement · cited by 12
Cited by1
Results whose statement or proof uses this declaration.
- DerivedCategory.Q_map_eq_of_homotopyproof · cited by 0