Theorems · Theorem · category theory
HomologicalComplexUpToQuasiIso.Q_inverts_homotopyEquivalences
∀ (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],
(HomologicalComplex.homotopyEquivalences C c).IsInvertedBy HomologicalComplexUpToQuasiIso.Q- Defined in
- Mathlib.Algebra.Homology.Localization
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites14
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.Preadditivestatement and proof · cited by 3,309
- HomologicalComplexstatement · cited by 1,691
- ComplexShapestatement and proof · cited by 1,684
- CategoryTheory.MorphismProperty.IsInvertedBystatement · cited by 118
- CategoryTheory.CategoryWithHomologystatement and proof · cited by 116
- CategoryTheory.Localization.invertsproof · cited by 63
- HomologicalComplex.quasiIsostatement and proof · cited by 42
- HomologicalComplex.homotopyEquivalencesstatement and proof · cited by 22
- CategoryTheory.MorphismProperty.HasLocalizationstatement and proof · cited by 15
- HomologicalComplexUpToQuasiIsostatement · cited by 12
- HomologicalComplexUpToQuasiIso.Qstatement and proof · cited by 11
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