Theorems · Theorem · category theory
HomotopyCategory.quotient_inverts_homotopyEquivalences
∀ {ι : Type u_2} (V : Type u) [inst : CategoryTheory.Category.{v, u} V] [inst_1 : CategoryTheory.Preadditive V]
(c : ComplexShape ι), (HomologicalComplex.homotopyEquivalences V c).IsInvertedBy (HomotopyCategory.quotient V c)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 29 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
- Quiver.Homproof · cited by 32,603
- CategoryTheory.Preadditivestatement and proof · cited by 3,309
- HomologicalComplexstatement and proof · cited by 1,691
- ComplexShapestatement and proof · cited by 1,684
- HomotopyCategorystatement · cited by 132
- CategoryTheory.MorphismProperty.IsInvertedBystatement · cited by 118
- HomotopyCategory.quotientstatement · cited by 109
- HomotopyEquiv.homproof · cited by 45
- HomotopyEquivproof · cited by 27
- HomologicalComplex.homotopyEquivalencesstatement and proof · cited by 22
Cited by3
Results whose statement or proof uses this declaration.
- HomotopyCategory.inverseImage_quotient_isomorphismsproof · cited by 2
- HomologicalComplex.isIso_quotient_map_iff_homotopyEquivalencesproof · cited by 1
- ComplexShape.strictUniversalPropertyFixedTargetQuotientproof · cited by 1