Theorems · Theorem · category theory
CategoryTheory.LocalizerMorphism.IsLocalizedEquivalence.isEquivalence
∀ {C₁ : Type u₁} {C₂ : Type u₂} {inst : CategoryTheory.Category.{v₁, u₁} C₁}
{inst_1 : CategoryTheory.Category.{v₂, u₂} C₂} {W₁ : CategoryTheory.MorphismProperty C₁}
{W₂ : CategoryTheory.MorphismProperty C₂} {Φ : CategoryTheory.LocalizerMorphism W₁ W₂}
[self : Φ.IsLocalizedEquivalence], (Φ.localizedFunctor W₁.Q W₂.Q).IsEquivalencethe induced functor on the constructed localized categories is an equivalence
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 80 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
- CategoryTheory.MorphismPropertystatement and proof · cited by 2,179
- CategoryTheory.LocalizerMorphismstatement and proof · cited by 161
- CategoryTheory.Functor.IsEquivalencestatement · cited by 111
- CategoryTheory.MorphismProperty.Qstatement · cited by 98
- CategoryTheory.MorphismProperty.Localizationstatement · cited by 72
- CategoryTheory.LocalizerMorphism.localizedFunctorstatement · cited by 29
- CategoryTheory.LocalizerMorphism.IsLocalizedEquivalencestatement and proof · cited by 18
Cited by1
Results whose statement or proof uses this declaration.
- CategoryTheory.LocalizerMorphism.isEquivalenceproof · cited by 0