Theorems · Definition · category theory
CategoryTheory.Localization.Construction.objEquiv
{C : Type uC} →
[inst : CategoryTheory.Category.{uC', uC} C] → (W : CategoryTheory.MorphismProperty C) → C ≃ W.LocalizationThe canonical bijection between objects in a category and its
localization with respect to a MorphismProperty W
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext, Quot.sound
- Assumes
- CategoryTheory.Category
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.Functor.objproof · cited by 19,642
- Equivstatement · cited by 8,337
- CategoryTheory.MorphismPropertystatement and proof · cited by 2,179
- CategoryTheory.MorphismProperty.Qproof · cited by 98
- CategoryTheory.MorphismProperty.Localizationstatement and proof · cited by 72
- CategoryTheory.Quotient.asproof · cited by 47
- CategoryTheory.Localization.Construction.LocQuiver.objproof · cited by 10
Cited by6
Results whose statement or proof uses this declaration.
- CategoryTheory.Localization.essSurjproof · cited by 16
- CategoryTheory.Localization.Construction.NatTransExtension.appproof · cited by 3
- CategoryTheory.Localization.Construction.NatTransExtension.app_eqproof · cited by 1
- CategoryTheory.Localization.Construction.natTrans_hcomp_injectiveproof · cited by 0
- CategoryTheory.Localization.Construction.objEquiv_applystatement and proof · cited by 0
- CategoryTheory.Localization.Construction.objEquiv_symm_applystatement and proof · cited by 0