Theorems · Definition · category theory
CategoryTheory.MorphismProperty.Localization
{C : Type uC} → [inst : CategoryTheory.Category.{uC', uC} C] → CategoryTheory.MorphismProperty C → Type uCThe localized category obtained by formally inverting the morphisms
in W : MorphismProperty C
- Cited by
- 72 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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.Quotientproof · cited by 48
- CategoryTheory.Localization.Construction.relationsproof · cited by 7
Cited by113
Results whose statement or proof uses this declaration.
- CategoryTheory.MorphismProperty.Qstatement · cited by 98
- CategoryTheory.Localization.Construction.liftstatement · cited by 12
- CategoryTheory.Functor.IsLocalization.of_equivalence_targetproof · cited by 8
- CategoryTheory.Localization.Construction.WhiskeringLeftEquivalence.functorstatement and proof · cited by 7
- CategoryTheory.Localization.Construction.WhiskeringLeftEquivalence.inversestatement · cited by 7
- CategoryTheory.Functor.IsLocalization.mk'statement and proof · cited by 6
- CategoryTheory.Localization.Construction.objEquivstatement and proof · cited by 5
- CategoryTheory.Localization.Construction.wIsostatement · cited by 5
- CategoryTheory.LocalizerMorphism.equiv_smallHomMapproof · cited by 4
- CategoryTheory.Localization.StrictUniversalPropertyFixedTarget.prodLift₁statement · cited by 4
- CategoryTheory.Localization.Construction.facstatement · cited by 3
- CategoryTheory.Localization.Construction.natTransExtensionstatement and proof · cited by 3