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Theorems · Definition · category theory

CategoryTheory.AreEqualizedByLocalization

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    CategoryTheory.MorphismProperty C → {X Y : C} → (X ⟶ Y) → (X ⟶ Y) → Prop

The property that two morphisms become equal in the localized category.

Defined in
Mathlib.CategoryTheory.Localization.Predicate
Cited by
5 results in Mathlib
Foundations
Depth 20 from the axioms · uses propext, Quot.sound
Assumes
CategoryTheory.Category
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

CategoryTheory.areEqualizedByLocalization_iff · cited by 6CategoryTheory.areEqualiz…HomRel.FactorsThroughLocalization · cited by 5HomRel.FactorsThroughLoca…CategoryTheory.AreEqualizedByLocalization.map_eq · cited by 4AreEqualizedByLocalizatio…ComplexShape.QFactorsThroughHomotopy.areEqualizedByLocalization · cited by 1QFactorsThroughHomotopy.a…CategoryTheory.AreEqualizedByLocalization.mk · cited by 0AreEqualizedByLocalizatio…CategoryTheory.AreEqualizedByLocalization.map_eq_of_isInvertedBy · cited by 0AreEqualizedByLocalizatio…ComplexShape.QFactorsThroughHomotopy.casesOn · cited by 0QFactorsThroughHomotopy.c…ComplexShape.QFactorsThroughHomotopy.recOn · cited by 0QFactorsThroughHomotopy.r…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor.map · cited by 8698Functor.mapCategoryTheory.MorphismProperty · cited by 2179CategoryTheory.MorphismPr…CategoryTheory.MorphismProperty.Q · cited by 98MorphismProperty.QCategoryTheory.AreEqualizedBy…CITED BYCITES

Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by8

Results whose statement or proof uses this declaration.