Theorems · Theorem · category theory

CategoryTheory.areEqualizedByLocalization_iff

∀ {C : Type u_1} {D : Type u_2} [inst : CategoryTheory.Category.{v_1, u_1} C]
  [inst_1 : CategoryTheory.Category.{v_2, u_2} D] (L : CategoryTheory.Functor C D)
  (W : CategoryTheory.MorphismProperty C) {X Y : C} (f g : X ⟶ Y) [L.IsLocalization W],
  CategoryTheory.AreEqualizedByLocalization W f g ↔ L.map f = L.map g

Defined in

Mathlib.CategoryTheory.Localization.Predicate

Cited by

6 results in Mathlib

Foundations

Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.IsLocalization