Theorems · Definition · category theory

CategoryTheory.Localization.uniq

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    {D₁ : Type u_4} →
      {D₂ : Type u_5} →
        [inst_1 : CategoryTheory.Category.{v_4, u_4} D₁] →
          [inst_2 : CategoryTheory.Category.{v_5, u_5} D₂] →
            (L₁ : CategoryTheory.Functor C D₁) →
              (L₂ : CategoryTheory.Functor C D₂) →
                (W' : CategoryTheory.MorphismProperty C) → [L₁.IsLocalization W'] → [L₂.IsLocalization W'] → D₁ ≌ D₂

If L₁ : C ⥤ D₁ and L₂ : C ⥤ D₂ are two localization functors for the same MorphismProperty C, this is an equivalence of categories D₁ ≌ D₂.

Defined in

Mathlib.CategoryTheory.Localization.Predicate

Cited by

17 results in Mathlib

Foundations

Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.IsLocalizationCategoryTheory.Functor.IsLocalization