Theorems · Definition · category theory

CategoryTheory.Localization.structuredArrowEquiv

{C : Type u_1} →
  {D : Type u_2} →
    {D' : Type u_3} →
      [inst : CategoryTheory.Category.{v_1, u_1} C] →
        [inst_1 : CategoryTheory.Category.{v_2, u_2} D] →
          [inst_2 : CategoryTheory.Category.{v_3, u_3} D'] →
            (W : CategoryTheory.MorphismProperty C) →
              (L : CategoryTheory.Functor C D) →
                (L' : CategoryTheory.Functor C D') →
                  [L.IsLocalization W] →
                    [L'.IsLocalization W] →
                      {X : C} →
                        CategoryTheory.StructuredArrow (L.obj X) L ≃ CategoryTheory.StructuredArrow (L'.obj X) L'

The bijection StructuredArrow (L.obj X) L ≃ StructuredArrow (L'.obj X) L' when L and L' are two localization functors for the same class of morphisms.

Defined in

Mathlib.CategoryTheory.Localization.StructuredArrow

Cited by

4 results in Mathlib

Foundations

Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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