Theorems · Definition · category theory

CategoryTheory.Localization.fac

{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] →
        {W : CategoryTheory.MorphismProperty C} →
          {E : Type u_3} →
            [inst_2 : CategoryTheory.Category.{v_3, u_3} E] →
              (F : CategoryTheory.Functor C E) →
                (hF : W.IsInvertedBy F) →
                  (L : CategoryTheory.Functor C D) →
                    [inst_3 : L.IsLocalization W] → L.comp (CategoryTheory.Localization.lift F hF L) ≅ F

The canonical isomorphism L ⋙ lift F hF L ≅ F for any functor F : C ⥤ E which inverts W, when L : C ⥤ D is a localization functor for W.

Defined in

Mathlib.CategoryTheory.Localization.Predicate

Cited by

10 results in Mathlib

Foundations

Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.IsLocalization