Theorems · Definition · category theory

CategoryTheory.Localization.lift

{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) →
                W.IsInvertedBy F → (L : CategoryTheory.Functor C D) → [L.IsLocalization W] → CategoryTheory.Functor D E

Given a localization functor L : C ⥤ D for W : MorphismProperty C and a functor F : C ⥤ E which inverts W, this is a choice of functor D ⥤ E which lifts F.

Defined in

Mathlib.CategoryTheory.Localization.Predicate

Cited by

9 results in Mathlib

Foundations

Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.IsLocalization