Theorems · Definition · category theory

CategoryTheory.Localization.StrictUniversalPropertyFixedTarget.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] →
        {L : CategoryTheory.Functor C D} →
          {W : CategoryTheory.MorphismProperty C} →
            {E : Type u_3} →
              [inst_2 : CategoryTheory.Category.{v_3, u_3} E] →
                CategoryTheory.Localization.StrictUniversalPropertyFixedTarget L W E →
                  (F : CategoryTheory.Functor C E) → W.IsInvertedBy F → CategoryTheory.Functor D E

any functor C ⥤ E which inverts W can be lifted as a functor D ⥤ E

Defined in

Mathlib.CategoryTheory.Localization.Predicate

Cited by

5 results in Mathlib

Foundations

Depth 5 from the axioms · uses no axioms

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Category