Theorems · Definition · category theory

CategoryTheory.Functor.essImage.liftFunctor

{J : Type u_1} →
  {C : Type u_2} →
    {D : Type u_3} →
      [inst : CategoryTheory.Category.{v_1, u_1} J] →
        [inst_1 : CategoryTheory.Category.{v_2, u_2} C] →
          [inst_2 : CategoryTheory.Category.{v_3, u_3} D] →
            (G : CategoryTheory.Functor J D) →
              (F : CategoryTheory.Functor C D) →
                [F.Full] → [F.Faithful] → (∀ (j : J), F.essImage (G.obj j)) → CategoryTheory.Functor J C

Lift a functor G : J ⥤ D to the essential image of a fully faithful functor F : C ⥤ D to a functor G' : J ⥤ C such that G' ⋙ F ≅ G. See essImage.liftFunctorCompIso.

Defined in

Mathlib.CategoryTheory.EssentialImage

Cited by

4 results in Mathlib

Foundations

Depth 21 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.FullCategoryTheory.Functor.Faithful