Theorems · Definition · category theory

CategoryTheory.Functor.essImage.liftFunctorCompIso

{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) →
                [inst_3 : F.Full] →
                  [inst_4 : F.Faithful] →
                    (hG : ∀ (j : J), F.essImage (G.obj j)) →
                      (CategoryTheory.Functor.essImage.liftFunctor G F hG).comp F ≅ G

A functor G : J ⥤ D to the essential image of a fully faithful functor F : C ⥤ D does factor through essImage.liftFunctor G F hG.

Defined in

Mathlib.CategoryTheory.EssentialImage

Cited by

2 results in Mathlib

Foundations

Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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