| import Mathlib | |
| open CategoryTheory | |
| variable {C D E : Type*} [Category C] [Category D] [Category E] | |
| namespace CategoryTheory | |
| class Functor.ReflectsSplitEpimorphismsToRegularEpimorphisms (F : Functor C D) : Prop where | |
| reflects : ∀ {X Y} {f : X ⟶ Y} [IsSplitEpi (F.map f)], Nonempty (RegularEpi f) | |
| end CategoryTheory | |
| variable (U : D ⥤ C) (V : E ⥤ C) (F : D ⥤ E) | |
| theorem exists_left_adjoint_of_comp_eq (h : F ⋙ V = U) (hU : U.IsRightAdjoint) (hV : V.IsRightAdjoint) | |
| (hV_refl : V.ReflectsSplitEpimorphismsToRegularEpimorphisms) : F.IsRightAdjoint := by | |
| sorry |