LeanCat / CAT_statement /S_0025.lean
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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