{C D : CategoryTheory.Cat} →
  (F : CategoryTheory.ReflQuiv.of ↑C ⟶ CategoryTheory.ReflQuiv.of ↑D) →
    (∀ {X Y Z : ↑C} (f : X ⟶ Y) (g : Y ⟶ Z),
        F.map (CategoryTheory.CategoryStruct.comp f g) = CategoryTheory.CategoryStruct.comp (F.map f) (F.map g)) →
      CategoryTheory.Functor ↑C ↑D