∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [CategoryTheory.IsCofilteredOrEmpty C]
  (F : CategoryTheory.Functor C (Type u_1)) (j : C), Directed (fun x1 x2 => x1 ⊇ x2) fun f => Set.range (F.map f.snd)