∀ {J : Type u} [inst : CategoryTheory.Category.{v_1, u} J] (F : CategoryTheory.Functor J (Type v))
  [CategoryTheory.IsCofilteredOrEmpty J],
  (∀ ⦃i j : J⦄ (f : i ⟶ j), Function.Surjective (F.map f)) → ∀ {i j : J} (f g : i ⟶ j), F.map f = F.map g