∀ {J : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} J],
  (∀ {α : Type u₁} (F : CategoryTheory.Functor J (CategoryTheory.Discrete α)) (j : J),
      Nonempty (F ≅ (CategoryTheory.Functor.const J).obj (F.obj j))) →
    CategoryTheory.IsPreconnected J