{J : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} J] →
    {C : Type u₃} →
      [inst_1 : CategoryTheory.Category.{v₃, u₃} C] →
        {F : CategoryTheory.Functor J C} →
          {t : CategoryTheory.Limits.Cocone F} →
            CategoryTheory.Limits.IsColimit t →
              ((CategoryTheory.coyoneda.obj (Opposite.op t.pt)).comp CategoryTheory.uliftFunctor.{u₁, v₃} ≅ F.cocones)