{J : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} J] →
    {C : Type u₃} →
      [inst_1 : CategoryTheory.Category.{v₃, u₃} C] →
        {F : CategoryTheory.Functor J C} →
          {X : C} → F.cocones.CorepresentableBy X → {Y : C} → (X ⟶ Y) → CategoryTheory.Limits.Cocone F