{C : Type u_1} →
  [inst : CategoryTheory.Category.{v, u_1} C] →
    [inst_1 : CategoryTheory.CartesianMonoidalCategory C] →
      (X : C) →
        (F : CategoryTheory.Functor Cᵒᵖ MonCat) →
          (F.comp (CategoryTheory.forget MonCat)).RepresentableBy X → CategoryTheory.MonObj X