∀ {C : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} C] [inst_1 : CategoryTheory.CartesianMonoidalCategory C]
  (X : C) (F : CategoryTheory.Functor Cᵒᵖ GrpCat) (α : (F.comp (CategoryTheory.forget GrpCat)).RepresentableBy X),
  CategoryTheory.CategoryStruct.comp
      (CategoryTheory.CartesianMonoidalCategory.lift
        (α.homEquiv.symm (α.homEquiv (CategoryTheory.CategoryStruct.id X))⁻¹) (CategoryTheory.CategoryStruct.id X))
      CategoryTheory.MonObj.mul =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.SemiCartesianMonoidalCategory.toUnit X) CategoryTheory.MonObj.one