∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.CartesianMonoidalCategory C] {G : C}
  [inst_2 : CategoryTheory.GrpObj G] [inst_3 : CategoryTheory.BraidedCategory C],
  CategoryTheory.IsCommMonObj G ↔
    CategoryTheory.GrpObj.commutator G =
      CategoryTheory.CategoryStruct.comp
        (CategoryTheory.SemiCartesianMonoidalCategory.toUnit (CategoryTheory.MonoidalCategoryStruct.tensorObj G G))
        CategoryTheory.MonObj.one