∀ (A : GrpCat),
  CategoryTheory.CategoryStruct.comp
      (CategoryTheory.CartesianMonoidalCategory.lift (fun x => x⁻¹)
        (CategoryTheory.CategoryStruct.id
          (MonTypeEquivalenceMon.inverse.obj ((CategoryTheory.forget₂ GrpCat MonCat).obj A)).X))
      CategoryTheory.MonObj.mul =
    CategoryTheory.CategoryStruct.comp
      (CategoryTheory.SemiCartesianMonoidalCategory.toUnit
        (MonTypeEquivalenceMon.inverse.obj ((CategoryTheory.forget₂ GrpCat MonCat).obj A)).X)
      CategoryTheory.MonObj.one