∀ (X : GrpCat),
  GrpCat.ofHom
      (MulEquiv.ulift.symm.toMonoidHom.comp
        ((GrpCat.Hom.hom (CategoryTheory.CategoryStruct.id X)).comp MulEquiv.ulift.toMonoidHom)) =
    CategoryTheory.CategoryStruct.id (GrpCat.of (ULift.{u_1, u_2} ↑X))