∀ {X Y : CommGrpCat} (x : CommGrpCat.uliftFunctor.obj X ⟶ CommGrpCat.uliftFunctor.obj Y),
  CommGrpCat.uliftFunctor.map
      (CommGrpCat.ofHom
        (MulEquiv.ulift.toMonoidHom.comp ((CommGrpCat.Hom.hom x).comp MulEquiv.ulift.symm.toMonoidHom))) =
    CommGrpCat.uliftFunctor.map
      (CommGrpCat.ofHom (MulEquiv.ulift.toMonoidHom.comp ((CommGrpCat.Hom.hom x).comp MulEquiv.ulift.symm.toMonoidHom)))