  We explain that a new theorem of Deligne on symmetric tensor categories
implies, in a straightforward manner, that any finite dimensional triangular
Hopf algebra over an algebraically closed field of characteristic zero has
Chevalley property, and in particular the list of finite dimensional triangular
Hopf algebras over such a field given in math.QA/0008232, math.QA/0101049 is
complete. We also use Deligne's theorem to settle a number of questions about
triangular Hopf algebras, raised in our previous publications, and generalize
Deligne's result to nondegenerate semisimple categories in characteristic $p$,
by using lifting methods developed in math.QA/0203060.
