## Are there any dominant pivotal functors such that the regular representation is not mapped onto a multiple of the regular representation?

This question is related to Pivotal functors of that are substantially different from finite group homomorphisms. A tensor functor F:C→D is called dominant (sometimes called “surjective”) if for any Y:D, there is an X:C such that Y is a subobject of FX. It is known (“On fusion categories” by Pavel Etingof, Dmitri Nikshych, and Viktor … Read more