It was recently brought to my attention that the Bag monad, also known as the MultiSet monad, is not polynomial on Set, but is Polynomial on the category of Groupoids, 3.10 Examples. I then started thinking about the category FinHilb, of finite-dimensional Hilbert spaces, and the fact that it has a dagger. This allows for the fact that the subcategory of just unitary isomorphisms as morphisms, (ie the core of Hilb) is a groupoid. I believe this means that the core of Hilb supports the polynomial functor of the Bag monad. Can someone show the form of this polynomial monad, and perhaps talk a bit about this monad?