I am looking to define a 2-category which has the following properties:

1. It's objects are finite dimensional hilbert spaces.
2. It is a groupoid.
3. It admits a polynomial monad that is the Bag or Multiset or "Free Commutative Monoid" monad.

Can someone define the category and also this polynomial monad?

One could see Jeffery Morton's comment here:

https://golem.ph.utexas.edu/category/2012/07/morton_and_vicary_on_the_categ.html

He is talking about this paper, and his comment contains the following statement:

Since C⊗sn≅C, this is just a sum of a bunch of 1-dimensional spaces, each of which describes an n-particle system, which again has only one state. The only thing to say about this state is that it has n particles in it. Jamie’s original paper explains this by means of a monad on Hilb, which is essentially the “free commutative monoid” monad: the Fock space is the free commutative monoid on C. This fact gives a bunch of special maps, including a bialgebra structure on the Fock space, and the raising and lowering operators can be constructed out of this. The commutation relations are a consequence of that.

If he is talking about $F$, Vicary clearly states that this is a comonad, so I am not sure if he is right.