[In this paper](https://arxiv.org/abs/1602.04324)  we see a Frobenius Monad in example 5.2.  Suppose we take Hilb as the underlying category.  Is this Frobenius Monad an internal category in [Hilb, Hilb]?  If you can show that it is an internal category, please give some data about that category.

Heunen and Tull have a [vaguely similar result](https://arxiv.org/pdf/1506.05028.pdf) in theorem 4.7.