In this paper 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.

In this paper 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 in theorem 4.7.

In this paper 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]? Is it a well recognizable category? What well recognizable category is it?

In this paper 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.