we believe its isomorphic representation in $\varepsilon_0$, which is quite natural, is worth investigating.

Towards the end of his book [@K03] (Sections 3.6.16-27), J. Kock discusses heuristically a project to describe geometrically the freely generated Frobenius monad, and leaves the matter as a challenge to the reader (Section 3.6.26). In this paper, one can find an answer to this challenge.

To make the hierarchy of ordinals in $\varepsilon_0$ collapse, and pass to something that amounts to *2Cob*, we need not assume commutativity. In the last two sections of this paper, we show how the notion of Frobenius algebra requires that the notion of Frobenius monad be extended with further assumptions, which produce the collapse of the hierarchy. The culprit for this collapse is the symmetry of $\mbox{\it Vect}_K$, without assuming that the Frobenius algebra is commutative (the Frobenius objects in symmetric monoidal categories of [@H04], Section 2, involve such a collapse too). We know that such a collapse must take place, but we do not know what should be its exact extent. In that context, we consider the collapse brought by the assumption of separability in Frobenius algebras, for which the exact categorial abstraction is the notion of separable matrix 