  This paper provides geometrical descriptions of the Frobenius monad freely
generated by a single object. These descriptions are related to results
connecting Frobenius algebras and topological quantum field theories. In these
descriptions, which are based on coherence results for self-adjunctions
(adjunctions where an endofunctor is adjoint to itself), ordinals in epsilon
zero play a prominent role. The paper ends by considering how the notion of
Frobenius algebra induces the collapse of the hierarchy of ordinals in epsilon
zero, and by raising the question of the exact categorial abstraction of the
notion of Frobenius algebra.
