establish is also the gist of the connection between the notions of Frobenius monad and two-dimensional topological quantum field theory (2TQFT). A 2TQFT may be understood as a functor from the category *2Cob*, whose arrows are cobordisms in dimension 2, to the category $\mbox{\it
Vect}_K$ of finite-dimensional vector spaces over the field $K$. In terms of category theory, a Frobenius algebra is characterized by a monoidal functor from the Frobenius monad freely generated by a single object to $\mbox{\it Vect}_K$, modulo the strictification of $\mbox{\it Vect}_K$ with respect to its monoidal structure given by the tensor product and $K$ (cf. the beginning of Section 7). A Frobenius algebra is the image of the object $1$ of the Frobenius monad. The main result here is that 2TQFTs correspond bijectively, modulo a skeletization of *2Cob*, to commutative Frobenius algebras. This result is stated officially as a result about equivalence of categories (see [@K03], Section 3.3).

An alternative result with the same mathematical content is that the free commutative Frobenius monad is isomorphic to the skeleton of *2Cob*. From that alternative result, the former result follows immediately. This alternative result may be conceived as a coherence result for commutative Frobenius monads.

Our coherence 