Frobenius algebras can be given a category-theoretic definition in terms of the category of vector spaces. This leads to a more general definition of Frobenius object in any monoidal category. In this talk, I will describe Frobenius objects in the category where the objects are sets and the morphisms are spans of sets. This category can be viewed as a toy model for the Wehrheim-Woodward symplectic category. The main result is that it is possible to construct a simplicial set that encodes the data of the Frobenius structure.

This work is an early step in a bigger program aimed at better understanding the relationship between Poisson geometry and topological field theory. Part of the talk will be devoted to giving an overview of this relationship and some of the questions surrounding it. This is based on joint work with Ivan Contreras and Molly Keller.