Abstract: 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 categories where the objects are sets and the morphisms are relations or spans. These categories can be viewed as toy models for the symplectic category. The main result is that, in both cases, it is possible to construct a simplicial set that encodes the data of the Frobenius structure. This work is a very small first step in a bigger program aimed at better understanding the relationship between Poisson geometry and two-dimensional topological field theory. Part of the talk will be devoted to giving an overview of this question as well as its analogue in dimension 3. This is based on work with Ruoqi Zhang and work in progress with Ivan Contreras and Molly Keller.