Ivan Contreras, Amherst College
Frobenius objects in the category of spans and the symplectic category
It is well known that Frobenius algebras are in correspondence with 2-dimensional TQFTs. In this talk, we introduce Frobenius objects in any monoidal category, and in particular in the category where objects are sets and morphisms are spans of sets. We prove the existence of a simplicial set that encodes the data of the Frobenius structure in this category. This serves as a (simplicial) toy model of the Wehrheim–Woodward construction for the symplectic category. This is part of a program that intends to describe, in terms of category theory, the relationship between symplectic groupoids and topological field theory via the Poisson sigma model. Based on joint work with Rajan Mehta and Molly Keller (Rev. in Math. Phys (34) 10 (2022)), with Rajan Mehta, Adele Long and Sophia Marx (https://arxiv.org/abs/2208.