arXiv subjects
Publications and source records attributed to Sophia E Marx.
We consider commutative Frobenius pseudomonoids in the bicategory of spans, and we show that they are in correspondence with 2-Segal cosymmetric sets. Such a structure can be interpreted as a coherent 2-dimensional topological quantum field theory taking values in the bicategory of spans. We also describe a construction that produces a 2-Segal cosymmetric set from any partial monoid equipped with a distinguished element.
In this survey article, we give an introduction to the notion of a 2-Segal set and prove that 2-Segal sets are equivalent to pseudomonoids in the bicategory of spans. The proof utilizes graphical techniques for 2-Segal sets and spans that should be useful in more general settings. There are procedures for obtaining an associative algebra from a 2-Segal set (satisfying finiteness conditions). We describe these procedures and give several examples of algebras arising from 2-Segal sets. Wherever possible, we avoid higher category theory so as to make the paper accessible to a wide audience.