Document Type
Article
Publication Date
5-2025
Abstract
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.
Keywords
2-Segal set, pseudomonoid, span, categorification, simplicial set
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Rights
Licensed to Smith College and distributed CC-BY 4.0 under the Smith College Faculty Open Access Policy.
Version
Author's Submitted Manuscript
Recommended Citation
Marx, Sophia E. and Mehta, Rajan Amit, "2-Segal Sets and Pseudomonoids in the Bicategory of Spans" (2025). Mathematics Sciences: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/mth_facpubs/213