2025/05/28 by Sophia E Marx, Marx, Sophia E, Rajan Amit Mehta +1
Computer Science · Decision Sciences · Mathematics · #18B10 #18B40 #18C40 #18N50 #Advanced Algebra and Logic #Algebraic Topology (math.AT) #Category Theory (math.CT) #FOS: Mathematics #Fuzzy and Soft Set Theory #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2505.22832
openalex publication_date 2025/05/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.