Document Type
Article
Publication Date
1-2025
Publication Title
Journal of Geometry and Physics
Abstract
In previous work by the first two authors, Frobenius and commutative algebra objects in the category of spans of sets were characterized in terms of simplicial sets satisfying certain properties. In this paper, we find a similar characterization for the analogous coherent structures in the bicategory of spans of sets. We show that commutative and Frobenius pseudomonoids in Span correspond, respectively, to paracyclic sets and Γ-sets satisfying the 2-Segal conditions. These results connect closely with work of the third author on A∞ algebras in ∞-categories of spans, as well as the growing body of work on higher Segal objects. Because our motivation comes from symplectic geometry and topological field theory, we emphasize the direct and computational nature of the classifications and their proofs.
Keywords
Spans, Topological quantum field theory, 2-categories, 2-Segal objects, Frobenius algebras, Commutative algebras, Mathematics, Category Theory
Volume
207
DOI
10.1016/j.geomphys.2024.105309
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.
Recommended Citation
Contreras, Ivan; Mehta, Rajan Amit; and Stern, Walker H., "Frobenius and Commutative Pseudomonoids in the Bicategory of Spans" (2025). Mathematics Sciences: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/mth_facpubs/182
Comments
Peer reviewed accepted manuscript.
v2: added section 3.5, improved exposition elsewhere in Section 3, various other minor edits. Final version; doi:10.1016/j.geomphys.2024.105309