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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2505.22832 |
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| _version_ | 1866909626499334144 |
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| author | Marx, Sophia E Mehta, Rajan Amit |
| author_facet | Marx, Sophia E Mehta, Rajan Amit |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_22832 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | 2-Segal sets and pseudomonoids in the bicategory of spans Marx, Sophia E Mehta, Rajan Amit Category Theory Algebraic Topology 18B10, 18B40, 18C40, 18N50 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. |
| title | 2-Segal sets and pseudomonoids in the bicategory of spans |
| topic | Category Theory Algebraic Topology 18B10, 18B40, 18C40, 18N50 |
| url | https://arxiv.org/abs/2505.22832 |