Cnossen, Bastiaan and Haugseng, Rune and Lenz, Tobias and Linskens, Sil (2025) Homotopical commutative rings and bispans. JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 111 (6): e70200. ISSN 0024-6107, 1469-7750
Full text not available from this repository. (Request a copy)Abstract
We prove that commutative semirings in a cartesian closed presentable infinity$\infty$-category, as defined by Groth, Gepner, and Nikolaus, are equivalent to product-preserving functors from the (2,1)-category of bispans of finite sets. In other words, we identify the latter as the Lawvere theory for commutative semirings in the infinity$\infty$-categorical context. This implies that connective commutative ring spectra can be described as grouplike product-preserving functors from bispans of finite sets to spaces. A key part of the proof is a localization result for infinity$\infty$-categories of spans, and more generally for infinity$\infty$-categories with factorization systems, that may be of independent interest.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | SPECTRAL MACKEY FUNCTORS; ALGEBRAIC K-THEORY; UNIVERSALITY |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Marc Hoyois |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 23 Jun 2026 06:21 |
| Last Modified: | 23 Jun 2026 06:23 |
| URI: | https://pred.uni-regensburg.de/id/eprint/67021 |
Actions (login required)
 |
View Item |
