Cnossen, Bastiaan and Lenz, Tobias and Ramzi, Maxime (2025) Universality of Barwick's Unfurling Construction. INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2025 (18): rnaf280. ISSN 1073-7928, 1687-0247
Full text not available from this repository. (Request a copy)Abstract
Given an $\infty $-category $\mathcal{C}$ with pullbacks, its $(\infty ,2)$-category $\textbf{Span}(\mathcal{C})$ of spans has the universal property of freely adding right adjoints to morphisms in $\mathcal{C}$ satisfying a Beck-Chevalley condition. We show that this universal property is implemented by an $(\infty ,2)$-categorical refinement of Barwick's unfurling construction: For any right adjointable functor $\mathcal{C} \to \textrm{Cat}_{\infty }$, the unstraightening of its unique extension to $\textbf{Span}(\mathcal{C})$ can be explicitly written down as another span $(\infty ,2)$-category, and on underlying $(\infty ,1)$-categories this recovers Barwick's construction. As an application, we show that the constructions of cartesian normed structures by Nardin-Shah and Cnossen-Haugseng-Lenz-Linskens coincide.
| Item Type: | Article |
|---|---|
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 17 Jun 2026 05:30 |
| Last Modified: | 17 Jun 2026 05:30 |
| URI: | https://pred.uni-regensburg.de/id/eprint/67018 |
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