Sphericalization and the Universal Spherical Adjunction
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866918501769281536 |
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| author | Abellán, Fernando Gödicke, Jonte |
| author_facet | Abellán, Fernando Gödicke, Jonte |
| contents | For every adjunction of stable $\infty$-categories -- or more generally, in any locally stable $(\infty,2)$-category -- we give a simple procedure for inverting the twist and cotwist functors associated to this adjunction. As a consequence, we obtain an explicit construction for a left and right adjoint to the inclusion of the $(\infty,2)$-category of spherical adjunctions of stable $\infty$-categories into all adjunctions. We utilize these adjoints to give a description of the walking spherical adjunction, a locally stable $(\infty,2)$-category which classifies spherical adjunctions, and to provide a synthetic proof of the fact that every spherical functor admits infinitely many left and right adjoints. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_15037 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Sphericalization and the Universal Spherical Adjunction Abellán, Fernando Gödicke, Jonte Category Theory Algebraic Topology Representation Theory For every adjunction of stable $\infty$-categories -- or more generally, in any locally stable $(\infty,2)$-category -- we give a simple procedure for inverting the twist and cotwist functors associated to this adjunction. As a consequence, we obtain an explicit construction for a left and right adjoint to the inclusion of the $(\infty,2)$-category of spherical adjunctions of stable $\infty$-categories into all adjunctions. We utilize these adjoints to give a description of the walking spherical adjunction, a locally stable $(\infty,2)$-category which classifies spherical adjunctions, and to provide a synthetic proof of the fact that every spherical functor admits infinitely many left and right adjoints. |
| title | Sphericalization and the Universal Spherical Adjunction |
| topic | Category Theory Algebraic Topology Representation Theory |
| url | https://arxiv.org/abs/2605.15037 |