Symmetry shifting for monoidal bicategories
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866908837467914240 |
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| author | Stenzel, Raffael |
| author_facet | Stenzel, Raffael |
| contents | We show that every braiding on a monoidal bicategory induces a monoidal structure on its bicategory of monoids, such that if the former is sylleptic or symmetric then the latter is braided or symmetric, respectively. This extends a classic theorem of Joyal and Street for monoidal categories. The proof presented in this paper is an application of the $\infty$-operadic Additivity Theorem and thereby averts any considerable calculations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_15358 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Symmetry shifting for monoidal bicategories Stenzel, Raffael Category Theory Quantum Algebra 18M05, 18M15, 18N10, 18N20, 18N70, 18N60 We show that every braiding on a monoidal bicategory induces a monoidal structure on its bicategory of monoids, such that if the former is sylleptic or symmetric then the latter is braided or symmetric, respectively. This extends a classic theorem of Joyal and Street for monoidal categories. The proof presented in this paper is an application of the $\infty$-operadic Additivity Theorem and thereby averts any considerable calculations. |
| title | Symmetry shifting for monoidal bicategories |
| topic | Category Theory Quantum Algebra 18M05, 18M15, 18N10, 18N20, 18N70, 18N60 |
| url | https://arxiv.org/abs/2602.15358 |