The higher algebra and geometry of monoidal bicategories
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866911449892257792 |
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| author | Stenzel, Raffael |
| author_facet | Stenzel, Raffael |
| contents | We show that braided, sylleptic and symmetric monoidal bicategories are precisely the $\mathsf{E}_k$-monoids in the cartesian monoidal $(\infty,1)$-category of bicategories for respective integers $k$. To manage the underlying computations, we use the geometry of the little cubes operads to mediate between the 2-dimensional algebra underlying the former and the $\infty$-categorical algebra underlying the latter. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_14424 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The higher algebra and geometry of monoidal bicategories Stenzel, Raffael Category Theory Algebraic Topology Quantum Algebra 18M05, 18M15, 18N10, 18N20, 18N70, 18N60 We show that braided, sylleptic and symmetric monoidal bicategories are precisely the $\mathsf{E}_k$-monoids in the cartesian monoidal $(\infty,1)$-category of bicategories for respective integers $k$. To manage the underlying computations, we use the geometry of the little cubes operads to mediate between the 2-dimensional algebra underlying the former and the $\infty$-categorical algebra underlying the latter. |
| title | The higher algebra and geometry of monoidal bicategories |
| topic | Category Theory Algebraic Topology Quantum Algebra 18M05, 18M15, 18N10, 18N20, 18N70, 18N60 |
| url | https://arxiv.org/abs/2602.14424 |