The higher algebra and geometry of monoidal bicategories

Raffael Stenzel

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arXiv · 2602.14424

The higher algebra and geometry of monoidal bicategories

Raffael Stenzel

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Abstract

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.

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Raffael Stenzel. 2026-02-16. The higher algebra and geometry of monoidal bicategories. https://arxiv.org/abs/2602.14424

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