Symmetry shifting for monoidal bicategories

Raffael Stenzel

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arXiv · 2602.15358

Symmetry shifting for monoidal bicategories

Raffael Stenzel

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Abstract

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.

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Raffael Stenzel. 2026-02-17. Symmetry shifting for monoidal bicategories. https://arxiv.org/abs/2602.15358

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