Symmetry shifting for monoidal bicategories
Category Theory
2026-02-18 v1 Quantum Algebra
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 -operadic Additivity Theorem and thereby averts any considerable calculations.
Cite
@article{arxiv.2602.15358,
title = {Symmetry shifting for monoidal bicategories},
author = {Raffael Stenzel},
journal= {arXiv preprint arXiv:2602.15358},
year = {2026}
}