Since an \(\mathbb A_2\otimes \mathbb E_1\)-structure on a given monoidal \(1\)-category is by corollary 7.4.15.([00FC]) precisely the data of a braiding, corollary 7.7.6 in particular implies the well-known observation (see [Lur17, Ex. 5.1.2.4]) that braided monoidal structures and \(\mathbb E_2\)-structures coinicide on ordinary \(1\)-categories.
Original source: arXiv:2401.02956v2
Original source · 2401.02956v2