ScalingStacks

Corollary 2.4.7.

Let \(\mathcal A\) with \(g \colon \mathcal A\rightarrow \mathcal D\) be a monoidal \(1\)-category over \(\mathcal D\). Then a prebraiding over \(\mathcal D\) on the identity functor \(\mathrm{Id}\colon \mathcal A\rightarrow\mathcal A\) is a braided monoidal structure on \(\mathcal A\) with the property that \(g\) is braided monoidal in the sense of [Eti+15, Def. 8.1.7.].