ScalingStacks

An \(\mathbb A_2 \otimes \mathbb E_1\)-structure on \(\mathcal A\) is a braiding on the monoidal category \(\mathcal A\), in the usual \(1\)-categorical sense. More precisely, the space \(\mathbb A_2(\mathcal A)\) of \(\mathbb A_2\)-structures on \(\mathcal A\) is discrete and equivalent to the set \(\mathrm{Braid}(\mathcal A)\) of braidings on \(\mathcal A\) defined in definition 2.4.8.