ScalingStacks

Warning 3.7. For every $\infty$-operad $\mathcal{O}$ and $d\geq 1$ we have $\left(h_{d}\mathcal{O}\right)^{\otimes}\simeq h_{d}\left(\mathcal{O}^{\otimes}\right)$, but for $d\leq 0$ we get something slightly different. The reason for this is that $\left(h_{d}\mathcal{C}\right)^{\otimes}$ corresponds to the application of $h_{d}$ fiber-wise to the map $p\colon\mathcal{O}^{\otimes}\to\mathbf{Fin}_{*}$. Since $\mathbf{Fin}_{*}$ is a 1-category, for $d\geq 1$ this is the same as applying $h_{d}$ to $p$, but for $d\leq 0$ it is not.