ScalingStacks

Remark 4.2.3. Note that applying the self-equivalence $(a,b)\mapsto(b,a)$ of ${\mathcal{U}}^{2}$ provides another lax action $E^{\prime}$ of ${\mathcal{U}}^{2}$ on ${\mathcal{W}}$. The corresponding differential category $\Delta_{E^{\prime}}{\mathcal{W}}$ is not equivalent to $\Delta_{E}{\mathcal{W}}$ in general.