ScalingStacks

Remark 4.4.3. Let us define a lax bi-$2$-representation $E_{i,j}=E_{2}^{j}F_{1}^{i}$ on ${\mathcal{W}}$ as deduced from the one defined in §4.2.1 by applying the swap automorphism of ${\mathcal{U}}\times{\mathcal{U}}$ (cf Remark 4.2.3).

There is a faithful differential functor $\Delta_{\lambda}{\mathcal{W}}\to\Delta_{E}{\mathcal{W}},\ (m,\varsigma)\mapsto(m,\varsigma_{1})$.