ScalingStacks

Let $Z_{1},\ldots,Z_{r}$ be the connected components of $Z$. The construction above induces an isomorphism of differential pointed categories (cf (7.4.2))

(7.4.5)

$${\mathcal{S}}^{\bullet}(Z_{1})\wedge\cdots\wedge{\mathcal{S}}^{\bullet}(Z_{r})\mathrel{\mathop{\kern 0.0pt\to}\limits^{\sim}}{\mathcal{S}}^{\bullet}(Z),\ (S_{1},\ldots,S_{r})\mapsto S_{1}\sqcup\cdots\sqcup S_{r}.$$