ScalingStacks

Let $Z_{1},\ldots,Z_{r}$ be the connected components of $Z$. The isomorphism (7.3.4) induces an isomorphism of pointed categories

(7.4.1)

$${\mathcal{P}}^{\bullet}(Z_{1})\wedge\cdots\wedge{\mathcal{P}}^{\bullet}(Z_{r})\mathrel{\mathop{\kern 0.0pt\to}\limits^{\sim}}{\mathcal{P}}^{\bullet}(Z).$$