ScalingStacks

The inclusions $Z_{i}\hookrightarrow Z$ induce pointed functors ${\mathcal{S}}^{\bullet}(Z_{i},1)\to{\mathcal{S}}^{\bullet}(Z,1)$ and give rise to an isomorphism of pointed categories

(7.3.4)

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