ScalingStacks

Corollary 3.1.9.

For \(\mathcal Z\in \mathrm{CAlg}(\mathcal S)\), proposition 3.1.8.([0036]) implies that there is an equivalence in \(\mathrm{CAlg}(\mathrm{Pr}^\mathrm{L})\): \[\mathcal C\otimes \mathrm{Mod}_\mathcal Z(\mathcal S) \simeq \mathcal C\otimes_{\mathcal S}\mathrm{Mod}_{\mathcal Z}(\mathcal S) \simeq \mathrm{Mod}_{\iota_{\mathcal C}(\mathcal Z)}(\mathcal C\otimes_\mathcal S\mathcal S) \simeq \mathrm{Mod}_{\iota_{\mathcal C}(\mathcal Z)}(\mathcal C).\]