ScalingStacks

Given \(\mathbb{K}\in \mathrm{CAlg}(\mathrm{Sp})\), definition 4.4.4 defines a large symmetric monoidal \(\mathrm{st}_{\mathbb{K}}^{B\mathcal Z}\)-enriched \(\infty\)-category \[\mathrm{Morita}^{\mathrm{c}}(\mathrm{Mod}_{\mathbb{K}}^{ \mathcal Z}) \in \mathrm{CAlg}(\widehat{\mathrm{Cat}}[\mathrm{st}_{\mathbb{K}}^{B\mathcal Z}])\] with a symmetric monoidal surjective-on-objects functor \(\mathrm{Alg}(\mathrm{Mod}_{\mathbb{K}}^{\mathcal Z}) \rightarrow\mathrm{Morita}^{\mathrm{cp}}(\mathrm{Mod}_{\mathbb{K}}^{ \mathcal Z})\), and such that the \(\mathrm{st}_{\mathbb{K}}^{B\mathcal Z}\)-enriched hom between \(A, B\) in \(\mathrm{Alg}(\mathrm{Mod}_{\mathbb{K}}^{\mathcal Z})\) is given by \[{}_A\mathrm{BMod}^{\mathrm{c}}_{B}(\mathrm{Mod}_{\mathbb{K}}^{\mathcal Z}) \in \mathrm{st}_{\mathbb{K}}^{B\mathcal Z},\] with the \(\mathrm{Perf}_{\mathbb{K}}\) and \(\mathcal Z\)-action induced by their respective actions on \(\mathrm{Mod}_{\mathbb{K}}^{\mathcal Z}\).