ScalingStacks

Given \(\mathbb{K}\in \mathrm{CAlg}(\mathrm{Sp}_{\geq 0})\), the symmetric monoidal inclusion \(\mathrm{Mod}_{\mathbb{K}}^{\geq 0, \mathcal Z} \hookrightarrow \mathrm{Mod}_{\mathbb{K}}^{\mathcal Z}\) from observation 3.5.17 induces a symmetric monoidal \(\mathrm{add}_{\mathbb{K}}^{B\mathcal Z}\)-enriched functor \[\mathrm{Morita}^{\mathrm{cp}}(\mathrm{Mod}_{\mathbb{K}}^{\geq 0, \mathcal Z}) \rightarrow\mathrm{Morita}^{\mathrm{c}}(\mathrm{Mod}_{\mathbb{K}}^{ \mathcal Z}),\] where \(\mathrm{Morita}^{\mathrm{c}}(\mathrm{Mod}_{\mathbb{K}}^{ \mathcal Z})\) is considered \(\mathrm{add}_{\mathbb{K}}^{B\mathcal Z}\)-enriched by transporting its \(\mathrm{st}_{\mathbb{K}}^{B\mathcal Z}\)-enrichment along the forgetful functor \(\mathrm{st}_{\mathbb{K}}^{B\mathcal Z}\rightarrow\mathrm{add}_{\mathbb{K}}^{B\mathcal Z}\).