ScalingStacks

Let \(\mathbb V\in \mathrm{CAlg}(\mathrm{Pr}^\mathrm{L})\) and let \(\widehat{\mathrm{Cat}}[\mathbb V]\) denote the \(\infty\)-category of large \(\mathbb V\)-enriched \(\infty\)-categories equipped with the enriched tensor product. The construction of an enriched \(\infty\)-category from a presentable module category then assembles into a lax symmetric monoidal faithful functor \[\mathrm{Mod}_{\mathbb V}(\mathrm{Pr}^\mathrm{L}) \rightarrow\widehat{\mathrm{Cat}}[\mathbb V].\] In particular, this induces a functor \[ \mathrm{CAlg}(\mathrm{Mod}_{\mathbb V}(\mathrm{Pr}^\mathrm{L})) \simeq \mathrm{CAlg}(\mathrm{Pr}^\mathrm{L})_{\mathbb V/} \rightarrow\mathrm{CAlg}(\widehat{\mathrm{Cat}}[\mathbb V]).\]