ScalingStacks

Any functor \(F \colon \mathcal C\rightarrow\mathcal D\) in \(\mathrm{CAlg}(\mathrm{Pr}^\mathrm{L})\) induces an equivalence in \(\mathrm{CAlg}(\mathrm{Pr}^\mathrm{L})\) \[\mathcal D\otimes_{\mathcal C}(\mathrm{Mod}_A(\mathcal C)) \simeq \mathrm{Mod}_{F(A)}(\mathcal D),\] where \(-\otimes_{\mathcal C}-\) denotes the pushout in \(\mathrm{CAlg}(\mathrm{Pr}^\mathrm{L})\), whose underlying presentable \(\infty\)-category is given by the relative tensor product in \(\mathrm{Pr}^\mathrm{L}\) [Lur17, Prop. 3.2.4.10], hence the notation.