ScalingStacks

Any algebra homomorphism \(f\colon A\rightarrow B\) in \(\mathrm{CAlg}(\mathcal C)\) induces a symmetric monoidal induction functor \(-\otimes_A B\colon \mathrm{Mod}_A(\mathcal C) \rightarrow\mathrm{Mod}_B(\mathcal C)\) that is left adjoint to the restriction functor along \(f\), and hence a morphism in \(\mathrm{CAlg}(\mathrm{Pr}^\mathrm{L})\).