ScalingStacks

By Observation B.1.20.([00K8]), the fully faithful inclusion \(\mathrm{Cat}_{(n,k)} \hookrightarrow \mathrm{Cat}_{(\infty, {k})}\) admits a left adjoint given by the formula \(\tau_n(\mathcal C) \coloneqq \mathrm{Fact}_n(\mathcal C\rightarrow{\sf pt})\).³² This left adjoint \(\tau_n\) is symmetric monoidal as it preserves products.