ScalingStacks

Let \(\mathcal K'\) be a small set of simplicial sets with containing \(\mathcal K\). Then the subcategory inclusion \(\mathrm{Cat}_{\infty}^{\mathcal K'} \rightarrow\mathrm{Cat}_{\infty}^{\mathcal K}\) admits a symmetric monoidal left adjoint \[\mathcal P_{\mathcal K}^{\mathcal K'}\colon \mathrm{Cat}_{\infty}^{\mathcal K} \rightarrow\mathrm{Cat}_{\infty}^{\mathcal K'}\] whose unit \(\mathcal C\rightarrow\mathcal P_{\mathcal K}^{\mathcal K'}(\mathcal C)\) for \(\mathcal C\in \mathrm{Cat}_{\infty}^{\mathcal K'}\) is a fully faithful functor.