ScalingStacks

For any \(j> k \geq 0\) and \(n\geq -2\), since the inclusion \(i_j \colon \mathrm{Cat}_{(\infty, {k})} \hookrightarrow \mathrm{Cat}_{(\infty, {j})}\) preserves \(n\)-factorizations (see observation 5.3.10), the diagram commutes. By adjunction, this induces for any \((\infty,j)\)-category \(\mathcal C\) a canonical functor of \((n,k)\)-categories \[ \tau_n \iota_k \mathcal C\rightarrow\iota_k \tau_n \mathcal C.\]