ScalingStacks

Observation 5.1.5.

For any \(j \geq k \geq 0\), the inclusion \(\mathrm{Cat}_{(\infty, {k})} \xhookrightarrow{i_j} \mathrm{Cat}_{(\infty, {j})}\) identifies \(\mathrm{Cat}_{(\infty, {k})}\) as the full subcategory of \(\mathrm{Cat}_{(\infty, {j})}\) on those \((\infty,j)\)-categories whose \(i\)-morphisms are all invertible for all \(i > k\) [GH15, Prop. 6.1.7(iv)].²³ We use this fact without further comment.