ScalingStacks

Notation 5.5.1.

For \(n, k \geq 0\), we let \(\mathrm{Ar}^{n}(\mathrm{Cat}_{(\infty, {k})}) \subseteq \mathrm{Ar}(\mathrm{Cat}_{(\infty, {k})})\) denote the full subcategory of the arrow category of \(\mathrm{Cat}_{(\infty, {k})}\) on the \(n\)-faithful functors. Moreover, for \(\mathcal D\in \mathrm{Cat}_{(\infty, {k})}\), we write \({(\mathrm{Cat}_{(\infty, {k})})}_{\small{/^{n}}{\mathcal D}} \subseteq {(\mathrm{Cat}_{(\infty, {k})})}_{\small{/^{\phantom{}}}{\mathcal D}}\) for the full subcategory of the over-category on the \(n\)-faithful functors \(\mathcal C\rightarrow\mathcal D\). In particular, \({(\mathrm{Cat}_{(\infty, {k})})}_{\small{/^{n}}{{\sf pt}}} = \mathrm{Cat}_{({n}, {k})}\).