Remark 4.7.4.2. In the situation of Definition 4.7.4.1, the dimension of the simplices under consideration is not fixed. That is, a simplicial set $S_{\bullet }$ is $\kappa $-small if and only if the disjoint union ${\coprod }_{m \geq 0} S_{m}^{\mathrm{nd}}$ is a $\kappa $-small set, where $S_{m}^{\mathrm{nd}} \subseteq S_{m}$ denotes the set of nondegenerate $m$-simplices of $S_{\bullet }$.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$