Remark 6.3.2.10 (Sizes of Localization). In the situation of Corollary 6.3.2.9, suppose that the simplicial set $\operatorname{\mathcal{C}}$ is $\kappa $-small, for some infinite cardinal $\kappa $. Then the simplicial set $\operatorname{\mathcal{D}}$ is also $\kappa $-small. This follows from the observation that $Q$ is a finite simplicial set (in fact, $Q$ has exactly eleven nondegenerate simplices).
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$