Remark 4.7.5.2. Let $\kappa $ be an uncountable cardinal, and let $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ be a categorical equivalence of simplicial sets. Then $\operatorname{\mathcal{C}}$ is essentially $\kappa $-small if and only if $\operatorname{\mathcal{D}}$ is essentially $\kappa $-small.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$