Remark 4.7.8.5 (Homotopy Invariance). Let $\kappa $ be an uncountable cardinal and let $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ be an equivalence of $\infty $-categories. Then $\operatorname{\mathcal{C}}$ is locally $\kappa $-small if and only if $\operatorname{\mathcal{D}}$ is locally $\kappa $-small.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$