Variant 8.3.5.7. Let $\kappa $ be an uncountable cardinal and let $\operatorname{\mathcal{C}}$ be an $\infty $-category which is locally $\kappa $-small. Then, in the statement of Proposition 8.3.5.6, we can replace $\operatorname{\mathcal{S}}$ with the $\infty $-category $\operatorname{\mathcal{S}}^{< \kappa }$ of $\kappa $-small spaces (Variant 5.5.4.12).
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$