Variant 9.2.2.11. Let $\kappa $ be a regular cardinal, let $Y$ be a set, and let $P(Y)$ be the partially ordered collection of all subsets of $Y$. Then a subset $X \subseteq Y$ is $\kappa $-small if and only if it is $\kappa $-compact when viewed as an object of the $\infty $-category $\operatorname{N}_{\bullet }( P(Y) )$.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$