Kerodon

$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$ $\newcommand\empty{}$
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$

Example 9.1.1.7. Let $(A, \leq )$ be a partially ordered set and let $\kappa $ be a cardinal. Then the $\infty $-category $\operatorname{N}_{\bullet }(A)$ is $\kappa $-filtered if and only if every $\kappa $-small subset $A_0 \subseteq A$ has an upper bound. If this condition is satisfied, we say that the partially ordered set $(A, \leq )$ is $\kappa $-directed.