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.
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