Example 7.2.5.9. Let $(A, \leq )$ be a partially ordered set. Combining Exercise 7.2.4.2 with Corollary 7.2.5.8, we see that the $\infty $-category $\operatorname{N}_{\bullet }(A)$ is filtered if and only if the partially ordered set $(A, \leq )$ is directed.
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