Example 7.6.6.10. Let $(Q, \leq )$ be a partially ordered set and let $\kappa $ be an infinite cardinal. Then the $\infty $-category $\operatorname{\mathcal{C}}= \operatorname{N}_{\bullet }(Q)$ is $\kappa $-complete if and only if every $\kappa $-small subset $S \subseteq Q$ has a greatest lower bound $\mathrm{inf}(S)$. Similarly, $\operatorname{\mathcal{C}}$ is $\kappa $-cocomplete if and only if every $\kappa $-small subset $S \subseteq Q$ has a least upper bound $\mathrm{sup}(S)$.
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