Example 9.1.4.10. Let $(P, \leq )$ and $(Q, \leq )$ be directed partially ordered sets and let $f: P \rightarrow Q$ be a nondecreasing function. Corollary 9.1.4.9 implies that the functor $\operatorname{N}_{\bullet }(f): \operatorname{N}_{\bullet }(P) \rightarrow \operatorname{N}_{\bullet }(Q)$ is right cofinal if and only if, for each $q \in Q$, there exists $p \in P$ satisfying $q \leq f(p)$.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$