Example 9.3.2.6. Let $\operatorname{\mathcal{C}}= \operatorname{N}_{\bullet }( \operatorname{\mathcal{C}}_0 )$ be the nerve of an ordinary category $\operatorname{\mathcal{C}}_0$. Then:
Every object of $\operatorname{\mathcal{C}}$ is discrete.
An object $X \in \operatorname{\mathcal{C}}$ is subterminal (in the sense of Definition 9.3.2.2) if and only if it is subterminal in the sense of classical category theory: that is, for every object $Y \in \operatorname{\mathcal{C}}$, there is at most one morphism from $Y$ to $X$.