Remark 10.2.3.9. In the formulation of Definition 10.2.3.4, we allow $n$ to be an arbitrary integer. However, for $n < 0$, the notion becomes degenerate: a simplicial object $X_{\bullet }$ is $n$-skeletal if and only if each $X_{m}$ is an initial object of $\operatorname{\mathcal{C}}$. In this case, $X_{\bullet }$ is an initial object in the $\infty $-category of simplicial objects $\operatorname{Fun}( \operatorname{N}_{\bullet }(\operatorname{{\bf \Delta }})^{\operatorname{op}}, \operatorname{\mathcal{C}})$.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$