Definition 10.2.3.4. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category and let $n$ be an integer. We say that a simplicial object $X_{\bullet }$ of $\operatorname{\mathcal{C}}$ is $n$-skeletal if the functor
\[ \operatorname{N}_{\bullet }( \operatorname{{\bf \Delta }})^{\operatorname{op}} \xrightarrow { X_{\bullet } } \operatorname{\mathcal{C}} \]
is left Kan extended from the full subcategory $\operatorname{N}_{\bullet }( \operatorname{{\bf \Delta }}^{\leq n})^{\operatorname{op}} \subseteq \operatorname{N}_{\bullet }( \operatorname{{\bf \Delta }})^{\operatorname{op}}$.