Definition 10.2.5.10. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category and let $n$ be an integer. We say that an augmented simplicial object $C_{\bullet }$ of $\operatorname{\mathcal{C}}$ is $n$-coskeletal if the functor
\[ C_{\bullet }: \operatorname{N}_{\bullet }( \operatorname{{\bf \Delta }}_{+} )^{\operatorname{op}} \rightarrow \operatorname{\mathcal{C}} \]
is right Kan extended from the full subcategory $\operatorname{N}_{\bullet }( \operatorname{{\bf \Delta }}_{+}^{\leq n} )^{\operatorname{op}}$.