Definition 10.2.3.18. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category, let $u: Y_{\bullet } \rightarrow X_{\bullet }$ be a morphism between simplicial objects of $\operatorname{\mathcal{C}}$, and let $n$ be an integer. We will say that $u$ exhibits $Y_{\bullet }$ as an $n$-skeleton of $X_{\bullet }$ if the following conditions are satisfied:
The simplicial object $Y_{\bullet }$ is $n$-skeletal.
For $0 \leq m \leq n$, the induced map $Y_{m} \rightarrow X_{m}$ is an isomorphism in the $\infty $-category $\operatorname{\mathcal{C}}$.