Definition 10.2.4.17. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category, let $u: X_{\bullet } \rightarrow Y_{\bullet }$ 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 $n$-coskeleton of $X_{\bullet }$ if the following conditions are satisfied:
The simplicial object $Y_{\bullet }$ is $n$-coskeletal.
For $0 \leq m \leq n$, the induced map $X_{m} \rightarrow Y_{m}$ is an isomorphism in the $\infty $-category $\operatorname{\mathcal{C}}$.