Kerodon

Remark 10.2.4.18. Definition 10.2.4.17 has an obvious counterpart for semisimplicial objects. If $u: X_{\bullet } \rightarrow Y_{\bullet }$ is a morphism between semisimplicial objects of an $\infty $-category $\operatorname{\mathcal{C}}$, we say that $u$ exhibits $Y_{\bullet }$ as an $n$-coskeleton of $X_{\bullet }$ if $Y_{\bullet }$ is $n$-coskeletal and the morphism $u$ induces an isomorphism $X_{m} \rightarrow Y_{m}$ for $0 \leq m \leq n$. By virtue of Proposition 10.2.4.15, this recovers Definition 10.2.4.17 in the case where $u$ arises from a morphism between simplicial objects of $\operatorname{\mathcal{C}}$.