Kerodon

Remark 10.2.5.17. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category and let $C_{\bullet }$ be an augmented simplicial object of $\operatorname{\mathcal{C}}$. For every integer $n$, the augmented simplicial object $C_{\bullet }$ is $n$-coskeletal (in the sense of Definition 10.2.5.10) if and only if its underlying augmented semisimplicial object is $n$-coskeletal (in the sense of Variant 10.2.5.14). For $n \leq -2$, this is trivial (see Example 10.2.5.12). For $n \geq -1$, it follows by combining Remark 10.2.5.15 with Proposition 10.2.4.15 (applied to the slice $\infty $-category $\operatorname{\mathcal{C}}_{ / C_{-1} }$).