Kerodon

Remark 10.2.3.15. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category and let $n$ be an integer. Using Proposition 10.2.3.14, we see that the condition that a simplicial object $X_{\bullet }$ of $\operatorname{\mathcal{C}}$ is $n$-skeletal depends only on the restriction of $X_{\bullet }$ to the (non-full) subcategory $\operatorname{N}_{\bullet }( \operatorname{{\bf \Delta }}_{\mathrm{surj}})^{\operatorname{op}} \subset \operatorname{N}_{\bullet }( \operatorname{{\bf \Delta }})^{\operatorname{op}}$ (see Notation 1.1.2.12). Stated more informally (and slightly incorrectly), the condition of $n$-skeletality depends only on the degeneracy operators of $X_{\bullet }$, and not on its face operators.