Kerodon

Remark 10.2.1.14. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category. Every augmented simplicial object of $\operatorname{\mathcal{C}}$ determines a simplicial object of $\operatorname{\mathcal{C}}$, by restriction along the inclusion of full subcategories $\operatorname{{\bf \Delta }}^{\operatorname{op}} \hookrightarrow \operatorname{{\bf \Delta }}^{\operatorname{op}}_{+}$. For this reason, we will sometimes use the notation $\overline{X}_{\bullet }$ to indicate an augmented simplicial object of $\operatorname{\mathcal{C}}$, to distinguish it from the underlying simplicial object $X_{\bullet } = \overline{X}_{\bullet }|_{ \operatorname{N}_{\bullet }( \operatorname{{\bf \Delta }}^{\operatorname{op}} )}$.