Definition 10.2.0.1 (Simplicial Objects). Let $\operatorname{\mathcal{C}}$ be an $\infty $-category. A simplicial object of $\operatorname{\mathcal{C}}$ is a functor from the $\infty $-category $\operatorname{N}_{\bullet }( \operatorname{{\bf \Delta }}^{\operatorname{op}} )$ to $\operatorname{\mathcal{C}}$. A cosimplicial object of $\operatorname{\mathcal{C}}$ is a functor from $\operatorname{N}_{\bullet }( \operatorname{{\bf \Delta }})$ to $\operatorname{\mathcal{C}}$.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$