Definition 10.2.2.1 (Semisimplicial Objects). Let $\operatorname{\mathcal{C}}$ be an $\infty $-category. A semisimplicial object of $\operatorname{\mathcal{C}}$ is a functor $\operatorname{N}_{\bullet }( \operatorname{{\bf \Delta }}_{\operatorname{inj}}^{\operatorname{op}} ) \rightarrow \operatorname{\mathcal{C}}$. A cosemisimplicial object of $\operatorname{\mathcal{C}}$ is a functor $\operatorname{N}_{\bullet }( \operatorname{{\bf \Delta }}_{\operatorname{inj}} ) \rightarrow \operatorname{\mathcal{C}}$.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$