Kerodon

$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$ $\newcommand\empty{}$
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$

Corollary 10.2.6.13. Let $X_{\bullet }$ be a split simplicial object of an $\infty $-category $\operatorname{\mathcal{C}}$. Then $X_{\bullet }$ admits a geometric realization $| X_{\bullet } |$. Moreover, the geometric realization of $X_{\bullet }$ is preserved by any functor of $\infty $-categories $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$.

Proof. The first assertion follows from Proposition 10.2.6.9, and the second from Remark 10.2.6.10. $\square$