Corollary 10.2.2.12. Let $X_{\bullet }$ be a semisimplicial object of a category $\operatorname{\mathcal{C}}$. Then an object $X \in \operatorname{\mathcal{C}}$ is a geometric realization of $X_{\bullet }$ (in the $\infty $-category $\operatorname{N}_{\bullet }(\operatorname{\mathcal{C}})$) if and only if it is a coequalizer of the face operators $d^{1}_0, d^{1}_1: X_1 \rightrightarrows X_0$.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$