Remark 10.2.2.26. In the situation of Proposition 10.2.2.25, the augmented semisimplicial object $\overline{X}_{\bullet }$ exhibits $X$ as a geometric realization of $X_{\bullet }$ (in the sense of Definition 10.2.1.16) if and only if it the morphism $\epsilon $ exhibits $X$ as a coequalizer of the face operators $d^{1}_0, d^{1}_1: X_1 \rightrightarrows X_0$.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$