Kerodon

Remark 10.2.2.10. Let $X_{\bullet }$ be a simplicial object of an $\infty $-category $\operatorname{\mathcal{C}}$. Corollary 10.2.2.7 asserts that an object $X \in \operatorname{\mathcal{C}}$ is a geometric realization of $X_{\bullet }$ (in the sense of Definition 10.2.1.3) if and only if it is a geometric realization of the underlying semisimplicial object of $X_{\bullet }$ (in the sense of Definition 10.2.2.9). In particular, $X_{\bullet }$ admits a geometric realization if and only if its underlying semisimplicial object admits a geometric realization.