Remark 10.2.1.8. Let $X_{\bullet }$ be a simplicial object of a category $\operatorname{\mathcal{C}}$. It follows from Exercise 10.2.1.6 that a geometric realization of $X_{\bullet }$ (if it exists) depends only on the pair of face operators $d^{1}_0, d^{1}_1: X_1 \rightrightarrows X_0$. Beware that, in the $\infty $-categorical setting, this is generally not true: the geometric realization $| X_{\bullet } |$ is sensitive to information about the entire simplicial object $X_{\bullet }$.
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