Notation 10.2.1.5. Let $X_{\bullet }$ be a simplicial object of an $\infty $-category $\operatorname{\mathcal{C}}$. It follows from Proposition 7.1.1.12 that, if $X_{\bullet }$ admits a geometric realization $X$, then the isomorphism class of $X$ is uniquely determined. To emphasize this, we will often denote $X$ by $| X_{\bullet } |$ and refer to it as the geometric realization of $X_{\bullet }$. Beware that, in the case where $\operatorname{\mathcal{C}}$ is (the nerve of) the category of sets, this is incompatible with the convention of Notation 1.2.3.3 (see Warning 10.2.1.4).
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