Definition 10.2.1.3 (Geometric Realization). Let $X_{\bullet }$ be a simplicial object of an $\infty $-category $\operatorname{\mathcal{C}}$. We will say that an object $X \in \operatorname{\mathcal{C}}$ is a geometric realization of $X_{\bullet }$ if it is a colimit of the diagram $X_{\bullet }: \operatorname{N}_{\bullet }( \operatorname{{\bf \Delta }}^{\operatorname{op}} ) \rightarrow \operatorname{\mathcal{C}}$.
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