Definition 10.2.5.1. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category and let $C_{\bullet }$ be an augmented simplicial object of $\operatorname{\mathcal{C}}$, which we identify with a simplicial object $C'_{\bullet }$ of the $\infty $-category $\operatorname{\mathcal{C}}_{ / C_{-1} }$ (see Remark 10.2.1.15). We will say that $C_{\bullet }$ is a Čechnerve if the simplicial object $C'_{\bullet }$ is a Čechnerve in the $\infty $-category $\operatorname{\mathcal{C}}_{/C_{-1} }$ (see Definition 10.2.4.1).
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