Remark 10.3.1.16. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category and let $f: X \rightarrow Y$ be a morphism of $\operatorname{\mathcal{C}}$. Suppose that $\operatorname{\mathcal{C}}$ admits finite limits, so that $f$ admits a Čechnerve $\operatorname{\check{C}}(X/Y)_{\bullet }$ (Proposition 10.2.5.6). If $Y$ is a subterminal object of $\operatorname{\mathcal{C}}$, then the underlying simplicial object of $\operatorname{\check{C}}(X/Y)_{\bullet }$ is also a Čechnerve of the object $X$. This follows by combining Remark 10.3.1.10 with Example 10.3.1.11.
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