Remark 11.3.0.1. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category which admits fiber products. Then Proposition 10.2.5.6 guarantees that every morphism $f: X \rightarrow Y$ of $\operatorname{\mathcal{C}}$ admits a Čechnerve. In this case, the proof of Proposition 10.2.6.21 shows that the restriction functor $\operatorname{Fun}'( \operatorname{N}_{\bullet }( \operatorname{{\bf \Delta }}_{\mathrm{min}}^{\operatorname{op}}), \operatorname{\mathcal{C}}) \rightarrow \operatorname{Fun}( \operatorname{N}_{\bullet }( \operatorname{Ret}^{\operatorname{op}}), \operatorname{\mathcal{C}})$ is a trivial Kan fibration.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$