Corollary 10.2.4.8. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category which admits finite products. Then the evaluation functor
\[ \operatorname{Fun}( \operatorname{N}_{\bullet }( \operatorname{{\bf \Delta }})^{\operatorname{op}} , \operatorname{\mathcal{C}}) \rightarrow \operatorname{\mathcal{C}}\quad \quad X_{\bullet } \mapsto X_{0} \]
admits a right adjoint, given on objects by the Čechnerve $X \mapsto \operatorname{\check{C}}_{\bullet }(X)$.