Corollary 5.3.5.11. Let $\operatorname{\mathcal{C}}$ be a category, let $U: \operatorname{\mathcal{E}}\rightarrow \operatorname{N}_{\bullet }(\operatorname{\mathcal{C}})$ be a cocartesian fibration of $\infty $-categories, and let $U': \operatorname{\mathcal{E}}' \rightarrow \operatorname{N}_{\bullet }(\operatorname{\mathcal{C}})$ be an isofibration of $\infty $-categories. Then the composite map
\begin{eqnarray*} \operatorname{Fun}_{ / \operatorname{N}_{\bullet }(\operatorname{\mathcal{C}}) }( \operatorname{\mathcal{E}}, \operatorname{\mathcal{E}}' ) & \xrightarrow {\theta } & \operatorname{Hom}_{ \operatorname{Fun}( \operatorname{\mathcal{C}}, \operatorname{Set_{\Delta }}) }( \operatorname{wTr}_{\operatorname{\mathcal{E}}/\operatorname{\mathcal{C}}}, \operatorname{wTr}_{\operatorname{\mathcal{E}}'/\operatorname{\mathcal{C}}} )_{\bullet } \\ & \rightarrow & \operatorname{Hom}_{ \operatorname{Fun}( \operatorname{\mathcal{C}}, \operatorname{Set_{\Delta }}) }( \operatorname{sTr}_{\operatorname{\mathcal{E}}/\operatorname{\mathcal{C}}}, \operatorname{wTr}_{\operatorname{\mathcal{E}}'/\operatorname{\mathcal{C}}} )_{\bullet } \end{eqnarray*}
is an equivalence of $\infty $-categories.