Notation 11.9.1.8. Let $U: \operatorname{\mathcal{E}}\rightarrow \operatorname{\mathcal{C}}$ be a cocartesian fibration of $\infty $-categories, let $L$ denote the collection of all $U$-cocartesian morphisms of $\operatorname{\mathcal{E}}$, and let $R$ denote the collection of all morphisms $f$ of $\operatorname{\mathcal{E}}$ such that $U(f)$ is an isomorphism in $\operatorname{\mathcal{C}}$. We let
denote the relative exponential of Construction 4.5.9.1. Evaluation at the vertices $0,1 \in \Delta ^1$ determines evaluation functors $\operatorname{ev}_0, \operatorname{ev}_1: \operatorname{Fun}( \operatorname{\mathcal{C}}\times \Delta ^1 / \operatorname{\mathcal{C}}, \operatorname{\mathcal{E}}) \rightarrow \operatorname{\mathcal{E}}$. Let $\widetilde{L}$ denote the collection of all morphisms $f$ of $\operatorname{Fun}( \operatorname{\mathcal{C}}\times \Delta ^1 / \operatorname{\mathcal{C}}, \operatorname{\mathcal{E}})$ such that $\operatorname{ev}_0(f)$ is $U$-cocartesian, and let $\widetilde{R}$ denote the collection of all morphisms $f$ of $\operatorname{Fun}( \operatorname{\mathcal{C}}\times \Delta ^1 / \operatorname{\mathcal{C}}, \operatorname{\mathcal{E}})$ such that $\operatorname{ev}_1(f)$ is an isomorphism. The evaluation maps $\operatorname{ev}_0$ and $\operatorname{ev}_1$ then induce a functor