Corollary 8.6.5.2. For every simplicial set $\operatorname{\mathcal{C}}$, the formation of cocartesian duals induces a bijection
\[ \xymatrix@C =50pt@R=50pt{ \{ \textnormal{Cocartesian fibrations $U: \operatorname{\mathcal{E}}\rightarrow \operatorname{\mathcal{C}}$} \} / \textnormal{Equivalence} \ar [d]^{\theta } \\ \{ \textnormal{Cocartesian fibrations $U^{\vee }: \operatorname{\mathcal{E}}^{\vee } \rightarrow \operatorname{\mathcal{C}}$} \} / \textnormal{Equivalence.} } \]