Kerodon

Corollary 8.6.6.5. Let $U: \operatorname{\mathcal{E}}\rightarrow \operatorname{\mathcal{C}}$ be a cocartesian fibration of simplicial sets, let $L$ be the collection of $U$-cocartesian edges of $\operatorname{\mathcal{E}}$, and let $\operatorname{\mathcal{E}}^{\vee }$ be the fiber product $\operatorname{\mathcal{C}}\times _{ \operatorname{Cospan}(\operatorname{\mathcal{C}}) } \operatorname{Cospan}^{L, \mathrm{all}}( \operatorname{\mathcal{E}})$. Then the projection map $U^{\vee }: \operatorname{\mathcal{E}}^{\vee } \rightarrow \operatorname{\mathcal{C}}$ is a cocartesian fibration, which is a cocartesian dual of $U$.