Remark 8.6.4.6. Let $U: \operatorname{\mathcal{E}}\rightarrow \operatorname{\mathcal{C}}$ and $U^{\vee }: \operatorname{\mathcal{E}}^{\vee } \rightarrow \operatorname{\mathcal{C}}$. In ยง8.6.6, we will show that $U^{\vee }$ is a cocartesian dual of $U$ (in the sense of Definition 8.6.4.1) if and only if the opposite fibration $U^{\vee , \operatorname{op}}: \operatorname{\mathcal{E}}^{\vee , \operatorname{op}} \rightarrow \operatorname{\mathcal{C}}^{\operatorname{op}}$ is a cartesian conjugate of $U$ (in the sense of Definition 8.6.1.1). See Proposition 8.6.6.1.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$