Corollary 8.6.2.4. Every cocartesian fibration of simplicial sets $U: \operatorname{\mathcal{E}}\rightarrow \operatorname{\mathcal{C}}$ admits a cartesian conjugate.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$
Proof. Using Corollary 5.6.7.3, we can choose a pullback diagram
\[ \xymatrix@R =50pt@C=50pt{ \operatorname{\mathcal{E}}\ar [d]^{U} \ar [r] & \operatorname{\mathcal{E}}' \ar [d]^{U'} \\ \operatorname{\mathcal{C}}\ar [r] & \operatorname{\mathcal{C}}', } \]
where $U'$ is a cocartesian fibration of $\infty $-categories. By virtue of Remark 8.6.1.4, it will suffice to show that $U'$ admits a cartesian conjugate, which follows from Proposition 8.6.2.3. $\square$