Question 11.5.0.59. Let $U: \operatorname{\mathcal{E}}\rightarrow \operatorname{\mathcal{C}}$ be a cocartesian fibration of $\infty $-categories. Can the $\infty $-category $\operatorname{\mathcal{E}}$ be reconstructed (up to equivalence) from the $\infty $-category $\operatorname{\mathcal{C}}$ and the homotopy transport representation $\operatorname{hTr}_{\operatorname{\mathcal{E}}/\operatorname{\mathcal{C}}}: \mathrm{h} \mathit{\operatorname{\mathcal{C}}} \rightarrow \mathrm{h} \mathit{\operatorname{QCat}}$?
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$