Kerodon

$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$ $\newcommand\empty{}$
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$

Exercise 7.4.3.8. Let $\overline{U}: \overline{\operatorname{\mathcal{E}}} \rightarrow \operatorname{\mathcal{C}}^{\triangleright }$ and $\overline{U}': \overline{\operatorname{\mathcal{E}}}' \rightarrow \operatorname{\mathcal{C}}^{\triangleright }$ be cocartesian fibrations of simplicial sets which are equivalent as inner fibrations over $\operatorname{\mathcal{C}}^{\triangleright }$ (in the sense of Definition 5.1.6.1). Show that $\overline{U}$ satisfies condition $(1)$ of Theorem 7.4.3.6 if and only if $\overline{U}'$ satisfies condition $(1)$ of Theorem 7.4.3.6.