Kerodon

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

Remark 5.4.7.12. Recall that every cartesian fibration of simplicial sets $\pi : \operatorname{\mathcal{E}}\rightarrow \operatorname{\mathcal{D}}$ has an underlying right fibration $\pi ': \operatorname{\mathcal{E}}' \rightarrow \operatorname{\mathcal{D}}$, given by restricting $\pi $ to the simplicial subset $\operatorname{\mathcal{E}}' \subseteq \operatorname{\mathcal{E}}$ spanned by those simplices $\sigma : \Delta ^ n \rightarrow \operatorname{\mathcal{E}}$ which carry each edge of $\Delta ^ n$ to $\pi $-cartesian edge of $\operatorname{\mathcal{E}}$. Corollary 5.4.7.11 asserts that, when $\pi $ is the cartesian fibration $\operatorname{Pith}( \operatorname{\mathcal{C}}_{/Z} ) \rightarrow \operatorname{Pith}(\operatorname{\mathcal{C}})$ associated to a choice of object $Z$ of an $(\infty ,2)$-category $\operatorname{\mathcal{C}}$, then $\pi '$ can be identified with the right fibration $\operatorname{Pith}(\operatorname{\mathcal{C}})_{/Z} \rightarrow \operatorname{Pith}(\operatorname{\mathcal{C}})$ supplied by Corollary 4.3.6.11; compare with Proposition 5.4.5.12.