Kerodon

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

Remark 5.2.5.3. Let $\pi : \operatorname{\mathcal{M}}\rightarrow \Delta ^1$ be a cocartesian fibration of $\infty $-categories. It follows from Corollary 5.2.5.2 that the $\infty $-category $\operatorname{\mathcal{M}}$ can be recovered (up to equivalence) from the $\infty $-categories $\operatorname{\mathcal{C}}= \{ 0\} \times _{\Delta ^1} \operatorname{\mathcal{M}}$, $\operatorname{\mathcal{D}}= \{ 1\} \times _{\Delta ^1} \operatorname{\mathcal{M}}$, and the covariant transport functor $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$. Similarly, if $\pi : \operatorname{\mathcal{M}}\rightarrow \Delta ^1$ is a cartesian fibration, then the $\infty $-category $\operatorname{\mathcal{M}}$ can be recovered from $\operatorname{\mathcal{C}}$, $\operatorname{\mathcal{D}}$, and the contravariant transport functor $G: \operatorname{\mathcal{D}}\rightarrow \operatorname{\mathcal{C}}$.