Kerodon

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

Corollary 5.1.1.10. Let $q: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ be an inner fibration of $\infty $-categories, where $\operatorname{\mathcal{D}}$ is a Kan complex, and let $e: X \rightarrow Y$ be a morphism fo $\operatorname{\mathcal{C}}$. The following conditions are equivalent:

$(1)$

The morphism $e$ is an isomorphism in $\operatorname{\mathcal{C}}$.

$(2)$

The morphism $e$ is $q$-cartesian.

$(3)$

The morphism $e$ is $q$-cocartesian.