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 of $\operatorname{\mathcal{C}}$. 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.