Kerodon

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Corollary 5.1.1.9. 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.