Example 8.1.9.7. Let $U: \operatorname{\mathcal{E}}\rightarrow \operatorname{\mathcal{C}}$ be an inner fibration of simplicial sets. Then $U$ is a cocartesian fibration if and only if every edge of $\operatorname{\mathcal{C}}$ admits $U$-cocartesian lifts. Similarly, $U$ is a cartesian fibration if and only if every edge of $\operatorname{\mathcal{C}}$ admits $U$-cartesian lifts.
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