Remark 5.1.4.5. Let $q: X \rightarrow S$ be an inner fibration of simplicial sets and let $e$ be an edge of $X$. If $q$ is a cartesian fibration, then $e$ is $q$-cartesian if and only if it is locally $q$-cartesian (see Corollary 5.1.3.9). Similarly, if $q$ is a cocartesian fibration, then $e$ is $q$-cocartesian if and only if it is locally $q$-cocartesian.
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