Remark 4.2.1.4. Let $f: X \rightarrow S$ be a morphism of simplicial sets. If $f$ is either a left fibration or a right fibration, then it is an inner fibration. In this case, if $S$ is an $\infty $-category, then $X$ is also an $\infty $-category (Remark 4.1.1.9).
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