Remark 4.1.0.9. Let $f: X \rightarrow S$ be a map of simplicial sets. Suppose that, for every simplex $\sigma : \Delta ^ n \rightarrow S$, the projection map $\Delta ^ n \times _{S} X \rightarrow \Delta ^ n$ is a left fibration (right fibration). Then $f$ is a left fibration (right fibration).

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