Definition 5.3.8.1. Let $U: \operatorname{\mathcal{E}}\rightarrow \operatorname{\mathcal{C}}$ be an inner fibration of simplicial sets. We say that $U$ is minimal if, for every $n$-simplex $\sigma : \Delta ^ n \rightarrow \operatorname{\mathcal{C}}$, the fiber product $\operatorname{\mathcal{E}}_{\sigma } = \Delta ^{n} \times _{\operatorname{\mathcal{C}}} \operatorname{\mathcal{E}}$ is a minimal $\infty $-category.
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