Warning 4.8.6.18. Let $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ be an inner fibration of $\infty $-categories and let $n \geq -1$ be an integer. If $F$ is essentially $n$-categorical, then each fiber $\operatorname{\mathcal{C}}_{D} = \{ D\} \times _{\operatorname{\mathcal{D}}} \operatorname{\mathcal{C}}$ of $F$ is a locally $(n-1)$-truncated $\infty $-category. Beware that the converse is false in general, even if $F$ is an isofibration. However, it holds under additional assumptions: see Variant 5.1.5.17.
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