Example 4.8.2.4. Let $n \geq -1$ be an integer and let $X$ be a Kan complex. Then $X$ is $n$-truncated (in the sense of Definition 3.5.7.1) if and only if it is locally $(n-1)$-truncated when regarded as an $\infty $-category (in the sense of Definition 4.8.2.1). This is reformulation of Example 3.5.9.18. See Corollary 4.8.3.11 for a more general statement.

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