Example 4.8.3.30. Let $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ be a functor of $\infty $-categories and let $n \geq 0$ be an integer. Suppose that $\operatorname{\mathcal{D}}$ is locally $(n-2)$-truncated. Then $F$ is $n$-faithful if and only if $\operatorname{\mathcal{C}}$ is locally $(n-2)$-truncated. This follows by Remark 4.8.3.29 in the special case $\operatorname{\mathcal{E}}= \Delta ^0$ (see Example 4.8.3.14).
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