Example 4.8.6.2. Let $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ be a functor of $\infty $-categories. Then:
The functor $F$ is essentially $0$-categorical if and only if it is faithful.
The functor $F$ is essentially $(-1)$-categorical if and only if it is fully faithful.
The functor $F$ is essentially $(-2)$-categorical if and only if it is an equivalence of $\infty $-categories. In this case, $F$ is also essentially $n$-categorical for any $n \leq -2$.
This is a restatement of Remark 4.8.5.11.