Example 4.8.6.3. Let $\operatorname{\mathcal{C}}$ be a simplicial set and let $F: \operatorname{\mathcal{C}}\rightarrow \Delta ^0$ be the projection map. Then $F$ is an $n$-categorical inner fibration if and only if $\operatorname{\mathcal{C}}$ is an $n$-category. For $n > 0$, this is immediate from the definitions. The cases $n = 0$, $n = -1$, and $n \leq -2$ follow from Proposition 4.7.7.16, Example 4.7.7.10, and Example 4.7.7.11, respectively.
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