Exercise 4.7.6.7. Let $\operatorname{\mathcal{C}}$ be a category. Show that the nerve $\operatorname{N}_{\bullet }(\operatorname{\mathcal{C}})$ is minimal in dimension $n$ for every integer $n > 0$ (see Proposition 4.8.3.1 for a more general statement). Consequently, the $\infty $-category $\operatorname{N}_{\bullet }(\operatorname{\mathcal{C}})$ is minimal if and only if, for every pair of isomorphic objects $X,Y \in \operatorname{\mathcal{C}}$, we have $X = Y$.
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