# Kerodon

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Example 1.3.5.4. Let $\operatorname{\mathcal{C}}$ be an ordinary category. Then the homotopy category of the $\infty$-category $\operatorname{N}_{\bullet }(\operatorname{\mathcal{C}})$ can be identified with $\operatorname{\mathcal{C}}$. In particular, for each $n \geq 0$, the homotopy category $\mathrm{h} \mathit{\Delta ^ n}$ can be identified with $[n] = \{ 0 < 1 < \cdots < n \}$.