Example 11.6.0.133. The contents of this tag are now contained in Proposition 1.4.5.7.
Let $\operatorname{\mathcal{C}}$ be an $\infty $-category. Then the homotopy category $\mathrm{h} \mathit{\operatorname{\mathcal{C}}}$ constructed in Definition 1.4.5.3 is also a homotopy category of $\operatorname{\mathcal{C}}$ in the sense of Definition 1.3.6.1. More precisely, the map $u: \operatorname{\mathcal{C}}\rightarrow \operatorname{N}_{\bullet }( \mathrm{h} \mathit{\operatorname{\mathcal{C}}} )$ of Construction 1.4.5.6 exhibits $\mathrm{h} \mathit{\operatorname{\mathcal{C}}}$ as a homotopy category of $\operatorname{\mathcal{C}}$, by virtue of Proposition 1.4.5.7.