Kerodon

$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$ $\newcommand\empty{}$
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$

Exercise 7.2.5.16. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category and let $n \geq 1$ be an integer. Show that the homotopy category $\mathrm{h} \mathit{\operatorname{\mathcal{C}}}$ satisfies condition $(\ast _ n)$ of Definition 7.2.5.1 if and only if $\operatorname{\mathcal{C}}$ satisfies condition $(\ast '_{n})$ of Lemma 7.2.5.13.