Remark 9.1.8.6. In the situation of Proposition 9.1.8.5, condition $(\ast )$ guarantees that each of the $\infty $-categories $\operatorname{\mathcal{E}}_{\alpha }$ has a final object (and is therefore $\mu $-filtered for any infinite cardinal $\mu $; see Example 9.1.1.6). Beware that these final objects need not be preserved by the transition maps $\operatorname{\mathcal{E}}_{\alpha } \rightarrow \operatorname{\mathcal{E}}_{\beta }$.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$