Corollary 9.2.8.7. The collection of essentially finite $\infty $-categories is closed under the formation of finite colimits (formed in the $\infty $-category $\operatorname{\mathcal{QC}}$).
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$
Corollary 9.2.8.7. The collection of essentially finite $\infty $-categories is closed under the formation of finite colimits (formed in the $\infty $-category $\operatorname{\mathcal{QC}}$).
Proof. Since the initial object $\emptyset \in \operatorname{\mathcal{QC}}$ is essentially finite, it will suffice to show that essential finiteness is closed under the formation of pushouts (see Corollary 7.6.2.30). This is a reformulation of Proposition 9.2.8.6 (see Example 7.6.3.4). $\square$