Remark 7.1.3.2. In the situation of Definition 7.1.3.1, the condition that $F$ preserves the (co)limit of a diagram $q: K \rightarrow \operatorname{\mathcal{C}}$ depends only on the diagram $q$, and not on the extension $\overline{q}$ (see Corollary 7.1.2.14).
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$