Remark 7.3.8.15. In the situation of Corollary 7.3.8.14, an object of $\operatorname{\mathcal{D}}$ is a colimit of the diagram $F$ if and only if it is a colimit of the diagram $F|_{ \operatorname{\mathcal{C}}^{0} }$. This follows by combining Corollaries 7.3.8.14 and 7.3.8.2.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$