Corollary 7.5.8.10. Let $\operatorname{\mathcal{C}}$ be a small category and let $\overline{\mathscr {F}}: \operatorname{\mathcal{C}}^{\triangleright } \rightarrow \operatorname{Kan}$ be a diagram of Kan complexes. Then $\overline{\mathscr {F}}$ is a categorical colimit diagram if and only if it is a homotopy colimit diagram.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$