Proposition 7.4.5.1. Let $U: \operatorname{\mathcal{E}}\rightarrow \operatorname{\mathcal{C}}$ be a cocartesian fibration between small simplicial sets, and let $\mathscr {F}: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{QC}}$ be a covariant transport representation of $U$. Then the diagram $\mathscr {F}$ admits a colimit in $\operatorname{\mathcal{QC}}$. Moreover, an object $\operatorname{\mathcal{D}}\in \operatorname{\mathcal{QC}}$ is a colimit of the diagram $\mathscr {F}$ if and only if it is equivalent to the localization $\operatorname{\mathcal{E}}[W^{-1}]$, where $W$ is the collection of all $U$-cocartesian morphisms of $\operatorname{\mathcal{E}}$.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$