Proposition 8.1.9.1. Let $U: \operatorname{\mathcal{E}}\rightarrow \operatorname{\mathcal{C}}$ be a cocartesian fibration of simplicial sets and let $W$ denote the collection of all $U$-cocartesian edges of $\operatorname{\mathcal{E}}$. Then the induced map $\operatorname{Cospan}^{\mathrm{all},W}( \operatorname{\mathcal{E}}) \rightarrow \operatorname{Cospan}(\operatorname{\mathcal{C}})$ is an inner fibration of simplicial sets.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$