Definition 8.6.9.5. Let $\operatorname{\mathcal{C}}$ and $\operatorname{\mathcal{D}}$ be $\infty $-categories, and suppose we are given a functor $\mathscr {K}: \operatorname{\mathcal{C}}\times \operatorname{\mathcal{C}}^{\operatorname{op}} \rightarrow \operatorname{\mathcal{D}}$. A coend of $\mathscr {K}$ is a colimit of the composite functor $\operatorname{Tw}( \operatorname{\mathcal{C}})^{\operatorname{op}} \rightarrow \operatorname{\mathcal{C}}\times \operatorname{\mathcal{C}}^{\operatorname{op}} \xrightarrow { \mathscr {K} } \operatorname{\mathcal{D}}$.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$