Definition 7.6.6.4. Let $\operatorname{\mathcal{C}}$ and $\operatorname{\mathcal{D}}$ be $\infty $-categories. We say that a functor $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ is continuous if it preserves $K$-indexed limits, for every small simplicial set $K$. We say that $F$ is cocontinuous if it preserves $K$-indexed colimits, for every small simplicial set $K$.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$