Kerodon

$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$ $\newcommand\empty{}$
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$

Example 9.1.7.8. Let $\operatorname{\mathcal{D}}$ be an $\infty $-category which admits finite colimits and small filtered colimits. Then $\operatorname{\mathcal{D}}$ admits all small colimits. Moreover, if $G: \operatorname{\mathcal{D}}\rightarrow \operatorname{\mathcal{E}}$ is a functor which preserves finite colimits and small filtered colimits, then $G$ preserves all small colimits. This follows by applying Corollary 9.1.7.7 in the special case $\kappa = \aleph _0$.