Kerodon

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

Example 7.1.3.5. Let $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ be any functor of $\infty $-categories. Then $F$ preserves $\Delta ^{0}$-indexed limits and colimits. By virtue of Example 7.1.2.10, this is equivalent to the observation that $F$ carries isomorphisms in $\operatorname{\mathcal{C}}$ to isomorphisms in $\operatorname{\mathcal{D}}$ (see Remark 1.4.1.6).