Kerodon

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

Remark 6.3.6.5. Let $X$ be a simplicial set. Then the projection map $X \rightarrow \Delta ^0$ is universally localizing if and only if $X$ is weakly contractible. This follows by combining Propositions 6.3.1.20 and 6.3.5.6.