Kerodon

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

Proposition 4.5.5.12. Let $X$ be a simplicial set. Then the comparison map $c_{X, \Delta ^0}: X \diamond \Delta ^{0} \rightarrow X \star \Delta ^{0} = X^{\triangleright }$ is a categorical equivalence of simplicial sets.