Proposition 4.5.8.12. 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.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$