Exercise 3.3.3.15. Let $X$ be a simplicial set. Show that $X$ is braced if and only if the inclusion functor $\operatorname{{\bf \Delta }}_{X}^{\mathrm{nd}} \hookrightarrow \operatorname{{\bf \Delta }}_{X}$ admits a left adjoint.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$