Remark 6.3.7.7. Recall that a simplicial set $S$ is braced if the collection of nondegenerate simplices of $S$ is closed under the face operators (Definition 3.3.1.1). Every nonsingular simplicial set is braced. However, the converse is false. For example, the quotient $\Delta ^1 / \operatorname{\partial \Delta }^{1}$ is braced, but is not nonsingular.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$