Remark 9.2.7.2. In the situation of Construction 9.2.7.1, vertices of the simplicial set $\operatorname{Sol}(\sigma )$ can be identified with solutions to the lifting problem $\sigma $ (in the sense of Definition 9.2.5.1). In particular, the lifting problem $\sigma $ admits a solution if and only if $\operatorname{Sol}(\sigma )$ is nonempty.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$