Corollary 3.3.1.10. The forgetful functor
\[ \{ \textnormal{Simplicial sets} \} \rightarrow \{ \textnormal{Semisimplicial sets} \} \]
has a left adjoint, given on objects by the construction $S_{\bullet } \mapsto S_{\bullet }^{+}$.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$