# Kerodon

$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$ $\newcommand\empty{}$

Corollary 3.3.1.9. Let $S_{\bullet }$ be a semisimplicial set. Then, for every simplicial set $Y_{\bullet }$, composition with the map $\iota : S_{\bullet } \hookrightarrow S^{+}_{\bullet }$ induces a bijection

$\xymatrix@R =50pt@C=50pt{ \{ \textnormal{Morphisms of simplicial sets f: S^{+}_{\bullet } \rightarrow Y_{\bullet }} \} \ar [d] \\ \{ \textnormal{Morphisms of semisimplicial sets f_0: S_{\bullet } \rightarrow Y_{\bullet }} \} . }$

Proof. Combine Proposition 3.3.1.5 with Proposition 3.3.1.7. $\square$