Exercise 1.3.1.5. Let $\operatorname{\mathcal{C}}$ be a category. Show that the restriction map
\[ \operatorname{Hom}_{\operatorname{Set_{\Delta }}}( \Delta ^{n}, \operatorname{N}_{\bullet }(\operatorname{\mathcal{C}}) ) \rightarrow \operatorname{Hom}_{\operatorname{Set_{\Delta }}}( \operatorname{\partial \Delta }^{n}, \operatorname{N}_{\bullet }(\operatorname{\mathcal{C}}) ) \]
is an injection for $n = 2$ and a bijection for $n > 2$.