Definition 3.5.3.1. Let $n$ be an integer and let $X$ be a simplicial set. We say that $X$ is $n$-coskeletal if, for every nonnegative integer $m > n$, the restriction map
\[ \theta _{m}: \operatorname{Hom}_{\operatorname{Set_{\Delta }}}( \Delta ^{m}, X ) \rightarrow \operatorname{Hom}_{\operatorname{Set_{\Delta }}}( \operatorname{\partial \Delta }^{m}, X) \]
is a bijection: that is, every morphism of simplicial sets $\operatorname{\partial \Delta }^{m} \rightarrow X$ extends uniquely to an $m$-simplex of $X$.