Exercise 3.5.4.11. Let $X$ be a Kan complex and let $n \geq -1$ be an integer. Show that $X$ is weakly $n$-coskeletal if and only if, for every 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 injective.
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