Example 9.2.3.4 (Contractible Kan Complexes). Let $\operatorname{\mathcal{C}}= \operatorname{Set_{\Delta }}$ be the category of simplicial sets and let $W$ be the collection of inclusion maps $\operatorname{\partial \Delta }^{n} \hookrightarrow \Delta ^{n}$. Then a simplicial set is weakly $W$-local if and only if it is a contractible Kan complex.
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