Example 9.2.3.2 (Kan Complexes). Let $\operatorname{\mathcal{C}}= \operatorname{Set_{\Delta }}$ be the category of simplicial sets and let $W$ be the collection of all horn inclusions $\Lambda ^{n}_{i} \hookrightarrow \Delta ^ n$, where $n > 0$ and $0 \leq i \leq n$. Then a simplicial set is weakly $W$-local if and only if it is a Kan complex.
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