Example 1.2.5.3 (Products of Kan Complexes). Let $\{ S_{\alpha } \} _{\alpha \in A}$ be a collection of simplicial sets parametrized by a set $A$, and let $S = \prod _{\alpha \in A} S_{\alpha }$ be their product. If each $S_{\alpha }$ is a Kan complex, then $S$ is a Kan complex. The converse holds provided that each $S_{\alpha }$ is nonempty.
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