Example 1.4.0.6 (Products of $\infty $-Categories). Let $\{ S_{\alpha } \} _{\alpha \in A}$ be a collection of simplicial sets parametrized by a set $A$, and let $S= \prod _{\alpha \in A} S_{\alpha }$ denote their product. If each $S_{\alpha }$ is an $\infty $-category, then $S$ is an $\infty $-category. The converse holds provided that each factor $S_{\alpha }$ is nonempty.
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