# Kerodon

$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$ $\newcommand\empty{}$

Example 1.1.9.4 (Products of Kan Complexes). Let $\{ S_{\alpha \bullet } \} _{\alpha \in A}$ be a collection of simplicial sets parametrized by a set $A$, and let $S_{\bullet } = \prod _{\alpha \in A} S_{\alpha \bullet }$ be their product. If each $S_{\alpha \bullet }$ is a Kan complex, then $S_{\bullet }$ is a Kan complex. The converse holds provided that each $S_{\alpha \bullet }$ is nonempty.