Warning 3.6.2.3. Let $X$ and $Y$ be simplicial sets. If neither $X$ or $Y$ is assumed to be finite, then the comparison map $\theta _{X,Y}: |X \times Y| \rightarrow |X| \times |Y|$ need not be a homeomorphism. For an explicit counterexample, we refer the reader to Section 5 of [MR48020].
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$