Kerodon

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

Warning 3.5.2.3. Let $X$ and $Y$ be simplicial sets. In general, the comparison map $\theta _{X,Y}: |X \times Y| \rightarrow |X| \times |Y|$ need not be a homeomorphism if neither $X$ or $Y$ is assumed to be finite. For an explicit counterexample, we refer the reader to Section 5 of [MR48020].