Remark 4.5.2.5 (Two-out-of-Three). Let $f: X \rightarrow Y$ and $g: Y \rightarrow Z$ be morphisms of simplicial sets. If any two of the morphisms $f$, $g$, and $g \circ f$ is a categorical equivalence, then so is the third. In particular, the collection of categorical equivalences is closed under composition.

$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$