Kerodon

$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$ $\newcommand\empty{}$
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$

Remark 3.4.5.3. Let $f: X_{} \rightarrow Y_{}$ and $g: Y_{} \rightarrow Z_{}$ be morphisms of semisimplicial sets. If any two of the morphisms $f$, $g$, and $g \circ f$ are weak homotopy equivalences, then so is the third (see Remark 3.1.6.15).