Remark 11.5.0.95 (Two-out-of-Six). Let $f: W_{} \rightarrow X_{}$, $g: X_{} \rightarrow Y_{}$, and $h: Y_{} \rightarrow Z_{}$ be morphisms of simplicial sets. If $g \circ f$ and $h \circ g$ are homotopy equivalences, then $f$, $g$, and $h$ are all homotopy equivalences.
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