Remark 11.10.7.10 (Two-out-of-Three). Let $S$ be a simplicial set, and let $f:X \rightarrow Y$ and $g: Y \rightarrow Z$ be morphisms in the slice category $(\operatorname{Set_{\Delta }})_{/S}$. If any two of the morphisms $f$, $g$, and $g \circ f$ is a covariant equivalence relative to $S$, then so is the third. Similarly, if any two of the morphisms $f$, $g$, and $g \circ f$ is a contravariant equivalence relative to $S$, then so is the third.
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