Definition 8.1.7.8. Let $\operatorname{\mathcal{C}}$ be a simplicial set and let $W$ be a collection of morphisms of $\operatorname{\mathcal{C}}$. We say that $W$ has the left two-out-of-three property if, for every $2$-simplex of $\operatorname{\mathcal{C}}$ with boundary indicated in by the diagram
\[ \xymatrix@R =50pt@C=50pt{ X \ar [rr]^{h} \ar [dr]^{f} & & Z \\ & Y, \ar [ur]_{g} & } \]
where $f$ belongs to $W$, $g$ belongs to $W$ if and only if $h$ belongs to $W$.