Example 1.1.4.15. When $n=2$, Proposition 1.1.4.13 asserts that morphisms of simplicial sets $\operatorname{\partial \Delta }^2 \rightarrow S$ can be identified with ordered triples $(g, h, f)$ of edges of $S$ having the property that $f$ and $h$ have the same source vertex $x \in S$, $g$ and $h$ have the same target vertex $z \in S$, and the target $y$ of $f$ coincides with the source of $g$; these relationships are summarized visually in the diagram
\[ \xymatrix { & y \ar [dr]^{g} & \\ x \ar [ur]^{f} \ar [rr]^{h} & & z. } \]