Example 1.5.2.14. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category. If we refer to a commutative diagram $\sigma :$
\[ \xymatrix@R =50pt@C=50pt{ & Y \ar [dr]^{g} & \\ X \ar [ur]^{f} \ar [rr]^{h} & & Z, } \]
then we mean that $\sigma $ is a $2$-simplex of $\operatorname{\mathcal{C}}$ satisfying $d^{2}_0(\sigma ) = g$, $d^{2}_1(\sigma ) =h$, and $d^{2}_2(\sigma ) = f$. In other words, we mean that $\sigma $ is a $2$-simplex which witnesses $h$ as a composition of $f$ and $g$, in the sense of Definition 1.4.4.1.