Exercise 4.8.0.2. Let $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ be a functor between categories. Show that $F$ is faithful if and only if, for every diagram $\sigma :$
\[ \xymatrix@R =50pt@C=50pt{ & Y \ar [dr]^{g} & \\ X \ar [ur]^{f} \ar [rr]^{h} & & Z } \]
in the category $\operatorname{\mathcal{C}}$, if $F(\sigma )$ is a commutative diagram in $\operatorname{\mathcal{D}}$, then $\sigma $ is also commutative.