covariant hom-functor as left-exact functor

Let \(\mathcal{C}\) be a finitely complete category. Then the covariant hom functor

\begin{align*} \mathrm{Hom}_{\mathcal{C}}(A,-): \mathcal{C} \rightarrow \mathrm{Set} \end{align*}

is a covariant left exact functor

follows from:

• Set as complete category
• left exact functor
• covariant left exact functor and exact sequence
• covariant hom-functor preserves small limits