functor preserving finite products

Let \(\mathcal{C}, \mathcal{D}\) be categories and \(\mathcal{F}: \mathcal{C} \rightarrow \mathcal{D}\) a functor. Then \(\mathcal{F}\) is said to be preserving finite products, if

\begin{align*} \mathcal{F}(\prod_{i \in I} A_i) = \prod_{i \in I}(\mathcal{F}(A_i)) \end{align*}