functor preserving finite colimits

Let \(\mathcal{C}, \mathcal{D}\) be categories. A functor \(\mathcal{F}: \mathcal{C} \rightarrow \mathcal{D}\) is said to preserve finite colimits, if for a finite colimits \(\mathrm{colim}_{\mathcal{J}}\) for some finite diagram \(\mathcal{J}\) the image

\begin{align*} \mathcal{F}(\mathrm{colim}_{\mathrm{J}}) \end{align*}

is a colimit for \(\mathcal{F} \circ \mathcal{J}\)