Equivalence of categories preserves colimits

Question

Is it true that if $F: \cal{C} \rightarrow \cal{D}$ is an equivalence of categories (I mean, is full, faithfull and essentially surjective over objects), then $F$ preserve colimits?

Answer 1

Yes.

In such a case $F$ has an inverse functor $G:\mathcal D\to\mathcal C$, such that $FG\simeq{\mathrm id}_{\mathcal D}$ and $GF\simeq{\mathrm id}_{\mathcal C}$, and it's easy to see that $G$ is both a left and right adjoint of $F$.

Consequently $F$ preserves all limits and colimits, and so does $G$.