Let $\mathcal{A}$ be a small category with some ( maybe none). What I would like to be able to do is add the rest of the colimits in a universal way. The Yoneda lemma will not work, since this simply adds all colimits formally. That is to say that you have new colimits that are different than the old. We do have maps from the newly created colimits to the old. The question is can we localize about these morphisms making the old and new colimits isomorphic?