When the exact completion of a category with weak finite limits is a Maľcev category, it is possible to combine the universal property of the exact completion and the universal property of the coequalizer completion. We use this fact to explain Freyd's representation theorems in abelian and Frobenius categories.
"Exact completion and representation in Abelian categories." Homology Homotopy Appl. 3 (3) 453 - 466, 2001.