# ct.category theory – Universal abelian category associated with an exact category

Let $$C$$ be the category of exact categories (choose a Grothendieck universe), whose morphisms are adjoined pairs. For a category $$C$$, let $$text {Ab} (C)$$ be the category of objects of the abelian group $$C$$. $$text {Ab} (C)$$ is an abelian category.

East $$text {Ab} (C)$$ the universal abelian category with a morphism $$p: C rightarrow text {Ab} (C)$$ in $$C$$?