 As a consequence of Gabriel–Popescu, one can show that every Grothendieck category is locally presentable.Every small abelian category formula_40 can be embedded in a Grothendieck category, in the following fashion.The category formula_82 of left-exact additive (covariant) functors formula_83 (where formula_84 denotes the category of abelian groups) is a Grothendieck category, and the functor formula_85, with formula_86, is full, faithful and exact.