PlanetPhysics/B Mod Category Equivalence Theorem

\begin{theorem}{\mathbf B-mod category equivalence theorem.}

Let be an abelian category with arbitrary direct sums (or coproducts). Also, let in be a compact projective generator and set . The functor yields an equivalence of categories between and the category . \end{theorem}

Proof. The proof proceeds in two steps. At the first step one shows that the functor is fully faithful, and therefore, at the second step one can apply the Abelian category equivalence lemma to yield the sought for equivalence of categories.