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
.
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.
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