Abstract
Let A be an abelian category. A Serre class or subcategory of A is a nonempty full subcategory S such that for every exact sequence $$0 \to A \to B \to C \to 0 $$ in A it is true that $$B \in \mathcal{S} \Leftrightarrow A \in \mathcal{S}\& C \in \mathcal{S}.$$
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