Algebra pp 498-519 | Cite as

Quotient Categories and Localizing Functors

  • Carl Faith
Part of the Die Grundlehren der mathematischen Wissenschaften book series (GL, volume 190)


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
$$B \in \mathcal{S} \Leftrightarrow A \in \mathcal{S}\& C \in \mathcal{S}.$$


Full Subcategory Abelian Category Torsion Theory Canonical Morphism Exact Functor 
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Copyright information

© Springer-Verlag, Berlin · Heidelberg 1973

Authors and Affiliations

  • Carl Faith
    • 1
  1. 1.Rutgers UniversityNew BrunswickUSA

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