A classification of torsion classes in abelian categories

Abstract

We give a classification of torsion classes (or nullity classes) in an abelian category by forming a spectrum of equivalence classes of premonoform objects. This is parallel to Kanda’s classification of Serre subcategories.

Keywords:

• Abelian category
• classification
• torsion theory

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 18E40
• 13D30

Acknowledgements

The authors thank Manuel Reyes, who gave us many interesting comments and helpful references. The authors also thank the referees for carefully reading the paper and for their useful suggestions.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by NSERC.