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Non-Abelian Torsion Theories

Published online by Cambridge University Press:  20 November 2018

Michael Barr
Michael Barr*
Affiliation:
McGill University, Montreal, Quebec
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Torsion theories have proved a very useful tool in the theory of abelian categories; for example, in one proof of Mitchell's embedding theorem (Bucur and Deleanu [3]) and in ring theory (Lambek [5]). It is the purpose of this paper to initiate an analogous theory for non-abelian categories. Originally we had hoped to prove the non-abelian analogue of Mitchell's theorem this way (Barr, [2, Theorem III (1.3)]), but so far this had not been possible. Nonetheless an interesting variety of examples fit into this theory.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 25 , Issue 6 , December 1973 , pp. 1224 - 1237
Copyright
Copyright © Canadian Mathematical Society 1973

References

1. Artin, M., Grothendieck Topologies (Harvard University Press, Boston, 1962).Google Scholar
2. Barr, M., Exact categories in Exact categories and categories of sheaves, Lecture Notes in Mathematics 236 (1971), 1–120.Google Scholar
3. Bucur, I. and Deleanu, A., Introduction to the theory of categories and functors (John Wiley & Sons, New York, 1968).Google Scholar
4. Kennison, J. F., Full reflective subcategories and generalized covering spaces, Illinois J. Math. 12 (1968), 353–365.Google Scholar
5. Lambek, J., Torsion theories, additive semantics and rings of quotients, Lecture Notes in Mathematics 177 (1971).Google Scholar
6. Lambek, J. and Rattray, B. A., Localization at infectives in complete categories, Mimeographed notes, 1972.Google Scholar
7. Ringel, C. R., Monofunctors as reflectors, Trans, Amer. Math. Soc. 161 (1971), 293–306.Google Scholar