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Torsion theories in homological categories. (English) Zbl 1123.18009

Homological categories were introduced by Borceux, Bourn, and Malcev in 2004. They generalize semi-abelian categories (in the sense of Janelidze, Marki, and Tholen) and admit a natural concept of short exact sequence so that the classical diagram lemmata of homological algebra remain valid in such a category. The necessity to consider homological categories rather than semi-abelian ones comes from the fact that if the objects of a semi-abelian category are endowed with a topology, they make up a homological category which need not to be semi-abelian [see F. Borceux and M. M. Clementino, Adv. Math. 190, No. 2, 425–453 (2005; Zbl 1069.54010)].
In the present paper, it is shown that Dickson’s concept of a torsion theory carries over to homological categories without change, and that the most basic properties of torsion theories also remain valid in this non-additive context.

MSC:

18E40 Torsion theories, radicals

Citations:

Zbl 1069.54010
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References:

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