Semi-localizations of semi-abelian categories. (English) Zbl 1339.18008
The main aim of the present paper is to present a theory of semi-localizations in regular categories (Section 2) which is an extension of some similar localizing processes applied in abelian categories. These are applied this to various particular, but important, cases of semi-abelian categories: exact Mal’tsev categories (Section 3), protomodular categories (Section 4), semi-abelian categories (Section 5). Moreover, it is well known that hereditary torsion theories play an important role in the study of abelian categories. In Section 6 a study of hereditary torsion theories in semi-abelian categories is realized.
Reviewer: Simion Sorin Breaz (Cluj-Napoca)
MSC:
| 18E40 | Torsion theories, radicals |
| 18B10 | Categories of spans/cospans, relations, or partial maps |
| 18A40 | Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.) |
| 08C05 | Categories of algebras |
Keywords:
semi-abelian category; protomodular category; Mal’tsev category; localization; semi-left-exact reflector; torsion theory; exact completionReferences:
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