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Categorical algebra Semi-abelian categories, semi-localizations and factorization systems
| Content Provider | Semantic Scholar |
|---|---|
| Author | Gran, Marino |
| Copyright Year | 2016 |
| Abstract | Semi-abelian categories [9] provide a suitable context to study the (co)homology of non-abelian algebraic structures (such as groups, Lie algebras, compact groups, crossed modules, cocommutative Hopf algebras), torsion theories, and commutators. In this mini-course a brief introduction to some elementary properties of these categories will be given, such as the validity of the classical homological lemmas and the isomorphism theorems from group theory [1]. In the last part we shall focus on more advanced aspects of the theory. These latter aspects will concern the relationship between torsion theories in semiabelian categories and semi-left-exact reflections in the sense of [5], and the correspondence with radicals, closure operators and factorizations systems [2, 4, 6]. An abstract characterization of semi-localizations of semi-abelian categories will be given [8], extending a known result in the abelian context [10]. If time permits the notion of action representable category [3] will be briefly introduced, and illustrated by some examples in the categories of groups, Lie algebras and crossed modules. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://www.mat.uc.pt/~phd_prog/summerschool2016/abstractGran.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
