Baer invariants in semi-abelian categories I:General theory

By Tomas Everaert, Tim Van der Linden. Theory and Applications of Categories, 2004

58 citations recorded by the source corpus.

Extending the work of Frohlich, Lue and Furtado-Coelho, we consider the theory of Baer invariants in the context of semi-abelian categories. Several exact sequences, relative to a subfunctor of the identity functor, are obtained. We consider a notion of commutator which, in the case of abelianization, corresponds to Smith’s. The resulting notion of centrality fits into Janelidze and Kelly’s theory of central extensions. Finally we propose a notion of nilpotency, relative to a Birkhoff subcategory of a semiabelian category.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/3746a5351c1cac41a846239b3701bc880b11ba19

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In Algebra and Number Theory

1. Marino Gran
2. Tim Van der Linden
3. Sandra Mantovani
4. Giuseppe Metere

In Geometry and Topology

1. Tim Van der Linden
2. Marino Gran
3. Sandra Mantovani
4. Giuseppe Metere

In Mathematical Physics

1. Tim Van der Linden
2. Marino Gran
3. Sandra Mantovani
4. Giuseppe Metere

Citations in the corpus

• On the second cohomology group in semi-abelian categories (2005, background): “through [ 21, Theorem 5.9 ], induces the exact sequence”
• Baer invariants in semi-abelian categories II: Homology (2004, unknown): “7 in [18], we get that ∆V (GX) = 0.”