Baer invariants in semi-abelian categories II: Homology

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

69 citations recorded by the source corpus.

This article treats the problem of deriving the reflector of a semi-abelian category Alpha onto a Birkhoff subcategory Beta of Alpha. Basing ourselves on Carrasco, Cegarra and Grandje´an’s homology theory for crossed modules, we establish a connection between our theory of Baer invariants with a generalization—to semi-abelian categories— of Barr and Beck’s cotriple homology theory. This results in a semi-abelian version of Hopf’s formula and the Stallings-Stammbach sequence from group homology.

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

View Paper: https://www.semanticscholar.org/paper/590e82793a0e381ba17313b79827df4d1d0d310b

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

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, methodology): “Several results, which are classical in the category of groups, can be extended to any semi-abelian category: among them, let us mention the 3× 3 Lemma, the Snake Lemma [9], the long exact homology sequence associated with a proper chain complex, or the Stallings-Stammbach five term exact sequence a”
• Baer invariants in semi-abelian categories I:General theory (2004, unknown): “1.4. In our forthcoming paper [ 16 ], we apply our theory of Baer invariants to obtain a generalization of Hopf’s formula [23] in integral homology of groups.”