Homology, Homotopy and Applications

Volume 9 (2007)

Number 1

On low-dimensional homology in categories

Pages: 275 – 293

DOI: https://dx.doi.org/10.4310/HHA.2007.v9.n1.a12

Authors

Tomas Everaert (Vakgroep Wiskunde, Faculteit Wetenschappen, Vrije Universiteit Brussel, Belgium)

Marino Gran (Lab. Math. Pures et Appliquées, Université du Littoral Côte d’Opale, Calais, France)

Abstract

The classical Stallings-Stammbach five-term exact sequence associated with a short exact sequence of groups is shown to exist in a general categorical context. This makes it possible to establish a new result relating low-dimensional homology and central series, which extends a well known result from the theory of groups.

Keywords

homology, category theory, Hopf formula, central series

2010 Mathematics Subject Classification

18G50, 20F14, 55N20

Published 1 January 2007