Homology, Homotopy and Applications

Volume 9 (2007)

Number 1

On low-dimensional homology in categories

Pages: 275 – 293

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


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)


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.


homology; category theory; Hopf formula; central series

2010 Mathematics Subject Classification

18G50, 20F14, 55N20

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