On low-dimensional homology in categories

Everaert, Tomas;Gran, Marino
(2007) Homology homotopy and applications — Vol. 9, n° 1, p. 275-293 (2007)

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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.
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Everaert, T., & Gran, M. (2007). On low-dimensional homology in categories. Homology homotopy and applications, 9(1), 275-293. https://doi.org/10.4310/HHA.2007.v9.n1.a12 (Original work published 2007)