Abstract
Chapter 4 put full emphasize on the notion of homological category, in which all traditional homological lemmas hold. In a finitely cocomplete Mal’cev category, we obtained results concerning commutators. With always in mind the generic example of the category of groups, we present here the notion of semi-abelian category, introduced in [60]: these categories constitute a context in which both aspects above can be developed. Unexpectedly, in this context, the notion of semi-direct product emerges naturally.
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© 2004 Springer Science+Business Media Dordrecht
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Borceux, F., Bourn, D. (2004). Semi-abelian categories. In: Mal’cev, Protomodular, Homological and Semi-Abelian Categories. Mathematics and Its Applications, vol 566. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-1962-3_6
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DOI: https://doi.org/10.1007/978-1-4020-1962-3_6
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-6551-3
Online ISBN: 978-1-4020-1962-3
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