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Introduction to semi-abelian categories

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If you have a question about this talk, please contact Julia Goedecke.

Semi-abelian categories were introduced by Janlidze, Marki and Tholen to solve MacLane’s longstanding problem of finding a framework that reflects the categorical properties of (all) groups as nicely as abelian categories do for abelian groups. Homological algebra can be studied very nicely in semi-abelian categories, but they also lend themselves to the study of radical theory, commutator theory and to other generalisations from group theory such as semi-direct products, actions and crossed modules.

In this talk I will give the definition of a semi-abelian category via the concept of protomodular categories introduced by Bourn, and will then explore the main properties which we use when working in this setting. I will also speak a little about exact sequences and homology.

This talk is part of the Category Theory Seminar series.

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