Introduction to semiabelian categories
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If you have a question about this talk, please contact Julia Goedecke.
Semiabelian 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 semiabelian categories, but they also lend themselves to the study of radical theory, commutator theory and to other generalisations from group theory such as semidirect products, actions and crossed modules.
In this talk I will give the definition of a semiabelian 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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