When is a double central extension universal?
(2015) 97th Peripatetic Seminar on Sheaves and Logic — Location: Louvain-la-Neuve (31.January.2015)
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- Abstract
- It is easy to prove that a double central extension over an object X which is initial amongst such is necessarily the zero double extension over X=0. This explains why it does not make sense to define universality of higher central extensions in the way done classically for one-fold central extensions. The aim of my talk is to introduce an appropriate notion of universality for higher central extensions which does extend the theory of one-fold central extensions and prefect objects to higher degrees in a non-trivial way. This work is done in semi-abelian categories, but the results are new even for groups. In particular, we shall see that a universal double central extension of X by H3(X) exists as soon as H2(X)=H1(X)=0. I will also describe a simple construction for such universal extensions. This is joint work with George Peschke.
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Citations
Van der Linden, T. (2015). When is a double central extension universal? 97th Peripatetic Seminar on Sheaves and Logic, Louvain-la-Neuve. https://hdl.handle.net/2078.5/63239