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## Hopf Formulae for TORAdd to your list(s) Download to your calendar using vCal - Julia Goedecke (University of Cambridge)
- Tuesday 14 March 2017, 14:15-15:15
- MR5, Centre for Mathematical Sciences.
If you have a question about this talk, please contact Tamara von Glehn. A Hopf formula expresses a homology object in terms of a projective
presentation, its kernel and certain (generalised) commutators. The
first one, for second group homology, was given by Hopf in 1942. Over
the last 13 years or so, Everaert, Gran, Van der Linden and others have
developed Hopf formulae in more general categorical contexts. One of
these general contexts is that of a semi-abelian category with a
Birkhoff subcategory where the reflector factors through a protoadditive
functor. In that generality, some elements of the Hopf formula are
necessarily very abstract. With Tim Van der Linden and Guram Donadze, I am studying the special situation of subvarieties of categories of
R-modules. Here we can find explicit and easy formulations of the
generalised commutators. Since the reflector in this situation turns out
to be tensoring, the resulting homology functors are Tor functors.
Through these fairly simple formulations we obtain new ways of
calculating, for example, homology of Lie algebras, and Hochschild
Homology of an associative unital algebra. More generally, we will be
able to cover the situation of any This talk is part of the Category Theory Seminar series. ## This talk is included in these lists:- All CMS events
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