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Higher central extensions via binary commutators
Description:  We prove that all semi-abelian categories with the Smith is Huq property satisfy the Commutator Condition: higher central extensions may be characterised in terms of binary (Huq or Smith) commutators. In fact, even binary Higgins commutators suffice. As a consequence, in presence of enough projectives we obtain explicit Hopf formulae for homology with coefficients in the abelianisation functor, and an interpretation of cohomology with coefficients in an abelian object in terms of equivalence classes of higher central extensions. We also give a counterexample against the Commutator Condition in the semi-abelian category of loops.
Date:  2012-02-20
Start Time:   14:30
Speaker:  Tim Van der Linden (Univ. catholique de Louvain, Belgium)
Institution:  Univ. catholique de Louvain, Belgium
Place:  Sala 5.5
Research Groups: -Algebra, Logic and Topology
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© 2012 Centre for Mathematics, University of Coimbra, funded by

Science and Technology Foundation

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