


Fundamental group functors and higher Hopf formulae



Description: 
In 1988, R. Brown and G. J. Ellis gave Hopf formulae for the integral homology of a group using topological methods. G. Janelidze first recognized that these descriptions are deeply connected with the categorical Galoistheoretic notion of covering morphism. Using this perspective, T. Everaert, M. Gran and T. Van der Linden proved that the same formulae can describe homology objects in a semiabelian context by taking a Birkhoff reflector as coefficient functor. It turns out that these homology objects coincide with the so called fundamental groups arising in categorical Galois theory. In my thesis, I have developed this approach to homology and I have showed that one can easily work with both a bigger class of reflectors (those which preserve pullbacks of split epimorphisms along regular epimorphisms) and a bigger class of categories (the homological categories in which every regular epimorphism is an effective descent morphism). Since then, using the concept of Kan extension, I have been able to improve my results. For instance, I have shown that the nth fundamental group functor is in fact a right pointwise Kan extension of a special kind and I have found as a result (not anymore as a definition) that it can be computed using nfold projective presentations. During my talk, I will present this new work.

Date: 
20140930

Start Time: 
14:30 
Speaker: 
Mathieu DuckertsAntoine (CMUC)

Institution: 
CMUC

Place: 
Sala 5.5

Research Groups: 
Algebra, Logic and Topology

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