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Protoadditive functors and abstract Galois groups

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A connection between the Galois-theoretic approach to semi-abelian homology and homological closure operators is established. In particular, a generalised Hopf formula for homology is obtained, allowing the choice of a new kind of functors as coefficients. A key role in this work is played by the notion of protoadditive functor, which makes it possible to calculate the abstract fundamental groups corresponding to several reflections in the categories of groups, rings, crossed modules and compact groups.

This is joint work with M. Duckerts and T. Everaert.

This talk is part of the Category Theory Seminar series.

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