Abstract
In this note some recent developments in the study of homology in semi-abelian categories are briefly presented. In particular the role of protoadditive functors in the study of Hopf formulae for homology is explained.
Highlights
The discovery of higher Hopf formulae for the homology of a group, due to Ronald Brown and Graham Ellis [6], has naturally led to some new perspectives in non-abelian homological algebra
The induced higher order central extensions are related to the BrownEllis Hopf-formulae, as explained below
Higher order central extensions can be defined for any semi-abelian category A ([27] e.g. the varieties of groups, rings, Lie algebras,crossed modules, compact groups, or any abelian category) and any Birkhoff subcategory B of A
Summary
The discovery of higher Hopf formulae for the homology of a group, due to Ronald Brown and Graham Ellis [6], has naturally led to some new perspectives in non-abelian homological algebra. The induced higher order central extensions are related to the BrownEllis Hopf-formulae, as explained below.
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