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

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Summary

Introduction

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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