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On satellites in semi-abelian categories: Homology without projectives

Published online by Cambridge University Press:  22 June 2009

JULIA GOEDECKE  and
TIM VAN DER LINDEN
JULIA GOEDECKE
Affiliation:
Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, Cambridge, CB3 0WB. e-mail: julia.goedecke@cantab.net
TIM VAN DER LINDEN
Affiliation:
Vakgroep Wiskunde, Vrije Universiteit Brussel, Pleinlaan 2, 1050 Brussel, Belgium. e-mail: tvdlinde@vub.ac.be
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Abstract

Working in a semi-abelian context, we use Janelidze's theory of generalised satellites to study universal properties of the Everaert long exact homology sequence. This results in a new definition of homology which does not depend on the existence of projective objects. We explore the relations with other notions of homology, and thus prove a version of the higher Hopf formulae. We also work out some examples.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 147 , Issue 3 , November 2009 , pp. 629 - 657
Copyright
Copyright © Cambridge Philosophical Society 2009

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