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arXiv · 0808.2798

On satellites in semi-abelian categories: Homology without projectives

Julia Goedecke·Tim Van der Linden
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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.

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Julia Goedecke, Tim Van der Linden. 2009-03-06. On satellites in semi-abelian categories: Homology without projectives. https://doi.org/10.1017/s0305004109990107

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