On satellites in semi-abelian categories: Homology without projectives

Details On satellites in semi-abelian categories: Homology without projectives On satellites in semi-abelian categories: Homology without projectives

2008-08-20

arxiv.org/abs/0808.2798v2

Math. Proc. Cambridge Philos. Soc. 147 (2009), no. 3, 629-657

Mathematics

Algebraic Topology

29 pages; major changes in Example 4.15, minor changes throughout the text

Scientific paper

10.1017/S0305004109990107

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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