On satellites in semi-abelian categories: Homology without projectives
Algebraic Topology
2010-06-10 v2 Category Theory
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.
Keywords
Cite
@article{arxiv.0808.2798,
title = {On satellites in semi-abelian categories: Homology without projectives},
author = {Julia Goedecke and Tim Van der Linden},
journal= {arXiv preprint arXiv:0808.2798},
year = {2010}
}
Comments
29 pages; major changes in Example 4.15, minor changes throughout the text