On satellites in semi-abelian categories: homology without projectives. (English) Zbl 1190.18006
In his thesis Everaert defined a new notion of homology sequence where the idea is to explain homology objects in term of higher-dimensional central and trivial extensions. In this paper, the authors use Janelidze’s general notion of satellites to study universal properties of the Everaert homology sequence where these universal properties may be interpreted as a new definition of homology. The advantage of such approach is that the existence of projective objects is not fundamental. However when the category has enough projectives, the resulting notion is still equivalent to Everaert, and thus prove a version of the higher Hopf formula.
Reviewer: Intan Muchtadi-Alamsyah (Bandung)
MSC:
| 18G30 | Simplicial sets; simplicial objects in a category (MSC2010) |
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