Limits and colimits of partial groups
Abstract
The purpose of this short paper is to analyse limits and colimits in the category $Part$ of partial groups, algebraic structures introduced by A. Chermak. The class of partial groups contains a subclass of objects corresponding to the class of transporter systems as defined by Oliver and Ventura. Special cases of such transporter systems are the centric linking systems associated to saturated fusion systems that were defined by Broto, Levi and Oliver. We will prove that $Part$ is both complete and cocomplete and, in addition, that the full subcategory of finite partial groups is both finitely complete and finitely cocomplete. A. González has proven that $Part$ is equivalent to a full subcategory of the category $sSet$ of simplicial sets. We will show that such subcategory is not closed under formation of colimits in $sSet$, so that a different construction must be taken into consideration.
 Publication:

arXiv eprints
 Pub Date:
 September 2021
 arXiv:
 arXiv:2109.12410
 Bibcode:
 2021arXiv210912410S
 Keywords:

 Mathematics  Group Theory;
 Mathematics  Algebraic Topology