Duality in non-abelian algebra I. From cover relations to grandis ex2-categories

Abstract

The aim of this series of papers is to develop a self-dual categorical approach to some topics in non-abelian algebra, which is based on replacing the framework of a category with that of a category equipped with a functot to it. The present paper gives some preliminary steps in this direction, where several known structures on a category, which arise in the categorical treatment of these topics, are viewed as such functors; as a result, we obtain some new conceptual links between these structures. © Zurab Janelidze and Thomas Weighill, 2014.