Chapter 7
Regular Groupoids

In this chapter we explain the construction of a regular groupoid starting from a family of groups which are indexed by a biordered set. The terminology pertaining to the theory of categories followed in the sequel is as given in [1]. Since we need the concepts of a morphism of presheaves (whose domains are not necessarily identical) and partial morphisms, we suitably redefine some of the concepts. The definitions stated here are for the category $\mathfrak{S}$ of groups.

In this chapter, unless otherwise specified, $E$ will stand for a biordered set and $\delta$ for a regular equivalence relation of $E$.