The set of objects of a groupoid may happen to be also a groupoid. A double groupoid is an even more involved entity. It consists of a set \(\mathcal Q\) with two groupoid structures, each of which has a different groupoid, say \(\mathcal H\) and \(\mathcal V\) , as its set of objects. These two base groupoids, however, have a common base \(\mathcal B\) . Accordingly, a double groupoid involves 4 sets intimately interconnected by 4 different groupoid structures. The arrows of a double groupoid \(\mathcal Q\) may be regarded informally as some kind of hyper-arrows, each of which can be visualized as a square consisting of two arrows of \(\mathcal H\) joining a pair of arrows of \(\mathcal V\) , or vice versa.