Cross-connection representation of regular semigroups

Normal categories, their normal duals and the local isomorphisms that existed between these categories were introduced by K.S.S. Nambooripad in [4] in order to construct the cross-connection semigroup. In this paper we recall that the principal left and right ideals of a regular semigroups are normal categories and provides the construction of the cross-connection semigroup termed as the cross-connection representation of a regular semigroup.