Underlying groupoids

Abstract

In this paper we describe a package XMOD [8] of functions for computing with crossed modules, their morphisms and derivations; $cat^1$-groups, their morphisms and sections, written using the GAP [7] group theory programming language. We have also enumerated the isomorphism classes of $cat^1$-groups in [1,4] and [2]. We gave the application algorithms and some mathematical results on $cat^1$-group structures in [3]. We also made a computational comment on pre-crossed modules, pre-$cat^1$ -groups and underlying grupoids in this paper.