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Calculations with finite groupoids and their homomorphisms

Version 1.54


Emma Moore

Chris Wensley
School of Computer Science, Bangor University,
Dean Street, Bangor, Gwynedd, LL57 1UT, U.K.


The groupoids package for GAP4 provides functions for the computation with groupoids (categories with every arrow invertible) and their morphisms; for graphs of groups, and graphs of groupoids. The most basic structure introduced is that of magma with objects, followed by semigroup with objects, then monoid with objects and finally groupoid which is a group with objects.

It provides normal forms for Free Products with Amalgamation and for HNN-extensions when the initial groups have rewrite systems and the subgroups have finite index.

The groupoids package was originally implemented in 2000 (as GraphGpd) when the first author was studying for a Ph.D. in Bangor.

The package was then renamed Gpd and version 1.07 was released in July 2011, to be tested with GAP 4.5. Gpd became an accepted GAP package in May 2015.

In April 2017 the package was renamed again, as groupoids.

Recent versions implement many of the constructions described in the paper [AW10] for automorphisms of groupoids.

The latest version is 1.54 of 29th November 2017.

Bug reports, comments, suggestions for additional features, and offers to implement some of these, will all be very welcome.

Please submit any issues at or send an email to the second author at


© 2000-2017 Emma Moore and Chris Wensley

groupoids is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version.


This documentation was prepared with the GAPDoc package [LN12] of Frank Lübeck and Max Neunhöffer.

The procedure used to mount new releases on GitHub uses the packages GitHubPagesForGAP [Hor14] and ReleaseTools of Max Horn.


1 Introduction
2 Many-object structures
3 Mappings of many-object structures
4 Groupoids
5 Homomorphisms of Groupoids
6 Graphs of Groups and Groupoids
7 Technical Notes
8 Development History

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