Calculations with finite groupoids and their homomorphisms

Version 1.74
Released 2024-01-23

This project is maintained by Chris Wensley

Build Status Code Coverage

The GAP 4 package ‘groupoids’


This package allows for the computation of finite groupoids: both connected, and with several components. Graphs of groups and graphs of groupoids are also constructed, allowing the calculation of normal forms for Free Products with Amalgamation and for HNN extensions when the initial groups have rewriting systems. This package was, until 2017, named Gpd.



The groupoids package is Copyright {\copyright} Chris Wensley and Emma Moore, 2000-2024.

‘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.

For details, see:


It is assumed that you have a recent working copy of GAP, and that this contains a full set of packages in the pkg directory, compiled as appropriate.

groupoids specifies two needed packages, FGA and utils, and some suggested packages, such as Semigroups and GAPDoc. These in turn need or suggest other packages. Some of these are loaded automatically when GAP starts.

The full list of packages which are loaded (in addition to those loaded automatically by GAP) when groupoids is loaded is as follows:

groupoids does not require any compilation, but those in the list above which require compilation are as follows:

Once these prerequisites are in place, proceed as follows:


If you have a question relating to groupoids, encounter any problems, or have a suggestion for extending the package in any way, please