groupoids

Calculations with finite groupoids and their homomorphisms

Version 1.54

29/11/2017

Abstract

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.

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

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

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.

Acknowledgements

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

2.1 Magmas with objects; arrows

  2.1-1 MagmaWithObjects
  2.1-2 Arrow
  2.1-3 IsSinglePiece

2.2 Semigroups with objects

2.2-1 SemigroupWithObjects

2.3 Monoids with objects

2.3-1 MonoidWithObjects

2.4 Generators of magmas with objects