GAP (groupoids) - Chapter 1: Introduction

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1 Introduction

### 1 Introduction

Groupoids are mathematical categories in which every arrow is invertible. The groupoids package provides functions for the computation with groupoids and their morphisms; for graphs of groups and graphs of groupoids. The package is far from complete, and development continues.

It was used by Emma Moore in her thesis [Moo01] to calculate normal forms for free products with amalgamation, and for HNN-extensions when the initial groups have rewriting systems.

The package may be obtained as a compressed tar file `groupoids-version.number.tar.gz` by ftp from one of the following sites:

- the groupoids GitHub site: https://github.com/gap-packages.github.io/groupoids/.

- any GAP archive, e.g. https://www.gap-system.org/Packages/packages.html;

The package also has a GitHub repository at: https://github.com/gap-packages/groupoids/.

The information parameter `InfoGroupoids` takes default value `1` which, for the benefit of new users, causes more messages to be printed out when operations fail. When raised to a higher value, additional information is printed out.

Help is available in the usual way.

    gap> LoadPackage( "groupoids" );

For version 1.05 the package was completely restructured, starting with magmas with objects and their mappings, and building up to groupoids via semigroups with objects and monoids with objects. From version 1.07 the package includes some functions to implement constructions contained in [AW10]. More functions will be released as soon as possible.

Once the package is loaded, it is possible to check the correct installation by running the test suite of the package with the command `ReadPackage("groupoids","tst/testing.g");` . Additional tests may be run using `ReadPackage("groupoids","tst/testextra.g");.` (The file `"tst/testall.g"` is used for automated testing.)

You may reference this package by mentioning [BMPW02], [Moo01] and [AW10].

Additional information can be found on the Computational Higher Dimensional Algebra website at: https://github.com/cdwensley.

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