GAP (Gpd) - Chapter 1: Introduction

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### 1. Introduction

Groupoids are mathematical categories in which every arrow is invertible. The Gpd share 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 [M01] to calculate normal forms for Free Products with Amalgamation, and for HNN-extensions, when the initial groups have rewrite systems.

Gpd is implemented using {\GAP}~4.4. Some of the utility functions in the XMod share package for crossed modules are used.

The information parameter `InfoGpd` 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( "gpd" );
    ------------------------------------------------------------
    loading XMod 2.007 for GAP 4.4 - Murat Alp and Chris Wensley
    ------------------------------------------------------------
    -----------------------------------------------------------
    loading Gpd 1.01 for GAP 4.4 - Emma Moore and Chris Wensley
    -----------------------------------------------------------
    true
    gap> ?Groupoid
    Help: several entries match this topic - type ?2 to get match [2]

    [1] Gpd: Groupoid
    [2] loops (not loaded): groupoid
    [3] Gpd: Groupoids
    [4] Gpd: Groupoids: their elements and attributes
    [5] Gpd: GroupoidByUnion
    [6] Gpd: GroupoidElement
    [7] Gpd: GroupoidMorphismByComponents
    [8] Gpd: GroupoidMorphism
    [9] Gpd: GroupoidsOfGraphOfGroupoids

You may reference this package by mentioning [BM+02] and [M01].

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