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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