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.
<P/>
It was used by Emma Moore in her thesis <Cite Key="emma-thesis" />
to calculate normal forms for <E>free products with amalgamation</E>,
and for <E>HNN-extensions</E>
when the initial groups have rewriting systems.
<P/>
The information parameter <C>InfoGroupoids</C> takes default value <C>1</C>
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.
<P/>
Help is available in the usual way.
<P/>
<Example>
<![CDATA[
gap> LoadPackage( "groupoids" );
]]>
</Example>
For version 1.05 the package was completely restructured,
starting with <E>magmas with objects</E> 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 for automorphisms and homotopies, as described in
<Cite Key="AlWe" />.
More functions will be released when time permits.
<P/>
Once the package is loaded, it is possible to check the installation
has proceeded correctly by running the test suite of the package with
the command <C> ReadPackage("groupoids","tst/testing.g"); </C>.
Additional tests may be run using
<C> ReadPackage("groupoids","tst/testextra.g");.</C>
(The file <C>"tst/testall.g"</C> is used for automated testing.)
<P/>
You may reference this package by mentioning <Cite Key="BrMoPoWe" />,
<Cite Key="emma-thesis" /> and <Cite Key="AlWe" />.
<P/>
Additional information on <E>Computational Higher Dimensional Algebra</E>
can be found in the notes on crossed modules at:
<URL>https://github.com/cdwensley/xmod-notes</URL>.
</Chapter>
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