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<div class="ChapSects"><a href="chap1_mj.html#X7DFB63A97E67C0A1">1 <span class="Heading">Introduction</span></a>
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<h3>1 <span class="Heading">Introduction</span></h3>

<p>Groupoids are mathematical categories in which every arrow is invertible. The <strong class="pkg">groupoids</strong> 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>

<p>It was used by Emma Moore in her thesis <a href="chapBib_mj.html#biBemma-thesis">[Moo01]</a> to calculate normal forms for <em>free products with amalgamation</em>, and for <em>HNN-extensions</em> when the initial groups have rewriting systems.</p>

<p>The package may be obtained as a compressed tar file <code class="file">groupoids-version.number.tar.gz</code> by ftp from one of the following sites:</p>


<ul>
<li><p>the <strong class="pkg">groupoids</strong> GitHub site: <span class="URL"><a href="https://github.com/gap-packages.github.io/groupoids/">https://github.com/gap-packages.github.io/groupoids/</a></span>.</p>

</li>
<li><p>any <strong class="pkg">GAP</strong> archive, e.g. <span class="URL"><a href="https://www.gap-system.org/Packages/packages.html">https://www.gap-system.org/Packages/packages.html</a></span>;</p>

</li>
</ul>
<p>The package also has a GitHub repository at: <span class="URL"><a href="https://github.com/gap-packages/groupoids/">https://github.com/gap-packages/groupoids/</a></span>.</p>

<p>The information parameter <code class="code">InfoGroupoids</code> takes default value <code class="code">1</code> 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>

<p>Help is available in the usual way.</p>


<div class="example"><pre>

<span class="GAPprompt">gap></span> <span class="GAPinput">LoadPackage( "groupoids" );</span>

</pre></div>

<p>For version 1.05 the package was completely restructured, starting with <em>magmas with objects</em> 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 <a href="chapBib_mj.html#biBAlWe">[AW10]</a>. More functions will be released when time permits.</p>

<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 <code class="code"> ReadPackage("groupoids","tst/testing.g"); </code>. Additional tests may be run using <code class="code"> ReadPackage("groupoids","tst/testextra.g");.</code> (The file <code class="code">"tst/testall.g"</code> is used for automated testing.)</p>

<p>You may reference this package by mentioning <a href="chapBib_mj.html#biBBrMoPoWe">[BMPW02]</a>, <a href="chapBib_mj.html#biBemma-thesis">[Moo01]</a> and <a href="chapBib_mj.html#biBAlWe">[AW10]</a>.</p>

<p>Additional information on <em>Computational Higher Dimensional Algebra</em> can be found in the notes on crossed modules at: <span class="URL"><a href="https://github.com/cdwensley/xmod-notes">https://github.com/cdwensley/xmod-notes</a></span>.</p>


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