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<TitlePage>
  <Title>
    groupoids
  </Title>
  <Subtitle>
    Calculations with finite groupoids and their homomorphisms
  </Subtitle>
  <Version>
    1.71
  </Version>
  <Author>
    Emma J. Moore<Alt Only="LaTeX"><Br/></Alt>

  </Author>
  <Author>
    Chris Wensley<Alt Only="LaTeX"><Br/></Alt>
<Address>
Dr. C.D. Wensley<Br/>
School of Computer Science and Electronic Engineering<Br/>
Bangor University<Br/>
Dean Street<Br/>
Bangor<Br/>
Gwynedd LL57 1UT<Br/>
UK<Br/>
</Address>
<Email>c.d.wensley@bangor.ac.uk</Email>
<Homepage>https://github.com/cdwensley</Homepage>

  </Author>
  <Date>
    7 August 2022
  </Date>
  <Abstract>
    The &groupoids; package provides functions for computation with
groupoids (categories with every arrow invertible) and their morphisms; for graphs of groups, and graphs of groupoids.
The most basic structure introduced is that of <E>magma with objects</E>, followed by <E>semigroup with objects</E>, then <E>monoid with objects</E> and finally <E>groupoid</E> which is a <E>group with objects</E>.
 <P/>It provides normal forms for Free Products with Amalgamation and for HNN-extensions when the initial groups have rewrite systems and the subgroups have finite index. This is described in Section <Ref Sect="sec-gphgps"/>. It is planned to move this section to a new package <Package>Rewriting</Package> in time for version 4.11 of &GAP;.
<P/>The &groupoids; package was originally implemented in 2000 (as <Package>GraphGpd</Package>) when the first author was studying for a Ph.D. in Bangor.
 <P/>The package was then renamed <Package>Gpd</Package> and version 1.07 was released in July 2011, ready for &GAP; 4.5.
 <P/><Package>Gpd</Package> became an accepted &GAP; package in May 2015.
 <P/>In April 2017 the package was renamed again, as <Package>groupoids</Package>.
 <P/>Recent versions implement many of the constructions described in the paper <Cite Key='AlWe' /> for automorphisms of groupoids.
 <P/>Bug reports, comments, suggestions for additional features, and offers to implement some of these, will all be very welcome.
 <P/>Please submit any issues at <URL>https://github.com/gap-packages/groupoids/issues/</URL> or send an email to the second author at <Email>c.d.wensley@bangor.ac.uk</Email>.
 <P/>
  </Abstract>
  <Copyright>
    &copyright; 2000-2019, Emma Moore and Chris Wensley.<P/>
The &groupoids; package is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version.

  </Copyright>
  <Acknowledgements>
    This documentation was prepared using the &GAPDoc; <Cite Key='GAPDoc'/> and &AutoDoc; <Cite Key='AutoDoc'/> packages.<P/>
The procedure used to produce new releases uses the package <Package>GitHubPagesForGAP</Package> <Cite Key='GitHubPagesForGAP' /> and the package <Package>ReleaseTools</Package>.<P/>
  </Acknowledgements>
  </TitlePage>