  
  
                                      [1X[5XGpd[105X[101X
  
  
              [1XGroupoids, graphs of groups, and graphs of groupoids[101X
  
  
                                  Version 1.46
  
  
                                   21/02/2017
  
  
                                   Emma Moore
  
                                 Chris Wensley
  
  
  
  Chris Wensley
      Email:    [7Xmailto:c.d.wensley@bangor.ac.uk[107X
      Homepage: [7Xhttp://pages.bangor.ac.uk/~mas023/[107X
      Address:  [33X[0;14YSchool of Computer Science, Bangor University,[133X
                [33X[0;14YDean Street, Bangor, Gwynedd, LL57 1UT, U.K.[133X
  
  
  
  -------------------------------------------------------
  [1XAbstract[101X
  [33X[0;0YThe  [5XGpd[105X  package  for  [5XGAP[105X4  provides  functions  for  the 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  [13Xmagma  with  objects[113X,  followed  by [13Xsemigroup with
  objects[113X, then [13Xmonoid with objects[113X and finally [13Xgroupoid[113X which is a [13Xgroup with
  objects[113X.[133X
  
  [33X[0;0YIt  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.[133X
  
  [33X[0;0YThe  [5XGpd[105X  package  was originally implemented in 2000 (as [5XGraphGpd[105X) when the
  first author was studying for a Ph.D. in Bangor.[133X
  
  [33X[0;0YVersion  1.07  was released in July 2011, to be tested with [5XGAP[105X 4.5. Version
  1.15  came  out  with  the  first  release  of [5XGAP[105X 4.5 in June 2012, and was
  submitted  for  official acceptance as a [5XGAP[105X package. [5XGpd[105X became an accepted
  [5XGAP[105X  package  in May 2015. The latest version is 1.46 of 21st February 2017,
  prepared for [5XGAP[105X 4.8.[133X
  
  [33X[0;0YRecent  versions  implement many of the constructions described in the paper
  [AW10] for automorphisms of groupoids.[133X
  
  [33X[0;0YBug reports, suggestions and comments are, of course, welcome. Please submit
  an  issue  at [7Xhttp://github.com/gap-packages/gpd/issues/[107X or send an email to
  the last author at [7Xmailto:c.d.wensley@bangor.ac.uk[107X.[133X
  
  
  -------------------------------------------------------
  [1XCopyright[101X
  [33X[0;0Y© 2000-2017 Emma Moore and Chris Wensley[133X
  
  [33X[0;0Y[5XGpd[105X  is  free  software;  you can redistribute it and/or modify it under the
  terms        of       the       GNU       General       Public       License
  ([7Xhttp://www.fsf.org/licenses/gpl.html[107X)  as  published  by  the Free Software
  Foundation;  either  version 2 of the License, or (at your option) any later
  version.[133X
  
  
  -------------------------------------------------------
  [1XAcknowledgements[101X
  [33X[0;0YThis  documentation  was  prepared  with  the [5XGAPDoc[105X package [LN12] of Frank
  Lübeck and Max Neunhöffer.[133X
  
  [33X[0;0YThe  procedure  used  to  mount  new  releases  on  GitHub uses the packages
  [5XGitHubPagesForGAP[105X [Hor14] and [5XReleaseTools[105X of Max Horn.[133X
  
  
  -------------------------------------------------------
  
  
  [1XContents (Gpd)[101X
  
  1 [33X[0;0YIntroduction[133X
  2 [33X[0;0YMany-object structures[133X
    2.1 [33X[0;0YMagmas with objects; arrows[133X
      2.1-1 MagmaWithObjects
      2.1-2 Arrow
      2.1-3 IsSinglePiece
    2.2 [33X[0;0YSemigroups with objects[133X
      2.2-1 SemigroupWithObjects
    2.3 [33X[0;0YMonoids with objects[133X
      2.3-1 MonoidWithObjects
    2.4 [33X[0;0YStructures with one or more pieces[133X
      2.4-1 DomainWithSingleObject
      2.4-2 UnionOfPieces
  3 [33X[0;0YHomomorphisms of many-object structures[133X
    3.1 [33X[0;0YHomomorphisms of magmas with objects[133X
      3.1-1 MagmaWithObjectsHomomorphism
    3.2 [33X[0;0YHomomorphisms of semigroups and monoids with objects[133X
    3.3 [33X[0;0YHomomorphisms to more than one piece[133X
      3.3-1 HomomorphismByUnion
  4 [33X[0;0YGroupoids[133X
    4.1 [33X[0;0YGroupoids: their properties and attributes[133X
      4.1-1 SinglePieceGroupoid
      4.1-2 ObjectList
      4.1-3 IsPermGroupoid
      4.1-4 UnionOfPieces
      4.1-5 HomogeneousGroupoid
    4.2 [33X[0;0YGroupoid elements; stars; costars; homsets[133X
      4.2-1 Arrow
      4.2-2 IdentityArrow
      4.2-3 Order
      4.2-4 ObjectStar
    4.3 [33X[0;0YSubgroupoids[133X
      4.3-1 Subgroupoid
      4.3-2 SubgroupoidWithRays
    4.4 [33X[0;0YLeft, right and double cosets[133X
      4.4-1 RightCoset
    4.5 [33X[0;0YConjugation[133X
      4.5-1 ConjugateArrow
      4.5-2 SinglePieceSubgroupoidByGenerators
      4.5-3 ConjugateGroupoid
  5 [33X[0;0YHomomorphisms of Groupoids[133X
    5.1 [33X[0;0YHomomorphisms from a connected groupoid[133X
      5.1-1 GroupoidHomomorphismFromSinglePiece
    5.2 [33X[0;0YHomomorphisms to a connected groupoid[133X
      5.2-1 HomomorphismToSinglePiece
    5.3 [33X[0;0YHomomorphisms to more than one piece[133X
      5.3-1 HomomorphismByUnion
    5.4 [33X[0;0YGroupoid automorphisms[133X
      5.4-1 GroupoidAutomorphismByObjectPerm
      5.4-2 [33X[0;0YAutomorphisms of a groupoid with rays[133X
      5.4-3 AutomorphismGroupOfGroupoid
      5.4-4 GroupoidAutomorphismByGroupAutos
      5.4-5 RootGroupHomomorphism
  6 [33X[0;0YGraphs of Groups and Groupoids[133X
    6.1 [33X[0;0YDigraphs[133X
      6.1-1 FpWeightedDigraph
    6.2 [33X[0;0YGraphs of Groups[133X
      6.2-1 GraphOfGroups
      6.2-2 IsGraphOfFpGroups
      6.2-3 RightTransversalsOfGraphOfGroups
    6.3 [33X[0;0YWords in a Graph of Groups and their normal forms[133X
      6.3-1 GraphOfGroupsWord
      6.3-2 ReducedGraphOfGroupsWord
    6.4 [33X[0;0YFree products with amalgamation and HNN extensions[133X
      6.4-1 FreeProductWithAmalgamation
      6.4-2 HnnExtension
    6.5 [33X[0;0YGraphsOfGroupoids and their Words[133X
      6.5-1 GraphOfGroupoids
      6.5-2 GraphOfGroupoidsWord
  7 [33X[0;0YTechnical Notes[133X
    7.1 [33X[0;0YMany object structures[133X
    7.2 [33X[0;0YMany object homomorphisms[133X
  8 [33X[0;0YDevelopment History[133X
    8.1 [33X[0;0YVersions of the Package[133X
    8.2 [33X[0;0YWhat needs to be done next?[133X
  
  
  [32X
