  
  
                                      [1X[5XGpd[0X[0X
  
  
              [1XGroupoids, graphs of groups, and graphs of groupoids[0X
  
  
                                  Version 1.03
  
  
                                  October 2007
  
  
                                   Emma Moore
  
                                 Chris Wensley
  
  
  
  Emma Moore
      Email:    [7Xmailto:emmajmoore@yahoo.co.uk[0X
  Chris Wensley
      Email:    [7Xmailto:c.d.wensley@bangor.ac.uk[0X
      Homepage: [7Xhttp://www.informatics.bangor.ac.uk/~cwensley/[0X
      Address:  School of Computer Science, Bangor University,
                Dean Street, Bangor, Gwynedd, LL57 1UT, U.K.
  
  
  
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  [1XAbstract[0X
  The  [5XGpd[0X  package  for  [5XGAP[0X4  provides  functions  for  the computation with
  groupoids  (categories with every arrow invertible) and their morphisms; for
  graphs of groups, and graphs of groupoids.
  
  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.
  
  The  [5XGpd[0X  package  was originally implemented in 2000 (as [5XGraphGpd[0X) when the
  first author was studying for a Ph.D. in Bangor.
  
  The current version is 1.03, released on October 8th 2007.
  
  Bug  reports,  suggestions  and  comments  are,  of  course, welcome. Please
  contact the second author at [7Xmailto:c.d.wensley@bangor.ac.uk[0X.
  
  
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  [1XCopyright[0X
  © 2000-2007 by Emma Moore and Chris Wensley
  
  We  adopt  the  copyright  regulations  of  [5XGAP[0X as detailed in the copyright
  notice in the [5XGAP[0X manual.
  
  
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  [1XContent (Gpd)[0X
  
  1. Introduction
  2. Groupoids
    2.1 Groupoids: their elements and attributes
      2.1-1 ConnectedGroupoid
      2.1-2 ComponentsOfGroupoid
      2.1-3 IsPermGroupoid
      2.1-4 GroupoidElement
      2.1-5 IsConnectedGroupoid
    2.2 Subgroupoids
      2.2-1 SubgroupoidByComponents
    2.3 Stars, Costars and Homsets
      2.3-1 ObjectStar
      2.3-2 IdentityElement
    2.4 Left, right and double cosets
      2.4-1 RightCoset
  3. Morphisms of Groupoids
    3.1 Morphisms to a connected groupoid
      3.1-1 MorphismOfConnectedGroupoids
      3.1-2 MorphismToConnectedGroupoid
      3.1-3 IsomorphismNewObjects
      3.1-4 InclusionMappingGroupoids
    3.2 General Morphisms and composites
      3.2-1 GroupoidMorphismByComponents
      3.2-2 IsGroupoidMorphism
      3.2-3 ImagesOfObjects
      3.2-4 Product
      3.2-5 InverseMorphism
  4. Graphs of Groups and Groupoids
    4.1 Digraphs
      4.1-1 FpWeightedDigraph
    4.2 Graphs of Groups
      4.2-1 GraphOfGroups
      4.2-2 IsGraphOfFpGroups
      4.2-3 RightTransversalsOfGraphOfGroups
    4.3 Words in a Graph of Groups and their normal forms
      4.3-1 GraphOfGroupsWord
      4.3-2 ReducedGraphOfGroupsWord
    4.4 Free products with amalgamation and HNN extensions
      4.4-1 FreeProductWithAmalgamation
      4.4-2 HnnExtension
    4.5 GraphsOfGroupoids and their Words
      4.5-1 GraphOfGroupoids
      4.5-2 GraphOfGroupoidsWord
  5. Development History
    5.1 Versions of the Package
    5.2 What needs to be done next?
  
  
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