  
  
                                   [1X XModAlg [101X
  
  
                      [1X Crossed Modules and Cat1-Algebras [101X
  
  
                                      1.23
  
  
                                3 December 2022
  
  
                                Zekeriya Arvasi
  
                                  Alper Odabas
  
  
  
  Zekeriya Arvasi
      Email:    [7Xmailto:zarvasi@ogu.edu.tr[107X
      Address:  [33X[0;14YProf. Dr. Z. Arvasi[133X
                [33X[0;14YOsmangazi University[133X
                [33X[0;14YArts and Sciences Faculty[133X
                [33X[0;14YDepartment of Mathematics and Computer Science[133X
                [33X[0;14YEskisehir[133X
                [33X[0;14YTurkey[133X
  
  
  Alper Odabas
      Email:    [7Xmailto:aodabas@ogu.edu.tr[107X
      Address:  [33X[0;14YDr. A. Odabas[133X
                [33X[0;14YOsmangazi University[133X
                [33X[0;14YArts and Sciences Faculty[133X
                [33X[0;14YDepartment of Mathematics and Computer Science[133X
                [33X[0;14YEskisehir[133X
                [33X[0;14YTurkey[133X
  
  
  
  -------------------------------------------------------
  [1XAbstract[101X
  [33X[0;0YThe  [5XXModAlg[105X package provides functions for computation with crossed modules
  of commutative algebras and cat[22X^1[122X-algebras.[133X
  
  [33X[0;0YBug reports, suggestions and comments are, of course, welcome. Please submit
  an  issue  on  GitHub  at [7Xhttps://github.com/gap-packages/xmodalg/issues/[107X or
  contact the second author at [7Xmailto:aodabas@ogu.edu.tr[107X.[133X
  
  
  -------------------------------------------------------
  [1XCopyright[101X
  [33X[0;0Y© 2014-2022, Zekeriya Arvasi and Alper Odabas.[133X
  
  [33X[0;0YThe  [5XXModAlg[105X 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.[133X
  
  
  -------------------------------------------------------
  [1XAcknowledgements[101X
  [33X[0;0YThis  documentation  was  prepared with the [5XGAPDoc[105X [LN17] and [5XAutoDoc[105X [GH17]
  packages.[133X
  
  [33X[0;0YThe   procedure   used   to   produce   new   releases   uses   the  package
  [5XGitHubPagesForGAP[105X [Hor17] and the package [5XReleaseTools[105X.[133X
  
  [33X[0;0YBoth      authors     are     very     grateful     to     Chris     Wensley
  ([7Xhttps://github.com/cdwensley[107X) for helpful suggestions.[133X
  
  [33X[0;0YThis  work  was partially supported by TÜBİTAK (The Scientific and Technical
  Research Council of Turkey), project number 107T542.[133X
  
  
  -------------------------------------------------------
  
  
  [1XContents (XModAlg)[101X
  
  1 [33X[0;0YIntroduction[133X
  2 [33X[0;0YAlgebras and their Actions[133X
    2.1 [33X[0;0YMultipliers[133X
      2.1-1 RegularAlgebraMultiplier
      2.1-2 IsAlgebraMultiplier
      2.1-3 MultiplierAlgebraOfIdealBySubalgebra 
      2.1-4 MultiplierAlgebra
      2.1-5 MultiplierHomomorphism
    2.2 [33X[0;0YCommutative actions[133X
      2.2-1 AlgebraActionByMultipliers
      2.2-2 AlgebraActionBySurjection
      2.2-3 SemidirectProductOfAlgebras
      2.2-4 SemidirectProductOfAlgebrasInfo
    2.3 [33X[0;0YLists of algebra homomorphisms[133X
      2.3-1 AllAlgebraHomomorphisms
  3 [33X[0;0YCat1-algebras[133X
    3.1 [33X[0;0YDefinitions and examples[133X
      3.1-1 Cat1Algebra
      3.1-2 Source
      3.1-3 Cat1AlgebraSelect
      3.1-4 SubCat1Algebra
    3.2 [33X[0;0YCat[22X^1-[122Xalgebra morphisms[133X
      3.2-1 Cat1AlgebraMorphism
      3.2-2 Source
      3.2-3 ImagesSource2DimensionalMapping
  4 [33X[0;0YCrossed modules[133X
    4.1 [33X[0;0YDefinition and Examples[133X
      4.1-1 XModAlgebra
      4.1-2 XModAlgebraByIdeal
      4.1-3 AugmentationXMod
      4.1-4 XModAlgebraByMultiplierAlgebra
      4.1-5 XModAlgebraBySurjection
      4.1-6 XModAlgebraByBoundaryAndAction
      4.1-7 XModAlgebraByModule
      4.1-8 Source
      4.1-9 SubXModAlgebra
    4.2 [33X[0;0Y(Pre-)Crossed Module Morphisms[133X
      4.2-1 XModAlgebraMorphism
      4.2-2 Kernel
      4.2-3 Image
      4.2-4 SourceHom
  5 [33X[0;0YConversion between cat1-algebras and crossed modules[133X
    5.1 [33X[0;0YEquivalent Categories[133X
      5.1-1 Cat1AlgebraOfXModAlgebra
      5.1-2 XModAlgebraOfCat1Algebra
  
  
  [32X
