\indexentry{License|hyperpage}{2}
\indexentry{InfoXMod@\texttt{InfoXMod}|hyperpage}{6}
\indexentry{crossed module|hyperpage}{7}
\indexentry{2d-domain|hyperpage}{7}
\indexentry{2d-group|hyperpage}{7}
\indexentry{XMod@\texttt  {XMod}|hyperpage}{7}
\indexentry{XModByBoundaryAndAction@\texttt  {XModByBoundaryAndAction}|hyperpage}{7}
\indexentry{XModByTrivialAction@\texttt  {XModByTrivialAction}|hyperpage}{7}
\indexentry{XModByNormalSubgroup@\texttt  {XModByNormalSubgroup}|hyperpage}{7}
\indexentry{XModByCentralExtension@\texttt  {XModByCentralExtension}|hyperpage}{7}
\indexentry{XModByAutomorphismGroup@\texttt  {XModByAutomorphismGroup}|hyperpage}{7}
\indexentry{XModByInnerAutomorphismGroup@\texttt  {XModByInnerAutomorphismGroup}|hyperpage}{7}
\indexentry{XModByGroupOfAutomorphisms@\texttt  {XModByGroupOfAutomorphisms}|hyperpage}{7}
\indexentry{XModByAbelianModule@\texttt  {XModByAbelianModule}|hyperpage}{7}
\indexentry{DirectProduct@\texttt  {DirectProduct}|hyperpage}{7}
\indexentry{Source@\texttt  {Source}|hyperpage}{8}
\indexentry{Range@\texttt  {Range}|hyperpage}{8}
\indexentry{Boundary@\texttt  {Boundary}|hyperpage}{8}
\indexentry{AutoGroup@\texttt  {AutoGroup}|hyperpage}{8}
\indexentry{XModAction@\texttt  {XModAction}|hyperpage}{8}
\indexentry{Size@\texttt  {Size}|hyperpage}{8}
\indexentry{Name@\texttt  {Name}|hyperpage}{8}
\indexentry{display a 2d-group|hyperpage}{8}
\indexentry{SubXMod@\texttt  {SubXMod}|hyperpage}{9}
\indexentry{TrivialSubXMod@\texttt  {TrivialSubXMod}|hyperpage}{9}
\indexentry{NormalSubXMods@\texttt  {NormalSubXMods}|hyperpage}{9}
\indexentry{pre-crossed module|hyperpage}{9}
\indexentry{PreXModByBoundaryAndAction@\texttt  {PreXModByBoundaryAndAction}|hyperpage}{9}
\indexentry{SubPreXMod@\texttt  {SubPreXMod}|hyperpage}{9}
\indexentry{Peiffer subgroup|hyperpage}{10}
\indexentry{PeifferSubgroup@\texttt  {PeifferSubgroup}|hyperpage}{10}
\indexentry{XModByPeifferQuotient@\texttt  {XModByPeifferQuotient}|hyperpage}{10}
\indexentry{IsPermXMod@\texttt  {IsPermXMod}|hyperpage}{10}
\indexentry{IsPcPreXMod@\texttt  {IsPcPreXMod}|hyperpage}{10}
\indexentry{cat1-group|hyperpage}{11}
\indexentry{Source@\texttt  {Source}|hyperpage}{11}
\indexentry{Range@\texttt  {Range}|hyperpage}{11}
\indexentry{TailMap@\texttt  {TailMap}|hyperpage}{11}
\indexentry{HeadMap@\texttt  {HeadMap}|hyperpage}{11}
\indexentry{RangeEmbedding@\texttt  {RangeEmbedding}|hyperpage}{11}
\indexentry{KernelEmbedding@\texttt  {KernelEmbedding}|hyperpage}{11}
\indexentry{Boundary@\texttt  {Boundary}|hyperpage}{11}
\indexentry{Name@\texttt  {Name}|hyperpage}{11}
\indexentry{Size@\texttt  {Size}|hyperpage}{11}
\indexentry{Cat1@\texttt  {Cat1}|hyperpage}{11}
\indexentry{PreCat1ByTailHeadEmbedding@\texttt  {PreCat1ByTailHeadEmbedding}|hyperpage}{11}
\indexentry{PreCat1ByEndomorphisms@\texttt  {PreCat1ByEndomorphisms}|hyperpage}{11}
\indexentry{PreCat1ByNormalSubgroup@\texttt  {PreCat1ByNormalSubgroup}|hyperpage}{11}
\indexentry{Cat1ByPeifferQuotient@\texttt  {Cat1ByPeifferQuotient}|hyperpage}{11}
\indexentry{Reverse@\texttt  {Reverse}|hyperpage}{11}
\indexentry{Cat1OfXMod@\texttt  {Cat1OfXMod}|hyperpage}{12}
\indexentry{XModOfCat1@\texttt  {XModOfCat1}|hyperpage}{12}
\indexentry{PreCat1OfPreXMod@\texttt  {PreCat1OfPreXMod}|hyperpage}{12}
\indexentry{PreXModOfPreCat1@\texttt  {PreXModOfPreCat1}|hyperpage}{12}
\indexentry{selection of a small cat1-group|hyperpage}{13}
\indexentry{Cat1Select@\texttt  {Cat1Select}|hyperpage}{13}
\indexentry{AllCat1sBasic@\texttt  {AllCat1sBasic}|hyperpage}{15}
\indexentry{2d-mapping|hyperpage}{16}
\indexentry{morphism of 2d-group|hyperpage}{16}
\indexentry{crossed module morphism|hyperpage}{16}
\indexentry{Source@\texttt  {Source}|hyperpage}{16}
\indexentry{Range@\texttt  {Range}|hyperpage}{16}
\indexentry{SourceHom@\texttt  {SourceHom}|hyperpage}{16}
\indexentry{RangeHom@\texttt  {RangeHom}|hyperpage}{16}
\indexentry{morphism|hyperpage}{16}
\indexentry{IsXModMorphism@\texttt  {IsXModMorphism}|hyperpage}{16}
\indexentry{IsPreXModMorphism@\texttt  {IsPreXModMorphism}|hyperpage}{16}
\indexentry{IsInjective@\texttt  {IsInjective}|hyperpage}{16}
\indexentry{IsSurjective@\texttt  {IsSurjective}|hyperpage}{16}
\indexentry{IsSingleValued@\texttt  {IsSingleValued}|hyperpage}{17}
\indexentry{IsTotal@\texttt  {IsTotal}|hyperpage}{17}
\indexentry{IsBijective@\texttt  {IsBijective}|hyperpage}{17}
\indexentry{IsEndo2dMapping@\texttt  {IsEndo2dMapping}|hyperpage}{17}
\indexentry{XModMorphism@\texttt  {XModMorphism}|hyperpage}{17}
\indexentry{XModMorphismByHoms@\texttt  {XModMorphismByHoms}|hyperpage}{17}
\indexentry{PreXModMorphism@\texttt  {PreXModMorphism}|hyperpage}{17}
\indexentry{PreXModMorphismByHoms@\texttt  {PreXModMorphismByHoms}|hyperpage}{17}
\indexentry{InclusionMorphism2dDomains@\texttt  {InclusionMorphism2dDomains}|hyperpage}{17}
\indexentry{InnerAutomorphismXMod@\texttt  {InnerAutomorphismXMod}|hyperpage}{17}
\indexentry{IdentityMapping@\texttt  {IdentityMapping}|hyperpage}{17}
\indexentry{IsomorphismPermObject@\texttt  {IsomorphismPermObject}|hyperpage}{17}
\indexentry{display a 2d-mapping|hyperpage}{17}
\indexentry{order of a 2d-automorphism|hyperpage}{17}
\indexentry{IsCat1Morphism@\texttt  {IsCat1Morphism}|hyperpage}{18}
\indexentry{IsPreCat1Morphism@\texttt  {IsPreCat1Morphism}|hyperpage}{18}
\indexentry{Cat1Morphism@\texttt  {Cat1Morphism}|hyperpage}{18}
\indexentry{Cat1MorphismByHoms@\texttt  {Cat1MorphismByHoms}|hyperpage}{18}
\indexentry{PreCat1Morphism@\texttt  {PreCat1Morphism}|hyperpage}{18}
\indexentry{PreCat1MorphismByHoms@\texttt  {PreCat1MorphismByHoms}|hyperpage}{18}
\indexentry{InclusionMorphism2dDomains@\texttt  {InclusionMorphism2dDomains}|hyperpage}{18}
\indexentry{InnerAutomorphismCat1@\texttt  {InnerAutomorphismCat1}|hyperpage}{18}
\indexentry{IdentityMapping@\texttt  {IdentityMapping}|hyperpage}{18}
\indexentry{IsomorphismPermObject@\texttt  {IsomorphismPermObject}|hyperpage}{18}
\indexentry{SmallerDegreePerm2dDomain@\texttt  {SmallerDegreePerm2dDomain}|hyperpage}{18}
\indexentry{operations on morphisms|hyperpage}{19}
\indexentry{CompositionMorphism@\texttt  {CompositionMorphism}|hyperpage}{19}
\indexentry{Kernel@\texttt  {Kernel}|hyperpage}{19}
\indexentry{Kernel2dMapping@\texttt  {Kernel2dMapping}|hyperpage}{19}
\indexentry{up 2d-mapping of 2d-group|hyperpage}{21}
\indexentry{Whitehead multiplication|hyperpage}{21}
\indexentry{IsDerivation@\texttt  {IsDerivation}|hyperpage}{21}
\indexentry{IsSection@\texttt  {IsSection}|hyperpage}{21}
\indexentry{IsUp2dMapping@\texttt  {IsUp2dMapping}|hyperpage}{21}
\indexentry{derivation, of crossed module|hyperpage}{21}
\indexentry{Whitehead monoid|hyperpage}{21}
\indexentry{regular derivation|hyperpage}{21}
\indexentry{Whitehead group|hyperpage}{21}
\indexentry{section, of cat1-group|hyperpage}{21}
\indexentry{Whitehead multiplication|hyperpage}{21}
\indexentry{DerivationByImages@\texttt  {DerivationByImages}|hyperpage}{21}
\indexentry{SectionByImages@\texttt  {SectionByImages}|hyperpage}{22}
\indexentry{SectionByDerivation@\texttt  {SectionByDerivation}|hyperpage}{22}
\indexentry{DerivationBySection@\texttt  {DerivationBySection}|hyperpage}{22}
\indexentry{RegularDerivations@\texttt  {RegularDerivations}|hyperpage}{23}
\indexentry{AllDerivations@\texttt  {AllDerivations}|hyperpage}{23}
\indexentry{RegularSections@\texttt  {RegularSections}|hyperpage}{23}
\indexentry{AllSections@\texttt  {AllSections}|hyperpage}{23}
\indexentry{ImagesList@\texttt  {ImagesList}|hyperpage}{23}
\indexentry{ImagesTable@\texttt  {ImagesTable}|hyperpage}{23}
\indexentry{CompositeDerivation@\texttt  {CompositeDerivation}|hyperpage}{24}
\indexentry{UpImagePositions@\texttt  {UpImagePositions}|hyperpage}{24}
\indexentry{UpGeneratorImages@\texttt  {UpGeneratorImages}|hyperpage}{24}
\indexentry{CompositeSection@\texttt  {CompositeSection}|hyperpage}{24}
\indexentry{WhiteheadGroupTable@\texttt  {WhiteheadGroupTable}|hyperpage}{24}
\indexentry{WhiteheadMonoidTable@\texttt  {WhiteheadMonoidTable}|hyperpage}{24}
\indexentry{WhiteheadPermGroup@\texttt  {WhiteheadPermGroup}|hyperpage}{24}
\indexentry{WhiteheadTransMonoid@\texttt  {WhiteheadTransMonoid}|hyperpage}{24}
\indexentry{actor|hyperpage}{26}
\indexentry{WhiteheadXMod@\texttt  {WhiteheadXMod}|hyperpage}{26}
\indexentry{LueXMod@\texttt  {LueXMod}|hyperpage}{26}
\indexentry{NorrieXMod@\texttt  {NorrieXMod}|hyperpage}{26}
\indexentry{ActorXMod@\texttt  {ActorXMod}|hyperpage}{26}
\indexentry{AutomorphismPermGroup@\texttt  {AutomorphismPermGroup}|hyperpage}{26}
\indexentry{crossed square|hyperpage}{26}
\indexentry{XModCentre@\texttt  {XModCentre}|hyperpage}{28}
\indexentry{InnerActorXMod@\texttt  {InnerActorXMod}|hyperpage}{28}
\indexentry{InnerMorphism@\texttt  {InnerMorphism}|hyperpage}{28}
\indexentry{induced crossed module|hyperpage}{29}
\indexentry{InducedXMod@\texttt  {InducedXMod}|hyperpage}{29}
\indexentry{InducedCat1@\texttt  {InducedCat1}|hyperpage}{29}
\indexentry{IsInducedXMod@\texttt  {IsInducedXMod}|hyperpage}{29}
\indexentry{IsInducedCat1@\texttt  {IsInducedCat1}|hyperpage}{29}
\indexentry{MorphismOfInducedXMod@\texttt  {MorphismOfInducedXMod}|hyperpage}{29}
\indexentry{AllInducedXMods@\texttt  {AllInducedXMods}|hyperpage}{31}
\indexentry{crossed module|hyperpage}{32}
\indexentry{cat2-group|hyperpage}{32}
\indexentry{3d-group|hyperpage}{32}
\indexentry{crossed pairing|hyperpage}{32}
\indexentry{XSq@\texttt  {XSq}|hyperpage}{33}
\indexentry{XSqByNormalSubgroups@\texttt  {XSqByNormalSubgroups}|hyperpage}{33}
\indexentry{ActorXSq@\texttt  {ActorXSq}|hyperpage}{33}
\indexentry{Transpose3dGroup@\texttt  {Transpose3dGroup}|hyperpage}{33}
\indexentry{Name@\texttt  {Name}|hyperpage}{33}
\indexentry{IsXSq@\texttt  {IsXSq}|hyperpage}{34}
\indexentry{Is3dObject@\texttt  {Is3dObject}|hyperpage}{34}
\indexentry{IsPerm3dObject@\texttt  {IsPerm3dObject}|hyperpage}{34}
\indexentry{IsPc3dObject@\texttt  {IsPc3dObject}|hyperpage}{34}
\indexentry{IsFp3dObject@\texttt  {IsFp3dObject}|hyperpage}{34}
\indexentry{IsPreXSq@\texttt  {IsPreXSq}|hyperpage}{34}
\indexentry{Up2dGroup@\texttt  {Up2dGroup}|hyperpage}{34}
\indexentry{Left2dGroup@\texttt  {Left2dGroup}|hyperpage}{34}
\indexentry{Down2dGroup@\texttt  {Down2dGroup}|hyperpage}{34}
\indexentry{Right2dGroup@\texttt  {Right2dGroup}|hyperpage}{34}
\indexentry{DiagonalAction@\texttt  {DiagonalAction}|hyperpage}{34}
\indexentry{XPair@\texttt  {XPair}|hyperpage}{34}
\indexentry{ImageElmXPair@\texttt  {ImageElmXPair}|hyperpage}{34}
\indexentry{morphism of 3d-group|hyperpage}{35}
\indexentry{crossed square morphism|hyperpage}{35}
\indexentry{3d-mapping|hyperpage}{35}
\indexentry{Source@\texttt  {Source}|hyperpage}{35}
\indexentry{Range@\texttt  {Range}|hyperpage}{35}
\indexentry{Up2dMorphism@\texttt  {Up2dMorphism}|hyperpage}{35}
\indexentry{Left2dMorphism@\texttt  {Left2dMorphism}|hyperpage}{35}
\indexentry{Down2dMorphism@\texttt  {Down2dMorphism}|hyperpage}{35}
\indexentry{Right2dMorphism@\texttt  {Right2dMorphism}|hyperpage}{35}
\indexentry{IsXSqMorphism@\texttt  {IsXSqMorphism}|hyperpage}{35}
\indexentry{IsPreXSqMorphism@\texttt  {IsPreXSqMorphism}|hyperpage}{35}
\indexentry{IsBijective@\texttt  {IsBijective}|hyperpage}{35}
\indexentry{IsEndomorphism3dObject@\texttt  {IsEndomorphism3dObject}|hyperpage}{35}
\indexentry{IsAutomorphism3dObject@\texttt  {IsAutomorphism3dObject}|hyperpage}{35}
\indexentry{crossed module of groupoids|hyperpage}{37}
\indexentry{crossed module over a groupoid|hyperpage}{37}
\indexentry{2d-domain with objects|hyperpage}{37}
\indexentry{PreXModWithObjectsObj@\texttt  {PreXModWithObjectsObj}|hyperpage}{37}
\indexentry{DiscreteNormalPreXModWithObjects@\texttt  {DiscreteNormalPreXModWithObjects}|hyperpage}{37}
\indexentry{PrintListOneItemPerLine@\texttt  {PrintListOneItemPerLine}|hyperpage}{38}
\indexentry{inclusion mapping|hyperpage}{38}
\indexentry{restriction mapping|hyperpage}{38}
\indexentry{InclusionMappingGroups@\texttt  {InclusionMappingGroups}|hyperpage}{38}
\indexentry{RestrictionMappingGroups@\texttt  {RestrictionMappingGroups}|hyperpage}{38}
\indexentry{MappingToOne@\texttt  {MappingToOne}|hyperpage}{38}
\indexentry{InnerAutomorphismByNormalSubgroup@\texttt  {InnerAutomorphismByNormalSubgroup}|hyperpage}{39}
\indexentry{IsGroupOfAutomorphisms@\texttt  {IsGroupOfAutomorphisms}|hyperpage}{39}
\indexentry{abelian module|hyperpage}{39}
\indexentry{AbelianModuleObject@\texttt  {AbelianModuleObject}|hyperpage}{39}
\indexentry{IsAbelianModule@\texttt  {IsAbelianModule}|hyperpage}{39}
\indexentry{AbelianModuleGroup@\texttt  {AbelianModuleGroup}|hyperpage}{39}
\indexentry{AbelianModuleAction@\texttt  {AbelianModuleAction}|hyperpage}{39}
\indexentry{distinct and common representatives|hyperpage}{40}
\indexentry{DistinctRepresentatives@\texttt  {DistinctRepresentatives}|hyperpage}{40}
\indexentry{CommonRepresentatives@\texttt  {CommonRepresentatives}|hyperpage}{40}
\indexentry{CommonTransversal@\texttt  {CommonTransversal}|hyperpage}{40}
\indexentry{IsCommonTransversal@\texttt  {IsCommonTransversal}|hyperpage}{40}
\indexentry{version 1 for \textsf{GAP} 3|hyperpage}{42}
\indexentry{version 2.001 for \textsf{GAP} 4|hyperpage}{42}
