  
  [1X24 [33X[0;0YCat-1-groups[133X[101X
  
  
  [1X24.1 [33X[0;0Y [133X[101X
  
  [1X24.1-1 AutomorphismGroupAsCatOneGroup[101X
  
  [33X[1;0Y[29X[2XAutomorphismGroupAsCatOneGroup[102X( [3XG[103X ) [32X function[133X
  
  [33X[0;0YInputs  a group [22XG[122X and returns the Cat-1-group [22XC[122X corresponding to the crossed
  module [22XG→ Aut(G)[122X.[133X
  
  [33X[0;0Y[12XExamples:[112X   1  ([7X../tutorial/chap6.html[107X) ,  2  ([7X../tutorial/chap12.html[107X) ,  3
  ([7X../www/SideLinks/About/aboutCrossedMods.html[107X) ,                           4
  ([7X../www/SideLinks/About/aboutquasi.html[107X) ,                                 5
  ([7X../www/SideLinks/About/aboutSimplicialGroups.html[107X) ,                      6
  ([7X../www/SideLinks/About/aboutIntro.html[107X) [133X
  
  [1X24.1-2 HomotopyGroup[101X
  
  [33X[1;0Y[29X[2XHomotopyGroup[102X( [3XC[103X, [3Xn[103X ) [32X function[133X
  
  [33X[0;0YInputs  a  cat-1-group [22XC[122X and an integer n. It returns the [22Xn[122Xth homotopy group
  of [22XC[122X.[133X
  
  [33X[0;0Y[12XExamples:[112X   1  ([7X../tutorial/chap6.html[107X) ,  2  ([7X../tutorial/chap12.html[107X) ,  3
  ([7X../www/SideLinks/About/aboutNonabelian.html[107X) ,                            4
  ([7X../www/SideLinks/About/aboutCrossedMods.html[107X) ,                           5
  ([7X../www/SideLinks/About/aboutquasi.html[107X) ,                                 6
  ([7X../www/SideLinks/About/aboutSimplicialGroups.html[107X) ,                      7
  ([7X../www/SideLinks/About/aboutIntro.html[107X) ,                                 8
  ([7X../www/SideLinks/About/aboutTensorSquare.html[107X) [133X
  
  [1X24.1-3 HomotopyModule[101X
  
  [33X[1;0Y[29X[2XHomotopyModule[102X( [3XC[103X, [3X2[103X ) [32X function[133X
  
  [33X[0;0YInputs  a  cat-1-group  [22XC[122X and an integer n=2. It returns the second homotopy
  group  of  [22XC[122X  as  a  G-module  (i.e.  abelian  G-outer group) where G is the
  fundamental group of C.[133X
  
  [33X[0;0Y[12XExamples:[112X             1             ([7X../tutorial/chap6.html[107X) ,             2
  ([7X../www/SideLinks/About/aboutCrossedMods.html[107X) [133X
  
  [1X24.1-4 QuasiIsomorph[101X
  
  [33X[1;0Y[29X[2XQuasiIsomorph[102X( [3XC[103X ) [32X function[133X
  
  [33X[0;0YInputs  a  cat-1-group  [22XC[122X and returns a cat-1-group [22XD[122X for which there exists
  some homomorphism [22XC→ D[122X that induces isomorphisms on homotopy groups.[133X
  
  [33X[0;0YThis function was implemented by [12XLe Van Luyen[112X.[133X
  
  [33X[0;0Y[12XExamples:[112X             1             ([7X../tutorial/chap12.html[107X) ,            2
  ([7X../www/SideLinks/About/aboutquasi.html[107X) ,                                 3
  ([7X../www/SideLinks/About/aboutSimplicialGroups.html[107X) [133X
  
  [1X24.1-5 ModuleAsCatOneGroup[101X
  
  [33X[1;0Y[29X[2XModuleAsCatOneGroup[102X [32X global variable[133X
  
  [33X[0;0YInputs  a  group  [22XG[122X,  an abelian group [22XM[122X and a homomorphism [22Xα: G→ Aut(M)[122X. It
  returns the Cat-1-group [22XC[122X corresponding th the zero crossed module [22X0: M→ G[122X.[133X
  
  [33X[0;0Y[12XExamples:[112X[133X
  
  [1X24.1-6 MooreComplex[101X
  
  [33X[1;0Y[29X[2XMooreComplex[102X( [3XC[103X ) [32X function[133X
  
  [33X[0;0YInputs a cat-1-group [22XC[122X and returns its Moore complex as a G-complex (i.e. as
  a complex of groups considered as 1-outer groups).[133X
  
  [33X[0;0Y[12XExamples:[112X[133X
  
  [1X24.1-7 NormalSubgroupAsCatOneGroup[101X
  
  [33X[1;0Y[29X[2XNormalSubgroupAsCatOneGroup[102X( [3XG[103X, [3XN[103X ) [32X function[133X
  
  [33X[0;0YInputs  a  group  [22XG[122X  with  normal  subgroup  [22XN[122X. It returns the Cat-1-group [22XC[122X
  corresponding th the inclusion crossed module [22XN→ G[122X.[133X
  
  [33X[0;0Y[12XExamples:[112X[133X
  
  [1X24.1-8 XmodToHAP[101X
  
  [33X[1;0Y[29X[2XXmodToHAP[102X( [3XC[103X ) [32X function[133X
  
  [33X[0;0YInputs  a  cat-1-group  [22XC[122X  obtained  from  the  Xmod  package  and returns a
  cat-1-group [22XD[122X for which IsHapCatOneGroup(D) returns true.[133X
  
  [33X[0;0YIt returns "fail" id [22XC[122X has not been produced by the Xmod package.[133X
  
  [33X[0;0Y[12XExamples:[112X 1 ([7X../www/SideLinks/About/aboutquasi.html[107X) [133X
  
