73.42 Image for a crossed module morphism

ImageXModMorphism( mor, S )

The image of a sub-crossed module S of X under a morphism mor : X to Y of crossed modules is the sub-crossed module of Y whose source is the image of S.source under mor.sourceHom and whose range is the image of S.range under mor.rangeHom. An appropriate name for the image is chosen automatically. A field .image is added to mor. Note that thjis function should be named XModMorphismOps.Image, but the command J := Image( mor, S ); does not work with version 3 of GAP.

    gap> subSX;
    Crossed module [c4->q8]
    gap> JX := ImageXModMorphism( mor, subSX );
    Crossed module [Im([c4->q8]) by <[q8->sl(2,3)] >-> [k4->a4]>]
    gap> RecFields( mor );
    [ "sourceHom", "rangeHom", "source", "range", "name", "isXModMorphism",
       "domain", "kernel", "image", "isMonomorphism", "isEpimorphism",
       "isIsomorphism", "isEndomorphism", "isAutomorphism", "operations" ]
    gap> XModPrint( JX );
    
    Crossed module [Im([c4->q8]) by <[q8->sl(2,3)] >-> [k4->a4]>] :-
    : Source group has parent ( s4 )  and has generators:
      [ (1,2)(3,4) ]
    : Range group has parent ( s4 )  and has generators:
      [ (1,2)(3,4), (1,3)(2,4) ]
    : Boundary homomorphism maps source generators to:
      [ (1,2)(3,4) ]
    : The automorphism group is trivial.