73.71 CompositeMorphism for cat1-groups

Cat1MorphismOps.CompositeMorphism( mu1,mu2 )

Morphisms mu_1 : C to D and mu_2 : D to E have a composite mu = mu_2 circ mu_1 : C to E whose source and range homomorphisms are the composites of those of mu_1 and mu_2. The example corresponds to that in refCompositeMorphism for crossed modules.

    gap> psi;
    Morphism of crossed modules <[c4->q8] >-> [c4->q8]>
    gap> inc;
    Morphism of crossed modules <[c4->q8] >-> [q8->sl(2,3)]>
    gap> mupsi := Cat1MorphismXModMorphism( psi );
    Morphism of cat1-groups
        <[Perm(q8 

X c4) ==> q8]>
    gap> muinc := Cat1MorphismXModMorphism( inc );
    Morphism of cat1-groups
        <[Perm(q8 

X q8) ==> sl(2,3)]>
    gap> mucomp := Cat1MorphismOps.CompositeMorphism( mupsi, muinc );
    Morphism of cat1-groups
        <[Perm(q8 

X q8) ==> sl(2,3)]>
    gap> muxcomp := Cat1MorphismXModMorphism( xcomp );;
    gap> mucomp = muxcomp;
    true   

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