CompositeMorphism( mor1, mor2 )
Morphisms mu_1 : X to Y and mu_2 : Y to Z have a composite mu = mu_2 circ mu_1 : X to Z whose source and range homomorphisms are the composites of those of mu_1 and mu_2.
In the following example we compose psi
with the inc
obtained previously.
gap > xcomp := XModMorphismOps.CompositeMorphism( psi, inc ); Morphism of crossed modules <[c4->q8] >-> [q8->sl(2,3)]> gap> XModMorphismPrint( xcomp ); Morphism of crossed modules :- : Source = Crossed module [c4->q8] with generating sets: [ (1,2,3,4)(5,8,7,6) ] [ (1,2,3,4)(5,8,7,6), (1,5,3,7)(2,6,4,8) ] : Range = Crossed module [q8->sl(2,3)] with generating sets: [ (1,2,3,4)(5,8,7,6), (1,5,3,7)(2,6,4,8) ] [ (1,2,3,4)(5,8,7,6), (1,5,3,7)(2,6,4,8), (2,5,6)(4,7,8)(9,10,11) ] : Source Homomorphism maps source generators to: [ (1,4,3,2)(5,6,7,8) ] : Range Homomorphism maps range generators to: [ (1,4,3,2)(5,6,7,8), (1,7,3,5)(2,8,4,6) ] : isXModMorphism? true
GAP 3.4.4