Cat1Morphism( C, D, L )
A morphism of cat1-groups is a pair of homomorphisms
rangeHom ], where
rangeHom are respectively
homomorphisms between the sources and ranges of C and D, which
commute with the two tail homomorphisms with the two head
homomorphisms and with the two embeddings.
In this implementation a morphism of cat1-groups
mu is a record with
mu.source, & the source cat1-group
mu.range, & the range cat1-group
mu.sourceHom, & a homomorphism from
mu.rangeHom, & a homomorphism from
mu.isCat1Morphism, & a Boolean flag, normally
mu.operations, & a special set of operations
mu.name, & a concatenation of the names of
Cat1Morphism requires as parameters two cat1-groups and
a two-element list containing the source and range homomorphisms. It
sets up the required fields for
mu, but does not check the axioms.
IsCat1Morphism function should be used to perform these checks.
Note that the
Cat1MorphismPrint function is needed to print out the
morphism in detail.
gap> GCCX := CCX.source; Perm(a4
X k4) gap> GAC := AC.source; a4 gap> genGAC := GAC.generators; [ (1,2,3), (2,3,4) ] gap> im := Sublist( GCCX.generators, [1..2] ); [ (2,4,3)(5,6,7), (2,3,4)(6,7,8) ]
gap> musrc := GroupHomomorphismByImages( genGAC, GCCX, gen, im );; gap> murng := InclusionMorphism( a4, a4 );; gap> mu := Cat1Morphism( AC, CCX, [ musrc, murng ] ); Morphism of cat1-groups <[a4 ==> a4]-->[Perm(a4
X k4) ==> a4]>
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