3 Homomorphisms of many-object structures
  
  A  homomorphism  f  from  a  magma  with objects M to a magma with objects N
  consists  of  a  map f_O from the objects of M to those of N together with a
  map f_A from the arrows of M to those of N which is compatible with tail and
  head and which preserves multiplication:
  
  
       f_A((a : u \to v)*f(b : v \to w)) ~=~ f_A(a*b : u \to w)
  
  
  with tail f_O(u) and head f_O(v).
  
  
  3.1 Homomorphisms of magmas with objects
  
  3.1-1 MagmaWithObjectsHomomorphism
  
  > MagmaWithObjectsHomomorphism( args ) _____________________________function
  > MagmaHomomorphismFromSinglePiece( src, rng, hom, imobs ) ________operation
  > HomomorphismToSinglePiece( src, rng, images ) ___________________operation
  > HomomorphismByUnion( src, rng, homs ) ___________________________operation
  
  As  usual,  there  are  a  variety  of  homomorphism constructors. The basic
  construction  is a homomorphism M -> N with both M and N connected, which is
  implemented  as IsHomomorphismToSinglePieceRep with attributes Source, Range
  and PieceImages. We require the following information:
  
  --    a  magma  homomorphism  f  from  the underlying of M to the underlying
        magma of N.
  
  --    a list imobs of the images of the objects of M;
  
  In the example we construct endomappings of m and M78.
  
  ---------------------------  Example  ----------------------------
    
    gap> tup1 := [ Tuple([m1,m2]), Tuple([m2,m1]), Tuple([m3,m4]), Tuple([m4,m3]) ]; 
    gap> f1 := GeneralMappingByElements( m, m, tup1 ); 
    f1 = <general mapping: m -> m >
    gap> IsMagmaHomomorphism( f1 ); 
    true
    gap> tup2 := [ Tuple([m1,m1]), Tuple([m2,m1]), Tuple([m3,m1]), Tuple([m4,m1]) ];; 
    gap> f2 := GeneralMappingByElements( m, m, tup2 );; 
    gap> IsMagmaHomomorphism( f2 );
    true 
    gap> map1 := HomomorphismFromSinglePiece( M78, M78, [-8,-7], f1 ); 
    magma with objects homomorphism : M78 -> M78
    gap> Display( map1 );
    Mapping to single piece magma:
    [ M78 ] -> [ M78 ]
    magma mapping: <mapping: m -> m >
       object map: [ -8, -7 ] -> [ -8, -7 ]
    Homomorphism to connected magma:
    [ M78 ] -> [ M78 ]
      object map = [ [ -8, -7 ], [ -8, -7 ] ]
    homomorphism = <homomorphism: m -> m >
    gap> idm := f1*f1;; 
    gap> idmap := HomomorphismFromSinglePiece( M78, M78, idm, [-7,-8] ); 
    gap> map2 := HomomorphismFromSinglePiece( M78, M78, f2, [-7,-8] ); 
    
  ------------------------------------------------------------------