diff --git a/doc/xmod.xml b/doc/xmod.xml
index 3f804fd..e8f0d3c 100644
--- a/doc/xmod.xml
+++ b/doc/xmod.xml
@@ -215,8 +215,9 @@ gap> SetName( S, "<e5>" );
 gap> RS := Cartesian( R, S );; 
 gap> SetName( RS, "GF(2^2)[k4] x <e5>" ); 
 gap> act := AlgebraAction( R, RS, S );;
-gap> bdy := AlgebraHomomorphismByFunction( S, R, r->r );
-MappingByFunction( <e5>, GF(2^2)[k4], function( r ) ... end )
+gap> bdy := AlgebraHomomorphismByImages( S, R, [e5], [e5] );
+[ (Z(2)^0)*<identity> of ...+(Z(2)^0)*f1+(Z(2)^0)*f2+(Z(2)^0)*f1*f2 ] -> 
+[ (Z(2)^0)*<identity> of ...+(Z(2)^0)*f1+(Z(2)^0)*f2+(Z(2)^0)*f1*f2 ]
 gap> IsAlgebraAction( act ); 
 true
 gap> IsAlgebraHomomorphism( bdy );
diff --git a/examples/cat1.g b/examples/cat1.g
index a49f794..f354683 100644
--- a/examples/cat1.g
+++ b/examples/cat1.g
@@ -50,7 +50,7 @@ SetName( S, "<e5>" );
 RS := Cartesian( R, S );; 
 SetName( RS, "GF(2^2)[k4] x <e5>" ); 
 act := AlgebraAction( R, RS, S );;
-bdy := AlgebraHomomorphismByFunction( S, R, r->r );
+bdy := AlgebraHomomorphismByImages( S, R, [e5], [e5] );
 IsAlgebraAction( act ); 
 IsAlgebraHomomorphism( bdy );
 XM := PreXModAlgebraByBoundaryAndAction( bdy, act );
diff --git a/examples/xmod.g b/examples/xmod.g
index d5931f1..d496101 100644
--- a/examples/xmod.g
+++ b/examples/xmod.g
@@ -47,7 +47,7 @@ SetName( S, "<e5>" );
 RS := Cartesian( R, S );; 
 SetName( RS, "GF(2^2)[k4] x <e5>" ); 
 act := AlgebraAction( R, RS, S );;
-bdy := AlgebraHomomorphismByFunction( S, R, r->r );
+bdy := AlgebraHomomorphismByImages( S, R, [e5], [e5] );
 IsAlgebraAction( act ); 
 IsAlgebraHomomorphism( bdy );
 XM := PreXModAlgebraByBoundaryAndAction( bdy, act );
diff --git a/tst/cat1.tst b/tst/cat1.tst
index cebe9b7..4d9e4f3 100644
--- a/tst/cat1.tst
+++ b/tst/cat1.tst
@@ -27,7 +27,7 @@ gap> e5 := Elements(R)[5];;
 gap> S := Subalgebra( R, [e5] );; 
 gap> SetName( S, "<e5>" );
 gap> act := AlgebraActionByMultipliers( R, S, R );;
-gap> bdy := AlgebraHomomorphismByFunction( S, R, s->s );;
+gap> bdy := AlgebraHomomorphismByImages( S, R, [e5], [e5] );;
 gap> IsAlgebraAction( act );; 
 gap> IsAlgebraHomomorphism( bdy );; 
 gap> XM := PreXModAlgebraByBoundaryAndAction( bdy, act );;
diff --git a/tst/convert.tst b/tst/convert.tst
index 91d708d..18aed73 100644
--- a/tst/convert.tst
+++ b/tst/convert.tst
@@ -21,7 +21,7 @@ gap> e5 := Elements(R)[5];;
 gap> S := Subalgebra( R, [e5] );; 
 gap> SetName( S, "<e5>" );
 gap> act := AlgebraActionByMultipliers( R, S, R );;
-gap> bdy := AlgebraHomomorphismByFunction( S, R, s->s );;
+gap> bdy := AlgebraHomomorphismByImages( S, R, [e5], [e5] );;
 gap> IsAlgebraAction( act );; 
 gap> IsAlgebraHomomorphism( bdy );; 
 gap> XM := PreXModAlgebraByBoundaryAndAction( bdy, act );;
diff --git a/tst/xmod.tst b/tst/xmod.tst
index 138229e..1c4082e 100644
--- a/tst/xmod.tst
+++ b/tst/xmod.tst
@@ -99,8 +99,9 @@ gap> e5 := Elements( R )[5];
 gap> S := Subalgebra( R, [e5] );;
 gap> SetName( S, "<e5>" );
 gap> act := AlgebraActionByMultipliers( R, S, R );;
-gap> bdy := AlgebraHomomorphismByFunction( S, R, s->s );
-MappingByFunction( <e5>, GF(2^2)[k4], function( s ) ... end )
+gap> bdy := AlgebraHomomorphismByImages( S, R, [e5], [e5] );
+[ (Z(2)^0)*<identity> of ...+(Z(2)^0)*f1+(Z(2)^0)*f2+(Z(2)^0)*f1*f2 ] -> 
+[ (Z(2)^0)*<identity> of ...+(Z(2)^0)*f1+(Z(2)^0)*f2+(Z(2)^0)*f1*f2 ]
 gap> IsAlgebraAction( act ); 
 true
 gap> IsAlgebraHomomorphism( bdy );