gap> LoadPackage( "CategoriesWithAmbientObjects", false );
true
gap> LoadPackage( "ModulePresentationsForCAP", ">= 2023.10-01", false );
true
gap> QQ := HomalgFieldOfRationalsInSingular( );;
gap> R := QQ * "x,y";
Q[x,y]
gap> M := AsLeftPresentation(
>   HomalgMatrix( "[ 1, x, 0, 1 ]", 2, 2, R ) );
<An object in Category of left presentations of Q[x,y]>
gap> Ag := CategoryWithAmbientObjects( CapCategory( M ) );
CategoryWithAmbientObjects( Category of left presentations of Q[x,y] )
gap> pi := AsGeneralizedMorphismByCospan( CoverByFreeModule( M ) );
<A morphism in Generalized morphism category of
 Category of left presentations of Q[x,y] by cospan>
gap> iota := PseudoInverse( pi );
<A morphism in Generalized morphism category of
 Category of left presentations of Q[x,y] by cospan>
gap> Mg := ObjectWithAmbientObject( iota, Ag );
<An object in Category of left presentations of Q[x,y]>
 with an ambient object
gap> Display( Mg );
1,x,
0,1

An object in Category of left presentations of Q[x,y]
gap> DisplayEmbeddingInAmbientObject( Mg );
0,0,
0,0

A monomorphism in Category of left presentations of Q[x,y]