gap> LoadPackage( "ModulePresentations" );
true
gap> LoadPackage( "QuotientCategories" );
true
gap> ZZ := HomalgRingOfIntegers( );
Z
gap> cat := LeftPresentations( ZZ );
Category of left presentations of Z
gap> epi := EpimorphismFromSomeProjectiveObject;;
gap> congruence_func := { alpha, beta } -> IsLiftable( alpha - beta, epi( Range( alpha ) ) );;
gap> quotient_cat := QuotientCategory( cat, congruence_func );
Quotient category( Category of left presentations of Z ) by congruence_func
gap> F := ProjectionFunctor( quotient_cat );;
gap> a := FreeLeftPresentation( 3, ZZ );
<A projective object in Category of left presentations of Z>
gap> quotient_a := ApplyFunctor( F, a );
<An object in Quotient category( Category of left presentations of Z ) by congruence_func>
gap> IsZero( quotient_a );
true