gap> LoadPackage( "FiniteCocompletions" );
true
gap> q := FinQuiver( "Q(SG,SR,TG,TR)[rhoS:SR->SG,rhoT:TR->TG,phi:SG->TG,chi:SR->TR]" );
FinQuiver( "Q(SG,SR,TG,TR)[rhoS:SR-≻SG,rhoT:TR-≻TG,phi:SG-≻TG,chi:SR-≻TR]" )
gap> P := PathCategory( q );
PathCategory(
FinQuiver( "Q(SG,SR,TG,TR)[rhoS:SR-≻SG,rhoT:TR-≻TG,phi:SG-≻TG,chi:SR-≻TR]" ) )
gap> C := P / [ [ P.rhoS * P.phi, P.chi * P.rhoT ] ];
PathCategory(
FinQuiver( "Q(SG,SR,TG,TR)[rhoS:SR-≻SG,rhoT:TR-≻TG,phi:SG-≻TG,chi:SR-≻TR]" ) )
/ [ rhoS⋅phi = chi⋅rhoT ]
gap> zz := HomalgRingOfIntegers( );
Z
gap> L := LinearClosure( zz, C );
Z-LinearClosure( PathCategory(
FinQuiver( "Q(SG,SR,TG,TR)[rhoS:SR-≻SG,rhoT:TR-≻TG,phi:SG-≻TG,chi:SR-≻TR]" ) )
/ [ rhoS⋅phi = chi⋅rhoT ] )
gap> A := AdditiveClosure( L );
AdditiveClosure( Z-LinearClosure( PathCategory(
FinQuiver( "Q(SG,SR,TG,TR)[rhoS:SR-≻SG,rhoT:TR-≻TG,phi:SG-≻TG,chi:SR-≻TR]" ) )
/ [ rhoS⋅phi = chi⋅rhoT ] ) )
gap> K := CoFreydCategory( A );
CoFreyd( AdditiveClosure( Z-LinearClosure( PathCategory(
FinQuiver( "Q(SG,SR,TG,TR)[rhoS:SR-≻SG,rhoT:TR-≻TG,phi:SG-≻TG,chi:SR-≻TR]" ) )
/ [ rhoS⋅phi = chi⋅rhoT ] ) ) )
gap> F := FreydCategory( K );
Freyd( CoFreyd( AdditiveClosure( Z-LinearClosure( PathCategory(
FinQuiver( "Q(SG,SR,TG,TR)[rhoS:SR-≻SG,rhoT:TR-≻TG,phi:SG-≻TG,chi:SR-≻TR]" ) )
/ [ rhoS⋅phi = chi⋅rhoT ] ) ) ) )
gap> S := CokernelObject( F.rhoS );
<An object in Freyd( CoFreyd( AdditiveClosure( Z-LinearClosure( PathCategory(
 FinQuiver( "Q(SG,SR,TG,TR)[rhoS:SR-≻SG,rhoT:TR-≻TG,phi:SG-≻TG,chi:SR-≻TR]" ) )
 / [ rhoS⋅phi = chi⋅rhoT ] ) ) ) )>
gap> T := CokernelObject( F.rhoT );
<An object in Freyd( CoFreyd( AdditiveClosure( Z-LinearClosure( PathCategory(
 FinQuiver( "Q(SG,SR,TG,TR)[rhoS:SR-≻SG,rhoT:TR-≻TG,phi:SG-≻TG,chi:SR-≻TR]" ) )
 / [ rhoS⋅phi = chi⋅rhoT ] ) ) ) )>
gap> psi := MorphismConstructor( S, K.phi, T );
<A morphism in Freyd( CoFreyd( AdditiveClosure( Z-LinearClosure( PathCategory(
 FinQuiver( "Q(SG,SR,TG,TR)[rhoS:SR-≻SG,rhoT:TR-≻TG,phi:SG-≻TG,chi:SR-≻TR]" ) )
 / [ rhoS⋅phi = chi⋅rhoT ] ) ) ) )>
gap> IsWellDefined( psi );
true
gap> CokernelObjectFunctorial( F.rhoS, F.phi, F.rhoT ) = psi;
true
gap> psi =
>   EvalString( CellAsEvaluatableString( psi, [ "F", "K", "A", "L", "C", "P" ] ) );
true