gap> LoadPackage( "FunctorCategories", false );
true
gap> T := FiniteCompletion( InitialCategory( ) );
FiniteCompletion( InitialCategory( ) )
gap> H := RangeCategoryOfHomomorphismStructure( T );
PreSheaves( InitialCategory( ), InitialCategory( ) )
gap> IsTerminalCategory( T );
true
gap> IsTerminalCategory( H );
true
gap> Display( T );
A CAP category with name FiniteCompletion( InitialCategory( ) ):

120 primitive operations were used to derive 624 operations for this category
which algorithmically
* IsCategoryWithDecidableColifts
* IsCategoryWithDecidableLifts
* IsFiniteCategory
* IsEquippedWithHomomorphismStructure
* IsLinearCategoryOverCommutativeRingWithFinitelyGeneratedFreeExternalHoms
* IsLeftClosedMonoidalCategory
* IsLeftCoclosedMonoidalCategory
* IsRigidSymmetricClosedMonoidalCategory
* IsRigidSymmetricCoclosedMonoidalCategory
* IsAbelianCategoryWithEnoughInjectives
* IsAbelianCategoryWithEnoughProjectives
* IsSymmetricClosedMonoidalLattice
* IsSymmetricCoclosedMonoidalLattice
* IsBooleanAlgebra
and furthermore mathematically
* IsDiscreteCategory
* IsFinitelyPresentedLinearCategory
* IsLinearClosureOfACategory
* IsLocallyOfFiniteInjectiveDimension
* IsLocallyOfFiniteProjectiveDimension
* IsTerminalCategory
* IsTotalOrderCategory
gap> i := InitialObject( T );
<An object in FiniteCompletion( InitialCategory( ) )>
gap> t := TerminalObject( T );
<An object in FiniteCompletion( InitialCategory( ) )>
gap> z := ZeroObject( T );
<A zero object in FiniteCompletion( InitialCategory( ) )>
gap> Display( i );
An object in CoPreSheaves( InitialCategory( ), InitialCategory( ) )
given by the above data

An object in FiniteCompletion( InitialCategory( ) ) given by the above data
gap> Display( t );
An object in CoPreSheaves( InitialCategory( ), InitialCategory( ) )
given by the above data

An object in FiniteCompletion( InitialCategory( ) ) given by the above data
gap> Display( z );
An object in CoPreSheaves( InitialCategory( ), InitialCategory( ) )
given by the above data

An object in FiniteCompletion( InitialCategory( ) ) given by the above data
gap> IsIdenticalObj( i, z );
false
gap> IsIdenticalObj( t, z );
false
gap> IsEqualForObjects( i, z );
true
gap> IsEqualForObjects( t, z );
true
gap> IsWellDefined( z );
true
gap> id_z := IdentityMorphism( z );
<A zero, identity morphism in FiniteCompletion( InitialCategory( ) )>
gap> fn_z := ZeroObjectFunctorial( T );
<A zero, isomorphism in FiniteCompletion( InitialCategory( ) )>
gap> IsWellDefined( fn_z );
true
gap> IsEqualForMorphisms( id_z, fn_z );
true
gap> IsCongruentForMorphisms( id_z, fn_z );
true