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# CAP, single 12
#
# DO NOT EDIT THIS FILE - EDIT EXAMPLES IN THE SOURCE INSTEAD!
#
# This file has been generated by AutoDoc. It contains examples extracted from
# the package documentation. Each example is preceded by a comment which gives
# the name of a GAPDoc XML file and a line range from which the example were
# taken. Note that the XML file in turn may have been generated by AutoDoc
# from some other input.
#
gap> START_TEST("cap12.tst");
# doc/_Chapter_Examples_and_Tests.xml:239-393
gap> LoadPackage( "CAP", false );
true
gap> T := TerminalCategoryWithMultipleObjects( );
TerminalCategoryWithMultipleObjects( )
gap> i := InitialObject( T );
<A zero object in TerminalCategoryWithMultipleObjects( )>
gap> t := TerminalObject( T );
<A zero object in TerminalCategoryWithMultipleObjects( )>
gap> z := ZeroObject( T );
<A zero object in TerminalCategoryWithMultipleObjects( )>
gap> Display( i );
InitialObject( )
gap> Display( t );
TerminalObject( )
gap> Display( z );
ZeroObject( )
gap> IsIdenticalObj( i, z );
false
gap> IsIdenticalObj( t, z );
false
gap> id_z := IdentityMorphism( z );
<A zero, identity morphism in TerminalCategoryWithMultipleObjects( )>
gap> fn_z := ZeroObjectFunctorial( T );
<A zero, isomorphism in TerminalCategoryWithMultipleObjects( )>
gap> IsEqualForMorphisms( id_z, fn_z );
false
gap> IsCongruentForMorphisms( id_z, fn_z );
true
gap> a := "a" / T;
<A zero object in TerminalCategoryWithMultipleObjects( )>
gap> Display( a );
a
gap> IsWellDefined( a );
true
gap> aa := ObjectConstructor( T, "a" );
<A zero object in TerminalCategoryWithMultipleObjects( )>
gap> Display( aa );
a
gap> IsEqualForObjects( a, aa );
true
gap> IsIsomorphicForObjects( a, aa );
true
gap> IsIsomorphism( SomeIsomorphismBetweenObjects( a, aa ) );
true
gap> b := "b" / T;
<A zero object in TerminalCategoryWithMultipleObjects( )>
gap> Display( b );
b
gap> IsEqualForObjects( a, b );
false
gap> IsIsomorphicForObjects( a, b );
true
gap> mor_ab := SomeIsomorphismBetweenObjects( a, b );
<A zero, isomorphism in TerminalCategoryWithMultipleObjects( )>
gap> IsIsomorphism( mor_ab );
true
gap> Display( mor_ab );
a
|
| SomeIsomorphismBetweenObjects
v
b
gap> Hom_ab := MorphismsOfExternalHom( a, b );;
gap> Length( Hom_ab );
1
gap> Hom_ab[1];
<A zero, isomorphism in TerminalCategoryWithMultipleObjects( )>
gap> Display( Hom_ab[1] );
a
|
| InterpretMorphismFromDistinguishedObjectToHomomorphismStructureAsMorphism
v
b
gap> Hom_ab[1] = mor_ab;
true
gap> HomStructure( mor_ab );
<A zero, identity morphism in TerminalCategoryWithSingleObject( )>
gap> m := MorphismConstructor( a, "m", b );
<A zero, isomorphism in TerminalCategoryWithMultipleObjects( )>
gap> Display( m );
a
|
| m
v
b
gap> IsWellDefined( m );
true
gap> n := MorphismConstructor( a, "n", b );
<A zero, isomorphism in TerminalCategoryWithMultipleObjects( )>
gap> Display( n );
a
|
| n
v
b
gap> IsEqualForMorphisms( m, n );
false
gap> IsCongruentForMorphisms( m, n );
true
gap> m = n;
true
gap> hom_mn := HomStructure( m, n );
<A zero, identity morphism in TerminalCategoryWithSingleObject( )>
gap> id := IdentityMorphism( a );
<A zero, identity morphism in TerminalCategoryWithMultipleObjects( )>
gap> Display( id );
a
|
| IdentityMorphism( a )
v
a
gap> m = id;
false
gap> id = MorphismConstructor( a, "xyz", a );
true
gap> zero := ZeroMorphism( a, a );
<A zero, isomorphism in TerminalCategoryWithMultipleObjects( )>
gap> Display( zero );
a
|
| ZeroMorphism( a, a )
v
a
gap> id = zero;
true
gap> IsLiftable( m, n );
true
gap> lift := Lift( m, n );
<A zero, isomorphism in TerminalCategoryWithMultipleObjects( )>
gap> Display( lift );
a
|
| Lift( m, n )
v
a
gap> IsColiftable( m, n );
true
gap> colift := Colift( m, n );
<A zero, isomorphism in TerminalCategoryWithMultipleObjects( )>
gap> Display( colift );
b
|
| Colift( m, n )
v
b
gap> DirectProduct( T, [ ] );
<A zero object in TerminalCategoryWithMultipleObjects( )>
gap> Equalizer( T, z, [ ] );
<A zero object in TerminalCategoryWithMultipleObjects( )>
gap> Coproduct( T, [ ] );
<A zero object in TerminalCategoryWithMultipleObjects( )>
gap> Coequalizer( T, z, [ ] );
<A zero object in TerminalCategoryWithMultipleObjects( )>
#
gap> STOP_TEST("cap12.tst", 1);
[ Dauer der Verarbeitung: 0.14 Sekunden
(vorverarbeitet)
]
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