JSci.maths.categories
Class Preorder

java.lang.Object
  JSci.maths.categories.Preorder

All Implemented Interfaces:

Category

public final class Preorder

extends java.lang.Object

implements Category

The Preorder class encapsulates preorders as categories.

Nested Class Summary

class	Preorder.Relation
class	Preorder.RelationSet

Nested classes inherited from class JSci.maths.categories.Category

Category.HomSet, Category.Morphism

Constructor Summary

Preorder(int n)
Constructs a preorder category.

Method Summary

java.lang.Object	cardinality(java.lang.Object a) Returns the cardinality of an object.
Category.HomSet	hom(java.lang.Object a, java.lang.Object b) Returns a hom-set.
Category.Morphism	identity(java.lang.Object a) Returns the identity morphism for an object.
java.lang.Object	initial()
int	ordinal() Returns the ordinal that this category represents.
java.lang.Object	terminal()

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

Preorder

public Preorder(int n)

Constructs a preorder category.

Method Detail

identity

public Category.Morphism identity(java.lang.Object a)

Returns the identity morphism for an object.

Specified by:

identity in interface Category

Parameters:

a - an Integer.

cardinality

public java.lang.Object cardinality(java.lang.Object a)

Returns the cardinality of an object.

Specified by:

cardinality in interface Category

Parameters:

a - an Integer.

Returns:

an Integer.

hom

public Category.HomSet hom(java.lang.Object a,
                           java.lang.Object b)

Returns a hom-set.

Specified by:

hom in interface Category

initial

public java.lang.Object initial()

terminal

public java.lang.Object terminal()

ordinal

public int ordinal()

Returns the ordinal that this category represents.