Category


1   package JSci.maths.categories;
2   
3   /**
4   * This interface defines a category.
5   * @jsci.planetmath Category
6   * @version 1.0
7   * @author Mark Hale
8   */
9   public interface Category {
10          /**
11          * Returns the identity morphism for an object.
12          */
13          Morphism identity(Object   a);
14          /**
15          * Returns the cardinality of an object.
16          * In general, this may not be an Integer.
17          */
18          Object   cardinality(Object   a);
19          /**
20          * Returns a hom-set.
21          */
22          HomSet hom(Object   a, Object   b);
23  
24          /**
25          * This interface defines a morphism in a category.
26          */
27          interface Morphism {
28                  /**
29                  * Returns the domain.
30                  */
31                  Object   domain();
32                  /**
33                  * Returns the codomain.
34                  */
35                  Object   codomain();
36                  /**
37                  * Maps an object from the domain to the codomain.
38                  */
39                  Object   map(Object   o);
40                  /**
41                  * Returns the composition of this morphism with another.
42                  */
43                  Morphism compose(Morphism m) throws UndefinedCompositionException;
44          }
45  
46          /**
47          * This interface defines a hom-set.
48          */
49          interface HomSet {}
50  }
51  
52
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