The Twelvefold Way

Items: Categories:

f : D → R, d=|D|, r=|R|
Items
Balls
Domain (D)		Categories
Urns
Range (R)		 Arbitrary
(unrestricted)		 Injective
(one-to-one)
 Surjective
(onto)
Labeled/Labeled
Unlabeled/Labeled
Labeled/Unlabeled
Unlabeled/Unlabeled