Species

A species of structures is a rule  which

1. Produces, for each finite set , a finite set ,

2. Produces, for each bijection , a function

(1)

The functions  should further satisfy the following functorial properties:

1. For all bijections  and ,

(2)

2. For the identity map ,

(3)

An element  is called an -structure on  (or a structure of species  on ). The function  is called the transport of -structures along .

REFERENCES:

Bergeron, F.; Labelle, G.; and Leroux, P. Combinatorial Species and Tree-Like Structures. Cambridge, England: Cambridge University Press, p. 5, 1998.