## 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

The functions should further satisfy the following functorial properties:

1. For all bijections and ,

2. For the Identity Map ,

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.