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 .