F(x) of a species F can be defined:
:where is the cardinality of for any set A having n elements; e.g., .

Some examples: writing ,
* The species of sets (traditionally called E, from the French "ensemble", meaning "set") is the functor which maps A to {A}. Then , so .
* The species S of permutations, described above, has . .
* The species T₂ of ordered pairs (2-tuples) is the functor taking a set A to A². Then and .

Calculus of species

1.Previous
3.Next