Combinatorial species(This article is about a concept in combinatorial mathematics. There is also an article on the concept of species used in biology.)
For example, the "species of permutations" maps each finite set A to the set of all permutations of A, and each bijection from A to another set B naturally induces a bijection from the set of all permutations of A to the set of all permutations of B. Similarly, the "species of partitions" can be defined by assigning to each finite set the set of all its partitions, and the "power set species" assigns to each finite set its power set.
- Need to explain how to add, multiply, compose, and differentiate combinatorial species.