Origin of Species
The proposal rests on the use of combinatorial species, introduced long ago by Andre Joyal, the great category theorist. A lot of our playing with trees and funny infinite sums in M theory is about combinatorial species, although we haven't yet worried about the exact relation. A species is just a functor from the groupoid of finite sets (and bijections) to itself. Recall that this groupoid is a lot like the finite ordinals, which correspond to cardinalities of sets. An example that often comes up in topos theory is the functor that sends each set to its power set, namely the set of all subsets of the set. This example illustrates the general idea of sending a collection of objects to another collection, equipped with some structure related to the original.