|Category theory is a flourishing branch of
mathematics that has the exploration of analogy as one of its major
uses. I will give a very brief and naive introduction to the concepts of
"category" and "functor". Then I will give simple definitions of a
"species of structure F" and a "structure of species F over a finite set
U", illustrated by numerous examples. I will then show what a
"molecular" species is, give all examples of molecular species on a
small number of elements, and use an example to show how every species
can be decomposed
into a "sum" of molecular species. From there I will show how to count
the number of molecular species that there can be on a given finite set
of n elements, and what two chemists found about that in 1929. To
conclude, I will mention what an atomic species is, and show how any
molecular species can be decomposed into a "product" of atomic species.
Where can we go from there? The answer during the talk!