The PROP for commutative monoids

Dear Categorists - A student of mine is wondering who first noticed this fact: if you take a skeleton of the category of finite sets and make it into a strict symmetric monoidal category using cartesian product, it's the "free strict symmetric monoidal category on a commutative monoid object". Or in other words, it's the PROP for commutative monoids. He noticed that in 2001, Teimuraz Pirashvili wrote a paper "On the PROP corresponding to bialgebras": http://arxiv.org/abs/math/0110014 Pirashvili says this fact is "well known", and gives a proof, but no reference. Can you help us dig deeper? It's just a matter of getting the history right. Best, jb [For admin and other information see: http://www.mta.ca/~cat-dist/ ]