What is the original reference where it was first proven that the generators and relations of the 2-dimensional cobordism category are those of commutative Frobenius algebras?
I've seen this article by Abrams being cited for it. But when I look into it I only find "Completeness of the relations follows easily by inspection" in proposition 12. I'm confused since I thought the completeness of relations was the only non-trivial part. The only place where I have seen something that looks like an actual proof is in this later article by Lauda and Pfeiffer in section 3.7, where they discuss 2-dimensional open-closed TQFT which obviously contains ordinary TQFT.