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](http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.29.4282&rep=rep1&type=pdf) 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](https://arxiv.org/pdf/math/0510664.pdf) in section 3.7, where they discuss 2-dimensional open-closed TQFT which obviously contains ordinary TQFT.



Original reference for generators and relations of 2-dimensional TQFT
Have you looked at Joachim Kock's book "[Frobenius algebras and 2D topological quantum field theories](https://mat.uab.cat/%7Ekock/TQFT.html)"?


