I know it has something to do with TFT, but precisely how? Here I copied down a paragraph in a (computer science paper? almost, theoretic physicist doing quantum computing) The last condition is really hard to believe. And why do they arise in nature? Here is why, it is related to 2d TFT. the circle gives the vector space, the merge and splitting of circle gives that algebra structure. Are this higher category enough? Why so simple? How about 3d picture?

I am lead to here because he says $QH^*(X)$ is a Frobenius algebra. Why? Where is the circle and where is the pair-of-pants? Well well, 3 point function defining product is crying out loudly saying “I am a pair-of-pants”.