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Names of references, and fixed arXiv link, while this is on the front page
LSpice
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The example I first learned was the following: a 2-D TQFT is equivalent to a Frobenius algebra.

This is discussed and stated as a folk theorem by Voronov in Topological field theories, string backgrounds and homotopy algebras; later, a careful proof was written up in Two dimensional topological quantum field theories and Frobenius algebras and published by Lowell Abrams. See also the book Frobenius algebras and 2D topological quantum field theories by Joachim Kock.

Paul Johnson
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