[Math] Examples of “folk theorems”

Question

In this post, Justin gives a quote about Raoul Bott that has this line in it:

He talked about 'folk' theorems… theorems everyone knew, but were never written down.

What are some good/interesting examples of these types of theorems?

Answer 1

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; later, a careful proof was written up and published by Lowell Abrams. See also the book by Joachim Kock.