In category theory there is a 'folk' model structure on the category Cat, where the weak equivalences are the equivalences of categories. There is a similar model structure on 2Cat, with weak equivalences being equivalences of 2-categories (weak ones, I presume) The former was not written down for a long time, but the latter was published by Steve Lack. Andre Joyal is not in favour of the name 'folk model structure', and there was discussion on this at the nForum (starting at that comment and continuing). That the existence of this model structure is a 'folk' theorem is a bit of folklore itself, as pointed out by Joyal at this comment.
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