I often will see the word "folklore" used in papers on category theory, e.g. in Barr's paper on Isbell Duality, he states a result, which he proves, is "folkloric", on page 512:
The following folkloric result goes back, in dual form in degree zero, to the fact that the diagonal chain complex associated to a double simplicial object is homotopic to its total complex
At first, I assumed it meant a result which everyone took as being true but no proof could be found in the publications (but not because a proof was't found). The term folklore makes me think it was a result found in the early days of research in category theory, 1950s-70s. It also has a disparaging tone to it, implying it might be untrue. But, it is true that "abstract nonsense" theorists are a self-disparaging bunch.
Could someone give me a good example of a result which has a folkloric feel to it?
Yes, "folklore" simply means "I think this result is well known, but I cannot find a paper that can be cited for it". The connotation is that the result has been known for some time by people in the field, but not often stated explicitly in writing, rather being passed down by word of mouth.
The term "folklore" is not limited in any way to category theory, it's common in many areas of research mathematics.