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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?

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    $\begingroup$ " But, it is true that "abstract nonsense" theorists are a disparaging bunch." Citation needed. $\endgroup$ – zibadawa timmy Sep 14 '14 at 1:42
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    $\begingroup$ Disparaging sense of humor. en.wikipedia.org/wiki/Abstract_nonsense The term is used endearingly... $\endgroup$ – Rachmaninoff Sep 14 '14 at 1:44
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    $\begingroup$ Why do you want to close this question? I can give you more examples of the use of "folkloric" in papers. I just want to know what is meant by such a statement, since it is used in publications. Please look at Barr's paper, page 512. $\endgroup$ – Rachmaninoff Sep 14 '14 at 1:47
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    $\begingroup$ You could actually quote a whole sentence using the word. That might help. $\endgroup$ – Thomas Andrews Sep 14 '14 at 1:52
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    $\begingroup$ @ThomasAndrews Point taken. $\endgroup$ – Rachmaninoff Sep 14 '14 at 1:58
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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.

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    $\begingroup$ We really need a modern EGA-like treatment of all major branches of mathematics in order to gather and organize these thousands of "folklore" results, so that they become citable and will survive future generations. $\endgroup$ – Martin Brandenburg Sep 14 '14 at 2:33
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    $\begingroup$ @MartinBrandenburg They'll survive because they're widely "cited" and the folklore theorem is typically stated when it's used. Anyone who reads 20th/21st-century mathematics comes across these results so they're not going to disappear for as long as people are using the results that depend on them. $\endgroup$ – David Richerby Sep 14 '14 at 11:01

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