Wikipedia:Articles for deletion/Gabriel–Popesco theorem


 * The following discussion is an archived debate of the proposed deletion of the article below. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in a deletion review).  No further edits should be made to this page.

The result was Withdrawn by nominator.  Running On Brains (talk) 20:57, 30 May 2012 (UTC)

Gabriel–Popesco theorem

 * – ( View AfD View log  •  Stats )

No indication of notability. I prodded this but it was de-prodded without explanation. A reference has since been added but it's not available online, and I suspect it neither calls the theorem the "Gabriel–Popesco theorem" or indicates its notability. A search for "Gabriel–Popesco theorem" turns up a different theorem. Pierre Gabriel lists two theorems with similar names, both of which redirect here. Could be this is being confused with something else. JohnBlackburne wordsdeeds 12:29, 26 May 2012 (UTC)


 * I've not checked notability but the theorem in the MIT lecture notes appears to be the same as the one in the article. Both talk about a functor of an Abelian category, defined through homomorphisms that is full and faithful and has a left-adjoint that is exact. Dricherby (talk) 14:11, 26 May 2012 (UTC)


 * Keep. The lecture notes cited in the nomination expressly reference "the classical Gabriel-Popesco theorem." GBooks and GScholar searches similarly turn up a convincing set of references to the term. Perhaps the article does not present the theorem correctly, or in its standard form, perhaps it does; but those are resolvable content issues, not grounds for deletion. Hullaballoo Wolfowitz (talk) 15:24, 26 May 2012 (UTC)


 * Forgive me if you already know this. It's pretty common in mathematics to restate theorems in the way that's most useful to the person applying the theorem. In some cases, there's really only one way to state the theorem but, in many cases there's no "standard form" as such. For example, even something like "There are infinitely many prime numbers" might get restated as "For any x, there is a prime p > x." Dricherby (talk) 17:58, 26 May 2012 (UTC)


 * comment so what is it called ? Gabriel–Popesco theorem or Gabriel-Popesco theorem for Ab5-categories (the name when I prodded it) or Gabriel–Popescu embedding theorem (the other of two links to it at Pierre Gabriel)? And I agree a theorem can be stated in many forms it's usual for well known theorems to be stated in a particular form, typically the form used when it was first proved.
 * But if these problems are resolved I still don't see that brief mentions of it establish notability. The paper it is from has been cited 40 times, less than once a year, so does not seem notable on academic grounds (not that there is a guideline for that: WP:PROF is for people).-- JohnBlackburne wordsdeeds 22:11, 26 May 2012 (UTC)


 * I'm not sure citation count means a lot. First, online coverage of older papers can be somewhat sketchy so there may be many more citations that just aren't in the database.  Second, once a result becomes sufficiently famous, people don't bother citing the paper it came from, especially if it's in textbooks.  For example, something like Hall's marriage theorem is used all the time but nobody bothers to cite Hall's paper any more because everyone knows what the marriage theorem is — but I've no idea whether the Gabriel-Popesco theorem is at that level.  Category theory is a very specialist area of mathematics that even most mathematicians know little or nothing about; to be honest, I don't think anyone who's not an expert in the area can really say whether this theorem is notable or not (which is why I'm not !voting). Dricherby (talk) 22:27, 26 May 2012 (UTC)
 * Note: This debate has been included in the list of Science-related deletion discussions.  • Gene93k (talk) 23:06, 26 May 2012 (UTC)
 * Whatever variant of the title is used, it should say Gabriel–Popesco, with an en-dash rather than a hyphen, if it's a conjunction of names of two persons, and Gabriel-Popesco, with a hyphen rather than an en-dash, if it's the hyphenated name of one person. Michael Hardy (talk) 02:45, 27 May 2012 (UTC)


 * Keep. This is an important theorem and "Gabriel-Popescu" is a rather standard name for it (and its generalizations). See for instance the use in Wendy Lowen, Michel Van den Bergh, "Deformation Theory of Abelian Categories", Transactions of the American Mathematical Society, Vol. 358, No. 12 (Dec., 2006), pp. 5441-5483 and Leovigildo Alonso Tarrío, Ana Jeremías López, María José Souto Salorio, "Construction of t-Structures and Equivalences of Derived Categories", Transactions of the American Mathematical Society, Vol. 355, No. 6 (Jun., 2003), pp. 2523-2543. The MIT-lectures notes referenced in the nomination also refer to (a slight generalization of) the same theorem. Generally, any theorem that has a name is worthy of coverage as people would want to look it up. Deleting the article would in no way help our readers or improve the encyclopedia. AxelBoldt (talk) 20:01, 27 May 2012 (UTC)


 * withdraw OK, not sure of the protocol for this but given the changes made to the article since nomination I'd like to withdraw my AfD nomination. Mostly it's now clear that there's not two or three theorems named after these two, just one, which means it's clearly the one being referred to and the references for it are sound. I'm still not convinced it's notable enough for it's own article, but it's certainly encyclopaedic so even if not worthy of a standalone article can be merged which does not need a deletion discussion.-- JohnBlackburne wordsdeeds 17:30, 30 May 2012 (UTC)
 * The above discussion is preserved as an archive of the debate. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in a deletion review). No further edits should be made to this page.