Timeline for What is Barr-Beck?
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
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| Oct 7, 2021 at 14:38 | comment | added | Tom Leinster | @TimCampion Thanks to varkor here, we now know that the "crude" as well as the "precise" monadicity theorems are due to Beck. (That's not to deny that other versions are due to Barr, of course.) So it's not accurate to say that Beck's original theorem was hard to use, because the crude/easy-to-use version was in fact the first theorem he stated. Of course, very few of us could have known this, because that note wasn't made publicly available until varkor and John Kennison dug it out this year. | |
| Feb 18, 2021 at 20:01 | answer | added | Noah Snyder | timeline score: 9 | |
| Feb 18, 2021 at 0:19 | history | became hot network question | |||
| Feb 17, 2021 at 23:17 | history | edited | Francesco Polizzi | CC BY-SA 4.0 |
added 5 characters in body
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| Feb 17, 2021 at 19:31 | comment | added | Friedrich Knop | Thanks. I informed the editors of MathSciNet. | |
| Feb 17, 2021 at 19:21 | comment | added | Yemon Choi | Just to confirm that they are indeed the same person, and the thesis has been re-typeset and disseminated as tac.mta.ca/tac/reprints/articles/2/tr2abs.html | |
| Feb 17, 2021 at 19:18 | vote | accept | Friedrich Knop | ||
| Feb 17, 2021 at 18:25 | answer | added | Alexander Campbell | timeline score: 25 | |
| Feb 17, 2021 at 16:43 | comment | added | Tim Campion | Recall that "triple" is just the old-timey way to say "monad". I don't know why Barr's name specifically is attached, but another great thing about Toposes, triples, and theories mentioned by Sasha above is that they prove maybe half a dozen different versions of the monadicity theorem. Beck's original version can be hard to use, sort of like the General Adjoint Functor Theorem -- the "special" versions have more restrictive, but easier-to-check, hypotheses. Maybe one particular version of the theorem is Barr's. | |
| Feb 17, 2021 at 16:42 | comment | added | Balazs | They must be the same mathematician: the author "Beck, Jon" (with Barr) of "Acyclic models and triples", 1966 must be the same as the author "Beck, Jonathan Mock" of TRIPLES, ALGEBRAS AND COHOMOLOGY, Thesis 1967. Wikipedia agrees, see article on "Jonathan Mock Beck (aka Jon Beck)". | |
| Feb 17, 2021 at 16:27 | answer | added | Carlo Beenakker | timeline score: 7 | |
| Feb 17, 2021 at 16:25 | comment | added | Sasha | If I remember correctly you can find the theorem in M. Barr, Ch. Wells, “Toposes, triples and theories”, Repr. Theory Appl. Categ., 12 (2005), 1–288. | |
| Feb 17, 2021 at 16:18 | history | asked | Friedrich Knop | CC BY-SA 4.0 |