Timeline for Why did Bourbaki's Élements omit the theory of categories?
Current License: CC BY-SA 4.0
45 events
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| Aug 18, 2019 at 22:30 | history | edited | YCor | CC BY-SA 4.0 |
made title less biased (Bourbaki didn't ignore categories, but didn't incorporate them in their books)
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| Aug 18, 2019 at 19:40 | review | Close votes | |||
| Aug 19, 2019 at 15:23 | |||||
| Aug 18, 2019 at 17:55 | history | reopened |
Francois Ziegler paul garrett Carlo Beenakker Fred Rohrer Emil Jeřábek |
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| Aug 16, 2019 at 19:41 | history | edited | Francois Ziegler |
edited tags
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| Aug 15, 2019 at 20:42 | history | made wiki | Post Made Community Wiki by Todd Trimble | ||
| Aug 15, 2019 at 20:02 | comment | added | AGenevois | An interesting discussion about Bourbaki can be found here: youtube.com/watch?v=QqR459KxDVU (in French). In particular, categories are mentioned. | |
| Aug 14, 2019 at 9:05 | review | Reopen votes | |||
| Aug 14, 2019 at 11:34 | |||||
| Apr 26, 2018 at 18:13 | review | Reopen votes | |||
| Apr 27, 2018 at 5:36 | |||||
| Apr 18, 2016 at 12:06 | comment | added | Fred Rohrer | Well, since very recently, the published Bourbaki treatise also introduces categories - cf. TA.II.3.1! | |
| Feb 9, 2015 at 15:36 | comment | added | Paul Taylor | The person who would have introduced Bourbaki to categories was Charles Ehresmann. He died in 1979 but he had a huge number of students, many of whom are still active, not least his widow, and could give an authoritative answer to this question. They should be allowed and invited to do so. | |
| Feb 7, 2015 at 22:38 | review | Reopen votes | |||
| Feb 7, 2015 at 23:06 | |||||
| Nov 4, 2013 at 6:44 | review | Reopen votes | |||
| Nov 5, 2013 at 13:30 | |||||
| Sep 10, 2013 at 13:01 | review | Reopen votes | |||
| Sep 10, 2013 at 16:24 | |||||
| Sep 9, 2013 at 12:58 | review | Reopen votes | |||
| Sep 9, 2013 at 14:29 | |||||
| May 25, 2013 at 1:44 | comment | added | Todd Trimble | @Wlodzimierz: some quick observations on "subjective and argumentative". I've been observing MO culture for a while; although I think the general question is interesting and worthwhile, the tone could suggest that you've already made up your mind what you think the answer should be. Also: a possibly problematic word is "ignore" (probably not literal, as all Bourbakistes were highly aware of categories). Asking "what is wrong with some guys?" and "preferring to bitch" might reinforce the impression of argumentativeness. (This is not to be critical; just pointing out possible red flags.) | |
| May 25, 2013 at 0:49 | comment | added | Włodzimierz Holsztyński | @quid, I'll be taking more time from now on before accepting an answer. Perhaps common sense should tell me this too. Thank you for your advice. About the closure, it'd be beneath me to try to reopen it (I prefer bitching about it :-). I am sorry to miss potentially more answers which would be so interesting to me. | |
| May 25, 2013 at 0:16 | comment | added | user9072 | @Wlodzimierz Holsztynski: in general I think you should not feel any pressure to accept an answer quickly (waiting a or even several days is certainly fine, in particular for somewhat open or vaguer questions). But thanks for the positive feedback. Regarding closure, three things: first, please, do not be upset about it. second, if you want you'd be able to vote to reopen (as it is your own question and you have 250+ points, link below the question), third you can if you like start a thread on meta (link at the top, extra signup but easy and instant) presenting an argument for reopening. | |
| May 24, 2013 at 23:40 | comment | added | Włodzimierz Holsztyński | Hi Michał, nice to see you again! But the question is already closed as "... argumentative"--what's wrong with some guys? (I hoped to learn quite a bit more). | |
| May 24, 2013 at 23:25 | history | edited | Włodzimierz Holsztyński | CC BY-SA 3.0 |
cosmetic
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| May 24, 2013 at 23:22 | comment | added | Michal R. Przybylek | @Wlod, nice question! And great to see you here :-) I learned much reading your posts on pl.sci.matematyka. | |
| May 24, 2013 at 22:58 | history | closed |
Theo Johnson-Freyd David White Alain Valette Qiaochu Yuan user6976 |
not constructive | |
| May 24, 2013 at 22:24 | history | edited | Włodzimierz Holsztyński | CC BY-SA 3.0 |
an invitation
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| May 24, 2013 at 22:16 | history | edited | Włodzimierz Holsztyński | CC BY-SA 3.0 |
Chronology
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| May 24, 2013 at 22:11 | comment | added | Fred Rohrer | @Ryan: I do not know if good old Nick is writing right now, but his newest book - the new edition of Algèbre VIII - appeared only last year. | |
| May 24, 2013 at 21:58 | comment | added | Włodzimierz Holsztyński | @Todd & @quid, when a good "Answer" appears to my "Question" then I feel a pressure to accept it without too much delay. I wish we could accept more than one "Answer". (And I truly liked @quid's answer). | |
| May 24, 2013 at 21:55 | comment | added | Włodzimierz Holsztyński | Thank you @Ryan for improving (correcting!) the title of my "Question". (I had some doubts myself too but was resigned to my inadequate English). | |
| May 24, 2013 at 21:47 | comment | added | Ryan Reich | No disrespect to the author, but I have altered the title a bit from "Why has Bourbaki ignored..." to "Why did Bourbaki ignore...". Normally this would be ambiguously wrong, but to the best of my knowledge Bourbaki is no longer writing :) | |
| May 24, 2013 at 21:46 | history | edited | Ryan Reich | CC BY-SA 3.0 |
Correct tense
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| May 24, 2013 at 21:20 | answer | added | Fred Rohrer | timeline score: 15 | |
| May 24, 2013 at 20:32 | answer | added | Colin McLarty | timeline score: 23 | |
| May 24, 2013 at 19:32 | comment | added | user9072 | I was also slightly suprised when seeing a relatively quick accept for this (type of) question. | |
| May 24, 2013 at 15:52 | answer | added | Todd Trimble | timeline score: 30 | |
| May 24, 2013 at 13:53 | answer | added | Ronnie Brown | timeline score: 11 | |
| May 24, 2013 at 11:22 | comment | added | Todd Trimble | It seems to me that quid's answer, while not bad, was accepted a bit prematurely. In particular, there are people who have made a careful study of the available historical record; among MO users, I think Colin McLarty would be in a position to give a more complete and authoritative answer. I will see whether I can contact him, to alert him to this thread. | |
| May 24, 2013 at 9:19 | comment | added | Brad Rodgers | @Qfwfq: At least some of the members of Bourbaki did not view what was being done as a pedagogical exercise. For instance, "People just misused [Bourbaki's] books; they were never meant for university teaching..." - JP Serre. (sms.math.nus.edu.sg/smsmedley/Vol-13-1/…) | |
| May 24, 2013 at 0:59 | vote | accept | Włodzimierz Holsztyński | ||
| May 24, 2013 at 0:23 | comment | added | Martin | @Wlodimierz Holsztynski: A related discussion can be read in Armand Borel's Twenty-five years with Nicolas Bourbaki ams.org/notices/199803/borel.pdf on page 378, where a short account of the story of the congrès du foncteur inflexible is given. It discusses Grothendieck's proposal how they should treat sheaf theory and why that route wasn't chosen. | |
| May 23, 2013 at 23:40 | answer | added | user9072 | timeline score: 32 | |
| May 23, 2013 at 23:33 | comment | added | Włodzimierz Holsztyński | @Michael, if you have any reference (link) to a discussion among Bourbaki about theory of category I would be interested and grateful for it. | |
| May 23, 2013 at 23:27 | comment | added | Włodzimierz Holsztyński | @Qfwfq: Bourbaki certainly was not afraid of being unorthodox, was revolutionary (which is hard to believe today :-). Many at the time, and later too (e.g. Vladimir Arnold) had strong misgivings about Bourbaki philosophy. Bourbaki was considered by them and many others (not me :-) anything but pedagogical. | |
| May 23, 2013 at 23:05 | comment | added | The User | @Charles Staats If I remember correctly, they did not use full ZFC in early editions, they left out the axiom of replacement and used epsilon calculus for cardinal assignment. However, I think you can do a lot of elementary, insightful category theory without talking about categories of categories or something like that. Well–you need classes. But I do not think Bourbaki was dogmatic about not using classes. | |
| May 23, 2013 at 22:43 | comment | added | Michael Greinecker | There are much more qualified people to comment here, but if I recall correctly, it was extensively discussed whether to include categories or not. | |
| May 23, 2013 at 22:36 | comment | added | Charles Staats | Another note is that something like the "category of sets" is not a set. To talk about it, you need some axioms other than the strict ZFC axioms on which all of Bourbaki's math is based. Thus, to discuss category theory in ways that include its current practice, Bourbaki would need either to augment the existing foundations in one way or another, or to adapt some sort of unconventional and probably very awkward conventions that would make their category theory work in ZFC, probably at the price of making it much harder to use. | |
| May 23, 2013 at 22:25 | comment | added | Qfwfq | Wasn't the Bourbaki treatise meant to be "pedagogical"? Perhaps (but I don't have objective information about this) at the time category theory was considered too advanced to be put in a foundational set of volumes... | |
| May 23, 2013 at 22:04 | history | asked | Włodzimierz Holsztyński | CC BY-SA 3.0 |