Dear Michael, Thank you for your "trying" to answer. I have waited for a few days for a "real" answer from Peter Johnstone to whom my question was, for obvious reasons, primarily addressed. When my mail to you was completed I received a very complete and nice answer from Ross Street, and then, two more by Marta Bunge. I want to thank them, and tell them that I shall try to give, in detail, complete answers to their mails.That is, if the "higher authorities" who control this list consider that this "mathematico- historical" disicussion could be as important as, say, the more than 20 mails devoted to the over all important discussion about role versus r\ole. I shall wait a week before answering Ross and Marta, in case I get more answers, and, who knows, one can always dream, one by "Peter Johnstone himself". I shall make do with your answer, but before I make a few comments about it, in order for you to understand them, it would be better to read carefully my comments on the "non-answer" by Johnstone to a question which concerned his book; After all "he" was responsible for not mentioning a 1970 "Comptes Rendus" note, very frequently referred to, and attributing the result to John Beck, without any reference to a published, or unpublished, paper of his. Not even to a paper of another author, dating of before 1970, and crediting John Beck with precisely, I insist on it, the same theorem that was given in my joint note with Roubaud, and which is attributed to Beck in "The Elephant"! He is no "baby in the woods", and if he writes something in an important book, published by Oxford University Press, he must be able to explain his decision. I hope to hear from him soon, and; since I am on this unpleasant matter, I hope he shall also answer the following questions: (i) In the long Appendix of his Topos Theory (TT), there is only one theorem.It is due to a student of mine, Jean Celeyrette, whose thesis is mentioned in the bibliography of (TT). Why has the name of J.Geleyrette totally disappeared from the much much longer bibliography of (El)? (ii) Same question about my Louvain paper on "Distributors" or "Profunctors", which he uses in an essential manner in (El) without ever mentioning my name. It was also in the bibligraphy of (TT) and again absent from the bibliography of (El) With the note on descent, and many other examples, this is getting to be "a habit" with Peter Johnstone. I advise him to lose very quickly such habits, they might become dangerous for one's health. ------------------------------------------------------------------------ - Considering what I said about Johnstone, you won't be surprised if I tell you that your answer does not fully satisfy me (and that is an understatement) Since oblique, bold, etc fonts are not accepted in this list, I shall write between quotation marks any parts of your mail I want to comment upon, and without quotation marks my comments. (i) "I certainly heard Jon lecture on this a number of times" What does your "this" precisely refer to? (ii) " PUblication? Lot's of luck. A quick glance at MathSciNet shows that there are an awful lot of J. Beck's, at least one J.M. Beck and at least one Jonathan Beck, but no paper by our Jon Beck on descent theory. As for precise statement, don't even think about it". I cannot, and will not, take this for an answer. My joint theorem with Roubaud is a precise statement, and so is its reformulation by Johnstone. He was obviously too young in 1970 to have heard it, if was the same, directly from Beck. How can he be sure it was the same, if you are not? Moreover I am vain enough to consider it was an important result, because it established a connection between two important theories, namely: descent and triples. There were enough good mathematicians in North America in the late 60's, and certainly, at least one of them, would have grasped its importance, and given one, or many, applications, as we did, Roubaud and myself, in the same note where we stated the theorem. Where are these applications? (iii) "But my recollection was only whether a triple could descend across a functor. There were cocyle conditions that were necessary and sufficient. I think the "Beck-Chevalley condition" was a simple example" I do not merely "think", I am sure, that I learnt Chevalley's condition, from Chevalley, in 1964. At that time fibered categories, "invented" by Grothendieck, were almost "unheard of" in the "North American" category community. The first reference I know of is Gray's paper in the 1965 conference of La Jolla, where he refers to Chevalley's lost notes for 1962 lectures at Berkeley. Even now, they are often presented in terms of "indexed categories", under the influence of W.V. Lawvere's 1971 "Perugia Notes". I thus doubt very much that, whatever Beck's talent,in 1964, when his PhD thesis was not yet completed, he might have had anything like Chevalley's condition for arbitrary fibrations. I "think" I was wrong to "compromise" and to accept that what I called the Chevalley Condifion should have Beck's name assocoated to it, and I'm sure that, from now on, I shall call Chevalley condition what was up to now called Beck-Chevalley condition, only because I insisted that it was historically a nonsense to call it, as the North American school did, "Beck" condition ! (iii) "At one point, Jon told my wife with some regret that, thanks to my insistence, he was finally published. He seemed constitutionally incapable of putting his thoughts in public." When and where was he "finally published"? (iv) "I think you can suppose that if PTJ couldn't find it, it isn't there except in the (increasingly feeble) memories of those who heard him." I do not merely "think", I know that you are a mathematician, (and that of course for me means a good one). Thus, if Beck's formulation had been so blatantly simple and precise as mine and Roubaud's you wouldn't need an effort of memory to remember it, with precision. And this is of course also true for many of the mathematicians "who heard him". Although I was not among the happy few who heard him, I don't need a great effort of memory to remember Beck' Triplability Theorem. I "think" also that Johnstone had better find a more credible justification than mere "hear so" and "think that", Jean Benabou, out of solidarity with the so-called "category-community" might not, even if he is angry, rise such a fuss. But Jacques Roubaud has no such solidarity, is very angry, and he is known, and respected, in "circles" much wider that the few handful of persons that some of us tend to "think of" as the center of the world. I do not "think", we are the center of the world, I am even sure, we are not !

Dear colleagues, I have had, so far, no less than 22 answers to my mail about references for the "Beck" theorem mentioned in the Elephant, all of them supporting Peter Johnstone. An I am not counting "references" which "referred" to other "reliable references" such as Dusko Pavlovic an Claudio Hermida in one of the THIRTEEN mails sent by Marta Bunge! I intend to answer in detail to all these mails. It might take a few days, because I don't have such a powerful team helping me in my research: bibliography, recollections, etc. It takes ALL of my time, 12 hours a day, but I enjoy EVERY MINUTE OF IT. I congratulate Peter Johnstone to have such a numerous and faithful army of supporters. But as you say in English: "The more the merrier". So Johnstone might use the delay before my answer to find a few dozen more supporters. It will make me even more happy, and I'm afraid he will need ALL the support he can get!

[Note from moderator: I agree with Dusko's remarks below. After 48 hours no further items will be posted in this thread. Moderate language will be used in any contributions posted during that time.] am i the only one who is not enjoying these arguments on CATEGORIES any more? i started worrying: ** is there something special in category theory that attracts all these ** argumentative people? is it that being argumentative somehow helps you ** with math, and then arguing with the symbols on a piece of paper and on ** the blackboards then somehow overflows into your social life?... and then i remembered that sometime in the early 90s, when the mailing lists started spreading, there were such flame wars on every mailing list. and they went on deep into the mid 90es. so i thought, maybe the category theorists are not more argumentative than other people. maybe it's just that some of them started using email a bit later, so they are discovering the medium of flame war just now. so i waved my hand. but now great jean benabou brought my little name into his argument, together with claudio hermida. i am not sure what he means, but it sounds like claudio and i are the examples of unreliable sources. well, honestly, jean, i really don't have the remotest idea what i have done to deserve the unhonorable mention. not having worked in anything related to this area for more than 10 years, and not having done much worth mentioning before that, AND not really depending on this community either for my job or for my reputation, i am simply just surprised... even after 10 min of scouring my memory, the only *remote* possibility that occurs to me is that i gave a talk in oberwolfach, cca 1994, describing the preservation conditions necessary and sufficient for descent, and effective descent ((monadicity is sufficient, but not necessary)). after my talk, or maybe in the middle, jean benabou stood up and said: "Mathematics Should Be Beautiful." i started mumbling that i was sorry if mine was so ugly ((was it my hand drawn diagrams on the slides?)), but that some people would say that mathematics should first of all be true... by which point we were both talking --- and max kelly hushed us both down. (we miss you, max!) i really really respect jean benabou's work. i also respect paul taylor's work. i have learned a great deal from both of them. but i really don't like how they argue their cases on this mailing list. (and if i am alone in that, then maybe i dont even belong here.) i agree that mathematics should be beautiful. short of that, since the truth doesn't always obey everyone's taste, math should at least be elegant, or decent. but if we are able to produce beautiful, or elegant, or at least decent mathematical arguments --- why is it that we generate such unpleasant nonmathematical arguments? can we please please stop? all the best, -- dusko On Fri, 9 Nov 2007, JeanBenabou wrote:

Dear colleagues,

I have had, so far, no less than 22 answers to my mail about references for the "Beck" theorem mentioned in the Elephant, all of them supporting Peter Johnstone. An I am not counting "references" which "referred" to other "reliable references" such as Dusko Pavlovic an Claudio Hermida in one of the THIRTEEN mails sent by Marta Bunge! I intend to answer in detail to all these mails. It might take a few days, because I don't have such a powerful team helping me in my research: bibliography, recollections, etc. It takes ALL of my time, 12 hours a day, but I enjoy EVERY MINUTE OF IT. I congratulate Peter Johnstone to have such a numerous and faithful army of supporters. But as you say in English: "The more the merrier". So Johnstone might use the delay before my answer to find a few dozen more supporters. It will make me even more happy, and I'm afraid he will need ALL the support he can get!