RE: References

RE: References

[Marta Bunge]

Dear Jean,

Here is what seems to be my 14th letter to you in this connection. It is a
friendly reminder that I did not "support" Peter Johnstone. Here is an
extract at the end of my November 4 official intervention ("Response to
Benabou") in categories.


>It seems then to be an error on the part of Peter Johnstone to have
>attributed Proposition 1.5.5 in E1 (page 297) to Beck and not to Benabou
>and Roubaud. At the end of this section on "Descent Conditions and Stacks"
>(page 303), the references given in El 1 are Bourn, Bunge and Pare, Giraud,
>Grothendieck, Reiterman and Tholen, but curiously enough, not
>Benabou-Roubaud. I am sure that Peter will repair this error should a
>second edition of the Elephant ever appear.

In fact, I do not think that Peter Johnstone "supports" himself in this
matter -- he has admitted the error. What more do you want him to say?


However, in view of the evidence, provided by Street and Lawvere, of the
possibility that Jon Beck may have discovered this theorem independently and
even talked about it, as the abstract in the Notices of the AMS (1967) seems
to indicate, it seems fair after all to add his name to yours in connection
with it. It is common pratice in mathematics to give credit for ideas
disseminated at lectures, even more so if these ideas are mentioned in an
abstract. This does not take away your own credit.

This is my very last letter on the subject, private or official.

With best wishes,
Marta




************************************************
Marta Bunge
Professor Emerita
Dept of Mathematics and Statistics
McGill University
805 Sherbrooke St. West
Montreal, QC, Canada H3A 2K6
Office: (514) 398-3810
Home: (514) 935-3618
marta.bunge@mcgill.ca
http://www.math.mcgill.ca/~bunge/
************************************************




>From: JeanBenabou <jean.benabou@wanadoo.fr>
>To: Categories <categories@mta.ca>
>Subject: categories: References
>Date: Fri, 9 Nov 2007 00:28:50 +0100
>
>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!
>
>
>

_________________________________________________________________
Express yourself with free Messenger emoticons. Check out
freemessengeremoticons.ca

Re: References

[Keith Harbaugh]

The recent postings of Jean Benabou have, it seems to me,
had at least two effects:

1. promoting a better understanding of
the historical truth
of how, in what order, and by whom various categorical ideas
were discovered and disseminated, and

2. in confronting possible inaccuracies
in some other mathematicians understanding of the same,
making some of those other mathematicians, and no doubt some bystanders,
uncomfortable (to say the least)
at the inflammatory tone of some of M. Benabou's remarks.

I think the first effect is salutary and beneficial to the understanding of
the past,
and thus also, to the future.
It would be unfortunate and, I believe, harmful,
to prevent M. Benabou from assisting the mathematical community
in obtaining better understanding of the categorical past.

On the other hand,
at least one thing should not have been said on this mailing list,
or elsewhere:
"I advise [Peter Johnstone] to lose very quickly such habits,
they might become dangerous for one's health."
(Benabou's message of November 3).
Threats, explicit or implict, to the reputation of individuals are
permissible
(one's reputation is a function of the collective body),
while threats to one's "health" are not.

As a proposal, and request to the moderator to modify
his "48 hour" limit imposed in his addition to Dusko Pavlovic's message of
November 9,
I suggest the following rule:

The discussion and argument may continue
to the point of diminishing returns (repetition and triviality).
Threats of illegal action (such as the one quoted above) will not be
allowed.
A positive and respectful tone,
accepting the good faith and intentions of all parties,
is required.

Again, the intent is to keep the good (increased understanding),
while avoiding the bad (unnecessary insults and threats).

By the way, I am, shall we say,
an interested bystander to the discussions on this list.
The fact that my contributions to category theory are nil
may, on the one hand,
mean that I do not have the right to intrude in this matter,
or on the other hand,
may mean that I can be more objective,
without axes to grind or anything to defend or assert.
You choose which to believe.

In any case, thanks to all parties,
Rosebrugh, Benabou, Johnstone and all the others
for your vast and much appreciated contributions
both to mathematical research and to this list.

Sincerely,
Keith Harbaugh

Re: References

[Dusko Pavlovic]

[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!
>
>
>

References

[JeanBenabou]

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!

Re: References

[jim stasheff]

Perhaps some one took notes on paper and hasn't thrown them out?
It would be great to ad them to Jon's small nachlass.

jim

On Nov 2, 2007, at 8:30 PM, Michael Barr wrote:

> I certainly heard Jon lecture on this a number of times.  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.  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.
>
> 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.
>
> 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.
>
> On Fri, 2 Nov 2007, JeanBenabou wrote:
>
>> Dear colleagues,
>>
>> I hope someone, and in particular Prof. Peter Johnstone, will help me
>> with the following information. I thought I had, with Jacques
>> Roubaud, proved in our joint note at the "Comptes Rendus" which I
>> mentioned in my previous mail proved a theorem on Monads and Descent.
>> I must have been mistaken, and also the many persons who quoted this
>> note, because in El Proposition 1.5.5 is the same theorem, but
>> attributed to J. Beck.
>>
>> I immediately "rushed" to the monumental bibliography of El to find
>> the reference, and there, big surprise, there was no J. Beck at all
>> among the 1262 references.
>>
>> Thus i'd greatly appreciate to have the date and paper of the paper
>> where Beck proved this theorem, and the precise statement he made, in
>> particular, did he prove his theorem in the general context of
>> fibered or indexed categories, or only in some very special case.
>>
>> Many thanks for your help
>>
>>
>
>

References

[JeanBenabou]

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 !

Re: References

[Michael Barr]

I certainly heard Jon lecture on this a number of times.  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.  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.

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.

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.

On Fri, 2 Nov 2007, JeanBenabou wrote:

> Dear colleagues,
>
> I hope someone, and in particular Prof. Peter Johnstone, will help me
> with the following information. I thought I had, with Jacques
> Roubaud, proved in our joint note at the "Comptes Rendus" which I
> mentioned in my previous mail proved a theorem on Monads and Descent.
> I must have been mistaken, and also the many persons who quoted this
> note, because in El Proposition 1.5.5 is the same theorem, but
> attributed to J. Beck.
>
> I immediately "rushed" to the monumental bibliography of El to find
> the reference, and there, big surprise, there was no J. Beck at all
> among the 1262 references.
>
> Thus i'd greatly appreciate to have the date and paper of the paper
> where Beck proved this theorem, and the precise statement he made, in
> particular, did he prove his theorem in the general context of
> fibered or indexed categories, or only in some very special case.
>
> Many thanks for your help
>
>

References

[JeanBenabou]

Dear colleagues,

I hope someone, and in particular Prof. Peter Johnstone, will help me
with the following information. I thought I had, with Jacques
Roubaud, proved in our joint note at the "Comptes Rendus" which I
mentioned in my previous mail proved a theorem on Monads and Descent.
I must have been mistaken, and also the many persons who quoted this
note, because in El Proposition 1.5.5 is the same theorem, but
attributed to J. Beck.

I immediately "rushed" to the monumental bibliography of El to find
the reference, and there, big surprise, there was no J. Beck at all
among the 1262 references.

Thus i'd greatly appreciate to have the date and paper of the paper
where Beck proved this theorem, and the precise statement he made, in
particular, did he prove his theorem in the general context of
fibered or indexed categories, or only in some very special case.

Many thanks for your help

References

[Eva SCHLAEPFER]

Hello,

can someone give me references for the following two constructions?

- in a closed monoidal category, the multiplication on the inner hom is
normally defined as the transpose of 

B tens (B -o B) tens (B -o B) ---> B tens (B -o B) ---> B

where tens is the tensor product, -o the inner hom, the first map ev tens
(B-o B) and the second ev.

- A,B,C objects in a monoidal category and A is a monoid. 
If B is an A-right-module in the sense that there is a morphism 
f: B tens A ---> B which satisfies certain axioms and C is a
A-left-module g:A tens C ---> C, then the quotient B tens_A C can be
defined as the coequalizer of the two
maps 
B tens g: B tens A tens C ---> B tens C   
and 
f tens C: B tens A tens C ---> B tens C

Thanks,

Eva Schlaepfer