Partial respponse to Jean Benabou

Partial respponse to Jean Benabou

[Prof. Peter Johnstone]

I intend in due course to reply to the long message posted by Jean Benabou
on 30 October. Unfortunately I am very busy at present (I am lecturing
six days a week this term) and I shall not have time to do so for a while.

However, Jean's evident desire for a quick response from me on the
subject of Proposition B1.5.5 in the Elephant cannot be ignored. Since I
wasn't around at the time this result was first proved, I had to rely
on the recollections of those older than myself as to its provenance:
I am grateful to Ross Street and Bill Lawvere for their recent postings
confirming the impression I received many years ago that Jon Beck had
indeed had this idea in the late 1960s. It seems clear from their
accounts that Beck had the idea independently of Benabou and Roubaud;
which of them had it first seems impossible to establish at this stage.

Since their work was independent, I should of course have credited
Benabou--Roubaud as well as Beck at this point in the text of the
Elephant, and I apologize for not having done so. The reason, I must
confess, was that I had simply not come across the Benabou--Roubaud
paper; clearly, this was a failure of due diligence on my part.

Incidentally, in reply to a comment in Marta Bunge's posting, I did
distribute draft copies of the Elephant to a number of colleagues, and
invite their comments, before it was published. None of them picked up
this particular point -- though I am not blaming them for that; the
fault was of course mine.

Regarding the fact that Celeyrette's thesis, and Jean's Louvain notes on
"Les Distributeurs", are not in the bibliography of the Elephant, there
is a simple reason for this: I decided at an early stage that, in order to
keep the size of the bibliography within bounds, it was necessary to limit
it to published books and papers, and to exclude unpublished theses and
other articles circulated only in preprint form. (Hence also the absence
of Beck from the bibliography.) I did relent in one or two cases
(actually as a result of comments from one of the people who saw the
drafts before publication) where a result appearing in someone's thesis,
and not subsequently published, was specifically referred to in the text.

Peter Johnstone