Re: Where does the term monad come from?
Michael Barr <barr <at> math.mcgill.ca>
2009-04-01 18:13:55 GMT
I have told this story many times, but I guess one more can't hurt. Of
course, it was originally used by Leibniz to describe the set of
infintesimals surrounding an ordinary point.
In the summer (or maybe late spring, the Oberwohlfach records will show
this) of 1966, there was a category meeting there. It was, as far as I
know, the third meeting ever devoted to categories. The first was the
first Midwest Category meeting, an invitation affair that consisted of
five people from Urbana (Jon Beck, John Gray, Alex Heller, Max Kelly, and
me), John Isbell and Fred Linton visiting Chicago that year, and a couple
people from U. Chicago, Mac Lane who was the host and arranged to pay our
expenses, Dick Swan, and maybe a couple others. The second was in La
Jolla and this was the third. The attendance consisted of practically
everyone in the world who had any interest in categories, with the notable
exception of Charles Ehresmann.
What, with one exception, most categorists call monads had by that time
been called "Standard constructions", "fundamental constructions" (in a
little-known paper by Jean-Marie Maranda pointed out to me by Peter
Huber), and, of course, "Triples". The latter was created by
Eilenberg-Moore and I once asked Sammy (who was known to agonize over good
terminology--e.g. "Exact") why. He answered that the concept seemed to be
of little importance, so he and John Moore spent no time on it! So much
for the predictive ability of a great mathematician.
At any rate, the big unanswered question of the meeting, where the
importance of the concept was becoming clear (Jon and I had proved our
Acyclic models theorem, for example, and the fact of the triplebleness of
compact Hausdorff spaces over sets, along with many mor familiar
examples), the search was on for a better name. We tried many ideas (mine
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