Re: dagger vs involutive

["Prof. Peter Johnstone" <P.T.Johnstone@dpmms.cam.ac.uk>]

Walter is of course quite right about triples vs. monads. But it is
interesting to compare that with the truly awful example of the
term "comma category" (and of course the 2-categorical notion of
"comma object" which it has spawned). The awfulness derives from the
fact that the term is derived not just from a particular notation,
but from an obsolete notation (Mac Lane, for example, despite his
sterling efforts to kill off "triple", uses the term "comma category"
in his book, even though his notation for it doesn't involve a comma).
How is it that we have never managed to find a more descriptive name
for this concept?

While I'm on the subject, does anyone out there know who invented the
terms "pullback" and "pushout"? They have always seemed to me to be
splendid examples of descriptive terminology, but I've never seen
them attributed to a particular person. (And yes, I know that Peter
Freyd invented "Doolittle diagram"; but that joke wouldn't have been
possible if "pullback" and "pushout" hadn't already been established
terminology.)

Peter Johnstone

On Mon, 5 Mar 2007 tholen@mathstat.yorku.ca wrote:

> Here is an outsider's view on the debate which is all about a
> formalistic (not to say meaningless) vs a meaningful name. There seem
> to be only very few occasions in mathematics when the formalistic name
> won, C*-algebras being a prominent example. In category theory, one is
> reminded of the hot debate of triples vs monads of the 60s and 70s. I
> guess that at the time of the "Zurich triple book" (SLNM 80) most
> people would have predicted that triples had already won the race. Mac
> Lane's book CWM appeared only 2 or 3 years later, after a vast amount
> of literature on triples. But he consistently used the meaningful name
> monad, even though (as far as I know) he had never directly published
> on the subject. You be the judge who won!
>
> Walter Tholen.
>
>
>