On 3/5/07, tholen@mathstat.yorku.ca <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
why only few? Recall the Poisson bracket, or Dirac's delta-function, or quaternions (though as a shorthand for 4D complex number it's probably more meaningful than triples) or, say, derivative, which is a basic notion in calculus yet is, in fact, quite a formalistic name. If to talk about general tendencies, then it seems the winner would be a formalistic term (unfortunately). Consider a competition between a meaningful yet too long, or hard to pronounce, or not smooth in some sense term and a meaningless yet short and energetic term, who would win? Many attempts to make terminology and notation in a particular domain entirely consistent failed as soon as they went beyond some reasonable level of consistency. Zinovy Diskin And aren't left-right adjoints, vertical-horizontal morphisms in fibrations of purely typographical ("blackboardial") origin? 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.