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.
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.
"after a vast amount of literature on triples" you should recall that also after a vast amount of literature on monads e.d.
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.
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.
Oh dear, I think I might have recently increased the set of synonyms. A couple of years ago, in conversation with Weng Kin Ho, I suggested the following terminology. Involutive category: a category C, with a functor c : C^op --> C and an isomorphism alpha : c^2 --> id_C Strictly involutive category: a category C with a functor c : C^op --> C such that c^2 = id_C Locally involutive category: a category C with an identity-on-objects functor c : C^op --> C such that c^2 = id_C. Weng Kin used this terminology in his PhD thesis (pp 17-18) http://www.cs.bham.ac.uk/~wkh/papers/thesis.pdf I wasn't aware of the other terminologies. Paul
participants (5)
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Eduardo Dubuc -
Paul B Levy -
Prof. Peter Johnstone -
tholen＠mathstat.yorku.ca -
Zinovy Diskin