In the film "A Beautiful Mind," the first indication that John Nash is regaining his abilities is a conversation with a student ("Galois extensions are really the same as covering spaces!" exclaims Toby, the student). The scene ends with Nash and the student bent over some papers and -- as I heard it -- the student says: "Functor...Two...Categories" (The film's not bad but its relation to Nash's life is tangential. If I had not absorbed a hint from a review, I think I might have stomped out in the middle because of the ridiculous portrayal of what mathematicians do. It turns out that the filmmakers are playing a game -- very effective with most of the audience -- in sliding between perceptions: ours and Nash's.)
I don't know quite what Peter's point is here: there is no difference between the spoken forms of "2-categories" and "two-categories". I think we all write "2-categories", as we write "n-categories" and "w-categories", where I am making-do with "w" for a lower-case Greek omega. Yet Blackwell, Power, and I, when we considered general questions about the algebras for 2-monads and the various kinds of strict and non-strict morphisms of these and some adjunctions between the 2-categories that arise, entitled our paper "Two-dimensional monad theory". I don't think "2-monad theory" would have represented our concerns as well, being capable of interpretation as meaning a wider study than ours, or a narrower one, depending on how it was taken by the reader. To the Australian Research Council, such work is described as research on two-dimensional universal algebra. What do others think? Regards - Max.
Max Kelly writes:
I don't know quite what Peter's point is here: there is no difference between the spoken forms of "2-categories" and "two-categories".
I forget who said what, but I think the issue was that when folks are talking in this movie, you can't easily tell whether they are saying "2-categories" or "two categories", i.e. a couple of categories. This problem comes up a lot in my life, and I am glad to see it finally showing up in a major motion picture! E.g., I must be careful never to say "functor between two categories", replacing it by "functor from one category to another". I would be shocked if they were talking about 2-categories in this movie. Even mentioning categories must seriously diminish their ticket sales, much less 2-categories. On a wholly different note, how are the category theorists in Sydney?
Just saw the movie last night and was alert to the `two' problem more problematic to me was the whole phrase functor (some preposition) 2 categories between? sounded more like `in'?? .oooO Jim Stasheff jds@math.unc.edu (UNC) Math-UNC (919)-962-9607 \ ( Chapel Hill NC FAX:(919)-962-2568 \*) 27599-3250 http://www.math.unc.edu/Faculty/jds On Mon, 31 Dec 2001, Max Kelly wrote:
I don't know quite what Peter's point is here: there is no difference between the spoken forms of "2-categories" and "two-categories". I think we all write "2-categories", as we write "n-categories" and "w-categories", where I am making-do with "w" for a lower-case Greek omega. Yet Blackwell, Power, and I, when we considered general questions about the algebras for 2-monads and the various kinds of strict and non-strict morphisms of these and some adjunctions between the 2-categories that arise, entitled our paper "Two-dimensional monad theory". I don't think "2-monad theory" would have represented our concerns as well, being capable of interpretation as meaning a wider study than ours, or a narrower one, depending on how it was taken by the reader. To the Australian Research Council, such work is described as research on two-dimensional universal algebra.
What do others think?
Regards - Max.
participants (4)
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baez＠math.ucr.edu -
JAMES STASHEFF -
maxk＠maths.usyd.edu.au -
Peter Freyd