Re: Two categories or 2-categories?

Re: Two categories or 2-categories?

[Max Kelly]

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.

Two categories or 2-categories

[baez]

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?  






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