FOM: category theory
awodey at cmu.edu
Tue Feb 22 10:22:21 EST 2000
> To: fom at math.psu.edu
> Subject: FOM: category theory, cohomology, group theory, and f.o.m.
> From: Stephen G Simpson <simpson at math.psu.edu>
> Date: Tue, 22 Feb 2000 00:21:24 -0500 (EST)
> In-Reply-To: <vkaputqwf5b.fsf at gs2.sp.cs.cmu.edu>
> Organization: Department of Mathematics, Pennsylvania State University
>Reply to Andrej Bauer's posting of Feb 21, 2000.
>You asked me to help you find the earlier FOM discussions of category
>theory. I think November 1997 to February 1998 was the most
>extensive. The conclusion was that category theory is no good as
>a global foundational setup, because (i) it is more complicated than
>set theory, (ii) it depends on set theory, (iii) it has no underlying
>or motivating foundational picture. There was also a lot of category
>theory discussion on FOM around April-May 1999, about small vs large
>categories, the set-theoretic basis of category theory, etc. Let's
>not go over all this ground again, unless you have some new point to
> > sets, classes and operations can be explained in terms of objects
> > and morphisms.
>No, they can't. This was well covered in the earlier FOM discussion.
As one who expended some effort trying to make the here-mentioned earlier
FOM discussions of category theory informative and productive, I must
register my objection to the moderator's formulation of their "conclusion".
Those were simply Steve Simpson's views, but the discussion never reached
anything like a satisfactory conclusion.
I do agree, however, that nothing is likely to be gained by going over it
Carnegie Mellon University
More information about the FOM