FOM: category theory

[Steve Awodey]

>      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
>      References:
>
>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
>make.
>
> > 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
again here.

Steve Awodey
Assistant Professor
Philosophy Department
Carnegie Mellon University