FOM: Re: Russell paradox for naive category theory
Todd Wilson
twilson at csufresno.edu
Tue May 11 18:34:41 EDT 1999
Stephen G Simpson 11 May 1999 15:15:22 (responding to Carsten Butz):
> > The Russell paradox for naive category theory you try to sell here
> > as new is at least 30 years old. ...
>
> You seem to be saying that my version of the Russell paradox for naive
> category theory (details in my posting of 11 May 1999 01:11:25) has
> been known for a long time. I feel that there is some reason to doubt
> what you are saying (see below). Therefore, I would appreciate a
> reference, even if the reference is only an informal allusion in some
> published paper, conference proceedings, newsgroup, oral history,
> report of an informal conversation, folklore, or whatever.
Here's one referece for this well-known piece of folklore (there are
no doubt others): it appears as an elementary exercise (3L, p. 37),
in the book "Abstract and Concrete Categories" by Adamek, Herrlich,
and Strecker:
3L. Quasicategories as Objects. Show that one cannot form the
"quasicategory of all quasicategories". [Hint: Russell's paradox
appears again.]
The context is a discussion on categories of categories. In Chapter 2
of this book (titled "Foundations"), a distinction is made between
sets, classes, and conglomerates, essentially adding one more level of
"largeness" to the usual one. These size distinctions lead to a
corresponding distinction between small categories, large categories,
and quasicategories.
--
Todd Wilson
Computer Science Department
California State University, Fresno
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