Date: Wed, 12 Apr 1995 23:53:35 -0300 (ADT)
Subject: Does Set exist outside Set?

Date: Tue, 11 Apr 95 22:50:05 PDT
From: Vaughan Pratt <pratt@cs.stanford.edu>


Can one prove the existence of Set in "any other" category?

More specifically, if category theory is developed *entirely* within
the topos of reflexive graphs (for a suitable notion of "entirely"),
can one still prove that there exists a category with four adjoints
left of Yoneda?  This is of course Rosebrugh and Woods' nifty one-axiom
characterization of Set, which one might call the uvwxy theorem.
(Automata theory also has a uvwxy theorem, namely the pumping lemma for
context-free languages, making the name context-sensitive...)

Vaughan Pratt