Subject: categories: The proposition O=H

From: Vaughan Pratt <[email-masked]>
Date: Tue, 27 Apr 2004 08:39:28 -0700

Anyone who's subscribed to this list long enough knows that I've been
sufficiently bothered by the disjunction "Sets or categories" as to pester
the list with my botherment periodically.  I bothered the FOM mailing list
with the same question for some years, with rather less civilized responses
on occasion -- that was quite a wild list for a while, but Martin Davis
seems to have done a good job of stabilizing it, too late unfortunately for
those of us who found the repartee counterproductive and moved on before
his administration.

My pestering is not so much to make a nuisance of myself as to get a
satisfactory answer.  So far the answers, on either side, have struck me
as entailing a certain acceptance of the local lore and wisdom bordering
on religion.

I would like to propose a middle ground on which set theorists and
category theorists can meet amicably.  The middle ground is expressed by
the proposition O=H, that objects and homobjects are of the same type.

One of "mathematics" or "short" is defined by the proposition that all
short definitions have been made, all short questions asked already, and
all short theorems either previously proved or now famous open problems.

Before pursuing this line of thought any further I'd like to ask whether
O=H is short in the above sense.  Has it been brought up before, and if so
what are the prevailing views on it?

Vaughan Pratt