Subject: categories: withdrawal of preprint

From: Susan Niefield <[email-masked]>
Date: Thu, 2 Jul 1998 22:10:56 -0400 (EDT)

The paper "Exponentiablity and Single Universes" by Marta Bunge and Susan
Niefield, recently announced on the site ww1.union.edu/~niefiels has been
temporarily withdrawn.  A revised version will be posted soon.  The paper
contained an erroneous result - namely, that for an arbitrary small
category B, the category UFL/B of Giraud-Conduche fibrations over B is a
topos.  A counterexample has been found by Peter Johnstone.

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From: Susan Niefield <[email-masked]>
Date: Tue, 21 Jul 1998 13:55:47 -0400 (EDT)

A revised version of the following reprint is available at

        http://www1.union.edu/~niefiels/ESU.ps
        http://www1.union.edu/~niefiels/ESU.dvi

EXPONENTIABILITY AND SINGLE UNIVERSES
by Marta BUNGE and Susan NIEFIELD

ABSTRACT - In this paper, we first consider known universes for pairs of
opposite notions such as those of discrete fibrations/discrete
opfibrations and of open/closed locale inclusions, and then extrapolate
these in order to introduce new single universes for open/closed
inclusions of subcategories and for functions/distributions on a topos.  A
key factor that these notions have in common is exponentiability in the
ambient category.  Along the way, we (1) prove that, for a factorization
linearly ordered small category B, the category of discrete
Giraud-Conduche fibrations over B is a (model generated) topos, (2)
characterize locally closed inclusions in the category Cat of small
categories, (3) investigate ``generalized coverings'' in topos theory,
including branched coverings, cuts, and complete spreads, and (4) examine
the preservations of exponetiability under the passage from Cat/B to the
category of Grothendieck toposes over the presheaves PB.