revised preprint available

[Susan Niefield <niefiels@union.edu>]

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.