Exponentiability and single universes

Citation
M. Bunge et S. Niefield, Exponentiability and single universes, J PURE APPL, 148(3), 2000, pp. 217-250
Citations number
39
Categorie Soggetti
Mathematics
Journal title
JOURNAL OF PURE AND APPLIED ALGEBRA
ISSN journal
00224049 → ACNP
Volume
148
Issue
3
Year of publication
2000
Pages
217 - 250
Database
ISI
SICI code
0022-4049(20000503)148:3<217:EASU>2.0.ZU;2-Y
Abstract
In this paper, we first consider known universes for pairs of opposite noti ons 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 fu nctions/distributions on a topos. Along the way, we (1) prove that, for a f actorization linearly ordered small category B, the category of discrete Gi raud-Conduche fibrations over B is a (model generated) topos, (2) character ize locally closed inclusions in the category Cat of small categories, and (3) investigate "generalized coverings" in topos theory as one of several p ossible single universes for local homeomorphisms and complete spreads over a topos. (C) 2000 Elsevier Science B.V. All rights reserved.