We introduce various notions of *partial topos*, i.e. `topos
without terminal object'. The strongest one, called *local topos*,
is motivated by the key examples of finite trees and sheaves with compact
support. Local toposes satisfy all the usual exactness properties of
toposes but are neither cartesian closed nor have a subobject classifier.
Examples for the weaker notions are local homeomorphisms and discrete
fibrations. Finally, for partial toposes with supports we show how they
can be completed to toposes via an inverse limit construction.

Keywords: fibred categories, partial toposes

2000 MSC: 18B25,18D30

*Theory and Applications of Categories*
, Vol. 11, 2003,
No. 13, pp 309-320.

http://www.tac.mta.ca/tac/volumes/11/13/11-13.dvi

http://www.tac.mta.ca/tac/volumes/11/13/11-13.ps

http://www.tac.mta.ca/tac/volumes/11/13/11-13.pdf

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/11/13/11-13.dvi

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/11/13/11-13.ps