Geodesic
Partial Toposes
Theory and applications of categories, Tome 11 (2003), pp. 309-320.

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

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.
Classification : 18B25, 18D30
Keywords: fibred categories, partial toposes 
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     author = {Jean B\'enabou and Thomas Streicher},
     title = {Partial {Toposes}},
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     year = {2003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2003_11_a12/}
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Jean Bénabou; Thomas Streicher. Partial Toposes. Theory and applications of categories, Tome 11 (2003), pp. 309-320. http://geodesic.mathdoc.fr/item/TAC_2003_11_a12/