Syntactic characterizations of properties of classifying toposes

Olivia Caramello

We give characterizations, for various fragments of geometric logic, of the class of theories classified by a locally connected (respectively connected and locally connected, atomic, compact, presheaf) topos, and exploit the existence of multiple sites of definition for a given topos to establish various results on quotients of theories of presheaf type.

Keywords: Grothendieck topos, site characterizations, geometric logic, presheaf topos

2000 MSC: 03G30, 18C10, 18B25

Theory and Applications of Categories, Vol. 26, 2012, No. 6, pp 176-193.

Published 2012-03-06.

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