Site characterizations for geometric invariants of toposes

Olivia Caramello

We discuss the problem of characterizing the property of a Grothendieck topos to satisfy a given `geometric' invariant as a property of its sites of definition, and indicate a set of general techniques for establishing such criteria. We then apply our methodologies to specific invariants, notably including the property of a Grothendieck topos to be localic (resp. atomic, locally connected, equivalent to a presheaf topos), obtaining explicit site characterizations for them.

Keywords: Grothendieck topos, site characterizations, geometric logic

2010 MSC: 03G30, 18C10, 18B25

Theory and Applications of Categories, Vol. 26, 2012, No. 25, pp 710-728.

Published 2012-11-23.

Revised 2013-02-20. Original version at

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