Site characterizations for geometric invariants of toposes

Details Site characterizations for geometric invariants of toposes Site characterizations for geometric invariants of toposes

2011-12-12

arxiv.org/abs/1112.2542v1

Mathematics

Category Theory

17 pages

Scientific paper

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.

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