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arXiv · 1505.04987

On toposes generated by cardinal finite objects

Simon Henry
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Abstract

We give a characterizations of toposes which admit a generating family of objects which are internally cardinal finite (i.e. Kuratowski finite and decidable) in terms of "topological" conditions. The central result is that, constructively, a hyperconnected separated locally decidable topos admit a generating family of cardinal finite objects. The main theorem is then a generalization obtained as an application of this result internally in the localic reflection of an arbitrary topos: a topos is generated by cardinal finite objects if and only if it is separated, locally decidable, and its localic reflection is zero dimensional.

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Simon Henry. 2016-04-05. On toposes generated by cardinal finite objects. https://arxiv.org/abs/1505.04987

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