On toposes generated by cardinal finite objects
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.
Keywords
Cite
@article{arxiv.1505.04987,
title = {On toposes generated by cardinal finite objects},
author = {Simon Henry},
journal= {arXiv preprint arXiv:1505.04987},
year = {2016}
}
Comments
18 pages. The logical framework has been clarified by the use of M.Shulman stack semantics. Proofs of the last section have been improved. Some typos corrected