On Sat, 31 Jul 2010, Andrej Bauer wrote:
The presheaf category of simplicial sets is the classifying topos for the theory L of a bounded linear order.
In general, there could be other theories which are "Morita equivalent" to L in the sense that their classifying toposes are equivalent to simplicial sets. Are any such known, preferably occurring in nature?
With kind regards,
Andrej
Of course you can write down different presentations for the theory classified by simplicial sets; any set of generators for the topos will give you one. But you're unlikely to find anything familiar: if there were a geometric theory "occurring in nature" whose category of models (in any topos) was equivalent to the category of bounded linear orders, that equivalence would almost certainly be well known. Peter Johnstone [For admin and other information see: http://www.mta.ca/~cat-dist/ ]