Re: What else do simplicial sets classify?

["Prof. Peter Johnstone" <P.T.Johnstone@dpmms.cam.ac.uk>]

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



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