What else do simplicial sets classify?

["Joyal, André" <joyal.andre@uqam.ca>]

Dear Andrej,

I do not know what you mean by a bounded linear order.

But I know that the topos of simplicial sets
is classifying strict intervals.

(an interval [a,b] is strict if its endpoint a and b are different)

  bounded linear orders = strict intervals?

Best, 
André

-------- Message d'origine--------
De: Andrej Bauer [mailto:andrej.bauer@andrej.com]
Date: sam. 31/07/2010 03:55
À: categories list
Objet : categories: What else do simplicial sets classify?
 
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

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