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 [For admin and other information see: http://www.mta.ca/~cat-dist/ ]