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The over-topos at a model

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The over-topos at a model
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31
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CC Attribution 3.0 Unported:
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For a model of a geometric theory in a Grothendieck topos, we can construct the over-topos of this model classifying homomorphisms above it. In this talk, we provide a site theoretic description of this construction. In the case of a set-valued model, a site will be provided by the category of global elements together with a certain antecedents topology, and we can describe a canonical geometric theory classified by this over-topos. In the general case, one must consider a more complicated category of generalized elements ; an antecedent topology then can be recovered through a notion of lifted topology, whose construction can be understood in the framework of stacks and comorphisms of sites. This is joint work with Olivia Caramello.