• Corpus ID: 233210515

The over-topos at a model

  title={The over-topos at a model},
  author={Olivia Caramello and Axel Osmond},
With a model of a geometric theory in an arbitrary topos, we associate a site obtained by endowing a category of generalized elements of the model with a Grothendieck topology, which we call the antecedent topology. Then we show that the associated sheaf topos, which we call the over-topos at the given model, admits a canonical totally connected morphism to the given base topos and satisfies a universal property generalizing that of the colocalization of a topos at a point. We first treat the… 



Denseness conditions, morphisms and equivalences of toposes.

We establish a general theorem providing necessary and sufficient explicit conditions for a morphism of sites to induce an equivalence of toposes. This results from a detailed analysis of arrows in

Sketches of an Elephant: a topos theory compendium. Vols. 1 and 2, vols. 43 and 44 of Oxford Logic Guides

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Università degli Studi dell'Insubria, via Valleggio 11, 22100 Como, Italy. E-mail address: olivia.caramello@uninsubria.it Institut des HautesÉtudes Scientifiques

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