在一个模型上的过度拓扑
The over-topos at a model
摘要：
与模型的几何理论在任意topos，我们关联的网站，通过赋予一类广义元素的模型与Grothendieck拓扑，我们称之为先行拓扑。然后，我们表明，相关联的层拓扑，我们称之为过拓扑在给定的模型，承认一个典型的全连通态射给给定的基础拓扑，并满足泛性质推广的一个拓扑的共定位在一个点。我们首先处理的情况下的基础拓扑的集，全球元素足以描述我们的网站的定义，在这种情况下，我们还介绍了一个几何理论分类的拓扑，其模型可以识别的模型同态对（内化）模型。然后，我们制定和证明的一般声明，在任意拓扑，其中涉及堆栈的广义元素的模型。最后，我们研究了几何和2-范畴方面的over-topos建设，展示它作为一个bilimit的双范畴的Grothendieck toposes。
英文摘要：
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 case of the base topos of sets, where global elements are sufficient to describe our site of definition; in this context, we also introduce a geometric theory classified by the over-topos, whose models can be identified with the model homomorphisms towards the (internalizations of the) model. Then we formulate and prove the general statement over an arbitrary topos, which involves the stack of generalized elements of the model. Lastly, we investigate the geometric and 2-categorical aspects of the over-topos construction, exhibiting it as a bilimit in the bicategory of Grothendieck toposes.
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