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Filter quotients and non-presentable (∞,1)-toposes
Journal of Pure and Applied Algebra ( IF 0.8 ) Pub Date : 2021-04-14 , DOI: 10.1016/j.jpaa.2021.106770
Nima Rasekh

We define filter quotients of (,1)-categories and prove that filter quotients preserve the structure of an elementary (,1)-topos and in particular lift the filter quotient of the underlying elementary topos. We then specialize to the case of filter products of (,1)-categories and prove a characterization theorem for equivalences in a filter product.

Then we use filter products to construct a large class of elementary (,1)-toposes that are not Grothendieck (,1)-toposes. Moreover, we give one detailed example for the interested reader who would like to see how we can construct such an (,1)-category, but would prefer to avoid the technicalities regarding filters.



中文翻译:

过滤商和不可表示的(∞,1)-求和

我们定义的过滤商 1个类别并证明过滤商保留了基本元素的结构 1个-topos,特别是提升基础基本topos的过滤商。然后,我们专门研究以下情况的过滤器产品1个类别并证明过滤器产品中的等价特征定理。

然后,我们使用过滤器产品来构造一大类基础 1个-格洛腾迪克以外的地方 1个-姿势 此外,我们为感兴趣的读者提供了一个详细的示例,希望了解我们如何构造这样一个1个-类别,但希望避免使用有关过滤器的技术。

更新日期:2021-04-14
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