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 -categories and prove that filter quotients preserve the structure of an elementary -topos and in particular lift the filter quotient of the underlying elementary topos. We then specialize to the case of filter products of -categories and prove a characterization theorem for equivalences in a filter product.
Then we use filter products to construct a large class of elementary -toposes that are not Grothendieck -toposes. Moreover, we give one detailed example for the interested reader who would like to see how we can construct such an -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 类别并证明过滤商保留了基本元素的结构 -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 -格洛腾迪克以外的地方 -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-类别,但希望避免使用有关过滤器的技术。