Filter Quotients and Non-Presentable $(\infty,1)$-Toposes

Nima Rasekh

doi:10.1016/j.jpaa.2021.106770

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arXiv · 2001.10088

Filter Quotients and Non-Presentable $(\infty,1)$-Toposes

Nima Rasekh

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Abstract

We define filter quotients of $(\infty,1)$-categories and prove that filter quotients preserve the structure of an elementary $(\infty,1)$-topos and in particular lift the filter quotient of the underlying elementary topos. We then specialize to the case of filter products of $(\infty,1)$-categories and prove a characterization theorem for equivalences in a filter product. Then we use filter products to construct a large class of elementary $(\infty,1)$-toposes that are not Grothendieck $(\infty,1)$-toposes. Moreover, we give one detailed example for the interested reader who would like to see how we can construct such an $(\infty,1)$-category, but would prefer to avoid the technicalities regarding filters.

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Nima Rasekh. 2020-01-27. Filter Quotients and Non-Presentable $(\infty,1)$-Toposes. https://doi.org/10.1016/j.jpaa.2021.106770

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