Filter quotients and non-presentable (∞, 1)-toposes

[摘要] We define filter quotients of (oo, 1)-categories and prove that filter quotients preserve the structure of an elementary (oo, 1)-topos and in particular lift the filter quotient of the underlying elementary topos. We then specialize to the case of filter products of (oo, 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 (oo, 1)-toposes that are not Grothendieck (oo, 1)-toposes. Moreover, we give one detailed example for the interested reader who would like to see how we can construct such an (oo, 1) category, but would prefer to avoid the technicalities regarding filters. (c) 2021 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

[发布日期] 2021-12-01

[关键词] Elementary topos theory;Higher category theory;Filter quotients