发表机构
Stockholm University（斯德哥尔摩大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文基于虚拟超范畴表示拓扑斯，以点的方式刻画几何态射类，引入虚拟超收缩概念，推广收缩与滤过余极限，并给出分离点类的新刻画。
AI 中文摘要
我们基于近期发展，即具有足够点的拓扑斯可表示为配备超收敛数据（又称虚拟超范畴）的点范畴，从而以点的方式刻画几何态射的通常类——满射、嵌入、超连通映射和局部映射。特别地，几何满射的刻画依赖于“虚拟超收缩”的概念，该概念推广了通常的收缩和滤过余极限，将Johnstone关于拓扑空间的子闭包概念范畴化，并为拓扑斯的分离点类提供了新的刻画。
英文摘要
We build on the recent development that toposes with enough points can be represented as categories of points equipped with ultraconvergence data (a.k.a. virtual ultracategories), characterizing usual classes of geometric morphisms --- surjections, embeddings, hyperconnected maps, and localic maps --- in terms of their points. In particular, the characterisation of geometric surjections relies on a notion of "virtual ultraretractions", which generalises usual retractions and filtered colimits, categorifies Johnstone's notion of subclosure for topological spaces, and provides a new characterisation of separating classes of points of a topos.
Comments35 pages
