正则范畴中的Aczel-Mendler互模拟
Aczel-Mendler Bisimulations in a Regular Category
AI总结：
本文在一般正则范畴和拓扑斯中推广Aczel-Mendler互模拟，证明其无需选择公理即可对复合封闭，并在温和条件下与其他余代数定义一致，最后给出多个实例。
摘要：
Aczel-Mendler互模拟是系统间多种计算关系的余代数扩展。通常假设底层范畴满足某种形式的选择公理，以使互模拟的集合具有理想性质，如对复合封闭。本文将该定义推广到一般正则范畴和拓扑斯中。我们证明这一定义：1）在不使用选择公理的情况下对复合封闭；2）在更温和的条件下与其他类型的余代数公式化一致；3）当范畴满足正则选择公理时与通常定义一致。特别地，拓扑斯情形在很大程度上依赖于幂对象，我们在此过程中恢复了若干有利性质。最后，我们描述了Stone空间、用于名字传递的拓扑斯以及环上模中的几个例子。
英文摘要：
Aczel-Mendler bisimulations are a coalgebraic extension of a variety of computational relations between systems. It is usual to assume that the underlying category satisfies some form of the axiom of choice, so that the collection of bisimulations enjoys desirable properties, such as closure under composition. In this paper, we accommodate the definition in general regular categories and toposes. We show that this general definition: 1) is closed under composition without using the axiom of choice, 2) coincides with other types of coalgebraic formulations under milder conditions, 3) coincides with the usual definition when the category satisfies the regular axiom of choice. In particular, the case of toposes heavily relies on power-objects, for which we recover some favourable properties along the way. Finally, we describe several examples in Stone spaces, toposes for name-passing, and modules over a ring.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
