论由蕴涵代数产生的范畴结构：从拓扑到装配
On categorical structures arising from implicative algebras: from topology to assemblies
AI总结：
本文将蕴涵代数分别作为 locale 和部分组合代数的推广，把类拓扑概念及装配范畴等结构抽象到任意蕴涵代数上，并系统研究其范畴性质与相互关系。
摘要：
蕴涵代数最近由 Miquel 引入，旨在提供一种统一的模型概念，涵盖最相关且最常用的模型，例如可实现性（经典的和直觉主义的）以及力迫。在这项工作中，我们首先将蕴涵代数视为 locale 的推广，并将若干类拓扑概念扩展到蕴涵代数的领域，同时给出各种具体例子。然后，我们将关注点转向把蕴涵代数视为部分组合代数的推广。我们将装配范畴、划分装配和 modest 集合的概念抽象到任意蕴涵代数上，并深入研究它们的范畴性质及相互关系。
英文摘要：
Implicative algebras have been recently introduced by Miquel in order to provide a unifying notion of model, encompassing the most relevant and used ones, such as realizability (both classical and intuitionistic), and forcing. In this work, we initially approach implicative algebras as a generalization of locales, and we extend several topological-like concepts to the realm of implicative algebras, accompanied by various concrete examples. Then, we shift our focus to viewing implicative algebras as a generalization of partial combinatory algebras. We abstract the notion of a category of assemblies, partition assemblies, and modest sets to arbitrary implicative algebras, and thoroughly investigate their categorical properties and interrelationships.
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。
