本项目将研究Quantaloid-enriched范畴(简称为Q-范畴)中的连续性、拓扑结构和范畴结构方面的性质，目标是建立基于Q-范畴的量化Domain理论基础，从而为应用量化Domain理论研究计算机程序设计语言的形式语义学提供数学基础。主要研究内容包括：(1)基于weight类的概念，建立Q-范畴的一般连续性理论，特别地建立定向连续Q-范畴的概念并研究其相关性质；(2)利用以Quantaloid为基础的Q-拓扑空间的概念，研究连续Q-范畴上的拓扑结构；(3)对特定的连续Q-范畴寻找其Cartesian闭子范畴；(4)讨论Q-范畴与概念格的关系，建立Q-范畴关于信息系统的表示。

This project will study the continuity, topological structures and categorical structures in quantaloid-enriched categories （Q-categories for short） with the purpose to establish the foundation for the study of quantitative domain theory through quantaloid-enriched categories. This will provide mathematical foundation for the application of quantitative domain theory in the study of the semantics of programming languages. The contents of the project include: (1) establishing the continuity theory for Q-categories based on the concept of weights, especially we will establish the directed continuity theory for Q-categories; (2) studying the topological structures in continuous Q-categories by the topological theory based on Q-categories; (3) searching Cartesian closed subcategories for certain continuous Q-categories; (4) studying the relations between Q-categories and concept lattices, and establishing the representation of Q-categories with respect to information systems.