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Modeling the integration between specifications and verification for cylindricity based on category theory

机译：基于类别理论的圆柱度规格与验证之间的集成建模

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Geometrical product specifications (GPS) is a standard system defined by ISO/TC213 which covers the standardization for micro- and macro-geometry specifications to make it suitable for the requirements of modern technologies. In addition, it integrates specifications and verification to make geometrical specifications more unambiguous and unique. Data modeling is a primary task in building an integrated information system for the application of geometrical characteristics consistent with the GPS standard system. It is feasible to extend this data modeling method to the whole GPS information system. This paper presents data modeling for the integration between specifications and verification for cylindricity consistent with GPS based on the category theory. The categorical data modeling method represents and stores all the elements and the relationships between them concerning the specifications and the verification process for cylindricity by categories, objects and morphisms; the established categories can be extended flexibly; the relationships between the objects were refined by pull back structures; and the manipulations of the model, such as query and the closure of query, are realized successfully by functor transforms in category theory.
机译：几何产品规范（GPS）是由ISO / TC213定义的标准系统，涵盖了微观和宏观几何规范的标准化，使其适合现代技术的要求。此外，它还集成了规格和验证，以使几何规格更加明确和独特。数据建模是构建集成信息系统以应用与GPS标准系统一致的几何特征的首要任务。将这种数据建模方法扩展到整个GPS信息系统是可行的。本文提出了一种基于类别理论的数据建模模型，用于规范与GPS圆柱度验证之间的集成。分类数据建模方法按类别，对象和形态来表示和存储所有有关规格和圆柱度验证过程的元素及其之间的关系;既定类别可以灵活扩展;对象之间的关系通过拉回结构得以完善。通过类别理论中的函子变换，成功实现了模型的查询，查询关闭等操作。

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