多模型数据转换的形式范畴理论框架
A Formal Category Theoretical Framework for Multi-model Data Transformations
摘要：
在多存储和多模型数据库管理系统中的数据集成和迁移过程从数据和模式转换中受益匪浅。转换的严格建模是一个复杂的问题。数据和模式转换领域散布着多种不同的转换框架、工具和映射。这些通常是特定领域的，缺乏坚实的理论基础。我们的第一个目标是为关系、图和层次数据模型和实例定义范畴理论基础。每个数据实例都被表示为一个称为函子的范畴理论映射。我们形式化的数据和模式转换为Kan升降机利用函表示的实例。Kan提升是一种范畴理论构造，它由两个满足某种泛性质的映射组成。在这项工作中，这两个映射对应于模式转换和数据转换。
英文摘要：
Data integration and migration processes in polystores and multi-model database management systems highly benefit from data and schema transformations. Rigorous modeling of transformations is a complex problem. The data and schema transformation field is scattered with multiple different transformation frameworks, tools, and mappings. These are usually domain-specific and lack solid theoretical foundations. Our first goal is to define category theoretical foundations for relational, graph, and hierarchical data models and instances. Each data instance is represented as a category theoretical mapping called a functor. We formalize data and schema transformations as Kan lifts utilizing the functorial representation for the instances. A Kan lift is a category theoretical construction consisting of two mappings satisfying a certain universal property. In this work, the two mappings correspond to schema transformation and data transformation.
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。
