论文标题
部分可观测时空混沌系统的无模型预测
A Formal Category Theoretical Framework for Multi-model Data Transformations
论文作者
论文摘要
多家房和多模型数据库管理系统中的数据集成和迁移过程极大地受益于数据和模式转换。转换的严格建模是一个复杂的问题。数据和模式转换字段散布着多个不同的变换框架，工具和映射。这些通常是特定领域的，缺乏固体理论基础。我们的第一个目标是为关系，图形和层次数据模型和实例定义类别理论基础。每个数据实例表示为称为函子的类别理论映射。当KAN使用功能形式表示该实例时，我们将数据和模式转换形式化。 kan升降机是一种理论构造类别，该构造由两个满足某个通用属性的映射组成。在这项工作中，两个映射对应于模式转换和数据转换。
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.
