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arXiv · 2201.04905

A Formal Category Theoretical Framework for Multi-model Data Transformations

Valter Uotila·Jiaheng Lu
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Abstract

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.

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Valter Uotila, Jiaheng Lu. 2022-01-13. A Formal Category Theoretical Framework for Multi-model Data Transformations. https://doi.org/10.1007/978-3-030-93663-1_2

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