Poly'21 @VLDB – A Formal Category Theoretical Framework for Multi-Model Data Transformations

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 naturally 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 certain constraints. The two mappings correspond to schema transformation and data transformation.

The link to the paper: https://sites.google.com/view/poly21/program