The 8th International Conference on Applied Category Theory (ACT) took place at the University of Florida on June 2-6, 2025. Prof. Jiaheng Lu attended this conference and gave a presentation on how to perform query processing for multi-model databases with category theory.
Multi-model databases are designed to store, manage, and query data in various models, such as relational, hierarchical, and graph data, simultaneously. Our research provides a theoretical basis for querying categorical databases. We propose two formal query languages: categorical calculus and categorical algebra, by extending relational calculus and relational algebra respectively. We demonstrate the equivalence between these two languages of queries. We propose a series of transformation rules of categorical algebra to facilitate query optimization. Finally, we analyze the expressive power and computation complexity for the proposed query languages.
Find the link of the full paper.