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.