Categorical Calculus and Algebra for Multi-Model Data
Abstract
Multi-model databases are designed to store, manage, and query data in various models, such as relational, hierarchical, and graph data, simultaneously. In this paper, we provide 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.
Cite
@article{arxiv.2603.10081,
title = {Categorical Calculus and Algebra for Multi-Model Data},
author = {Jiaheng Lu},
journal= {arXiv preprint arXiv:2603.10081},
year = {2026}
}
Comments
In Proceedings ACT 2025, arXiv:2603.07595. arXiv admin note: substantial text overlap with arXiv:2504.09515