Categorical Calculus and Algebra for Multi-Model Data

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 multi-model databases within the categorical paradigm.We propose two formal query languages: categorical calculus and categorical algebra, by extending relational calculus and relational algebra respectively for multi-model databases.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.