Deconstructing UML, Part 1: Modeling Classes with Categories

Published

May 13, 2021

Author(s)

Sarala Padi, Spencer J. Breiner, Eswaran Subrahmanian, Ram D. Sriram

Abstract

In this paper we analyze elements of the Unified Modeling Language (UML), specifically the class diagram, and propose an simplified alternative language based on a branch of mathematics called category theory (CT). We argue that modeling in CT provides a richer and more precise formal structure than UML, while still supporting many of the intuitive and diagrammatic features which engineers appreciate in UML. Deep ties connect CT to formal logic, physics and computer science, helping to connect our CT-based models to simulation and implementation. We proceed by walking through the constructs of the class diagram and showing how the same information can be captured using CT constructions. As we do, we see that some UML constructs are redundant while others smuggle in assumptions which ought to be made explicit. Thus we argue that the use of CT in information modeling can make our models less ambiguous, more precise and more formal.

Citation

NIST Interagency/Internal Report (NISTIR) - 8358

Report Number

8358

NIST Pub Series

NIST Interagency/Internal Report (NISTIR)

Pub Type

NIST Pubs

Download Paper

https://doi.org/10.6028/NIST.IR.8358

Local Download

Keywords

Unified Modeling Language, Class Diagram, Category Theory, Semantics of UML

Citation

Padi, S. , Breiner, S. , Subrahmanian, E. and Sriram, R. (2021), Deconstructing UML, Part 1: Modeling Classes with Categories, NIST Interagency/Internal Report (NISTIR), National Institute of Standards and Technology, Gaithersburg, MD, [online], https://doi.org/10.6028/NIST.IR.8358, https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=931719 (Accessed November 4, 2025)