Towards a unified framework for decomposability of processes

TL;DR

This paper explores the concept of process decomposability within monoidal categories, providing formal definitions and arguing for a structuralistic interpretation, with implications for mathematical modeling and engineering applications.

Contribution

It offers a precise definition of process decomposability in monoidal categories and critiques common interpretations of parallel processes, emphasizing a structuralistic perspective.

Findings

Provides formal definitions of process decomposability

Argues against viewing parallel processes as coupled

Highlights advantages of category theory for modeling

Abstract

The concept of process is ubiquitous in science, engineering and everyday life. Category theory, and monoidal categories in particular, provide an abstract framework for modelling processes of many kinds. In this paper, we concentrate on sequential and parallel decomposability of processes in the framework of monoidal categories: We will give a precise definition, what it means for processes to be decomposable. Moreover, through examples, we argue that viewing parallel processes as coupled in this framework can be seen as a category mistake or a misinterpretation. We highlight the suitability of category theory for a structuralistic interpretation of mathematical modelling and argue that for appliers of mathematics, such as engineers, there is a pragmatic advantage from this.