  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.
