# Processes come intuitively

Processes come intuitively to us; descriptions of processes appear independently all across science and engineering, in the form of diagrams, flowcharts or prose. We draw them all the time, but that does not mean that we always know how to interpret them: many engineering diagrams do not have clear formal semantics, so we relegate them to serve just for intuition and inspiration.

Diagrams deserve better: we wlil lift diagrams from mere intuitions to mathematical structures themselves – we will defend the legitimate and exceptional conceptual mathematics we now have to talk about processes and diagrams. Our framework for process theories is that of monoidal cateogries: processes that compose sequentially and in parallel, passing resources around, form symmetric monoidal categories; diagrams that depict these exchanges are no less than a sound and complete formal syntax for symmetric monoidal categories.