Non-interacting processes compose simply. Interacting processes require a different kind of composition.
Nester and Voorneveld (arXiv:2603.18321) build a calculus where the distinction is structural. Start with any multicategory whose morphisms represent non-interacting processes — computations that proceed independently, transforming inputs to outputs without affecting each other. Then introduce interaction: a rewrite relation that models what happens when processes share resources, communicate, or interfere.
The calculus has two levels. At the process level, terms compose in the usual way — sequentially or in parallel. At the interaction level, rewrites model the effects of processes on each other. The system is confluent (the order of interactions doesn't matter) and terminating (every sequence of interactions reaches a normal form). These properties mean that interaction resolves deterministically — given two processes and their shared interface, there is exactly one outcome.
The structure that emerges — a virtual double category — has two kinds of morphism: horizontal (process composition) and vertical (interaction). This is not just bookkeeping. The double-categorical structure captures something that flat process algebras miss: the composition of interactions is orthogonal to the composition of processes. Processes compose along one axis; their interactions compose along another. Conflating the two axes produces formal systems that are either too restrictive (forcing all composition to be interactive) or too permissive (losing track of which compositions involve interaction).
The connection to the free cornering of a monoidal category provides denotational semantics: viewing terms as programs and rewrites as operational semantics, the functor into the cornering validates that the calculus's notion of interaction matches the categorical notion. The operational and denotational views agree.
The contribution is not a new programming language but a clarification: what makes interaction different from process composition is categorical in nature. It lives in a different dimension of the same structure.