Categorical Structure of Asynchrony

We investigate a categorical framework for the semantics of asynchronous communication in networks of parallel processes. Abstracting from a category of asynchronous labeled transition systems, we formulate the notion of a categorical model of asynchrony as a uniformly traced monoidal category with diagonals, such that every morphism is total and the focus is equivalent to a category of complete partial orders. We present a simple, non-deterministic, cpo-based model that satisfies these requirements, and we discuss how to refine this model by an observational congruence. We also present a general construction of passing from deterministic to non-deterministic models, and more generally, from non-linear to linear structure on a category.