Observers, experiments and agents: a comprehensive approach to parallelism

The aim of this paper is to introduce an enriched categorical approach which provides a unifying theory for many notions of parallelism and concurrency. Our constructions are based on a concept of observational equivalence induced by a set of observers, which perform experiments over agents. The outcome of those experiments is a set of computations together with an agreement information. In order to model parallel agents and their behaviours we use categories enriched over a bicategory. They provide an abstract framework with entities at three levels: i) observers at level 0, ii) experiments at level 1, and iii) computing agents at level 2. This comprehensive framework is parametric with respect to the nature of the observers, which may observe totally or partially ordered sets of actions in a discrete or continuous manner. The relationship between various models for parallelism can be expressed in terms of the change of the base bicategory of observers.