Situated Transition Systems

We construct a monoidal category of open transition systems that generate material history as transitions unfold, which we call situated transition systems. The material history generated by a composite system is composed of the material history generated by each component. The construction is parameterized by a symmetric strict monoidal category, understood as a resource theory, from which material histories are drawn. We pay special attention to the case in which this category is compact closed. In particular, if we begin with a compact closed category of integers then the resulting situated transition systems can be understood as systems of double-entry bookkeeping accounts.