A categorical construction for modelling causal structures within a general class of process theories

A categorical semantics for causal structure

We present a categorical construction for modelling causal structures within a general class of process theories that include the theory of classical probabilistic processes as well as quantum theory.Unlike prior constructions within categorical quantum mechanics, the objects of this theory encode fine-grained causal relationships between subsystems and give a new method for expressing and deriving consequences for a broad class of causal structures.We show that this framework enables one to define families of processes which are consistent with arbitrary acyclic causal orderings.In particular, one can define one-way signalling (a.k.a.