Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 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. semi-causal) processes, non-signalling
processes, and quantum $n$-combs. Furthermore, our framework is general enough
to accommodate recently-proposed generalisations of classical and quantum
theory where processes only need to have a fixed causal ordering locally, but
globally allow indefinite causal ordering.
  To illustrate this point, we show that certain processes of this kind, such
as the quantum switch, the process matrices of Oreshkov, Costa, and Brukner,
and a classical three-party example due to Baumeler, Feix, and Wolf are all
instances of a certain family of processes we refer to as $\textrm{SOC}_n$ in
the appropriate category of higher-order causal processes. After defining these
families of causal structures within our framework, we give derivations of
their operational behaviour using simple, diagrammatic axioms.

10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
15
The categories of this paper are: nucl-ex
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph