  We highlight the underlying category-theoretic structure of measures of
information flow. We present an axiomatic framework in which communication
systems are represented as morphisms, and information flow is characterized by
its behavior when communication systems are combined. Our framework includes a
variety of discrete, continuous, and, conjecturally, quantum information
measures. It also includes some familiar mathematical constructs not normally
associated with information, such as vector space dimension. We discuss these
examples and prove basic results from the axioms.
