The Category-Theoretic Arithmetic of Information

Details The Category-Theoretic Arithmetic of Information The Category-Theoretic Arithmetic of Information

2008-03-25

arxiv.org/abs/0803.3608v3

Mathematics

Category Theory

v3: Changed presentation and incorporated reviewers' suggestions

Scientific paper

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.

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