The Category-Theoretic Arithmetic of Information

2008/03/25 by Benjamin Allen, Allen, Benjamin
Computer Science · Mathematics · #18A99 #94A17 #Category Theory (math.CT) #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #cs.IT #math.CT #math.IT #msc:18A99 #msc:94A17

paper · pdf · doi:10.48550/arxiv.0803.3608

v3: Changed presentation and incorporated reviewers' suggestions

arxiv created 2008/07/21 · arxiv updated 2009/12/01

Abstract

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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