The Category-Theoretic Arithmetic of Information

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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.
v3: Changed presentation and incorporated reviewers' suggestions

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Category Theory, Information Theory, 18A99; 94A17

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http://salesiana.dossiersoluciones.com/handle/123456789/165276

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0803.3608
 http://arxiv.org/abs/0803.3608

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arXiv