The Category-Theoretic Arithmetic of Information Export

@misc{citeulike:2599233, abstract = {The concept of information has found application across the sciences. However, the conventional measures of information are not appropriate for all situations, and a more general mathematical concept is needed. In this work we give axioms that characterize the arithmetic of information, i.e. the way that pieces of information combine with each other. These axioms allow for a general notion of information functions, which quantify the information transmitted by a communication system. In our formalism, communiation systems are repersented as category-theoretic morphisms between information sources and destinations. Our framework encompasses discrete, continuous, and quantum information measures, as well as familiar mathematical functions that are not usually associated with information. We discuss these examples and prove basic results on the general behavior of infomration.}, archivePrefix = {arXiv}, author = {Allen, Benjamin}, citeulike-article-id = {2599233}, citeulike-linkout-0 = {http://arxiv.org/abs/0803.3608}, citeulike-linkout-1 = {http://arxiv.org/pdf/0803.3608}, day = {26}, eprint = {0803.3608}, keywords = {axiomatic, category\_theory, communication, information}, month = {Mar}, posted-at = {2008-03-28 00:19:15}, priority = {0}, title = {The Category-Theoretic Arithmetic of Information}, url = {http://arxiv.org/abs/0803.3608}, year = {2008} }

TY - ELEC ID - citeulike:2599233 L3 - citeulike-article-id:2599233 N2 - The concept of information has found application across the sciences. However, the conventional measures of information are not appropriate for all situations, and a more general mathematical concept is needed. In this work we give axioms that characterize the arithmetic of information, i.e. the way that pieces of information combine with each other. These axioms allow for a general notion of information functions, which quantify the information transmitted by a communication system. In our formalism, communiation systems are repersented as category-theoretic morphisms between information sources and destinations. Our framework encompasses discrete, continuous, and quantum information measures, as well as familiar mathematical functions that are not usually associated with information. We discuss these examples and prove basic results on the general behavior of infomration. TI - The Category-Theoretic Arithmetic of Information KW - axiomatic KW - category_theory KW - communication KW - information AU - Allen, Benjamin PY - 2008/Mar/26/ UR - http://arxiv.org/abs/0803.3608 ER -