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Information Operators in Categorical Information Spaces
Department of Mathematics, University of California, Los Angeles, 405 Hilgard Ave., Los Angeles, CA 90095, USA
Received: 4 October 2010; in revised form: 28 October 2010 / Accepted: 29 October 2010 / Published: 18 November 2010
Abstract: The general theory of information (GTI) is a synthetic approach, which reveals the essence of information, organizing and encompassing all main directions in information theory. On the methodological level, it is formulated as system of principles explaining what information is and how to measure information. The goal of this paper is the further development of a mathematical stratum of the general theory of information based on category theory. Abstract categories allow us to construct flexible models for information and its flow. Now category theory is also used as unifying framework for physics, biology, topology, and logic, as well as for the whole mathematics, providing a base for analyzing physical and information systems and processes by means of categorical structures and methods. There are two types of representation of information dynamics, i.e., regularities of information processes, in categories: the categorical representation and functorial representation. Here we study the categorical representations of information dynamics, which preserve internal structures of information spaces associated with infological systems as their state/phase spaces. Various relations between information operators are introduced and studied in this paper. These relations describe intrinsic features of information, such as decomposition and complementarity of information, reflecting regularities of information processes.
Keywords: information; information operator; category; functor; composition; knowledge; cognition; order
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MDPI and ACS Style
Burgin, M. Information Operators in Categorical Information Spaces. Information 2010, 1, 119-152.
Burgin M. Information Operators in Categorical Information Spaces. Information. 2010; 1(2):119-152.
Burgin, Mark. 2010. "Information Operators in Categorical Information Spaces." Information 1, no. 2: 119-152.