Information Operators in Categorical Information Spaces

The general theory of information (GTI) is a synthetic approach, which revealsthe essence of information, organizing and encompassing all main directions ininformation theory. On the methodological level, it is formulated as system of principlesexplaining what information is and how to measure information. The goal of this paper isthe further development of a mathematical stratum of the general theory of informationbased on category theory. Abstract categories allow us to construct flexible models forinformation and its flow. Now category theory is also used as unifying framework forphysics, biology, topology, and logic, as well as for the whole mathematics, providing abase for analyzing physical and information systems and processes by means of categoricalstructures and methods. There are two types of representation of information dynamics, i.e., regularities of information processes, in categories: the categorical representation andfunctorial representation. Here we study the categorical representations of informationdynamics, which preserve internal structures of information spaces associated withinfological systems as their state/phase spaces. Various relations between informationoperators are introduced and studied in this paper. These relations describe intrinsicfeatures of information, such as decomposition and complementarity of information, reflecting regularities of information processes