The mathematical stratum of the General Theory of Information (GTI) builds mathematical models of information, information processes and information processing systems. According to the basic principles of GTI, information is intrinsically related to transformations. That is why portions of information are modeled by information operators in infological system representation spaces or simply in information spaces. Informally, an information space is a space where information functions (acts). In the formalized approach, information spaces are constructed as state or phase spaces of infological systems. It is possible to use different mathematical structures for state/phase representation. Thus, the mathematical stratum of the GTI is build as an operator theory in information spaces based on principles of this theory, which are translated into postulates and axioms.
There are two types of mathematical models of information: (1) information processes and (2) information processing systems. This separation results in two approaches: functional and categorical.
In the functional approach, the information space is represented by functional spaces, such as Hilbert spaces or Banach spaces, while portions of information are modeled by operators in these spaces.
In the categorical approach, information spaces are represented by abstract categories (Burgin 2010b). There are two forms of information dynamics depiction in categories: the categorical and functorial representations. The categorical representation of information dynamics preserves internal structures of information spaces associated with infological systems as their state or phase spaces. In it, portions of information are modeled by categorical information operators. The functorial representation of information dynamics preserves external structures of information spaces associated with infological systems as their state or phase spaces. In it, portions of information are modeled by functorial information operators.
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