Method of Additional Structures on the Objects of a Monoidal Kleisli Category as a Background for Information Transformers Theory
Abstract
Category theory provides a compact method of encoding mathematical structures in a uniform way, thereby enabling the use of general theorems on, for example, equivalence and universal constructions. In this article we develop the method of additional structures on the objects of a monoidal Kleisli category. It is proposed to consider any uniform class of information transformers (ITs) as a family of morphisms of a category that satisfy certain set of axioms. This makes it possible to study in a uniform way different types of ITs, e.g., statistical, multivalued, and fuzzy ITs. Proposed axioms define a category of ITs as a monoidal category that contains a subcategory (of deterministic ITs) with finite products. Besides, it is shown that many categories of ITs can be constructed as Kleisli categories with additional structures.
Keywords
Cite
@article{arxiv.math-ph/0211067,
title = {Method of Additional Structures on the Objects of a Monoidal Kleisli Category as a Background for Information Transformers Theory},
author = {P. V. Golubtsov and S. S. Moskaliuk},
journal= {arXiv preprint arXiv:math-ph/0211067},
year = {2007}
}
Comments
59 pages, Latex, no figures