Method of Additional Structures on the Objects of a Monoidal Kleisli Category as a Background for Information Transformers Theory
<|reference_start|>Method of Additional Structures on the Objects of a Monoidal Kleisli Category as a Background for Information Transformers Theory: 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.<|reference_end|>
@article{golubtsov2002method,
    title={Method of Additional Structures on the Objects of a Monoidal Kleisli
  Category as a Background for Information Transformers Theory},
    author={P. V. Golubtsov, S. S. Moskaliuk},
    journal={Hadronic Journal, V.25, No.2,179-238 (2002)},
    year={2002},
    archivePrefix={arXiv},
    eprint={math-ph/0211067},
    primaryClass={math-ph cs.MA math.CT math.MP}
}