Monoidal Kleisli Category as a Background for Information Transformers Theory

We consider any uniform class of information transformers (ITs) as a family of morphisms of a monoidal category that contains a subcategory (of deterministic ITs) with finite products and satisfies certain set of axioms. Besides, many IT-categories can be constructed as Kleisli categories. The ingredients for this construction are: a base category (of deterministic ITs); a functor, producing objects of “distributions”; a natural transformation, representing “independent product of distributions”. The paper also generalizes Bayesian approach to decision-making problems and studies informativeness of ITs. It shows that classes of equivalent ITs form a partially ordered bounded Abelian monoid. Several examples of concrete IT-categories are examined.