Peter V. Golubtsov
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.