Axiomatic Description of Categories of Information Transformers

It is proposed to consider any uniform class of information transformers (ITs) as a family of morphisms of a category that satisfy a certain set of axioms. The paper defines basic concepts for information transformers and studies their main properties in terms of categories of ITs. In particular it generalizes the Bayesian approach to decision-making problems. It also introduces two different approaches to comparison of informativeness of ITs and investigates their interrelations. It is shown that classes of ITs of equivalent informativeness form a partially ordered bounded Abelian monoid. Several examples of concrete categories of information transformers are examined.