A Categorial Approach to Information: Information Transformers, Informativeness, and Decision-Making Problems

Document Type

Presentation Abstract

Presentation Date

3-28-2011

Abstract

In this presentation I will discuss a mathematical structure suitable for studying systems which somehow deal with information. I will show that the appropriate structure is a category which satisfies some additional axioms. Within such category we will be able to introduce problems of decision making (or information processing) and address a question: what does it mean that one source of information is more informative than the other. We will see that many such categories can be constructed as monoidal Kleisli categories. The key ingredients for this construction are: a base category with products ("deterministic" morphisms), a functor, producing objects of "distributions" and a natural transformation, representing "independent product of distributions". Several examples of such categories will be discussed.

Additional Details

Monday, 28 March 2011
3:10 p.m. in Math 103
4:00 p.m. Refreshments in Math Lounge 109

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