The concept of information has found application across the sciences. However, the conventional measures of information are not appropriate for all situations, and a more general mathematical concept is needed. In this work we give axioms that characterize the arithmetic of information, i.e. the way that pieces of information combine with each other. These axioms allow for a general notion of information functions, which quantify the information transmitted by a communication system. In our formalism, communication systems are represented as category-theoretic morphisms between information sources and destinations. Our framework encompasses discrete, continuous, and quantum information measures, as well as familiar mathematical functions that are not usually associated with information. We discuss these examples and prove basic results on the general behavior of information.
It looks like a discussion about this is starting over at the n-Category Café. If I didn’t have to spend today cutting down a 12-page paper to eight pages for an overpriced book of conference proceedings which nobody will read, I’d totally be writing more about it!