Networking academia: Categories as a cross-disciplinary research language

A network culture is emerging in human society. It takes on a wide variety of forms, from the online social networks between individuals, to information networks (e.g. Lokey's Business Wire), to virtual trading floors for financial securities, to global delivery networks of goods and services: everyone is linking up. In order to efficiently study this phenomenon, one must construct rigorous definitions which are general enough to encompass many different types of networks, but precise enough to allow researchers in disparate fields to accurately communicate and compare their findings. Although definitions for various kinds of networks have been made, they are neither rigorous nor broadly applicable, resulting in a lack of good communication between distinct fields. Category theory may be useful in solving this problem. Category theory is a branch of mathematics designed to provide a unifying language for all of mathematics. It has revolutionized mathematical research since its invention in the 1940s and has begun breaking ground in computer science and physics as well, which is evidence of its generality and applicability. I believe that category theory could play an even broader role in academia at large. The goal of this project is to apply category theory to the theory of networks in order to provide a rigorous yet flexible set of rules for specifying and studying networks in a broad array of social and physical settings. I hope to devise a common language for economists, computer scientists, linguists, mathematicians, and researchers in many other fields, which in turn will strengthen the network that is academia itself.