UC Irvine

Category theory has been advocated as a replacement for set theory as the foundation for mathematics. It is claimed that as a foundation set theory is both inadequate and inappropriate. Set theory is considered inadequate because it cannot produce all of the mathematical objects of interest. Set theory is considered inappropriate because it provides a poor framework for mathematical research. In this dissertation, I argue that category theory is subject to exactly the same objections by considering the use of category theory for work in graph theory.