Functorial Knot Theory

Abstract

The thesis titled \Functorial Knot Theory", expository in nature, aims to show some recent connections between Knot theory and Category theory. In the rst part we discuss how the language of categories and functors e ectively enhances the development of new knot invariants such as Jones polynomial and Khovanov homology. The second part demonstrates the surprising application of knot theory in proving some important coherence theorems in category theory.