This project is concerned with classifying semisimple, braided tensor categories that are generated by a single object X with a prescribed decomposition of the tensor square of X with itself. The principal investigator will also work on the question of strictness of braided categories and their characterization in terms of balancing phases. A category is a collection of objects, together with a collection of maps and a rule of composition of maps. One example is the set of functions on subsets of the real line using the usual composition of functions. Categories were originally defined to fill a foundational role in mathematics. However, current research in category theory is concerned with categories with structure. This area has potential impact on a number of different areas of mathematics, as well as theoretical physics.
