The mathematical concept of symmetry is a group acting on a set. In many modern problems in math and physics, sets are replaced by categories. In contrast to sets, categories encode both objects and relations between them. This makes the notion of symmetry for categories more subtle. The result is the notion of a "2-group". In this project we study explicit 2-group actions on categories. The methods will involve computations in group cohomology.
Required: 417. Recommended: 423, 428 (category theory). A knowledge of group actions is essential. A familiarity with categories would be helpful.