Aspects of duality in 2-categories

The notion of ‘duality’ plays an important role in quantum algebra and topological quantum field theory, as has been particularly emphasized by Baez and Dolan. One aspect of this is the idea of duals for morphisms in a 2-category, which is a generalization of the idea of rigidity in monoidal categories. I will introduce the notion of an ‘even-handed structure’ on a 2-category as a coherent means of turning right adjoints into left adjoints, and explain how this works in various examples such as fusion categories, braided monoidal categories, 2-Hilbert spaces and derived categories having a ‘trivial Serre functor’.