3-dimensional defect TQFTs and their tricategories

Understand

We initiate a systematic study of 3-dimensional `defect' topological quantum field theories, that we introduce as symmetric monoidal functors on stratified and decorated bordisms.

• For every such functor we construct a tricategory with duals, which is the natural categorification of a pivotal bicategory.
• This captures the algebraic essence of defect TQFTs, and it gives precise meaning to the fusion of line and surface defects as well as their duality operations.
• As examples, we discuss how Reshetikhin-Turaev and Turaev-Viro theories embed into our framework, and how they can be extended to defect TQFTs.