Theoretical physics

Algebraic number

Pure mathematics

Construct (python library)

Topological quantum field theory

Dual polyhedron

Field (mathematics)

Duality (order theory)

Computer science

Categorification

Physics

Mathematics

Mathematical analysis

Combinatorics

Functor

Programming language

Topology (electrical circuits)

Algebra over a field

Advances in Mathematics

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.

3-dimensional defect TQFTs and their tricategories