Extended 3-dimensional bordism as the theory of modular objects

Abstract

A modular object in a symmetric monoidal bicategory is a Frobenius algebra object whose product and coproduct are biadjoint, equipped with a braided structure and a compatible twist, satisfying rigidity, ribbon, pivotality, and modularity conditions. We prove that the oriented 3-dimensional bordism bicategory of 1-, 2-, and 3-manifolds is the free symmetric monoidal bicategory on a single anomaly-free modular object.

64 pages

References in corpus (2)

• Quasistrict symmetric monoidal 2-categories via wire diagrams
• On unitary 2-representations of finite groups and topological quantum field theory

Cited by in corpus (2)

• Symmetries and defects in three-dimensional topological field theory
• Morita Bicategories of Algebras and Duality Involutions