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A modular object in a symmetric monoidal bicategory is a Frobenius algebraobject whose product and coproduct are biadjoint, equipped with a braidedstructure and a compatible twist, satisfying rigidity, ribbon, pivotality, andmodularity conditions. We prove that the oriented 3-dimensional bordismbicategory of 1-, 2-, and 3-manifolds is the free symmetric monoidal bicategoryon a single anomaly-free modular object.

Extended 3-dimensional bordism as the theory of modular objects