We prove coherence theorems for dualizable objects in monoidal bicategories and for fully dualizable objects in symmetric monoidal bicategories, describing coherent dual pairs and coherent fully dual pairs. These are structures one can attach to an object which we show are property-like and equivalent to, respectively, dualizability and full dualizability. In the latter case, our work reduces the two-dimensional Cobordism Hypothesis of Baez-Dolan to a comparison problem between two explicitly defined bicategories.
Keywords: monoidal bicategories, dualizable objects, fully dualizable objects
2020 MSC: 18N10, 18N20
Theory and Applications of Categories, Vol. 38, 2022, No. 9, pp 257-310.
Published 2022-02-01.
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