A coherent dual of an object lifts to a coherent dual of a bimodule over Frobenius algebras; zigzag 2-isos need special Frobenius sections, and special Frobenius algebras in 2Vect are rigid.
Rigid and separable algebras in fusion 2-categories
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Frobenius Algebras and Dual Bimodules in Monoidal 2-Categories
A coherent dual of an object lifts to a coherent dual of a bimodule over Frobenius algebras; zigzag 2-isos need special Frobenius sections, and special Frobenius algebras in 2Vect are rigid.