Dualizations and antipodes (Q1404247)

The authors define and study left dualisations for pseudomonoids in right autonomous bicategories. A pseudomonoid with a left dualisation is called left autonomous. Examples are given by left autonomous monoidal \({\mathcal V}\)-categories in enriched category theory and by quasi-Hopf algebras. There is an analogous notion of right dualisation, and a pseudomonoid with both left and right dualisations is called autonomous. The authors develop a notion of autonomous monoidal lax functor. They also develop a representation theory for monoidal bicategories and apply it to quasi-Hopf algebras.