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Duals and invertibility

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If you have a question about this talk, please contact Nathan Bowler.

It is a classical fact that certain transformations in monoidal categories are forced to be invertible in the presence of duals (e.g., monoidal transformations between strong monoidal functors, lax braidings). This phenomenon also happens in Hopf algebra theory, where a lax braiding (a.k.a. (co)quasi-triangular structure) on a Hopf algebra is automatically (convolution-)invertible. In this talk we exploit the notion of a dual pairing in a pseudomonoid in a monoidal bicategory in order to give generalisations of the examples above. In particular we show that for an autonomous pseudomonoid the lax centre coincides with the centre, and that a lax braiding is always invertible (a braiding). The techniques we use allow us to deduce the results from the classical case of monoidal categories.

This talk is part of the Category Theory Seminar series.

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