University of Cambridge > Talks.cam > Category Theory Seminar > Duals and invertibility

Duals and invertibility

Add to your list(s) Download to your calendar using vCal

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.

Tell a friend about this talk:

This talk is included in these lists:

Note that ex-directory lists are not shown.

 

© 2006-2019 Talks.cam, University of Cambridge. Contact Us | Help and Documentation | Privacy and Publicity