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SUMMARY:Duals and invertibility - Ignacio Lopez Franco (University of Camb
 ridge)
DTSTART:20101109T141500Z
DTEND:20101109T151500Z
UID:TALK27858@talks.cam.ac.uk
CONTACT:Nathan Bowler
DESCRIPTION:It is a classical fact that certain transformations in monoida
 l 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 braidi
 ng (a.k.a. (co)quasi-triangular structure) on a Hopf algebra is automatica
 lly (convolution-)invertible. In this talk we exploit the notion of a dual
  pairing in a pseudomonoid in a monoidal bicategory in order to give gener
 alisations of the examples above. In particular we show that for an autono
 mous pseudomonoid the lax centre coincides with the centre\, and that a la
 x braiding is always invertible (a braiding). The techniques we use allow 
 us to deduce the results from the classical case of monoidal categories.\n
 [This is joint work with R. Street and R. J. Wood].
LOCATION:MR3\, Centre for Mathematical Sciences
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