JOOST VERCRUYSSE (Vrije Universiteit Brussel):
KLEISLI HOPF ALGEBRAS
Starting with a monoidal monad M on a braided monoidal category A, we
consider the associated Kleisli category. This Kleisli category turns out
to be again a braided monoidal category, and Hopf algebras in this new
category will be termed Kleisli Hopf algebras. The purpose of this talk is
to show that multiplier Hopf algebras and infinite Drinfel'd doubles arise
as natural examples of our theory under a correct choice of M and A. This
is joint work (in progress) with Kris Janssen.
10 November 2009 (10:15 room 322)
JOOST VERCRUYSSE (Vrije Universiteit Brussel):
GALOIS THEORY IN BICATEGORIES
We develop a Galois (descent) theory for comonads within the framework of
bicategories. We give generalizations of Beck's theorem and the
Joyal-Tierney theorem. Many examples are provided, including classical
descent theory, Hopf-Galois theory over Hopf algebras and Hopf algebroids,
Galois theory for corings and group-corings, and Morita-Takeuchi theory
for corings. As an application we construct a new type of comatrix corings
based on (dual) quasi bialgebras. (Joint work with Jose
Gomez-Torrecillas.)