Galois theory in bicategories

Details Galois theory in bicategories Galois theory in bicategories

2007-11-22

arxiv.org/abs/0711.3642v1

Mathematics

Rings and Algebras

39 pages

Scientific paper

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.

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