Pretorsors and equivalences
Abstract
Properties of (most general) noncommutative torsors or AB torsors are analysed. Starting with pretorsors it is shown that they are equivalent to a certain class of Galois extensions of algebras by corings. It is shown that a class of faithfully flat pretorsors induces equivalences between categories of comodules of associated corings. It is then proven that AB torsors correspond to monoidal functors (and, under some additional conditions, equivalences) between categories of comodules of bialgebroids.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 July 2006
 arXiv:
 arXiv:math/0607529
 Bibcode:
 2006math......7529B
 Keywords:

 Mathematics  Quantum Algebra;
 Mathematics  Rings and Algebras;
 16W30 (Primary);
 58B34 (Secondary)
 EPrint:
 34 pages, LaTeX file v2: Def 5.1 corrected v3: Examples added in Sec 3 and minor changes in the layout v4: Corrections in Lemmata 2.2 and 3.7