Pre-torsors and equivalences

Details Pre-torsors and equivalences Pre-torsors and equivalences

2006-07-21

arxiv.org/abs/math/0607529v4

J. Algebra 317 (2007), 544-580. Corrigendum. J. Algebra 319 (2008), 1339-1340

Mathematics

Quantum Algebra

34 pages, LaTeX file v2: Def 5.1 corrected v3: Examples added in Sec 3 and minor changes in the layout v4: Corrections in Lemm

Scientific paper

10.1016/j.jalgebra.2007.08.023;

Properties of (most general) non-commutative torsors or A-B torsors are analysed. Starting with pre-torsors 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 pre-torsors induces equivalences between categories of comodules of associated corings. It is then proven that A-B torsors correspond to monoidal functors (and, under some additional conditions, equivalences) between categories of comodules of bialgebroids.

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