Pre-torsors and equivalences

Gabriella Böhm, Tomasz Brzeziński

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)544-580
Number of pages37
JournalJournal of Algebra
Volume317
Issue number2
DOIs
Publication statusPublished - Nov 15 2007

Fingerprint

Torsor
Equivalence
Coring
Comodule
Galois Extension
Functor
Algebra

Keywords

  • ×-Hopf algebra
  • (Monoidal) equivalence
  • (Pre-)torsor
  • Bi-Galois object
  • Bialgebroid
  • Comodule
  • Coring
  • Galois extension

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

Pre-torsors and equivalences. / Böhm, Gabriella; Brzeziński, Tomasz.

In: Journal of Algebra, Vol. 317, No. 2, 15.11.2007, p. 544-580.

Research output: Contribution to journalArticle

Böhm, Gabriella ; Brzeziński, Tomasz. / Pre-torsors and equivalences. In: Journal of Algebra. 2007 ; Vol. 317, No. 2. pp. 544-580.
@article{d839ec122680495d93f3c6f3ae6ca2f3,
title = "Pre-torsors and equivalences",
abstract = "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.",
keywords = "×-Hopf algebra, (Monoidal) equivalence, (Pre-)torsor, Bi-Galois object, Bialgebroid, Comodule, Coring, Galois extension",
author = "Gabriella B{\"o}hm and Tomasz Brzeziński",
year = "2007",
month = "11",
day = "15",
doi = "10.1016/j.jalgebra.2007.08.023",
language = "English",
volume = "317",
pages = "544--580",
journal = "Journal of Algebra",
issn = "0021-8693",
publisher = "Academic Press Inc.",
number = "2",

}

TY - JOUR

T1 - Pre-torsors and equivalences

AU - Böhm, Gabriella

AU - Brzeziński, Tomasz

PY - 2007/11/15

Y1 - 2007/11/15

N2 - 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.

AB - 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.

KW - ×-Hopf algebra

KW - (Monoidal) equivalence

KW - (Pre-)torsor

KW - Bi-Galois object

KW - Bialgebroid

KW - Comodule

KW - Coring

KW - Galois extension

UR - http://www.scopus.com/inward/record.url?scp=35348962638&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=35348962638&partnerID=8YFLogxK

U2 - 10.1016/j.jalgebra.2007.08.023

DO - 10.1016/j.jalgebra.2007.08.023

M3 - Article

AN - SCOPUS:35348962638

VL - 317

SP - 544

EP - 580

JO - Journal of Algebra

JF - Journal of Algebra

SN - 0021-8693

IS - 2

ER -