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semitransitive coring

Let kk be a (commutative) field and RR a kk-algebra.

An RR-coring CC is semi-transitive if the category M f CM^C_f of CC-comodules which are finitely generated as modules over RR

  • M f CM^C_f is artinian and noetherian (has all objects of finite composition length), all its objects are projective as RR-modules, and all its hom-spaces are finite dimensional over kk
  • the category of all CC-comodules is Ind-generated by M f CM^C_f (Every CC-comodule is a filtered colimit of CC-comodules finitely generated as RR-modules)

It appears that semi-transitive corings are those corings which can be reconstructed from fiber functors on categories which are artinian, noetherian and with finite dimensional hom-spaces.

  • A. Bruguières, Théorie tannakienne non commutative, Comm. Algebra 22, 5817–5860, 1994

  • K. Szlachanyi, Fiber functors, monoidal sites and Tannaka duality for bialgebroids, arxiv/0907.1578

Created on June 4, 2011 20:59:28 by Zoran Škoda (31.45.129.40)