Abstract
LetC be a neutral Tannakian category over a fieldk. By a theorem of Saavedra Rivano there exists a commutative Hopf algebraA overk such thatC is equivalent to the category of finite dimensional rightA-comodules. We review Saavedra Rivano’s construction of the bialgebraA and show thatA has still an antipode if the symmetry condition on the monoidal structure ofC is removed.
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References
P. Deligne,Catégories Tannakiennes, preprint.
P. Deligne and J. Milne,Tannakian Categories, Lecture Notes in Math.900, Springer-Verlag, Berlin, 1982, pp. 101–228.
N. Saavedra Rivano,Catégories Tannakiennes, Lecture Notes in Math.265, Springer-Verlag, Berlin, 1972.
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Ulbrich, KH. On hopf algebras and rigid monoidal categories. Israel J. Math. 72, 252–256 (1990). https://doi.org/10.1007/BF02764622
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DOI: https://doi.org/10.1007/BF02764622