On hopf algebras and rigid monoidal categories
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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.
Keywords
Hopf Algebra Monoidal Category Canonical Isomorphism Dual Object Monoidal Structure
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References
- 1.P. Deligne,Catégories Tannakiennes, preprint.Google Scholar
- 2.P. Deligne and J. Milne,Tannakian Categories, Lecture Notes in Math.900, Springer-Verlag, Berlin, 1982, pp. 101–228.Google Scholar
- 3.N. Saavedra Rivano,Catégories Tannakiennes, Lecture Notes in Math.265, Springer-Verlag, Berlin, 1972.zbMATHGoogle Scholar
Copyright information
© The Weizmann Science Press of Israel 1990