Tannaka Reconstruction of Weak Hopf Algebras in Arbitrary Monoidal Categories

Details Tannaka Reconstruction of Weak Hopf Algebras in Arbitrary Monoidal Categories Tannaka Reconstruction of Weak Hopf Algebras in Arbitrary Monoidal Categories

2009-03-02

arxiv.org/abs/0903.0208v1

Mathematics

Category Theory

16 pages, a great many figures

Scientific paper

We introduce a variant on the graphical calculus of Cockett and Seely for monoidal functors and illustrate it with a discussion of Tannaka reconstruction, some of which is known and some of which is new. The new portion is: given a separable Frobenius functor F: A --> B from a monoidal category A to a suitably complete or cocomplete braided autonomous category B, the usual formula for Tannaka reconstruction gives a weak bialgebra in B; if, moreover, A is autonomous, this weak bialgebra is in fact a weak Hopf algebra.

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