Tannaka Reconstruction of Weak Hopf Algebras in Arbitrary Monoidal Categories

Abstract

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.

16 pages, a great many figures

Cited by in corpus (2)

• Fiber functors, monoidal sites and Tannaka duality for bialgebroids
• The Tannaka representation theorem for separable Frobenius functors