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arXiv · 0907.1578

Fiber functors, monoidal sites and Tannaka duality for bialgebroids

K. Szlachanyi
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Abstract

What are the fiber functors on small additive monoidal categories C which are not abelian? We give an answer which leads to a new Tannaka duality theorem for bialgebroids generalizing earlier results by Phung Ho Hai. The construction reveals a sheaf theoretic interpretation in so far as the reconstructed bialgebroid H has comodule category equivalent to the category of T-sheaves w.r.t. a monoidal Grothendieck topology on C. We also prove an existence theorem for fiber functors on small additive monoidal categories with bounded fusion and weak kernels. For certain autonomous categories a generalized Ulbrich Theorem can be formulated which relates fiber functors to Hopf algebroid Galois extensions.

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K. Szlachanyi. 2009-07-09. Fiber functors, monoidal sites and Tannaka duality for bialgebroids. https://arxiv.org/abs/0907.1578

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