Tannaka Duality, Coclosed Categories and Reconstruction for Nonarchimedean Bialgebras

The topic of this paper is a generalization of Tannaka duality to coclosed categories. As an application we prove reconstruction theorems for coalgebras (bialgebras, Hopf algebras) in categories of topological vector spaces over a nonarchimedean field K. In particular, our results imply reconstruction and recognition theorems for categories of locally analytic representations of compact p-adic groups, which was the major motivation for this work. Also, as an example, we discuss a certain (trivial) extension of the geometric Satake correspondence.