Tannaka duality, coclosed categories and reconstruction for nonarchimedean bialgebras

TL;DR

This paper extends Tannaka duality to coclosed categories and establishes reconstruction theorems for nonarchimedean bialgebras, with applications to topological vector spaces and p-adic group representations.

Contribution

It generalizes Tannaka duality to coclosed categories and proves reconstruction theorems for coalgebras and bialgebras in nonarchimedean settings.

Findings

Reconstruction theorems for nonarchimedean coalgebras and bialgebras

Recognition theorems for categories of locally analytic p-adic group representations

Extension of Tannaka duality to coclosed categories

Abstract

The topic of this paper is a generalization of Tannaka duality to coclosed categories. As an application we prove reconstruction theorems for coalgebras (and bialgebras) 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.