Nonarchimedean coalgebras and coadmissible modules

We show that basic notions of locally analytic representation theory can be reformulated in the language of topological coalgebras (Hopf algebras) and comodules. We introduce the notion of admissible comodule and show that it corresponds to the notion of admissible representation in the case of topological Hopf algebra of locally analytic functions on a compact $p$-adic group.