A comonadicity theorem for partial comodules

Abstract

We show that the category of partial comodules over a Hopf algebra H is comonadic over Vect_k and provide an explicit construction of this comonad using topological vector spaces. The case when H is finite-dimensional is treated in detail. A study of partial representations of linear algebraic groups is initiated; we show that a connected linear algebraic group does not admit partiality.