On comonadicity of the extension-of-scalars functors

Building on a categorical approach of G. Janelidze and W. Tholen to descent theory for modules, we show how this theory can be presented at the level of enriched categories. Specializing to the monoidal category of bimodules over a separable algebra this gives a criterion for comonadicity of the extension-of-scalars functor associated to an extension of (not necessarily commutative) rings. As an application of this criterion, some known results on the comonadicity of such functors are obtained.