An equivalence for categories of modules over a complete discrete valuation

An equivalence is presented between two categories closely related to the category of valuated vector spaces. This equivalence is then recast in terms of short exact sequences of modules. A new class of mixed modules is introduced, whose members we call A-Warfield, and, in particular, it is shown that an isomorphism between the endomorphism rings of two A-Warfield modules is induced by an isomorphism of their underlying modules.