On a Duality with “Less than Usual” Reflexive Abstract Modules

In this paper we study dualities between categories of topological and abstract modules. Under a few conditions, any such duality is a restriction of the natural duality between the full subcategories Refl( _RK and Refl (K_A ) of K-reflexive modules, given by the functors Chom_R(−K) and Hom( _A −K) for a certain bimodule _RK_A . We are interested in the case where the class Refl(K_A ) of reflexive abstract modules is only contained in the class of modules cogenerated by K_A .