The fundamental connection between the reflexivity of an object and the compatibility relation (Q2755000)

The author generalizes the concept of reflexivity from topological vector spaces to the setting of concrete categories with dual space functors. He also defines, in terms of compatible objects, when such a category has representation theorems. He connects these concepts in a number of theorems and corollaries and subsequently considers some applications, notably to locally compact abelian groups, locally convex topological vector spaces and topological abelian groups satisfying the Pontryagin duality theorem.