On reflexivity of objects in some specific categories (Q920365)

The note contains the result about the sufficient conditions for standard covariant HOM-functors \(Hom_ A(.,X): A\to B\) \([Hom_ B(.,X): B\to A]\) to be naturally equivalent for concrete categories A and B. As a consequence, the characterizations of reflexivity in some particular categories are given in the following form: \(A^*\) is reflexive iff \(A^{**}\) is the same [in categories TOP, E-mod of right (left) E-module over ring E and M of left Banach E-modules over \(C^*\)-algebra E], appealing to naturally arising E-homomorphisms from A into \(A^{**}\) with \(A^{**}\) endowed with an appropriate topology.