  Given a pair of adjoint functors between two arbitrary categories it induces
mutually inverse equivalences between the full subcategories of the initial
ones, consisting of objects for which the arrows of adjunction are
isomorphisms. We investigate some cases in which these subcategories may be
better characterized. One application is the construction of cellular
approximations. Other is the definition and the characterization of (weak)
*-objects in the non additive case.
