Closure properties associated to natural equivalences (Q1946806)

Consider two abelian categories and a pair of (covariant and additive) adjoint functors between them. Call static (adstatic) those objects for which the counit (respectively the unit) of this adjunction is an isomorphism. Thus the full subcategories of static and adstatic objects are maximal with the property that the restrictions of initial functors still induce equivalences between them. In the paper under review there are found necessary and sufficient conditions for the subcategory of adstatic objects to be closed under factor objects satisfying the additional property that the corresponding unit of adjunction is a monomorphism. It turns out that the closure of the subcategory of adstatic objects under factors with above additional property is also linked to the closure of the class of static objects under factor objects modulo subobjects satisfying a dual property, namely the corresponding counit is an epimorphism. The results are accompanied by a number of examples.