Localizations, colocalizations and non additive ∗-objects

摘要

Given two arbitrary categories, a pair of adjoint functors between them induces three pairs of full subcategories, as follows: the subcategories of reflexive objects, that is objects for which the unit (respectively counit) of the adjunction is an isomorphism; the subcategories of local (respectively colocal) objects w.r.t. these adjoint functors; the subcategories of cogenerated (respectively generated) objects w.r.t. this adjoint pair, namely objects for which the unit (counit) of the adjunction is a monomorphism (an epimorphism). We investigate some cases in which the subcategory of reflexive objects coincide with the subcategory of (co)local objects or with the subcategory of (co)generated objects. As an application we define and characterize (weak) ∗-objects in the non additive case, more precisely weak ∗-acts.