ALGEBRAIC HULLS OF ADJOINT FUNCTORS AS INJECTIVE HULLS

摘要

For each adjoint functorU: A #x2192; XwhereXis an (#x3F5;, M)-category having enough #x3F5;-projectives, we construct an (#x3F5;, M)-algebraic hullE: (A, U) #x2192; (#xC2;, #xDB;), i.e., (#xC2;, #xDB;) is (epsiv; M)-algebraic andEhas a certain denseness property. We show that there is a conglomerate of functors overXwith respect to which the (#x3F5; M)-algebraic categories are exactly the injective objects and characterize (#x3F5; M)-algebraic hulls as injective hulls.