ALGEBRAIC HULLS OF ADJOINT FUNCTORS AS INJECTIVE HULLS

Abstract

For each adjoint functor U: A → X where X is an (ϵ, M)-category having enough ϵ-projectives, we construct an (ϵ, M)-algebraic hull E: (A, U) → (Â, Û), i.e., (Â, Û) is (epsiv; M)-algebraic and E has a certain denseness property. We show that there is a conglomerate of functors over X with respect to which the (ϵ M)-algebraic categories are exactly the injective objects and characterize (ϵ M)-algebraic hulls as injective hulls.