Localization at Injectives in Complete Categories

We consider a complete category <!-- MATH $\mathcal{A}$ --> . For each object of <!-- MATH $\mathcal{A}$ --> we define a functor <!-- MATH $Q:\mathcal{A} \to \mathcal{A}$ --> and obtain a necessary and sufficient condition on for , after restricting its codomain, to become a reflector of <!-- MATH $\mathcal{A}$ --> onto the limit closure of . In particular, this condition is satisfied if is injective in <!-- MATH $\mathcal{A}$ --> with regard to equalizers. Among the special cases of such reflectors are: the reflector onto torsion-free divisible objects associated to an injective in <!-- MATH $\operatorname{Mod} R$ --> ; the Samuel compactification of a uniform space; the Stone-Čech compactification.