2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/125093We prove that, under suitable assumptions on a category C, the existence of supercompact cardinals implies that every absolute epireflective class of objects of C is a small-orthogonality class. More precisely, if L is a localization functor on an accessible category C such that the unit morphism X \to LX is an extremal epimorphism for all X, and the class of L-local objects is defined by an absolute formula with parameters, then the existence of a supercompact cardinal above the cardinalities of the parameters implies that L is a localization with respect to some set of morphisms.15 pagesCategory Theory18A40, 18C35, 03E55, 03C55, 55P60text