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Epireflections and supercompact cardinals

Joan Bagaria·Carles Casacuberta·Adrian R. D. Mathias
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Abstract

We 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.

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Joan Bagaria, Carles Casacuberta, Adrian R. D. Mathias. 2007-03-05. Epireflections and supercompact cardinals. https://arxiv.org/abs/math/0703119

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