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Epireflections and supercompact cardinals |
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| Authors: | Joan Bagaria Adrian RD Mathias |
| Institution: | a ICREA (Institució Catalana de Recerca i Estudis Avançats) and Departament de Lògica, Història i Filosofia de la Ciència, Universitat de Barcelona, Montalegre 6, 08001 Barcelona, Spain b Departament d’Àlgebra i Geometria, Universitat de Barcelona, Gran Via de les Corts Catalanes 585, 08007 Barcelona, Spain c ERMIT, Université de la Réunion, Avenue René Cassin 15, F-97715 Saint Denis de la Réunion, France |
| Abstract: | We prove that the existence of arbitrarily large supercompact cardinals implies that every absolute epireflective class of objects in a balanced accessible category is a small-orthogonality class. In other words, if L is a localization functor on a balanced accessible category such that the unit morphism X→LX is an epimorphism for all X and the class of L-local objects is defined by an absolute formula, then the existence of a sufficiently large supercompact cardinal implies that L is a localization with respect to some set of morphisms. |
| Keywords: | 03E55 03C55 18A40 18C35 55P60 |
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