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Epireflections and supercompact cardinals

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 smallorthogonality 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.
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https://hal.univ-reunion.fr/hal-01186171
Contributor : Nicolas Alarcon <>
Submitted on : Monday, June 7, 2021 - 1:35:09 PM
Last modification on : Wednesday, June 30, 2021 - 9:40:07 PM

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Joan Bagaria, Carles Casacuberta, Adrian R D Mathias. Epireflections and supercompact cardinals. Journal of Pure and Applied Algebra, Elsevier, 2009, 213 (7), pp.1208-1215. ⟨10.1016/j.jpaa.2008.11.046⟩. ⟨hal-01186171⟩

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