Epireflections and supercompact cardinals
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→...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2007 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:44042 |
| Acceso en línea: | https://ddd.uab.cat/record/44042 |
| Access Level: | acceso abierto |
| Palabra clave: | Nombres cardinals Categories (Matemàtica) Homotopia |
| Sumario: | 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→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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