Epireflections和超紧基数
Epireflections and supercompact cardinals
摘要：
我们证明了，在适当的假设下，超紧基数的存在意味着C的对象的每个绝对表反射类是一个小正交类。更精确地说，如果L是可达范畴C上的局部化函子，使得单位态射X \to LX是所有X的极满态射，并且L-局部对象的类由带参数的绝对公式定义，那么存在一个超紧基数高于参数基数意味着L是关于某个态射集的局部化。
英文摘要：
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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