Totality of product completions
نویسندگان
چکیده
Categories whose Yoneda embedding has a left adjoint are known as total categories and are characterized by a strong cocompleteness property. We introduce the notion of multitotal category A by asking the Yoneda embedding A → [Aop,Set] to be right multiadjoint and prove that this property is equivalent to totality of the formal product completion ΠA of A. We also characterize multitotal categories with various types of generators; in particular, the existence of dense generators is inherited by the formal product completion iff measurable cardinals cannot be arbitrarily large.
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تاریخ انتشار 2010