两类代数Domain范畴的等价

Equivalences for Two Algebraic Domain Categories

首先证明了一个Domain范畴与它的等价范畴有相同的笛卡儿闭性,其次通过引入两类新的偏序集即L-偏序集和B-偏序集,构造了范畴LPOSA(由L-偏序集与逼近关系组成)和范畴BPOSA(由B-偏序集与逼近关系组成),并证明了它们分别与代数L-domain范畴ALD和代数bc-domain范畴ABD等价．

First it is obtained that a domain category has the same cartesian closedness with its equivalences, which perhaps provide a helpful way to investigate the cartesian closedness of some domain category. Then two kinds of new posets are defined and thus two kinds of new categories are constructed. They are finally proved to be respectively equivalent with the category ALD of all algebraic L-domains and the category ABD of all algebraic bc-domains.