偏序集范畴的Cartesian闭性

Cartesian closedness of the category of posets

作者讨论了偏序集范畴的Cartesian闭性,给出了偏序集范畴的满子范畴具有Cartesian闭性的充分必要条件.特别地,作者证明了交连续半格(不要求定向完备性)范畴是Cartesian闭范畴,L-CDCPO范畴是L-POSET范畴的极大Cartesian闭子范畴.

In this paper, the authors investigate the Cartesian closedness of the category of posets, and obtain the sufficient and necessary condition such that a full subcategory of POSET is Cartesian closed. Particularly, they show that the category of meet-continuous semilattices is Cartesian closed and L-CDCPO is the largest cartesian closed full subcategory of L-POSET.