Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4952228 | Theoretical Computer Science | 2017 | 11 Pages |
Abstract
Amadio (1991) [3] and Curien (1998) [4] raised the question of whether the category of stable bifinite domains (SB for short) in sense of Amadio-Droste is the largest Cartesian closed full subcategory of the category of Ï-algebraic meet-cpos with CM functions (Ï-SAM for short). In the second part of this paper, we prove that for any Ï-algebraic meet-cpo D and certain non-distributive finite poset MË, if [DâcMË], [[DâcMË]âc[DâcMË]] and [[[DâcMË]âcMË]âc[[DâcMË]âcMË]] are Ï-algebraic, then we have that (1) D is finitary; (2) if D is not stable bifinite, then [[DâcMË]âc[DâcMË]] is not finitary. So, the category SB is a maximal Cartesian closed full subcategory of Ï-SAM, which gives a partial solution to the problem posed by Amadio and Curien.
Keywords
Related Topics
Physical Sciences and Engineering
Computer Science
Computational Theory and Mathematics
Authors
Xiaoyong Xi, Qingyu He, Lingyun Yang,