Exponentiable morphisms of domains

F. CAGLIARI, S. MANTOVANI
2008 Mathematical Structures in Computer Science  
Given a map f in the category ω-Cpo of ω-complete posets, exponentiability of f in ω-Cpo easily implies exponentiability of f in the category Pos of posets, while the converse is not true. We find then the extra conditions needed on f exponentiable in Pos to be exponentiable in ω-Cpo, showing the existence of partial products of the two-point ordered set S = {0 < 1} (Theorem 1.8). Using this characterization and the embedding via the Scott topology of ω-Cpo in the category Top of topological
more » ... ces, we can compare exponentiability in each setting, obtaining that a morphism in ω-Cpo, exponentiable both in Top and in Pos, is exponentiable also in ω-Cpo. Furthermore we show that the exponentiability in Top and in Pos are independent from each other. (2000) : 06B30, 06B35, 18B30, 18D15, 54F05. Mathematics Subject Classifications
doi:10.1017/s0960129508006786 fatcat:6jskbx4y5zb3xklgohlsthyzwa