Adjoint relations for the category of local dcpos | ||
| Categories and General Algebraic Structures with Applications | ||
| مقاله 7، دوره 7، Special Issue on the Occasion of Banaschewski's 90th Birthday (II) - شماره پیاپی 1، مهر 2017، صفحه 89-105 اصل مقاله (883.04 K) | ||
| نوع مقاله: Research Paper | ||
| نویسندگان | ||
| Bin Zhao؛ Jing Lu؛ Kaiyun Wang* | ||
| Shaanxi Normal University | ||
| چکیده | ||
| In this paper, we consider the forgetful functor from the category {\bf LDcpo} of local dcpos (respectively, {\bf Dcpo} of dcpos) to the category {\bf Pos} of posets (respectively, {\bf LDcpo} of local dcpos), and study the existence of its left and right adjoints. Moreover, we give the concrete forms of free and cofree $S$-ldcpos over a local dcpo, where $S$ is a local dcpo monoid. The main results are: (1) The forgetful functor $U$ : {\bf LDcpo} $\longrightarrow$ {\bf Pos} has a left adjoint, but does not have a right adjoint; (2) The inclusion functor $I$ : {\bf Dcpo} $\longrightarrow$ {\bf LDcpo} has a left adjoint, but does not have a right adjoint; (3) The forgetful functor $U$ : {\bf LDcpo}-$S$ $\longrightarrow$ {\bf LDcpo} has both left and right adjoints; (4) If $(S,\cdot,1)$ is a good ldcpo-monoid, then the forgetful functor $U$: {\bf LDcpo}-$S$ $\longrightarrow$ {\bf Pos}-$S$ has a left adjoint. | ||
تازه های تحقیق | ||
Dedicated to Bernhard Banaschewski on the occasion of his $90^{th}$ birthday | ||
| کلیدواژهها | ||
| Dcpo؛ local dcpo؛ $S$-ldcpo؛ forgetful functor | ||
| مراجع | ||
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