%0 Journal Article
%T Adjoint relations for the category of local dcpos
%J Categories and General Algebraic Structures with Applications
%I Shahid Beheshti University
%Z 2345-5853
%A Zhao, Bin
%A Lu, Jing
%A Wang, Kaiyun
%D 2017
%\ 07/01/2017
%V 7
%N Special Issue on the Occasion of Banaschewski's 90th Birthday (II)
%P 89-105
%! Adjoint relations for the category of local dcpos
%K Dcpo
%K local dcpo
%K $S$-ldcpo
%K forgetful functor
%R
%X 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} hasboth 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.
%U http://cgasa.sbu.ac.ir/article_43374_e3ba4928af107559409d8a2f182b5716.pdf