Shahid Beheshti UniversityCategories and General Algebraic Structures with Applications2345-58537Special Issue on the Occasion of Banaschewski's 90th Birthday (II)20170701Adjoint relations for the category of local dcpos8910543374ENBinZhaoShaanxi Normal UniversityJingLuShaanxi Normal UniversityKaiyunWangShaanxi Normal UniversityJournal Article20161020In 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:<br /> (1) The forgetful functor $U$ : {bf LDcpo} $longrightarrow$ {bf Pos} has a left adjoint, but does not have a right adjoint;<br />(2) The inclusion functor $I$ : {bf Dcpo} $longrightarrow$ {bf LDcpo} has a left adjoint, but does not have a right adjoint;<br />(3) The forgetful functor $U$ : {bf LDcpo}-$S$ $longrightarrow$ {bf LDcpo} has<br />both left and right adjoints;<br />(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.http://cgasa.sbu.ac.ir/article_43374_e3ba4928af107559409d8a2f182b5716.pdf