TY - JOUR
ID - 43374
TI - Adjoint relations for the category of local dcpos
JO - Categories and General Algebraic Structures with Applications
JA - CGASA
LA - en
SN - 2345-5853
AU - Zhao, Bin
AU - Lu, Jing
AU - Wang, Kaiyun
AD - Shaanxi Normal University
Y1 - 2017
PY - 2017
VL - 7
IS - Special Issue on the Occasion of Banaschewski's 90th Birthday (II)
SP - 89
EP - 105
KW - Dcpo
KW - local dcpo
KW - $S$-ldcpo
KW - forgetful functor
DO -
N2 - 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.
UR - http://cgasa.sbu.ac.ir/article_43374.html
L1 - http://cgasa.sbu.ac.ir/article_43374_e3ba4928af107559409d8a2f182b5716.pdf
ER -