Limits and Colimits in the Category of Pre-Directed Complete Pre-Ordered Sets

In this paper, some categorical properties of the category pre-dcpo of all predcpos; pre-ordered sets which are also pre-directed complete, with pre-continuous maps between them is considered. in particular, we characterize products and coproducts in this category. furthermore, we show that this category is neither complete nor cocomplete. also, epimorphisms and monomorphisms in pre-dcpo are described. finally, some adjoint relations between the category pre-dcpo and others are considered. more precisely, we consider the forgetful functors between this category and some well-known categories, and study the existence of their left and right adjoints.