The Category of Semitopological S-Acts
Behnam Khosravi · 2009
Let S-Top be the category of topological S-acts over a topological semigroup S and S-SemiTop be the category of semitopological S-acts over a semitopological semigroup S. It is obvious that any topological S-act is a semitopological S-act, however we will see that the converse is not true in general. In this note, we study the universal objects in the category of semitopological S-acts and introduce them completely. Furthermore, we study the left and right adjoint situation between the category of topological S-acts and the category of semitopological S-acts over a topological semigroup S. Similarly, we present the left adjoint to the inclusion functor from the category of topological semigroups (groups) to the category of semitopological semigroups (groups). Finally as a result of this study, we partially answer to this question that when the point convergence topology is admissible?