چکیده
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In this paper, we dene the category PosAct-S of all poset acts; an S-act in the category Pos, with
action preserving monotone maps between them. Also, we study the existence of the free and cofree
objects in the categories PosAct-S. More precisely, we consider all forgetful functors between these
categories and the categories Act-S of S-acts, Pos of posets, and Set of sets, and study the existence of
their left and right adjoints.
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