عنوان مجله
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Tamkang Journal of Mathematics
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چکیده
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In this paper, first the congruences in the category PosAct-S of all
poset acts over a pomonoid S; an S-act in the category Pos of all posets, with
action preserving monotone maps between them, are introduced. Then, we study
the existence of the free and cofree objects in the category PosAct-S. More precisely,
we consider all forgetful functors between this category and the categories Pos-S of
all S-posets, Pos of all posets, Act-S of all S-acts, and Set of all sets, and we study
the existence of their left and right adjoints. It is shown that the category Pos-S is
a full reflective and coreflective subcategory of PosAct-S.
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