In this paper, recalling the category FPos-S of all S-fuzzy posets, and action-preserving monotone maps between them, some categorical properties of the category FPos-S is considered. In particular, we characterize products, coproducts, equalizers, coequalizers, pullbacks and pushouts in this category. Also, we consider all forgetful functors between the category FPos-S and the categories FPos of fuzzy posets, Pos-S of S-posets, Pos of posets, Act-S of S-acts and Set of sets, and study the existence of their left and right adjoints.
