The Category of S-Fuzzy Posets

In this paper, we define and consider, the category FPos-S of all S-fuzzy posets and action-preserving monotone maps between them. S-fuzzy poset congruences which play an important role in studying the categorical properties of S-fuzzy posets are introduced. More precisely, the correspondence between the S-fuzzy poset congruences and the fuzzy action and order preserving maps is discussed. We characterize S-fuzzy poset congruences on the Sfuzzy posets in terms of the fuzzy pseudo orders. Some categorical properties of the category FPos-S of all S-fuzzy posets 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. Finally, epimorphisms, monomorphisms and order embeddings in FPos and FPos-S are studied.