Leila Shahbaz - Department of Mathematics, University of Maragheh, Maragheh, ۵۵۱۸۱-۸۳۱۱۱, Iran.

In this paper, we define and consider, the category {\bf 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 thecategorical 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 S-fuzzy posets in terms of the fuzzy pseudo orders. Some categorical properties of the category {\bf 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 {\bf FPos}-S and the categories {\bf FPos} of fuzzy posets, {\bf Pos}-S of S-posets, {\bf Pos} of posets, {\bf Act}-S of S-acts  and {\bf Set} of sets and study the existence of their left and right adjoints. Finally, epimorphisms, monomorphisms and order embeddings in {\bf FPos} and {\bf FPos}-S are studied.

Fuzzy poset, S-fuzzy congruence, Free object, Cofree object, Adjoint pair