University of MaraghehSahand Communications in Mathematical Analysis2322-580720320230401The Category of $S$-Fuzzy Posets15717770454610.22130/scma.2023.1983286.1222ENLeilaShahbazDepartment of Mathematics, University of Maragheh, Maragheh, 55181-83111, Iran.0000-0001-6312-6231Journal Article20221224In 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 the<br />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 $S$-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.https://scma.maragheh.ac.ir/article_704546_862d46534148ae2743fef130a0478714.pdf