%0 Journal Article
%T The Category of $S$-Fuzzy Posets
%J Sahand Communications in Mathematical Analysis
%I University of Maragheh
%Z 2322-5807
%A Shahbaz, Leila
%D 2023
%\ 04/01/2023
%V 20
%N 3
%P 157-177
%! The Category of $S$-Fuzzy Posets
%K Fuzzy poset
%K $S$-fuzzy congruence
%K Free object
%K Cofree object
%K Adjoint pair
%R 10.22130/scma.2023.1983286.1222
%X 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.
%U https://scma.maragheh.ac.ir/article_704546_862d46534148ae2743fef130a0478714.pdf