عنوان مجله
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Sahand Communications in Mathematical Analysis
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کلیدواژهها
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Fuzzy poset, S-fuzzy congruence, Free object, Cofree object, Adjoint pair
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چکیده
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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.
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