Morita Theory for The Category of Fuzzy S-acts
نویسنده
چکیده
In this paper, we give the properties of tensor product and study the relationship between Hom functors and left (right) exact sequences in FS-Act. Also, we get some necessary conditions for equivalence of two fuzzy Sacts category. Moreover, we prove that two monoids S and T are Morita equivalent if and only if FS-Act and FT -Act are equivalent.
منابع مشابه
Fuzzy Acts over Fuzzy Semigroups and Sheaves
lthough fuzzy set theory and sheaf theory have been developed and studied independently, Ulrich Hohle shows that a large part of fuzzy set theory is in fact a subfield of sheaf theory. Many authors have studied mathematical structures, in particular, algebraic structures, in both categories of these generalized (multi)sets. Using Hohle's idea, we show that for a (universal) algebra $A$, th...
متن کاملPOWERSET OPERATOR FOUNDATIONS FOR CATALG FUZZY SET THEORIES
The paper sets forth in detail categorically-algebraic or catalg foundations for the operations of taking the image and preimage of (fuzzy) sets called forward and backward powerset operators. Motivated by an open question of S. E. Rodabaugh, we construct a monad on the category of sets, the algebras of which generate the fixed-basis forward powerset operator of L. A. Zadeh. On the next step, w...
متن کاملCategorically-algebraic topology and its applications
This paper introduces a new approach to topology, based on category theory and universal algebra, and called categorically-algebraic (catalg) topology. It incorporates the most important settings of lattice-valued topology, including poslat topology of S.~E.~Rodabaugh, $(L,M)$-fuzzy topology of T.~Kubiak and A.~v{S}ostak, and $M$-fuzzy topology on $L$-fuzzy sets of C.~Guido. Moreover, its respe...
متن کاملCOGENERATOR AND SUBDIRECTLY IRREDUCIBLE IN THE CATEGORY OF S-POSETS
In this paper we study the notions of cogenerator and subdirectlyirreducible in the category of S-poset. First we give somenecessary and sufficient conditions for a cogenerator $S$-posets.Then we see that under some conditions, regular injectivityimplies generator and cogenerator. Recalling Birkhoff'sRepresentation Theorem for algebra, we study subdirectlyirreducible S-posets and give this theo...
متن کاملFUZZY ORDERED SETS AND DUALITY FOR FINITE FUZZY DISTRIBUTIVE LATTICES
The starting point of this paper is given by Priestley’s papers, where a theory of representation of distributive lattices is presented. The purpose of this paper is to develop a representation theory of fuzzy distributive lattices in the finite case. In this way, some results of Priestley’s papers are extended. In the main theorem, we show that the category of finite fuzzy Priestley space...
متن کامل