‎ in the present article‎, ‎we study some categorical properties of the category {$bf‎ cpo_{sep}$-$s$} of all {separately strict $s$-cpo's}; cpo's equipped with‎ a compatible right action of a separately strict cpo-monoid $s$ which is‎ strict continuous in each component‎. ‎in particular‎, we show that this category is reflective and coreflective in the‎ category of $s$-cpo's‎, ‎find the free a...

in this paper, some categorical properties of the category ${bf cpo}_{{bf act}text{-}s}$ of all {cpo $s$-acts}, cpo's equipped with actions of a monoid $s$ on them, and strict continuous action-preserving maps between them is considered. in particular, we describe products and coproducts in this category, and consider monomorphisms and epimorphisms. also, we show that the forgetful functor from...

The paper is devoted to a concept of a fuzzy ordered set and partially ordered set category fuzzyfication. The aim of this work is to define a fuzzy order relation on a usual set, on an L-valued set and on an L-set. Using the fuzzy order relation we construct fuzzy POS category and study the connection between this categories and SET(L).

As an application of the dual equivalence between the category of L-spatialC-objects and the category of L-sober C-M-L-spaces, it is shown in this paper that for a fixed augmented partially ordered set A, there exists a dual equivalence between the category of A-spatial augmented partially ordered sets and the category of A-sober A-valued spaces. Then, with regard to this duality, for a fixed (...

Let L be the ordered set of isomorphism types of finite lattices, where the ordering is by embeddability. We study first-order definability in this ordered set. Our main result is that for every finite lattice L, the set {l, l} is definable, where l and l are the isomorphism types of L and its opposite (L turned upside down). We shall show that the only non-identity automorphism of L is the map...

In this paper,  it is shown that the category of $L$-ordered fuzzifying convergence spaces contains the category of pretopological $L$-ordered fuzzifying convergence spaces as a bireflective subcategory and the latter contains the category of topological $L$-ordered fuzzifying convergence spaces as a bireflective subcategory. Also, it is proved that the category of $L$-ordered fuzzifying conver...

In this paper, we have focused to study convex L-subgroups of an Lordered group. First, we introduce the concept of a convex L-subgroup and a convex L-lattice subgroup of an L-ordered group and give some examples. Then we find some properties and use them to construct convex L-subgroup generated by a subset S of an L-ordered group G . Also, we generalize a well known result about the set of all...

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...

the paper deals with special types of $l$-ordered sets, $l$-fuzzy complete lattices, and fuzzy directed complete posets.first, a theorem for constructing monotone maps is proved, a characterization for monotone maps on an $l$-fuzzy complete lattice is obtained, and it's proved that if $f$ is a monotone map on an $l$-fuzzy complete lattice $(p;e)$, then the least fixpoint of $f$ is meet of ...