Given a poset P , the set, Γ(P), of all Scott closed sets ordered by inclusion forms a complete lattice. A subcategory C of Pos d (the category of posets and Scott-continuous maps) is said to be Γ-faithful if for any posets P and Q in C, Γ(P) ∼ = Γ(Q) implies P ∼ = Q. It is known that the category of all continuous dcpos and the category of bounded complete dcpos are Γ-faithful, while Pos d is ...

The category, or class of algebras, in the title is denoted by $bf W$. A hull operator (ho) in $bf W$ is a reflection in the category consisting of $bf W$ objects with only essential embeddings as morphisms. The proper class of all of these is $bf hoW$. The bounded monocoreflection in $bf W$ is denoted $B$. We classify the ho's by their interaction with $B$ as follows. A ``word'' is a function ...

By constructions in monoid and group theory we exhibit an adjunction between the category of partially ordered monoids and lazy monoid homomorphisms, and the category of partially ordered groups and group homomorphisms, such that the unit of the adjunction is injective. We also prove a similar result for sets acted on by monoids and groups. We introduce the new notion of lazy homomorphism for a...

We introduce H-fields as ordered differential fields of a certain kind. Hardy fields extending R, as well as the field of logarithmicexponential series over R are H-fields. We study Liouville extensions in the category ofH-fields, as a step towards a model theory ofH-fields. The main result is that an H-field has at most two Liouville closures.

Let P be a finite partially ordered set, briefly a finite poset. We will show that for any P -persistent object X in the category of finite topological spaces, there is a P− weighted graph, whose clique complex has the same P -persistent homology as X.

In this paper we prove a cancellation law in the category (1) of partially ordered sets and (2) of T0 spaces, the respective conditions on the common factor being that it have (1) an irreducible bottom element and (2) an irreducible bottom element in its specialization order.

Following the results obtained in Preord and in Cat, we characterize the effective étale-descent morphisms inM -Ord, the category ofM -ordered sets for a given monoid M . Furthermore we show that in M -Ord every effective descent morphism is effective for étale-descent (while the converse is false), and we generalize it to a more general context of relational algebras.

This paper presents an investigation of many valued lattices from the point of view of enriched category theory. For a bounded partially ordered set P , the conditions for P to become a lattice can be postulated as existence of certain adjunctions. Reformulating these adjunctions, by aid of enriched category theory, in many valued setting, two kinds of many valued lattices, weak -lattices and -...

We introduce -algebras and -algebras as semantic domains for data re nement of imperative programming languages. The functorial semantics of -calculus is given by using the adjunction between the category of -algebras and the category of small locally ordered categories. We de ne the notion of upward and downward simulation between the interpretations of atomic commands, and re nements between ...

We find the injective hulls of partially ordered monoids in the category whose objects are po-monoids and submultiplicative order-preserving functions. These injective hulls are with respect to a special class of monics called “embeddings”. We show as well that the injective objects with respect to these embeddings are precisely the quantales.