We prove a categorical duality between class of abstract algebras partial functions and (small) topological categories. The are the isomorphs collections closed under operations composition, antidomain, range, preferential union (or ‘override’). categories those whose space objects is Stone space, source map local homeomorphism, target open, all arrows epimorphisms.

In this paper we construct new categorical models for the identity types of Martin-Löf type theory, in the categories Top of topological spaces and SSet of simplicial sets. We do so building on earlier work of Awodey and Warren, which has suggested that a suitable environment for the interpretation of identity types should be a category equipped with a weak factorisation system in the sense of ...

BACKGROUND Application oriented ontologies are important for reliably communicating and managing data in databases. Unfortunately, they often differ in the definitions they use and thus do not live up to their potential. This problem can be reduced when using a standardized and ontologically consistent template for the top-level categories from a top-level formal foundational ontology. This wou...

In this paper, we introduce the concept of the generalized topological molecular lattices as a generalization of Wang's topological molecular lattices,  topological spaces, fuzzy topological spaces, L-fuzzy topological spaces and soft topological spaces. Topological molecular lattices were defined by closed elements, but in this new structure we present the concept of the open elements and defi...

For many years, it was thought that Landau's theory of symmetry breaking could describe essentially all phases and phase transitions. However, in the last twenty years, it has become clear that at zero temperature, quantum mechanics allows for the possibility of new phases of matter beyond the Landau paradigm. In this thesis, we develop a general theoretical framework for these "exotic phases" ...

The geometric and algebraic properties of Gray categories with duals are investigated by means of a diagrammatic calculus. The diagrams are three-dimensional stratifications of a cube, with regions, surfaces, lines and vertices labelled by Gray category data. These can be viewed as a generalisation of ribbon diagrams. The Gray categories present two types of duals, which are extended to functor...

in this paper we introduce the concept of topological number for locally convex topological spaces and prove some of its properties. it gives some criterions to study locally convex topological spaces in a discrete approach.

Our work over the past years shows that not only the collection of (for instance) all topological spaces gives rise to a category, but also each topological space can be seen individually as a category by interpreting the convergence relation x −→ x between ultrafilters and points of a topological space X as arrows in X. Naturally, this point of view opens the door to the use of concepts and id...

in this paper we find sufficient conditions on primitive inverse topological semigroup s under which: the inversion inv : (h(s)) (h(s)) is continuous; we show that every topologically periodic countable compact primitive inverse topological semigroups with closed h-classes is topologically isomorphic to an orthogonal sum p i2= bi (gi) of topological brandt extensions bi (gi) of countably compac...