By Gelfand-Neumark duality, the category C∗Alg of commutative C∗algebras is dually equivalent to the category of compact Hausdorff spaces, which by Stone duality, is also dually equivalent to the category uba` of uniformly complete bounded Archimedean `-algebras. Consequently, C∗Alg is equivalent to uba`, and this equivalence can be described through complexification. In this article we study u...

Inthispaper, (L,M)-fuzzy domain finiteness and (L,M)-fuzzy restricted hull spaces are introduced, and several characterizations of the category (L,M)-CS of (L,M)-fuzzy convex spaces are obtained. Then, (L,M)-fuzzy stratified (resp. weakly induced, induced) convex spaces are introduced. It is proved that both categories, the category (L,M)-SCS of (L,M)-fuzzy stratified convex spaces and the cate...

The aim of this paper is to study the categorical relations betweenmatroids, Goetschel-Voxman’s fuzzy matroids and Shi’s fuzzifying matroids.It is shown that the category of fuzzifying matroids is isomorphic to that ofclosed fuzzy matroids and the latter is concretely coreflective in the categoryof fuzzy matroids. The category of matroids can be embedded in that offuzzifying matroids as a simul...

This work is a contribution to a recent field, Directed Algebraic Topology. Categories which appear as fundamental categories of ‘directed structures’, e.g. ordered topological spaces, have to be studied up to appropriate notions of directed homotopy equivalence, which are more general than ordinary equivalence of categories. Here we introduce past and future equivalences of categories—sort of ...

In this paper, for a complete residuated lattice L, we present the categorical properties of ?-neighborhood spaces and their relationships to neighborhood stratified L-neighborhood spaces. The main results are: (1) category is topological category; (2) can be embedded in as reflective subcategory, when L meet-continuous lattice, subcategory; (3) continuous (resp., spaces) simultaneously corefle...

The problem of extending to graph grammars the unfolding semantics originally developed by Winskel for (safe) Petri nets has been faced several times along the years, both for the single-pushout and double-pushout approaches, but only partial results were obtained. In this paper we fully extend Winskel’s approach to single-pushout grammars providing them with a categorical concurrent semantics ...