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On two epireflective subcategories of the category of 2T 0-fuzzy bitopological spaces
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: AnuruddhaS. Khastgir ArunK. SrivastavaThe motivation for the present work is provided by Giuli and Salbany's work on the category BTOP 0 of T 0?bitopological spaces wherein they identified a cogenerator Q and a closure operator and used these to obtain, among other things,... -
Homomorphisms of complete distributive lattices
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: A. Pultr J. Sichler V. TrnkováThe category of all complete distributive lattices and their complete homomorphisms is universal, and this is also true for the category of all complete distributive lattices whose morphisms preserve complete joins, finite meets and an additional nullary operation. A survey... -
Compactness with Respect to a Convergence Structure
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Josef SlapalA convergence structure for a category is given by determining convergent nets and their limits for each object of this category under validity of some basic convergence axioms. The nets considered are obtained as a categorical generalization of the usual... -
On the Relationship Between Several Basic Categories in Fuzzy Topology
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Dexue ZhangIn this paper, a process, which associates with every fibre-small topo- logical category A and every completely distributive lattice L another topological category called the co-tower extension of A, is introduced to investigate the relationship between several basic categories in... -
The Kleisli Category is a Category Of Fractions
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: E. Giuli K.A. Hardie J.J.C. VermeulenWe consider a generalised notion of category of fractions associated with a class Φ of permitted replacement situations between zig-zags in a category C. The Kleisli category associated with a monad [T, η, μ] in C is shown to be... -
On the genus of fibrations for which the fibre is a product of Eilenberg-Maclane spaces.
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: J.-B. GatsinziWe give an upper bound for the genus of a rational fibration of which the fibre is a product of even Eilenberg-Maclane spaces. -
Categories of Dicompact bi-T 2 texture spaces and a Banach-Stone theorem
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Filiz Yildiz LawrenceM. BrownThe principal aim of this paper is to consider various aspects of the theory of dicompact bi-T 2 texture spaces, and place them in a categorical setting. It culminates in a version of the Banach-Stone theorem. On the way, a... -
Lattice-Valued Convergence Ring and Its Uniform Convergence Structure
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: T.M.G. Ahsanullah --- Department of Mathematics, Saudi ArabiaConsidering L a frame, we introduce the notion of stratified L-neighborhood topological ring, produce some characterization theorems including its Luniformizability. With the help of the notions of stratified convergence structures attributed to Gunther Jäger [10], we introduce and study various... -
TRACES OF EPIMORPHISM CLASSES
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Lutz Schroder --- Department of Mathematics and Computer Science, University of Bremen, Bremen, Germany,Classes of morphisms that occur as preimages of the class of all epi-morphisms, of all extremal epimorphisms, respectively of all retractions under some faithful functor are characterized by suitable closure properties. The corresponding question for regular or strict epimorphisms is... -
On coreflective hulls in [0, 1]-
TOP and s[0, 1]-TOP Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Veena Singh --- Department of Mathematics, India ArunK. Srivastava --- Department of Mathematics and Centre for Interdisciplinary Mathematical Sciences, Faculty of Science, IndiaIn this paper, we find the coreflective hull of the category of indiscrete [0, 1]-topological spaces in the category [0, 1]-TOP of [0, 1]-topological spaces. We also show that the coreflective hull of a single-point s[0, 1]-topological space in the... -
Frame valued stratified generalized convergence groups
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: T.M.G. Ahsanullah Jawaher Al-MufarrijFollowing the notion of stratified L-fuzzy convergence space of Gunther Jäger [Quaest. Math. 24 (2001), 501–517], we introduce the notion of a stratified L-generalized convergence group, and look into some other objects, namely, stratified L-Kent convergence groups, and stratified L-principal... -
Functorial relationships between lattice-valued topology and topological systems
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: J.T. Denniston S.E. RodabaughThis paper investigates functorial relationships between lattice-valued topology (arising from fuzzy sets and fuzzy logic) and topological systems (arising from topological and localic aspects of domains and finite observational logic in computer science). Two such relationships are embeddings from TopSys... -
On minimum proper essential extensions in a category
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Anthony W. Hager --- Wesleyan University, USA Brian Wynne --- Lehman College, CUNY, USAIn a concrete category A satisfying certain natural conditions, we investigate minimum proper essential extenstions (A-mpee’s) and how this relates to atoms in the complete lattice hoA of hull operators on A (if A # is the category with... -
On presheaf submonads of quantale-enriched categories
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Maria Manuel Clementino --- University of Coimbra, Portugal Carlos Fitas --- University of Coimbra, PortugalThis paper focuses on the presheaf monad, or the free cocompletion monad, and its submonads on the realm of V-categories, for a quantale V . First we present two characterisations of presheaf submonads, both using V-distributors: one based on admissible... -
The monoidal nature of the Feistel-Toffoli construction
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Hans-E. Porst --- Stellenbosch University, South AfricaThe Feistel-Toffoli construction of a bijective Boolean function out of an arbitrary one, a fundamental tool in reversible computing and in cryptography, has recently been analyzed (see [12]) to be a special instance of the construction of a monoid homomorphism... -
On binary matrix properties
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Michael Hoefnagel --- Stellenbosch University, South Africa Pierre-Alain Jacqmin --- Université catholique de Louvain, Belgium Zurab Janelidze --- Stellenbosch University, South Africa Emil van der Walt --- Stellenbosch University, South AfricaThe so-called matrix properties of finitely complete categories are a special type of exactness properties that can be encoded as extended matrices of integers. The relation of entailment of matrix properties gives an interesting preorder on the set of such... -
Lax pullback complements in partial morphism categories
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: S.N. Hosseini --- Mahani Mathematical Research Center, Shahid Bahonar University of Kerman, Iran L. Yeganeh --- Mahani Mathematical Research Center, Shahid Bahonar University of Kerman, IranThe goal of this article is to characterize the lax pullback complement of a given partial morphism along a total morphism, in an -partial morphism category, where is an exponentiable stable system. To achieve this, we first show that if... -
Precover completing domains in exact categories
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Septimiu Crivei --- Babeş-Bolyai University, Str. M. Kogălniceanu 1, Romania Robert Pop --- Babeş-Bolyai University, Str. M. Kogălniceanu 1, RomaniaSubprojectivity domains may be generalized to precover completing domains, not only in module categories, but also in additive (exact) categories. This is the setting in which we give several general properties of precover completing domains and we study objects having...