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A Characterization of the Prime Closed Filter Compactification of a Topological Space
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: H.L. Bentley H. HerrlichThe prime compactification whose points are the prime closed filters can be defined for a general topological space and is naturally functorial. We derive several properties of this compactification and present a characterization. -
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... -
Additive Families of GLn-Invariants of Schur Functors
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Arnold Keet --- Mathematics Department, Van der Sterr Building, South AfricaWe extend the symbolic method of [5] to invariants for the action of the general linear group on any Schur or co-Schur functor. We apply this symbolic method to prove that certain families of invariants of the Schur (co-Schur) functors... -
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... -
Topological systems versus attachment relations
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Cosimo Guido --- Department of Mathematics “Ennio De Giorgi”, Italy Sergey A. Solovyov --- Department of Mathematics and Statistics, Faculty of Science, Czech RepublicThe manuscript makes a category-theoretic comparison between the concepts of topological system of S. Vickers and attachment relation of C. Guido. With the help of the recent definition of the notions in the framework of an arbitrary variety of algebras,... -
Pre-rigid monoidal categories
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Alessandro Ardizzoni --- University of Turin, Italy Isar Goyvaerts --- Vrije Universiteit Brussel, Claudia Menini --- University of Ferrara, ItalyLiftable pairs of adjoint functors between braided monoidal categories in the sense of [GV1] provide auto-adjunctions between the associated categories of bialgebras. Motivated by finding interesting examples of such pairs, we study general pre-rigid monoidal categories. Roughly speaking, these are... -
The ℓp -metrization of functors with finite supports
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Taras Banakh --- Ivan Franko National University of Lviv, Ukraine Viktoria Brydun --- Ivan Franko National University of Lviv, Lesia Karchevska --- , Ukraine Mykhailo Zarichnyi --- Ivan Franko National University of Lviv, UkraineLet p ∈ [1, ∞] and F : Set → Set be a functor with finite supports in the category Set of sets. Given a non-empty metric space (X, dX), we introduce the distance on the functor-space FX as the... -
Lax comma categories of ordered sets
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Maria Manuel Clementino --- University of Coimbra, Portugal Fernando Lucatelli Nunes --- Universiteit Utrecht, NederlandLet Ord be the category of (pre)ordered sets. Unlike Ord/X , whose behaviour is well-known, not much can be found in the literature about the lax comma 2-category Ord//X . In this paper we show that the forgetful functor Ord//X... -
Topogenous orders and related families of morphisms
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: David Holgate --- University of the Western Cape, South Africa Minani Iragi --- Brno University of Technology, Czech RepublicIn a category with a proper ()-factorization system, we study the notions of strict, co-strict, initial and final morphisms with respect to a topogenous order. Besides showing that they allow simultaneous study of four classes of morphisms obtained separately with...