35 Result(s)

Article

Categorical Extension of Dualities: From Stone to de Vries and Beyond, I

Propounding a general categorical framework for the extension of dualities, we present a new proof of the de Vries Duality Theorem for the category KHaus of compact Hausdorff spaces and their continuous maps, as ...

Georgi Dimov, Elza Ivanova-Dimova, Walter Tholen in Applied Categorical Structures (2022)

Article

Met-Like Categories Amongst Concrete Topological Categories

When replacing the non-negative real numbers with their addition by a commutative quantale \(\mathsf{V}\) ...

Walter Tholen in Applied Categorical Structures (2018)

Article

The Fundamental Group as the Structure of a Dually Affine Space

This paper dualizes the setting of affine spaces as originally introduced by Diers for application to algebraic geometry and expanded upon by various authors, to show that the fundamental groups of pointed top...

Eraldo Giuli, Walter Tholen in Applied Categorical Structures (2016)

Article

Categorically Proper Homomorphisms of Topological Groups

We extend the Dikranjan-Uspenskij notions of c-compact and h-complete topological group to the morphism level, study the stability properties of the newly defined types of maps, such as closure under direct pr...

Wei He, Walter Tholen in Applied Categorical Structures (2016)

Article

Nullstellen and Subdirect Representation

David Hilbert’s solvability criterion for polynomial systems in n variables from the 1890s was linked by Emmy Noether in the 1920s to the decomposition of ideals in commutative rings, which in turn led Garret Bir...

Walter Tholen in Applied Categorical Structures (2014)

Article

Foreword

George Janelidze, Martin Hyland, Michael Johnson… in Applied Categorical Structures (2011)

Article

Lawvere Completion and Separation Via Closure

For a quantale \(\mathsf{V}\) , first a closure-theoretic approach to completeness and separation in

Dirk Hofmann, Walter Tholen in Applied Categorical Structures (2010)

Article

A Topologist’s View of Chu Spaces

For a symmetric monoidal-closed category \(\mathcal{X}\) and any object K, the category of K-Chu spaces is small-topolo...

Eraldo Giuli, Walter Tholen in Applied Categorical Structures (2007)

Article

Universality of Coproducts in Categories of Lax Algebras

Categories of lax \((T,V\,)\) -algebras are shown to have pullback-stable coproducts if \(T\) preserves inverse images. The general result not on...

Mojgan Mahmoudi, Christoph Schubert, Walter Tholen in Applied Categorical Structures (2006)

Article

Preface

George Janelidze, Bodo Pareigis, Walter Tholen in Applied Categorical Structures (2004)

Article

One Setting for All: Metric, Topology, Uniformity, Approach Structure

For a complete lattice V which, as a category, is monoidal closed, and for a suitable Set-monad T we consider (T,V)-algebras and introduce (T,V)-proalgebras, in generalization of Lawvere's presentation of metric ...

Maria Manuel Clementino, Dirk Hofmann, Walter Tholen in Applied Categorical Structures (2004)

Article

Injective hulls are not natural

In a category with injective hulls and a cogenerator, the embeddings into injective hulls can never form a natural transformation, unless all objects are injective. In particular, assigning to a field its alg...

Jiří Adámek, Horst Herrlich, Jiří Rosický, Walter Tholen in algebra universalis (2002)

Article

Weak Factorization Systems and Topological Functors

Weak factorization systems, important in homotopy theory, are related to injective objects in comma-categories. Our main result is that full functors and topological functors form a weak factorization system i...

Jiří Adámek, Horst Herrlich, Jiří Rosický, Walter Tholen in Applied Categorical Structures (2002)

Article

What is a Quotient Map with Respect to a Closure Operator?

It is shown that there is no good answer to the question of the title, even if we restrict our attention to S et-based topological categories. Although very closely related, neither the natural notion of c-finali...

Maria Manuel Clementino, Eraldo Giuli, Walter Tholen in Applied Categorical Structures (2001)

Article

Openness with Respect to a Closure Operator

We study the notions of closed, open, initial and final morphism with respect to a closure operator and show that they have a perfectly symmetric pullback behaviour. We also investigate their interaction with ...

Eraldo Giuli, Walter Tholen in Applied Categorical Structures (2000)

Article

Representation of Relations by Partial Maps

With the notions of partial morphism and relation to be understood with respect to a class M of monomorphisms in a finitely complete category C, we give sufficient conditions for the graph functor Par(C) → Rel(C)...

**aomin Dong, Walter Tholen in Applied Categorical Structures (2000)

Chapter

Representation of Relations by Partial Maps

With the notions of partial morphism and relation to be understood with respect to a class M of monomorphisms in a finitely complete category C, we give sufficient conditions for the graph functor Par(C) → Rel(C)...

**aomin Dong, Walter Tholen in Papers in Honour of Bernhard Banaschewski (2000)

Article

Separated and Connected Maps

Using on the one hand closure operators in the sense of Dikranjan and Giuli and on the other hand left- and right-constant subcategories in the sense of Herrlich, Preuß, Arhangel'skii and Wiegandt, we apply tw...

Maria Manuel Clementino, Walter Tholen in Applied Categorical Structures (1998)