On exponentiability of étale algebraic homomorphisms (with Dirk Hofmann and George Janelidze)
Preprint 11-35, DMUC

Abstract: In this paper we show that Cagliari-Mantovani result stating that, in the category of compact Hausdorff spaces, every étale map is exponentiable can be formulated in a general category Alg(T) of Eilenberg-Moore T-algebras, for a monad T, and proved in case T satisfies the so-called Beck-Chevalley condition. For that, Alg(T) is embedded in the (topological) category RelAlg(T) of relational T-algebras, where a suitable notion of étale morphism can be studied, it is shown that morphisms between T-algebras are exponentiable in RelAlg(T), and, moreover, these exponentials belong to Alg(T) whenever the morphisms are étale.
 

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Fibrewise injectivity and Kock-Z"oberlein monads (with Francesca Cagliari and Sandra Mantovani)
Journal of Pure and Applied Algebra (accepted)
Preprint 11-32, DMUC

Abstract: Using Escardó's characterization of injectivity via Kock-Z"oberlein monads, we introduce suitable monads in comma categories of topological spaces that yield characterizations of fibrewise injectivity in topological T0-spaces, with respect to the class of embeddings, and of dense, of flat and of completely flat embeddings. Characterizations, in the category of topological spaces, of injective maps with respect to the same classes of embeddings follow easily from the results obtained for T0-spaces. Moreover, it is shown that, together with the corresponding embeddings, injective continuous maps form a weak factorization system in the category of topological (T0-)spaces and continuous maps.

Descent morphisms and a van Kampen Theorem in categories of lax algebras (with Dirk Hofmann)
Topology and its Applications, available online

A note on effective descent morphisms of topological spaces and relational algebras
(with George Janelidze)
Topology and its Applications 158 (2011), 2431-2436.

On the completion monad via the Yoneda embedding in quasi-uniform spaces
(with Dirk Hofmann)
Topology and its Applications 158 (2011), 2423-2430.

A note on the categorical van Kampen Theorem
Topology and its Applications 158 (2011) 926-929.

On regular and homological closure operators
(with Gonçalo Gutierres)
Cahiers de Topologie et Géométrie Différentielle Catégoriques LI (2010) 127-142.

On the categorical meaning of Hausdorff and Gromov distances, I 
(with Andrei Akhvlediani and Walter Tholen)
Topology and its Applications 157 (2010) 1275-1295.

Lawvere completeness in topology
(with Dirk Hofmann)
Applied Categorical Structures 17 (2009) 175-210.

Exponentiable functors between quantaloid-enriched categories
(with Dirk Hofmann and Isar Stubbe)
Applied Categorical Structures 17 (2009) 91-101.

Relative injectivity as cocompleteness for a class of distributors
(with Dirk Hofmann)
Theory and Applications of Categories 21 (2009), 210-230.
 
Protolocalisations of homological categories
(with Francis Borceux, Marino Gran and Lurdes Sousa)
Journal of Pure and Applied Algebra 212 (2008) 1898–1927.

On some special classes of continuous maps
(with Dirk Hofmann)
Chapter 39, Part 4, of  Open Problems in Topology 2, pages 367-376, edited by Elliott Pearl, Elsevier 2007.

Torsion theories and radicals  in normal categories
(with Dikran Dikranjan and Walter Tholen)
Journal of Algebra 305 (2006) 98-129.
 
Topological protomodular algebras
(with Francis Borceux)
Topology and its Applications 153 (2006) 3085-3100.

Exponentiation in V-categories
(with Dirk Hofmann)
Topology and its Applications 153 (2006) 3113-3128.

Topological semi-abelian algebras 
(with Francis Borceux)
Advances in Mathematics 190 (2005) 425-453.

Local homeomorphisms via ultrafilter convergence 
(with Dirk Hofmann and George Janelidze)
Proceedings of the American Mathematical Society 133 (2005), 917-922.

Effective descent morphisms in categories of lax algebras
(with Dirk Hofmann)
Applied Categorical Structures 12 (2004) 413-425. 

On extensions of lax monads
(with Dirk Hofmann)
Theory and Applications of Categories 13 (2004) 41-60.

One setting for all: metric, topology, uniformity, approach structure
(with Dirk Hofmann and Walter Tholen)
Applied Categorical Structures 12 (2004) 127-154. Abstract   

A Functional Approach to General Topology
(with Eraldo Giuli and Walter Tholen),
in: Categorical Foundations. Special Topics in Order, Topology, Algebra, and Sheaf Theory,    
Encyclopedia of Mathematics and its Applications 97, Cambridge University Press (2004), pp. 103-163.

Exponentiability in categories of lax algebras  
(with Dirk Hofmann and Walter Tholen)
Theory and Applications of Categories 11 (2003) 337-352.

Metric, Topology and Multicategory - A Common Approach
(with Walter Tholen)
Journal of Pure and Applied Algebra 179 (2003) 13-47.

Topological features of lax algebras
(with Dirk Hofmann)
Applied Categorical Structures 11 (2003) 267-286.

The convergence approach to exponentiable maps
(with Dirk Hofmann and Walter Tholen)
Portugaliæ Mathematica 60 (2003) 139-160.

On limit stability of special classes of continuous maps
(with Dirk Hofmann)
Topology and its Applications 125 (2002) 471-488.

Triquotient maps via ultrafilter convergence
(with Dirk Hofmann)
Proceedings of the American Mathematical Society 130 (2002) 3423-3431.

On finite triquotient maps
Journal of Pure and Applied Algebra 168 (2002) 387-389.

A note on local compactness
(with Walter Tholen)
Rendiconti dell'Istituto di Matematica dell'Universita di Trieste, Suppl. 2, XXXII (2001) 17-31.

On connectedness via closure operators
Applied Categorical Structures 9 (2001) 539-556.

What is a quotient map with respect to a closure operator?
(with Eraldo Giuli and Walter Tholen)
Applied Categorical Structures 9 (2001) 139-151.

Separated and connected maps
(with Walter Tholen)
Applied Categorical Structures 6 (1998) 373-401.

A Characterization of the Vietoris Topology
(with Walter Tholen)
Topology Proceedings 22 (1997) 71-95.

Separation versus connectedness
(with Walter Tholen)
Topology and its Applications 75 (1997) 143-181.

Tychonoff's Theorem in a Category
(with Walter Tholen)
Proceedings of the American Mathematical Society 124 (1996) 3311-3314.

Topology in a Category: Compactness
(with Eraldo Giuli and Walter Tholen)
Portugaliæ Mathematica 53 (1996) 397-433.

On categorical notions of compact object
Applied Categorical Structures 4 (1996) 15-29.

Constant morphisms and constant subcategories
Applied Categorical Structures 3 (1995) 119-137.

On connectedness and disconnectedness
in: Topology with Applications (Szekszard, Hungary, 1993)
Mathematical Studies 4 (Bolyai Society), pgs. 71-82.

Weakly hereditary regular closure operators
Topology and its Applications 49 (1993) 129-139.

Hausdorff separation in categories
Applied Categorical Structures 1 (1993) 285-295.

T0- and T1-reflections
Comment. Mathematicae Universitatis Carolinae 33 (1992) 493-504.