Dirk Hofmann I am Assistant Professor at the Department of Mathematics of the University of Aveiro. Contact: Departamento de Matemática Universidade de Aveiro 3810-193 Aveiro Portugal Phone: (+351) 234 370 681 Email: dirk@ua.pt The picture was taken during my talk at CT2007 in Carvoeiro (Portugal) by J. Koslowski.

Research

My research interests focus on the development and application of categorical methods in Mathematics, more specifically in Algebra and Topology.

Publications

• Gonçalo Gutierres and Dirk Hofmann,
  Approaching metric domains, (pdf)
  accepted for publication in Appl. Categ. Structures;
  arXiv:math.GN/1103.4744
• Dirk Hofmann and Paweł Waszkiewicz,
  A duality of quantale-enriched categories, (pdf)
  accepted for publication in J. Pure Appl. Algebra;
  arXiv:math.CT/1009.3892
• Maria Manuel Clementino and Dirk Hofmann,
  Descent morphisms and a van Kampen theorem in categories of lax algebras, (pdf)
  accepted for publication in Topology Appl.;
  Technical Report 11-01, University of Coimbra, 2011.
• Dirk Hofmann and Walter Tholen,
  Lax algebra meets topology, (pdf)
  accepted for publication in Topology Appl.
• Dirk Hofmann and Maria Manuel Clementino,
  On the completion monad via the Yoneda embedding in quasi-uniform spaces, (pdf)
  Topology Appl. 158 (17) (2011), 2423–2430,
• Dirk Hofmann and Paweł Waszkiewicz,
  Approximation in quantale-enriched categories, (pdf)
  Topology Appl., 158 (8) (2011), 963–977.
• Dirk Hofmann and Isar Stubbe,
  Towards Stone duality for topological theories, (pdf)
  Topology Appl. 158 (7) (2011), 913–925.
• Dirk Hofmann, Injective Spaces via Adjunction, (pdf)
  J. Pure Appl. Algebra 215 (3) (2011), 283–302.
• Dirk Hofmann and Walter Tholen,
  Lawvere completion and separation via closure, (pdf)
  Appl. Categ. Structures 18 (2010), 259–287.
• Eraldo Giuli and Dirk Hofmann,
  Affine sets: the structure of complete objects and duality, (pdf)
  Topology Appl. 156 (2009), 2129–2136.
• Gonçalo Gutierres and Dirk Hofmann,
  Sequential convergence via Galois Correspondences, (pdf)
  Acta Math. Hungar. 123 (2009), 187–202.
• Maria Manuel Clementino and Dirk Hofmann,
  Lawvere completeness in Topology, (pdf)
  Appl. Categ. Structures 17 (2009), 175–210.
• Maria Manuel Clementino and Dirk Hofmann,
  Relative injectivity as cocompleteness for a class of distributors, (pdf)
  Theory Appl. Categ. 21 (2009), 210–230.
• Maria Manuel Clementino, Dirk Hofmann and Isar Stubbe,
  Exponentiable functors between quantaloid-enriched categories, (pdf)
  Appl. Categ. Structures 17 (2009), 91–101.
• Dirk Hofmann, Topological theories and closed objects, (pdf)
  Adv. Math. 215 (2007), 789–824.
• Gonçalo Gutierres and Dirk Hofmann,
  Axioms for sequential convergence, (pdf)
  Appl. Categ. Structures 15 (2007), no. 5-6, 599–614.
• Dirk Hofmann, Exponentiation for unitary structures, (pdf)
  Topology Appl. 153 (2006), 3180–3202.
• Maria Manuel Clementino and Dirk Hofmann,
  Exponentiation in V-categories, (pdf)
  Topology Appl. 153 (2006), 3113–3128.
• Dirk Hofmann and Walter Tholen,
  Kleisli operations for topological spaces, (pdf)
  Topology Appl. 153 (2006), 2952–2961.
• Dirk Hofmann, An algebraic description of topological quotient maps, (pdf)
  J. Pure Appl. Algebra 199 (2005), 71–86.
• Maria Manuel Clementino, Dirk Hofmann and George Janelidze,
  Local homeomorphisms via ultrafilter convergence, (pdf)
  Proc. Amer. Math. Soc. 133 (2005), no. 3, 917–922.
• Maria Manuel Clementino and Dirk Hofmann,
  On extensions of lax monads, (pdf)
  Theory Appl. Categ. 13 (2004), No. 3, 41–60.
• Maria Manuel Clementino and Dirk Hofmann,
  Effective descent morphisms in categories of lax algebras, (pdf)
  Appl. Categ. Structures 12 (2004), no. 5-6, 413–425.
• Maria Manuel Clementino, Dirk Hofmann and Walter Tholen,
  One setting for all: metric, topology, uniformity, approach structure, (pdf)
  Appl. Categ. Structures 12 (2004), no. 2, 127–154.
• Maria Manuel Clementino, Dirk Hofmann and Walter Tholen,
  Exponentiability in categories of lax algebras, (pdf)
  Theory Appl. Categ. 11 (2003), No. 15, 337–352.
• Maria Manuel Clementino and Dirk Hofmann,
  Topological features of lax algebras, (pdf)
  Appl. Categ. Structures 11 (2003), no. 3, 267–286.
• Maria Manuel Clementino, Dirk Hofmann and Walter Tholen,
  The convergence approach to exponentiable maps, (pdf)
  Port. Math. (N.S.) 60 (2003), no. 2, 139–160.
• Maria Manuel Clementino and Dirk Hofmann,
  Triquotient maps via ultrafilter convergence, (pdf)
  Proc. Amer. Math. Soc. 130 (2002), no. 11, 3423–3431.
• Maria Manuel Clementino and Dirk Hofmann,
  On limit stability of special classes of continuous maps, (pdf)
  Topology Appl. 125 (2002), no. 3, 471–488.
• Dirk Hofmann, A generalisation of the duality compactness theorem, (pdf)
  J. Pure Appl. Algebra 171 (2002), no. 2-3, 205–217.
• Dirk Hofmann, On a generalisation of the Stone-Weierstrass theorem, (pdf)
  Appl. Categ. Structures 10 (2002), no. 6, 569–592.

Other Publications

• Maria Manuel Clementino and Dirk Hofmann,
  On some special classes of continuous maps, (pdf)
  In Elliott Pearl, editor, Open Problems in Topology II, chapter 4, pages 367–376, Elsevier, 2007.
• Natürliche Dualitäten und das verallgemeinerte Stone-Weierstraß Theorem (pdf german)
  (Natural Dualities and the generalised Stone-Weierstraß Theorem),
  Ph.D. thesis, University of Bremen, Germany, June 1999.
• Ringe stetiger Funktionen (Rings of continuous functions), (pdf german)
  Diploma thesis, University of Bremen, Germany, October 1995.

Submitted Articles

• Probabilistic metric spaces as enriched categories (with Carla David Reis), (pdf)
  arXiv:math.GN/1201.1161.
• On exponentiability of étale algebraic homomorphisms (with Maria Manuel Clementino and George Janelidze), (pdf)
  Technical Report 11–35, University of Coimbra, 2011.
• Duality for distributive spaces, (pdf)
  arXiv:math.CT/1009.3892.
• A four for the price of one duality principle for distributive spaces, (pdf)
  arXiv:math.GN/1102.2605.

Slides of some talks

• Dualities for distributive spaces, (pdf)
  2011 Spring Southeastern AMS Sectional Meeting, Statesboro, GA, March 12 – 13, 2011.
• Duality-TV, (pdf)
  Workshop on Categorical Topology, Ponta Delgada, Azores, March 18 – 20, 2010.
• ’Distributors at work’ in Topology, (pdf)
  24^st Summer Conference on Topology and its Applications, Brno, Czech Republic, July 14 – 17, 2009.
• Completely Distributive Spaces, (pdf)
  CT09, Capetown, South Africa, June 29 – July 4, 2009.
• Continuous V-categories, (pdf)
  Domains IX, Brighton, UK, September 22 – 24, 2008.

Last change: January 6, 2012.

This document was translated from L^AT_EX by H^EV^EA.