Dirk Hofmann

I am Assistant Professor at the Department of Mathematics of the University of Aveiro.

picdirk.jpeg

The picture was taken during CT2015 at the University of Aveiro.

Contact:

Departamento de Matemática
Universidade de Aveiro
3810-193 Aveiro
Portugal
Phone: (+351) 234 370 681
Email: dirk@ua.pt (please note this)

Research

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

I am Editor of Theory and Applications of Categories and Honorary Associate Editor of Categories and General Algebraic Structures with Applications.

From June 14 - 19, 2015, we organised here at the University of Aveiro the conference Category Theory 2015. The conference webpage can be found here.

Since February 2017 we (together with Uwe Kähler) run a seminar for PhD-students (within our research unit CIDMA), the program is here.

Publications

For my work, I use Arch Linux (with i3 windows manager), Latex, Emacs (including Reftex, Auctex, Org-mode and many other packages) and Git. I cannot imagine doing research without these free tools.

  • Dirk Hofmann, Renato Neves and Pedro Nora,
    Limits in Categories of Vietoris Coalgebras, (pdf)
    Technical report, arXiv:cs.LO/1612.03318, 2017.
  • Dirk Hofmann and Isar Stubbe,
    Topology from enrichment: the curious case of partial metrics, (pdf)
    Cahiers de Topologie et Géométrie Différentielle Catégoriques (in press).
  • Dirk Hofmann, Renato Neves and Pedro Nora,
    Generating the algebraic theory of C(X): the case of partially ordered compact spaces, (pdf)
    Theory and Applications of Categories, 33 (12) (2018), 276–295.
  • Dirk Hofmann and Pedro Nora,
    Enriched Stone-type dualities, (pdf)
    Advances in Mathematics 330 (2018) 307–360.
  • Dirk Hofmann and Carla Reis,
    Convergence and quantale-enriched categories, (pdf)
    Categories and General Algebraic Structures with Applications (in press).
  • Dirk Hofmann and Lurdes Sousa,
    Aspects of algebraic algebras, (pdf)
    Logical Methods in Computer Science 13 (3) (2017), 1-25.
  • Maria Manuel Clementino and Dirk Hofmann,
    The Rise and Fall of V-functors, (pdf)
    Fuzzy Sets and Systems 321 (2017), 29-49.
  • Maria Manuel Clementino, Dirk Hofmann and George Janelidze,
    On exponentiable morphisms in classical algebra, (pdf)
    Applied Categorical Structures 24 (5) (2016), 733-742.
  • Dimitri Chikhladze, Maria Manuel Clementino and Dirk Hofmann,
    Representable (T,V)-categories, (pdf)
    Applied Categorical Structures 23 (6) (2015), 829-858.
  • Dirk Hofmann and Gavin J. Seal,
    A cottage industry of lax extensions, (pdf)
    Categories and General Algebraic Structures with Applications 3 (1) (2015), 113-151.
  • Dirk Hofmann and Gavin J. Seal,
    Exponentiable approach spaces, (pdf)
    Houston Journal of Mathematics 41 (3) (2015), 1051-1062.
  • Dirk Hofmann and Pedro Nora,
    Dualities for modal algebras from the point of view of triples, (pdf)
    Algebra Universalis 73 (3) (2015), 297-320.
  • Dirk Hofmann, Frédéric Mynard and Gavin Seal,
    Exponential Kleisli monoids as Eilenberg-Moore algebras, (pdf)
    Applied Categorical Structures 23 (2) (2015), 137-157.
  • Dirk Hofmann and Pedro Nora,
    Some notes on Esakia spaces, (pdf)
    Textos de Matemática - Universidade de Coimbra 46 (2014), 201-220.
  • Maria Manuel Clementino, Dirk Hofmann and Andrea Montoli,
    Covering morphisms in categories of relational algebras, (pdf)
    Applied Categorical Structures 22 (5) (2014), 767-788.
  • Dirk Hofmann, The enriched Vietoris monad on representable spaces, (pdf)
    Journal of Pure and Applied Algebra 218 (12) (2014), 2274-2318.
  • Maria Manuel Clementino, Dirk Hofmann and George Janelidze,
    The monads of classical algebra are seldom weakly cartesian, (pdf)
    Journal of Homotopy and Related Structures 9 (1) (2014), 175-197.
  • Dirk Hofmann and Manuel A. Martins,
    On a coalgebraic view on logic, (pdf)
    Journal of Logic and Computation 23 (5) (2013), 1097-1106.
  • Gonçalo Gutierres and Dirk Hofmann,
    Approaching metric domains, (pdf)
    Applied Categorical Structures 21 (6) (2013), 617-650.
  • Dirk Hofmann, A four for the price of one duality principle for distributive spaces, (pdf)
    Order 30 (2) (2013), 643-655.
  • Maria Manuel Clementino, Dirk Hofmann and George Janelidze,
    On exponentiability of étale algebraic homomorphisms, (pdf)
    Journal of Pure and Applied Algebra 217 (7) (2013), 1195-1207.
  • Dirk Hofmann, Duality for distributive spaces, (pdf)
    Theory and Applications of Categories 28 (3) (2013), 66-122.
  • Dirk Hofmann and Carl David Reis,
    Probabilistic metric spaces as enriched categories, (pdf)
    Fuzzy Sets and Systems 210 (2013), 1-21.
  • Maria Manuel Clementino and Dirk Hofmann,
    Descent morphisms and a van Kampen theorem in categories of lax algebras, (pdf)
    Topology and its Applications 159 (9) (2012), 2310-2319.
  • Dirk Hofmann and Walter Tholen,
    Lax algebra meets topology, (pdf)
    Topology and its Applications 159 (9) (2012), 2434-2452.
  • Dirk Hofmann and Paweł Waszkiewicz,
    A duality of quantale-enriched categories, (pdf)
    Journal of Pure and Applied Algebra 216 (8-9) (2012), 1866-1878.
  • Maria Manuel Clementino and Dirk Hofmann,
    On the completion monad via the Yoneda embedding in quasi-uniform spaces, (pdf)
    Topology and its Applications 158 (17) (2011), 2423-2430.
  • Dirk Hofmann and Paweł Waszkiewicz,
    Approximation in quantale-enriched categories, (pdf)
    Topology and its Applications, 158 (8) (2011), 963-977.
  • Dirk Hofmann and Isar Stubbe,
    Towards Stone duality for topological theories, (pdf)
    Topology and its Applications 158 (7) (2011), 913-925.
  • Dirk Hofmann, Injective Spaces via Adjunction, (pdf)
    Journal of Pure and Applied Algebra 215 (3) (2011), 283-302.
  • Dirk Hofmann and Walter Tholen,
    Lawvere completion and separation via closure, (pdf)
    Applied Categorical Structures 18 (2010), 259-287.
  • Eraldo Giuli and Dirk Hofmann,
    Affine sets: the structure of complete objects and duality, (pdf)
    Topology and its Applications 156 (2009), 2129-2136.
  • Gonçalo Gutierres and Dirk Hofmann,
    Sequential convergence via Galois Correspondences, (pdf)
    Acta Mathematica Hungarica 123 (2009), 187-202.
  • Maria Manuel Clementino and Dirk Hofmann,
    Lawvere completeness in Topology, (pdf)
    Applied Categorical Structures 17 (2009), 175-210.
  • Maria Manuel Clementino and Dirk Hofmann,
    Relative injectivity as cocompleteness for a class of distributors, (pdf)
    Theory and Applications of Categories 21 (2009), 210-230.
  • Maria Manuel Clementino, Dirk Hofmann and Isar Stubbe,
    Exponentiable functors between quantaloid-enriched categories, (pdf)
    Applied Categorical Structures 17 (2009), 91-101.
  • Dirk Hofmann, Topological theories and closed objects, (pdf)
    Advances in Mathematics 215 (2007), 789-824.
  • Gonçalo Gutierres and Dirk Hofmann,
    Axioms for sequential convergence, (pdf)
    Applied Categorical Structures 15 (2007), no.5-6, 599-614.
  • Dirk Hofmann, Exponentiation for unitary structures, (pdf)
    Topology and its Applications 153 (2006), 3180-3202.
  • Maria Manuel Clementino and Dirk Hofmann,
    Exponentiation in V-categories, (pdf)
    Topology and its Applications 153 (2006), 3113-3128.
  • Dirk Hofmann and Walter Tholen,
    Kleisli operations for topological spaces, (pdf)
    Topology and its Applications 153 (2006), 2952-2961.
  • Dirk Hofmann, An algebraic description of topological quotient maps, (pdf)
    Journal of Pure and Applied Algebra 199 (2005), 71-86.
  • Maria Manuel Clementino, Dirk Hofmann and George Janelidze,
    Local homeomorphisms via ultrafilter convergence, (pdf)
    Proceedings of the American Mathematical Society 133 (2005), no. 3, 917-922.
  • Maria Manuel Clementino and Dirk Hofmann,
    On extensions of lax monads, (pdf)
    Theory and Applications of Categories 13 (2004), No. 3, 41-60.
  • Maria Manuel Clementino and Dirk Hofmann,
    Effective descent morphisms in categories of lax algebras, (pdf)
    Applied Categorical 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)
    Applied Categorical Structures 12 (2004), no. 2, 127-154.
  • Maria Manuel Clementino, Dirk Hofmann and Walter Tholen,
    Exponentiability in categories of lax algebras, (pdf)
    Theory and Applications of Categories 11 (2003), No. 15, 337-352.
  • Maria Manuel Clementino and Dirk Hofmann,
    Topological features of lax algebras, (pdf)
    Applied Categorical Structures 11 (2003), no. 3, 267-286.
  • Maria Manuel Clementino, Dirk Hofmann and Walter Tholen,
    The convergence approach to exponentiable maps, (pdf)
    Portugaliae Mathematica (N.S.) 60 (2003), no. 2, 139-160.
  • Maria Manuel Clementino and Dirk Hofmann,
    Triquotient maps via ultrafilter convergence, (pdf)
    Proceedings of the American Mathematical Society 130 (2002), no. 11, 3423-3431.
  • Maria Manuel Clementino and Dirk Hofmann,
    On limit stability of special classes of continuous maps, (pdf)
    Topology and its Applications 125 (2002), no. 3, 471-488.
  • Dirk Hofmann, A generalisation of the duality compactness theorem, (pdf)
    Journal of Pure and Applied Algebra 171 (2002), no. 2-3, 205-217.
  • Dirk Hofmann, On a generalisation of the Stone-Weierstrass theorem, (pdf)
    Applied Categorical Structures 10 (2002), no. 6, 569-592.

Other Publications

  • Dirk Hofmann, Gavin J. Seal and Walter Tholen (eds),
    Monoidal Topology. A Categorical Approach to Order, Metric, and Topology, (pdf)
    Cambridge University Press, 2014.
    Authors: Maria Manuel Clementino, Eva Colebunders, Dirk Hofmann, Robert Lowen, Rory Lucyshyn-Wright, Gavin J. Seal and Walter Tholen.
  • 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.
  • Injective spaces via adjunction, (pdf english) (pdf portuguese)
    Scientific report for my Habilitation (“Agregação”), University of Aveiro, Portugal, January 2015.
  • 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.

Slides of some talks

Author: Dirk Hofmann

Created: 2018-08-05 Sun 16:44

Emacs 26.1 (Org mode 9.1.9)

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