Dirk Hofmann

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.

• Sergey Goncharov, Dirk Hofmann, Pedro Nora, Lutz Schröder and Paul Wild
  Relators and notions of simulation revisited, (pdf)
  arXiv: 2502.01790 [cs.LO] (2025).
• Maria Manuel Clementino, Dirk Hofmann, and Walter Tholen
  Cauchy convergence in V-normed categories, (pdf)
  arXiv: 2404.09032 [math.CT] (2024).
• Sergey Goncharov, Dirk Hofmann, Pedro Nora, Lutz Schröder and Paul Wild
  Quantalic Behavioural Distances, (pdf)
  arXiv: 2202.07069 [math.CT] (2022).
  
  
• Sergey Goncharov, Dirk Hofmann, Pedro Nora, Lutz Schröder and Paul Wild
  Identity-preserving lax extensions and where to find them, (pdf)
  In: ed. by Olaf Beyersdorff, Michał Pilipczuk, Elaine Pimentel, and Nguyễn Kim Thắng. Vol. 327. Leibniz International Proceedings in Informatics (LIPIcs). Schloss Dagstuhl Leibniz-Zentrum für Informatik, 40:1–40:20. arXiv: 2410.14440 [cs.LO]. 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025).
• Marco Abbadini and Dirk Hofmann
  Barr-coexactness for metric compact Hausdorff spaces, (pdf)
  Theory and Applications of Categories, 44 (6) (2025), 196-226.
• Maria Manuel Clementino, Carlos Fitas, and Dirk Hofmann
  A variety of co-quasivarieties, (pdf)
  Topology and its Applications (online) (2025)
  
• Sergey Goncharov, Dirk Hofmann, Pedro Nora, Lutz Schröder and Paul Wild
  A Point-free Perspective on Lax extensions and Predicate liftings, (pdf)
  Mathematical Structures in Computer Science, 34 (2) (2024), 1-30.
• Dirk Hofmann and Pedro Nora
  Duality theory for enriched Priestley spaces, (pdf)
  Journal of Pure and Applied Algebra, 227 (3) (2023), 107231.
• Jonas Forster, Sergey Goncharov, Dirk Hofmann, Pedro Nora, Lutz Schröder, and Paul Wild
  Quantitative Hennessy-Milner Theorems via Notions of Density, (pdf)
  In: ed. by Bartek Klin and Elaine Pimentel. Vol. 252. Leibniz International Proceedings in Informatics (LIPIcs). Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 22:1–22:20. arXiv: 2207.09187 [cs.LO]. Proceedings of the conference in Computer Science Logic 2023 (CSL23).
• Sergey Goncharov, Dirk Hofmann, Pedro Nora, Lutz Schröder, and Paul Wild
  Kantorovich Functors and Characteristic Logics for Behavioural Distances, (pdf)
  In: Foundations of Software Science and Computation Structures. Ed. by Orna Kupferman and Pawel Sobocinski. Vol. 13992. Lecture Notes in Computer Science. 46–67. 26th International Conference, FoSSaCS 2023, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2023, Paris, France, April 2227, 2023, Proceedings.
• Dirk Hofmann and Pedro Nora,
  Hausdorff Coalgebras, (pdf)
  Applied Categorical Structures, 28 (5) (2020), 773–806.
• Maria Manuel Clementino, Dirk Hofmann and Willian Ribeiro,
  Cartesian closed exact completions in topology, (pdf)
  Journal of Pure and Applied Algebra, 224 (2) (2020), 610–629.
• Dirk Hofmann, Renato Neves and Pedro Nora,
  Limits in Categories of Vietoris Coalgebras, (pdf)
  Mathematical Structures in Computer Science, 29 (4) (2019), 552–587.
• Dirk Hofmann and Isar Stubbe,
  Topology from enrichment: the curious case of partial metrics, (pdf)
  Cahiers de Topologie et Géométrie Différentielle Catégoriques, LIX (4) (2018), 307–353.
• 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 9 (1) (2018), 77–138.
• 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.

• 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.

• Duality theory, convergence, and enriched categories, (pdf)
  CT 2017 - International Category Theory Conference, Vancouver, Canada, July 16 - 22, 2017.
• Enriched perspectives on duality theory, (pdf)
  37th Linz Seminar on Fuzzy Set Theory, Linz, Austria, February 7 - 10, 2017.
• 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)
  24st Summer Conference on Topology and its Applications, Brno, Czech Republic, July 14 – 17, 2009.
• Completely Distributive Spaces, (pdf)
  CT 2009 - International Category Theory Conference, Capetown, South Africa, June 29 - July 4, 2009.
• Continuous V-categories, (pdf)
  Domains IX, Brighton, UK, September 22 - 24, 2008.
• Topological spaces, categorically, (pdf)
  CT 2007 – International Category Theory Conference, Carvoeiro, Algarve, Portugal, June 18 – 23, 2007.