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
  Quantalic Behavioural Distances, (pdf)
  arXiv: 2202.07069 [math.CT] (2022).
• Sergey Goncharov, Dirk Hofmann, Pedro Nora, Lutz Schröder and Paul Wild
  A Point-free Perspective on Lax extensions and Predicate liftings, (pdf)
  arXiv: 2112.12681 [math.CT] (2021).
• Dirk Hofmann and Pedro Nora
  Duality theory for enriched Priestley spaces, (pdf)
  arXiv: 2009.02303 [math.CT] (2020).
• 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.