Dirk Hofmann
I am Associate Professor at the Department of Mathematics of the University of Aveiro.
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.
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.
- 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.
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.
Slides of some talks
- 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.