Categorical Methods in Algebra, Topology, and Analysis
Supported by NSERC
Current and Recent Post-Doctoral Visitors
Renier Jansen (November 2023, visiting from the University of the Free State)
Muhammad Qasim (September 2023 - June 2024, visiting from NUST, Islamabad)
Fernando Lucatelli Nunes (July - September 2023, visiting from Utrecht University)
Amir Homayoun Nejah (July 2021 - June 2022, visiting from Shahid Beheshti University)
Leila Yeganeh (January 2020 - January 2021, visiting from Kerman University)
Paolo Perrone (September-December 2019, visiting from Max-Planck-Institut, Leipzig)
Amir Shir Ali Nasab (March-June 2018, visiting from Kerman University)
Hongliang Lai (2015-16, visiting from Sichuan University)
Lili Shen (2014-16, visiting from Sichuan University)
Current and Recent Doctoral Students
Matheus Duzi Ferreira Costa (July 2022 - June 2023, visiting from the University of Sao Paulo)
Pedro Nora (November 2017, visiting from the University of Aveiro)
Leila Yeganeh (2017, visiting from Kerman University)
Former Doctoral Students
See the Math 07 Page
Dean's Undergraduate Research Awardee
Jiyu (Gates) Wang (Summer 2018)
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Books (> 2000)
| Monoidal Topology. A Categorical Approach to Order, Metric, and Topology. Edited by Dirk Hofmann, Gavin J. Seal and Walter Tholen. Encyclopedia of Mathematics and its Applications 153, Cambridge University Press, 2014. |
| Categorical Foundations. Special Topics in Order, Topology, Algebra, and Sheaf Theory. Edited by Maria-Cristina Pedicchio and Walter Tholen. Encyclopedia of Mathematics and Its Applications 97, Cambridge University Press, 2004. |
| Galois Theory, Hopf Algebras, and Semiabelian Categories. Edited by George Janelidze, Bodo Pareigis and Walter Tholen. Fields Institute Communications 43, American Mathematical Society, 2004. |
Research Articles (> 2000)
| Cauchy convergence in V-normed categories. With M.M. Clementino and D. Hofmann. https://arxiv.org/abs/2404.09032
On the metrical and quantalic versions of the *-autonomous category of Sup-lattices. Theory and Applications of Categories 40(7) (2024) 227--248. http://www.tac.mta.ca/tac/volumes/40/7/40-07abs.html Groupoids and skeletal categories form a pretorsion theory in Cat. Advances in Mathematics 426 (2023) 109110. With F. Borceux, F. Campanini and M. Gran. https://arxiv.org/abs/2207.08487 Smallness in Topology. Quaestiones Mathematicae 46 (2023) 13-39. With J. Adamek, M. Husek, and J. Rosicky. https://arxiv.org/abs/2302.00050 A categorical review of complete regularity. Topology Proceedings 61 (2023) 305-340. With A. H. Nejah. http://arxiv.org/abs/2202.10278 Categorical extensions of dualities: from Stone to de Vries and beyond, II. Topology and its Applications 340 (2023) 108712. With G. Dimov and E. Ivanova-Dimova. http://arxiv.org/abs/2109.07172 Quotients of span categories that are allegories and the representation of regular categories. Applied Categorical Structures 30 (2022) 1177-1201, https://doi.org/10.1007/s10485-022-09687-9 . With S. N. Hosseini, A. R. Shir Ali Nasab and L. Yeganeh. http://arxiv.org/abs/2112.04599 Kan extensions are partial colimits. Applied Categorical Structures 30 (2022) 685--753. With P. Perrone. arXiv The comprehensive factorization of Burroni's T-functors. Theory and Applications of Categories 36(8) (2021) 206-249. With L. Yeganeh. pdf arXiv Diagrams, fibrations, and the decomposition of colimits. With G. Peschke. Diagrams, Fibrations, and the Decomposition of Colimits arXiv Categorical extensions of dualities: from Stone to de Vries and beyond, I. Applied Categorical Structures 30(2) (2021) 287--329 . With G. Dimov and E. Ivanova-Dimova. arXiv Semi-reflective extensions of dualities and a new approach to the Fedorchuk duality, Topology and its Applications 281 (2020) 107207. With G. Dimov and E. Ivanova-Dimova. arXiv |
| Fraction, restriction and range categories from non-monic classes of morphisms, Journal of Pure and Applied Algebra 224(9) (2020) 106361. arXiv (previous version: Abandoning monomorphisms: partial maps, fractions and factorization arXiv). With S.N. Hosseini and A.R. Shir Ali Nasab. |
| Order-enriched solid functors, Commentationes Mathematicae Universitatis Carolinae 60(4) (2019) 553-580. With Lurdes Sousa. arXiv |
| Metagories, Topology and its Applications 273 (2020). With Jiyu Wang. pdf |
| Lax pullback complements and pullbacks of spans, Theory and Applications of Categories 33(16) (2018) 445-475. With S.N. Hosseini and L. Yeganeh. pdf |
| Met-like categories amongst concrete topological categories, Applied Categorical Structures 26(5) (2018) 1095--1111 pdf |
| Quantalic topological theories, Tbilisi Mathematical Journal 10(3) (2017) 223-237. pdf |
| A note on the topologicity of quantale-valued topological spaces, Logical Methods in Computer Science 13(3) (2017) 3861. With Hongliang Lai. V-TopNoChoice |
| Monads on Q-Cat and their lax extensions to Q-Dist, Journal of Pure and Applied Algebra 222 (2018) 2143-2163. With Hongliang Lai. mon_ext_Q-cat |
| Approximate injectivity, Applied Categorical Structures 26(4) (2018) 699-716. With J. Rosicky. approx4 |
| Lax distributive laws for topology, II, Theory and Applications of Categories 32 (2017) 736-768. With Lili Shen and Hongliang Lai. LaxDistLaws.II |
| Quantale-valued topological spaces via closure and convergence, Topology and its Applications 230 (2017) 599-620. ith H. Lai. V-App0929 |
| Lax distributive laws for topology I, Cahiers de Topologie et Géométrie Différentielle Catégoriques 60(3) (2019) 311-364. LaxDistLaws |
| The fundamental group as the structure of a dually affine space, Applied Categorical Structures 24 (2016) 509-520. With E. Giuli. DuallyAffine |
| A mathematical tribute to Reinhard Börger, Cahiers de Topologie et Géométrie Différentielle Catégoriques 57(4) (2016) 295-314, ReinhardBoergerTribute |
| Categorically proper homomorphisms of topological groups, Applied Categorical Structures 24 (2016) 715-732. With W. He. C-perfect_131015 |
| Limits and colimits of quantaloid-enriched categories and their distributors, Cahiers de Topologie et Géom. Différentielle Catégoriques 56(3) (2015) 209-231. With L. Shen. Limits_and_colimits_of_quantaloidenriched_categories_and_their_distributors |
| Topological categories, quantaloids and Isbell adjunctions Topology and its Applications 200 (2016) 2012-236. With L. Shen. concrete_categories_preprint |
| From lax monad extensions to topological theories, Textos de Matematica (Coimbra) 46 (2014) 99-123. With M. M. Clementino. ClementinoTholen |
| Dual closure operators and their applications, Journal of Algebra 439 (2015) 373-416. With D. Dikranjan. Dclop-20June2014 |
| Nullstellen and subdirect representation, Applied Categorical Structures 22 (2014) 907-929. nullstMarch2013bis |
| Proper maps and the Kuratowski-Mrowka Theorem, Theory and Applications of Categories 27 (2013) 327-346. With Maria Manuel Clementino. Kuratowski_Mrowka |
| Lax algebra meets topology, Topology and its Applications 159 (2012) 2434-2452, with Dirk Hofmann. alg_meets_top_final |
| Kleisli enriched, Journal of Pure and Applied Algebra 216 (2012) 1920-1931. kleisli |
| Closure operators and their middle-interchange law, Topology and its Applications 158 (2011) 2437-2441. middle-interchange |
| On the categorical meaning of Hausdorff and Gromov distances, I, Topology and its Applications 157 (2010) 1275-1295. With Andrei Akhvlediani and Maria Manuel Clementino. Hausdorff and Gromov |
| Ordered topological structures, Topology and its Applications 156 (2009) 2149-2157. ots_d3_reworded |
| Ideal determined categories, Cahiers Topologie Géométrie Différentielle Catégoriques 51 (2010). With G. Janelidze, L. Marki and A. Ursini. Microsoft Word - JMTU_200907302200 |
| Strongly separable morphisms in general categories, Theory and Applications of Categories 23 (2009) 136-149. With G. Janelidze.Strongly-separable-20090731a |
| Injectivity versus exponentiability, Cahiers Topologie Géométrie Différentielle Catégoriques 59 (2008) 228-240. Injectivity_vs_exponentiability |
| Lawvere completion and separation via closure, Applied Categorical Structures. With Dirk Hofmann. lcosureAPCS_rev |
| A topologist's view of Chu spaces, Applied Categorical Structures 15 (2007) 573-598. With Eraldo Giuli. chu_tholen |
| Factorization, fibration and torsion, Journal of Homotopy Theory and Related Structures 2 (2007) 295-314. With J. Rosicky'. TF2 |
| Natural weak factorization systems, Archivum Mathematicum 42 (2006) 397-408. With Marco Grandis. Natwfs |
| Characterization of torsion theories in general categories, Contemporary Mathematics 431 (2007). With George Janelidze. CTTGC . |
| Torsion theories and radicals in normal categories, Journal of Algebra 305 (2006) 98-129. With M. M. Clementino and D. Dikranjan. TT |
| Universality of coproducts in categories of lax algebras, Applied Categorical Structures 14 (2006) 243-249. With M. Mahmoudi and C. Schubert. UnivCoprod_final |
| Facets of descent III: Monadic descent for rings and algebras, Applied Categorical Structures 12 (2004) 461-477. With G. Janelidze facets3 |
| Classification of closure operators for categories of topological spaces. In: Categorical Structures and Their Applications, edited by W. Gähler and G. Preuss, pp69-98 (World Scientific, Singapore 2004). With D. Dikranjan and S. Watson. DTW_sub |
| Kleisli operations for topological spaces, Topology and its Applications 153 (2006) 2952-2961. With D. Hofmann. kleislitopdirk |
| Descent Equivalence, Cahiers Topologie Géom. Différentielle Catégoriques 44 (2004) 301-352. With X. Guo and M. Sobral. DesEqu |
| One setting for all: metric, topology, uniformity, approach structure, Applied Categorical Structures 12 (2004) 127-154. With M. M. Clementino and D. Hofmann. ProMat_V_
Metric , topology and multicategory--A common approach. Journal of Pure and Applied Algebra 179 (2003) 13-47. With M.M. Clementino. doi_10.1016_S0022-4049(02)00246-3 |
| Exponentiability in categories of lax algebras, Theory and Applications of Categories 11 (2003) 337-352. With M. M. Clementino and D. Hofmann. pproducts |
| The convergence approach to exponentiable maps, Portugaliae Mathematica 60 (2003) 139-160. With M.M. Clementino and D. Hofmann. Convexp |
| Left-determined model categories and universal homotopy theories, Transactions of the American Mathematical Society 355 (2003) 13-47. With J. Rosicky'. HOM |
| Semi-abelian categories, Journal of Pure and Applied Algebra 168 (2002) 367-386. With G. Janelidze and L. Ma'rki. semiabelian2000 |
| Weak factorization systems and topological functors, Applied Categorical Structures 10 (2002) 237-249. With J. Ada'mek, H. Herrlich, and J. Rosicky'. ahrt3 (3) |
| Lax factorization algebras, Journal of Pure and Applied Algebra 175 (2002) 355-382. With J. Rosicky'. laxalg |
| Injective hulls are not natural, Algebra Universalis 48 (2002) 379-388. With J. Ada'mek, H. Herrlich and J. Rosicky'. article |
| On a generalized small-object argument for the Injective Subcategory Problem, Cahiers de Topologie et Géométrie Différentielle Catégoriques 43 (2002) 83-106, with J. Ada'mek, H. Herrlich, and J. Rosicky'. ahrt2 (1) |
| Free Quillen factorization systems, Georgian Mathematical Journal 9 (2002) 807-820. With A. Pultr. Quillen |
| Essential weak factorization systems, Contributions to General Algebra 13 (2001) 321-333. newessential |
| Perfect Maps are exponentiable - categorically, Theory and Applications of Categories 8 (2001) 321-333. With Gunther Richter. pdf |
| A note on local compactness, Rendiconti dell'Istituto di Matematica dell' Universita' di Trieste, Suppl. 2, 32 (2001) 17-31. With M.M. Clementino. loc-comp-latest |
| Atlantis Preface Introduction I II chapter3 IV V VI VII VIII |
Some oldies that are harder to find elsewhere:
| Relative Bildzerlegungen und algebraische Kategorien, Ph. D. thesis (Muenster 1974). PhD_Thesis |
| Reinhard Boerger's Master's thesis: Kongruenzrelationen auf Kategorien, Diplomarbeit, Muenster 1977. Available at BörgerThesis2
Cantor's diagonal principle for categories. English translation of "Cantors Diagonalprinzip fuer Kategorien", Mathematische Zeitschrift 160:135-138, 1978. With R. Boerger. Translated and commented by G.C.L. Brummer, August 2005. pdf Birkhoff's Theorem for categories, in: Lecture Notes in Mathematics 915 (Springer, Berlin 1982), pp 351--357. Birkhoff |
| Factorizations, fibres and connectedness, in: Proceedings of the Conference on Categorical Topology, Toledo 1983 (Heldermann, Berlin 1984), pp 549--566. FactsFibsConns |
| Concrete dualities, in: Category Theory at Work (Heldermann, Berlin 1991), pp 111--136. With H.-E. Porst. DualitiesPorstTholen
Categorical algebraic properties. A compendium on amalgamation, congruence extension, epimorphisms, residual smallness, and injectivity. Studia Scientiarum Mathematicarum Hungarica 18 (1983): 79--141. With E.W. Kiss, L. Marki, P. Prohle. kmpt_pp79-111 kmpt_pp111-141 |
General Mathematical Interest Articles
| Saunders Mac Lane 1909-2005, Meeting a Grand Leader. Scientiae Matematicae Japonicae 19 (2006) 13-24. Saunders Mac Lane |
| Mathematics: Beauty and the Beast. PublicLectureBeautyBeast |
Upcoming and Recent Conferences
PSSL 106, Brno (Czech Republic). Presentation: Quantale-weighted categories PSSL106
--Topology, Algebra, Categories in Logic (TACL 2022), June 2022, Coimbra (Portugal). Minicourse: From metric spaces to quantale-enriched categories TACL School 2022
-- 5th Workshop on Categorical Algebra, Gargnano (Italy), April 2022. Presentation: Another categorical look at monoids, quantales, metrics, etc. CatAlg2022
-- Algebra, Topology and Dynamical Systems (ATDS 2020, Conference in Honour of Dikran Dikranjan), Udine (Italy), July 28-31, 2020. Postponed to September 2021. Minicourse: Topological vistas from considering spaces as small categories. Udine2021slides
-International Conference on Category Theory (CT 2020), Genoa (Italy), June 21-27, 2020. Postponed to September 2021. Presentation: Monoidal topology: advances and challenges. CT20->21_tholen
--2020 Summer Conference on Topology and its Applications, Youngstown (OH) (USA), July 13-17, 2020. Special Session on Enriched Categories and Topology (organized by D. Hofmann, U. Hoehle, I. Stubbe, W. Tholen). Postponed to 2023.
-- Applied Category Theory 2019, Oxford (U.K.), July 15-19, 2019, University of Oxford. Presentation: Approximate composition. ACT2019TholenSlides
-- Category Theory 2019, Edinburgh (U.K.), July 7-13, 2019, University of Edinburgh.. Presentation: Functorial decomposition of colimits (joint work with George Peschke). CT2019TholenSlides
-- Topology, Algebra, and Categories in Logic, Nice (France), June 17-21, 2019, Universite' Cote d'Azur. Presentation on: Semi-reflective extensions of dualities and a new approach to the Fedorchuk duality (joint work with G. Dimov and E Ivanova-Dimova). TACL2019Tholen
-- PSSL 105 (105th Peripatetic Seminar on Sheaves and Logic), Palermo (Italy), May 17-19, 2019, University of Palermo. Presentation on: Abandoning monomorphisms: partial maps, fractions and factorizations (joint work with S. N. Hosseini and A.R. Shir Ali Nasab). PSSL105Tholen
-- Workshop on Algebra, Logic and Topology, Coimbra (Portugal), September 27-29, 2018, University of Coimbra, organized by M. M. Clementino, M. J. Ferreira, J. Picado, S. Pinto and M Sobral. Presentation: Metagories (joint work J. Wang) Metagories13Oct2018
-- Category Theory 2018, Ponta Delgada (Azores, Portugal), July 08-14, 2018, University of Azores, organized by M. M. Clementino et al. Presentation: Remarks on weighted categories and the non-symmetric Pompeiu-Hausdorff-Gromov metric.
-- CatAlg2018 - 4th Workshop on Categorical Algebra, Gargnano (Italy), May 28- June 01, 2018, Universita degli Studi di Milano, organized by A. S. Cigoli, S. Mantovani, G. Metere , A. Montoli. Presentation: Factorizations then and now Gargnano2018
Past Conferences
| Category Theory 2006 (CT06), White Point (Nova Scotia), 25 June - 01 July 2006, Dalhousie University, organized by Robert Dawson, Dorette Pronk and Peter Selinger. Presentation: Mac Lane and Factorizations. PresentationCT2006[94] |
| Summer Conference on Topology and Its Applications, Satesboro GA, 6-9 July 2006, Georgia Southern University, organized by Martha Abell, Francis Jordan, Frederic Mynard, and Sze-Man Ngai. Presentation: Macro- and Micro-Aspects of Categorical Topology . |
| Summer School on Contemporary Categorical Methods in Algebra and Topology, Haute-Bodeux (Belgium), 3-10 June 2007, Université Catholique de Louvain, organized by Francis Borceux. Lectures on Lax-algebraic methods in General Topology: Lecture 1, Lecture 2. |
| Category Theory 2007 (CT07), Algarve (Portugal), 17-23 June, University of the Algarve, organized by Diana Rodelo et al. Presentation: Topology for V-categories and (T,V)-categories. |
| Categorical Methods in Algebra, Topology and Computer Science, Coimbra (Portugal), 26-28 October 2007, University of Coimbra, organized by Maria Manuel Clementino and Lurdes Sousa. |
| Mathematical Applications of Category Theory, London (Ontario), 8-10 December 2007, Special Session at the Winter Meeting of the Canadian Mathematical Society, organized by F. William Lawvere and Walter Tholen. |
| Aspects of Contemporary Topology III, Antwerp (Belgium), 9-15 December 2007, University of Antwerp, organized by Eva Colebunders , Bob Lowen, Mark Sioen and Stijn Verwulgen. |
| Advances in Set-Theoretic Topology, Erice (Sicily, Italy), 9-19 June 2008, International School of Mathematics "G. Stampacchia", organized by Gino Tironi et al. |
| International Category Theory Conference (CT08), Calais (France), 23-28 June 2008, Université du Littoral, organized by Dominique Bourn and Marino Gran. Presentation: Injectivity, exponentiability, and completeness (Slides 1-4, 5-8, 9-12,13-16, 17-20, 21-24, 25-27). |
| Conference in honour of Francis Borceux and Dominique Bourn, Brussels (Belgium), 10-11 October 2008. Organized by Marino Gran, Rudger Kieboom and Enrico Vitale. Presentation: On the categorical meaning of Hausdorff and Gromov distances (Slides 0-2, 3-6, 7-11). |
| 88th Peripatetic Seminar on Sheaves and Logic - in Honour of Martin Hyland and Peter Johnstone, Cambridge (UK), 4-5 April 2009. Organized by Eugenia Cheng and Andy Pitts. |
| International Conference in Category Theory (CT09), 29 June - 4 July 2009, University of Cape Town (South Africa). Organized by George Janelidze et al. |
| 24th Summer Conference on Topology and its Applications, Brno (Czech Republic), 14-17 July 2009. Organized by Josef Slapal. |
| Aspects of Contemporary Topology IV, Antwerp (Belgium), 14-18 December 2009, University of Antwerp. Organized by Eva Colebunders , Bob Lowen, Mark Sioen. |
| Conference on Categorical Topology, in honour of Eraldo Giuli, Ponta Delgada (Portugal), 18-20 March 2010. Organized by Margerida Dias, et al. |
| 91st Peripatetic Seminar on Sheaves and Logic, Amsterdam (The Netherlands), 27-28 November 2010, University of Amsterdam. Organized by Raul Leal Rodriguez, et al. |
| AMS Sectional Meeting (#1068), Section on Categorical Topology, Statesboro (GA), 12-13 March 2011, University of Southern Georgia. Organized by Frederic Mynard and Gavin Seal. |
| Mathematics Conference, Schenectady (NY), 30 April - 1 May 2011, Union College. Organized by Susan Niefield, et al. |
| International Category Theory Meeting (CT2011), Vancouver (BC), 18-23 July 2011, University of British Columbia. Organized by John MacDonald, et al. Presentation on Topology in categories of (T,V)-categories. |
| Workshop on Category Theory (Conference in honour of George Janelidze), Coimbra (Portugal), 9-13 July 2012. Organized by Maria Manuel Clementino, et al. Presentation: A personal glance at George's category theory. PresentationCoimbra2012 |
| 85th Workshop on General Algebra (Arbeitstagung Allgemeine Algebra), Luxemburg, 31 January - 2 February 2013. Organized by Erkko Lehtonen, et al. Presentation on Nullstellen and Subdirect Representation. |
| Workshop on Algebra and Topology, Coimbra (Portugal), February 2013. |
| International Category Theory Meeting (CT 2014), Cambridge (U.K.), July 2014. Presentation on Concordant and Monotone Maps in (Extensive) Categories. |
| 3rd Workshop on Categorical Algebra, Gargnano (Italy), April 2015. |
| Joint Intnl. Meeting AMS-EMS-Portuguese Math. Soc., Special Session on Categorical Methods in in Algebra and Topology, Porto (Portugal), June 2015. |
| International Category Theory Meeting (CT 2015), Aveiro (Portugal), July 2015. |
| 1st Pan-Pacific Conference on Topology and Applications, Zhang Zhou (China), 25--30 November 2015. Presentation on Monoidal Topology 1stPanPacificTop |
| Symposium on Algebra, Topology and Category Theory, on the Occasion of the 90th Birthday of Bernhard Banaschewski, Cape Town (South Africa), March 2016. |
| International Category Theory Meeting (CT 2016), Halifax (Canada), July 2016. |
| 32nd Summer Conference on Topology and Its Applications, Dayton OH (U.S.A.), June 2017. Presentation on Order, Distance, Closure and Convergence: Reconciling Competing Fundamental Topological Concepts. WT SummerTopology2017 |
