Mini Curriculum
International Dual Degree
Workshop Haute Bodeux 07


Categorical Methods in Algebra, Topology, and Analysis 

Supported by NSERC


Current and Recent Doctoral Students

Pedro Nora (November 2017, visiting from the University of Aveiro)

Leila Yeganeh (2017, visiting from Kerman University)

Former Doctoral Students

See the Math Genealogy Page

Current and Recent Post-Doctoral Visitors

Amir Shr 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)

Dean's Undergraduate Research Awardee

Jiyu (Gates) Wang (Summer 2018)


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)

Semi-reflective extensions of dualities and a new approach to the Fedorchuk duality, with G. Dimov and E. Ivanova-Dimova. arXiv
Abandoning monomorphisms: partial maps, fractions and factorizations, with S.N. Hosseini and A.R. Shir Ali Nasab. arXiv
Order-enriched solid functors, with Lurdes Sousa. arXiv
Metagories, with Jiyu Wang. pdf
Lax pullback complements and pullbacks of spans, with S. N. Hosseini and L. Yeganeh, Theory and Applications of Categories 33(16) (2018) 445-475.  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. pdf
Monads on Q-Cat and their lax extensions to Q-Dist, Journal of Pure and Applied Algebra 222 (2018) 2143-2163, with Hongliang Lai. pdf
Approximate injectivity, Applied Categorical Structures 26(4) (2018) 699-716, with J. Rosicky.  pdf
Lax distributive laws for topology, II, Theory and Applications of Categories 32 (2017) 736-768, with Lili Shen and Hongliang Lai. pdf
Quantale-valued topological spaces via closure and convergence, Topology Applications 230 (2017) 599-620, with H. Lai. pdf
Lax distributive laws for topology, I. pdf
The fundamental group as the structure of a dually affine space, Applied Categorical Structures 24 (2016) 509-520, with E. Giuli. pdf
A mathematical tribute to Reinhard Brger,Cahiers Topologie Gom. Diffrentielle Catgoriques 57(4) (2016) 295-314, pdf 
Categorically proper homomorphisms of topological groups, Applied Categorical Structures 24 (2016) 715-732, with W. He. pdf
Limits and colimits of quantaloid-enriched categories and their distributors, Cahiers Topologie Gom. Diffrentielle Catgoriques 56(3) (2015) 209-231, with L. Shen. pdf
Topogical categories, quantaloids and Isbell adjunctions Topology and its Applications 200 (2016) 2012-236, with L. Shen. pdf
From lax monad extensions to topological theories, Textos Matematicos 46 (2014) 99-123, with M. M. Clementino. pdf
Dual closure operators and their applications, Journal of Algebra 439 (2015) 373-416, with D. Dikranjan. pdf
Nullstellen and subdirect representation, Applied Categorical Structures 22 (2014) 907-929. pdf
Proper maps and the Kuratowski-Mrowka Theorem, Theory and Applications of Categories 27 (2013) 327-346, with Maria Manuel Clementino. pdf
Lax algebra meets topology, Topology and its Applications 159 (2012) 2434-2452, with Dirk Hofmann. pdf
Kleisli enriched, Journal of Pure and Applied Algebra 216 (2012) 1920-1931. pdf
Closure operators and their middle-interchange law, Topology and its Applications 158 (2011) 2437-2441, pdf
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. pdf
Ordered topological structures, Topology and its Applications 156 (2009) 2149-2157. pdf
Ideal determined categories, Cahiers Topologie Gom. Diffrentielle Catgoriques 51 (2010), with G. Janelidze, L. Marki and A. Ursini. pdf
Strongly separable morphisms in general categories, Theory Appl. Categories 23 (2009) 136-149, with G. Janelidze. pdf
Injectivity versus exponentiability, Cahiers Topologie Gom. Diffrentielle Catgoriques 59 (2008) 228-240. pdf
Lawvere completion and separation via closure, Applied Categorical Structures, with Dirk Hofmann. pdf
A topologist's view of Chu spaces, Applied Categorical Structures 15 (2007) 573-598, with Eraldo Giuli. pdf
Factorization, fibration and torsion, J. Homotopy Theory and Related Structures (to appear), with J. Rosicky'. pdf
Natural weak factorization systems, Archivum Mathematicum 42 (2006) 397-408, with Marco Grandis. pdf
Characterization of torsion theories in general categories, Contemporary Mathematics  (to appear), with George Janelidze. pdf, ps.
Torsion theories and radicals in normal categories, Journal of Algebra 305 (2006) 98-129, with M. M. Clementino and D. Dikranjan. pdf.
Universality of coproducts in categories of lax algebras, Applied Categorical Structures 14 (2006) 243-249, with M. Mahmoudi and C. Schubert. pdf.
Facets of descent III: Monadic descent for rings and algebras, Applied Categorical Structures 12 (2004) 461-477,  with G. Janelidze ps, pdf.
Classification of closure operators for categories of topological spaces. In: Categorical Structures and Their Applications, edited by W. Ghler and G. Preuss, pp69-98 (World Scientific, Singapore 2004), with D. Dikranjan and S. Watson. pdf, ps.
Kleisli operations for topological spaces, Topology and its Applications 153 (2006) 2952-2961, with D. Hofmann pdf.
Descent Equivalence, Cahiers Topologie Gom. Diffrentielle Catgoriques 44 (2004) 301-352, with X. Guo and M. Sobral. ps, pdf.
One setting for all: metric, topology, uniformity, approach structure, Applied Categorical Structures 12 (2004) 127-154, with M. M. Clementino and D. Hofmann. pdf.
Exponentiability in categories of lax algebras, Theory and Applications of Categories 11 (2003) 337-352, with M. M. Clementino and D. Hofmann. pdf.
The convergence approach to exponentiable maps, Math. Portugaliae 60 (2003) 139-160, with M.M. Clementino and D. Hofmann. pdf
Left-determined model categories and universal homotopy theories Transactions American Math. Soc. 355 (2003) 13-47, with J. Rosicky'. ps, pdf.
Semi-abelian categories, J. Pure Appl. Algebra 168 (2002) 367-386, with G. Janelidze and L. Ma'rki. ps
Weak factorization systems and topological functors, Appl. Categorical Structures 10 (2002) 237-249, with J. Ada'mek, H. Herrlich, and J. Rosicky'. ps
Lax Factorization Algebras J. Pure Appl. Algebra 175 (2002) 355-382 with J. Rosicky'. ps, pdf.
Injective hulls are not natural, Algebra Universalis 48 (2002) 379-388 with J. Ada'mek, H. Herrlich and J. Rosicky'. ps
On a generalized Small-Object Argument for the Injective Subcategory Problem, Cahiers Topologie Geom. Differentielle Categoriques 43 (2002) 83-106, with J. Ada'mek, H. Herrlich, and J. Rosicky'. ps
Free Quillen factorization systems, Georgian J. Math. 9 (2002) 807-820, with A. Pultr. pdf.
Essential weak factorization systems Contributions to General Algebra 13 (2001) 321-333. ps
Perfect Maps are exponentiable - categorically, Theory Appl. Categories 8 (2001) 321-333, with G\"unther Richter. ps
A note on local compactness, Rendiconti Ist. Mat. Univ. Trieste Suppl. 2, 32 (2001) 17-31, with M.M. Clementino. ps
Atlantis  Preface Introduction I II III IV V VI VII VIII

Some oldies that are harder to find elsewhere:

Relative Bildzerlegungen und algebraische Kategorien, Ph. D. thesis (Muenster 1974). pdf
Birkhoff's Theorem  for categories, in: Lecture Notes in Math. 915 (Springer, Berlin 1982), pp 351--357. pdf
Factorizations, fibres and connectedness, in: Proc. Conf. Categorical Topology, Toledo 1983 (Heldermann, Berlin 1984), pp 549--566. pdf
Concrete dualities, in: Category Theory at Work (Heldermann, Berlin 1991), pp 111--136, with H.-E. Porst. pdf


General Mathematical Interest Articles

Saunders Mac Lane 1909-2005, Meeting a Grand Leader. Scientiae Matematicae Japonicae 19 (2006) 13-24 pdf
Mathematics: Beauty and the Beast. ppt


Upcoming and Recent Conferences

-- 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.

--  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


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 .
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, Universit 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, Universit 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.
Workshop on Category Theory (Conference in honour of George Janelidze), Coimbra (Portugal), 9-13 July 2012. Organized by Maria Manuel Clementino, et al.
85th Workshop on General Algebra (Arbeitstagung Allgemeine Algebra), Luxemburg, 31 January - 2 February 2013. Organized by Erkko Lehtonen, et al.
Workshop on Algebra and Topology, Coimbra (Portugal), February 2013.
International Category Theory Meeting (CT 2014), Cambridge (U.K.), July 2014.
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.
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.



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