Categorical Methods in Algebra, Topology, and
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
Current and Recent Post-Doctoral Visitors
Amir Shr Ali Nasab (March-June 2018, visiting from
Hongliang Lai (2015-16, visiting from Sichuan
Lili Shen (2014-16, visiting from Sichuan University)
Dean's Undergraduate Research Awardee
Jiyu (Gates) Wang (Summer 2018)
Books (> 2000)
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
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
|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
|Approximate injectivity, Applied Categorical Structures 26(4)
(2018) 699-716, with J. Rosicky.
|Lax distributive laws for topology, II, Theory and Applications
of Categories 32 (2017) 736-768, with Lili Shen and Hongliang
|Quantale-valued topological spaces via closure and convergence, Topology
Applications 230 (2017) 599-620, with H.
|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
Börger,Cahiers Topologie Géom. Différentielle
Catégoriques 57(4) (2016)
295-314, pdf |
|Categorically proper homomorphisms of topological groups, Applied
Categorical Structures 24 (2016) 715-732, with W.
|Limits and colimits of quantaloid-enriched categories and their
distributors, Cahiers Topologie Géom. Différentielle
Catégoriques 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.
|From lax monad extensions to topological theories, Textos
Matematicos 46 (2014) 99-123, with M. M.
|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
|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 Géom. Différentielle
Catégoriques 51 (2010), with G. Janelidze, L. Marki and A. Ursini.
|Strongly separable morphisms in general categories, Theory Appl.
Categories 23 (2009) 136-149, with G. Janelidze.
|Injectivity versus exponentiability, Cahiers Topologie Géom. Différentielle
Catégoriques 59 (2008) 228-240.
|Lawvere completion and separation via closure, Applied Categorical
Structures, with Dirk Hofmann.
|A topologist's view of Chu spaces, Applied Categorical Structures
15 (2007) 573-598, with Eraldo Giuli.
|Factorization, fibration and torsion, J. Homotopy Theory and
Related Structures (to appear), with J. Rosicky'.
|Natural weak factorization systems, Archivum Mathematicum 42
(2006) 397-408, with Marco Grandis.
|Characterization of torsion theories in general categories,
Contemporary Mathematics (to appear), with
George Janelidze. pdf,
|Torsion theories and radicals in normal categories, Journal of
Algebra 305 (2006) 98-129, with M. M. Clementino and D. Dikranjan.
|Universality of coproducts in categories of lax algebras, Applied
Categorical Structures 14 (2006) 243-249, with M. Mahmoudi and C. Schubert.
|Facets of descent III: Monadic descent for rings and algebras,
Applied Categorical Structures 12 (2004) 461-477, with G. Janelidze ps,
|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.
|Kleisli operations for topological spaces, Topology and its Applications
153 (2006) 2952-2961, with D.
|Descent Equivalence, Cahiers Topologie Géom. Différentielle
Catégoriques 44 (2004) 301-352, with X. Guo and M. Sobral.
|One setting for all: metric, topology, uniformity, approach structure,
Applied Categorical Structures 12 (2004) 127-154, with M. M. Clementino and D. Hofmann.
|Exponentiability in categories of lax algebras, Theory and
Applications of Categories 11 (2003) 337-352, with M. M. Clementino
and D. Hofmann.
|The convergence approach to exponentiable maps, Math. Portugaliae
60 (2003) 139-160, with M.M. Clementino and D. Hofmann.
|Left-determined model categories and universal homotopy theories
Transactions American Math. Soc. 355 (2003) 13-47, with J. Rosicky'.
|Semi-abelian categories, J. Pure Appl. Algebra 168 (2002)
367-386, with G. Janelidze and L. Ma'rki.
|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'.
|Injective hulls are not natural, Algebra Universalis 48 (2002)
379-388 with J. Ada'mek, H. Herrlich and J. Rosicky'.
|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'.
|Free Quillen factorization systems, Georgian J. Math. 9 (2002)
807-820, with A. Pultr.
|Essential weak factorization systems Contributions to General
Algebra 13 (2001) 321-333.
|Perfect Maps are exponentiable - categorically, Theory Appl.
Categories 8 (2001) 321-333, with G\"unther Richter.
|A note on local compactness, Rendiconti Ist. Mat. Univ. Trieste
Suppl. 2, 32 (2001) 17-31, with M.M. Clementino.
Introduction I II
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
|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
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:
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
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
2006 (CT06), White Point (Nova Scotia), 25 June - 01 July 2006,
Dalhousie University, organized by Robert Dawson, Dorette Pronk and Peter
Mac Lane and
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.|
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.|
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
|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,
Seminar on Sheaves and Logic - in Honour of Martin Hyland and Peter
Johnstone, Cambridge (UK), 4-5 April 2009. Organized by Eugenia Cheng and
|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
|Conference on Categorical
Topology, in honour of Eraldo Giuli, Ponta Delgada (Portugal), 18-20
March 2010. Organized by Margerida Dias, et al.|
Peripatetic Seminar on Sheaves and Logic, Amsterdam (The
Netherlands), 27-28 November 2010, University of Amsterdam. Organized
by Raul Leal Rodriguez, et al.|
Meeting (#1068), Section on Categorical Topology, Statesboro (GA),
12-13 March 2011, University of Southern Georgia. Organized by
Frederic Mynard and Gavin Seal.|
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.|
on Category Theory (Conference in honour of George Janelidze), Coimbra (Portugal),
2012. Organized by Maria Manuel Clementino, et al.|
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.),
|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),
|International Category Theory Meeting (CT 2015), Aveiro (Portugal),
|1st Pan-Pacific Conference on Topology and Applications, Zhang Zhou
(China), 25--30 November 2015. Presentation on Monoidal
|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),
|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.|