

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 PostDoctoral Visitors
Amir Shr Ali Nasab (MarchJune 2018, visiting from
Kerman University)
Hongliang Lai (201516, visiting from Sichuan
University)
Lili Shen (201416, 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 MariaCristina 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)
 Semireflective extensions of dualities and a new approach to the Fedorchuk duality,
with G. Dimov and E. IvanovaDimova. arXiv 
 Abandoning monomorphisms: partial maps, fractions and
factorizations, with S.N. Hosseini and A.R. Shir Ali Nasab. arXiv 
 Orderenriched 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) 445475. pdf 
 Metlike categories amongst concrete topological categories,
Applied Categorical Structures 26(5) (2018) 10951111
pdf 
 Quantalic topological theories, Tbilisi Mathematical Journal
10(3) (2017) 223237. pdf 
 A note on the topologicity of quantalevalued topological spaces, Logical
Methods in Computer Science 13(3) (2017) 3861,
with Hongliang Lai. pdf 
 Monads on QCat and their lax extensions to QDist, Journal of
Pure and Applied Algebra 222 (2018) 21432163, with Hongliang
Lai. pdf 
 Approximate injectivity, Applied Categorical Structures 26(4)
(2018) 699716, with J. Rosicky.
pdf 
 Lax distributive laws for topology, II, Theory and Applications
of Categories 32 (2017) 736768, with Lili Shen and Hongliang
Lai. pdf 
 Quantalevalued topological spaces via closure and convergence, Topology
Applications 230 (2017) 599620, 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) 509520, with E. Giuli. pdf 
 A mathematical tribute to Reinhard
Börger,Cahiers Topologie Géom. Différentielle
Catégoriques 57(4) (2016)
295314, pdf 
 Categorically proper homomorphisms of topological groups, Applied
Categorical Structures 24 (2016) 715732, with W.
He. pdf 
 Limits and colimits of quantaloidenriched categories and their
distributors, Cahiers Topologie Géom. Différentielle
Catégoriques 56(3) (2015)
209231, with L. Shen. pdf 
 Topogical categories, quantaloids and Isbell adjunctions Topology and its
Applications 200 (2016) 2012236, with L.
Shen. pdf 
 From lax monad extensions to topological theories, Textos
Matematicos 46 (2014) 99123, with M. M.
Clementino. pdf 
 Dual closure operators and their applications, Journal of Algebra
439 (2015) 373416, with D. Dikranjan. pdf 
 Nullstellen and subdirect representation, Applied Categorical
Structures 22 (2014) 907929. pdf 
 Proper maps and the KuratowskiMrowka Theorem, Theory and
Applications of Categories 27 (2013) 327346, with Maria Manuel
Clementino. pdf 
 Lax algebra meets topology, Topology and its
Applications 159 (2012) 24342452, with Dirk Hofmann. pdf 
 Kleisli enriched, Journal of Pure and Applied Algebra 216
(2012) 19201931. pdf 
 Closure operators and their middleinterchange law, Topology and its
Applications 158 (2011) 24372441, pdf 
 On the categorical meaning of Hausdorff and Gromov distances, I, Topology and its
Applications 157 (2010) 12751295, with Andrei Akhvlediani and
Maria Manuel Clementino. pdf 
 Ordered topological structures, Topology and its Applications
156 (2009) 21492157. pdf 
 Ideal determined categories, Cahiers Topologie Géom. Différentielle
Catégoriques 51 (2010), with G. Janelidze, L. Marki and A. Ursini.
pdf 
 Strongly separable morphisms in general categories, Theory Appl.
Categories 23 (2009) 136149, with G. Janelidze.
pdf 
 Injectivity versus exponentiability, Cahiers Topologie Géom. Différentielle
Catégoriques 59 (2008) 228240.
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) 573598, 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) 397408, 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) 98129, with M. M. Clementino and D. Dikranjan.
pdf. 
 Universality of coproducts in categories of lax algebras, Applied
Categorical Structures 14 (2006) 243249, with M. Mahmoudi and C. Schubert.
pdf. 
 Facets of descent III: Monadic descent for rings and algebras,
Applied Categorical Structures 12 (2004) 461477, with G. Janelidze ps,
pdf. 
 Classification of closure operators for categories of topological
spaces. In: Categorical Structures and Their Applications, edited
by W. Gähler and G. Preuss, pp6998 (World Scientific, Singapore 2004),
with D. Dikranjan and S. Watson.
pdf,
ps. 
 Kleisli operations for topological spaces, Topology and its Applications
153 (2006) 29522961, with D.
Hofmann pdf.

 Descent Equivalence, Cahiers Topologie Géom. Différentielle
Catégoriques 44 (2004) 301352, with X. Guo and M. Sobral.
ps,
pdf. 
 One setting for all: metric, topology, uniformity, approach structure,
Applied Categorical Structures 12 (2004) 127154, with M. M. Clementino and D. Hofmann.
pdf. 
 Exponentiability in categories of lax algebras, Theory and
Applications of Categories 11 (2003) 337352, with M. M. Clementino
and D. Hofmann.
pdf. 
 The convergence approach to exponentiable maps, Math. Portugaliae
60 (2003) 139160, with M.M. Clementino and D. Hofmann.
pdf 
 Leftdetermined model categories and universal homotopy theories
Transactions American Math. Soc. 355 (2003) 1347, with J. Rosicky'.
ps,
pdf. 
 Semiabelian categories, J. Pure Appl. Algebra 168 (2002)
367386, with G. Janelidze and L. Ma'rki.
ps 
 Weak factorization systems and topological functors, Appl.
Categorical Structures 10 (2002) 237249, with J. Ada'mek, H. Herrlich,
and J. Rosicky'. ps

 Lax Factorization Algebras J. Pure Appl. Algebra 175 (2002)
355382 with J. Rosicky'.
ps,
pdf. 
 Injective hulls are not natural, Algebra Universalis 48 (2002)
379388 with J. Ada'mek, H. Herrlich and J. Rosicky'.
ps 
 On a generalized SmallObject Argument for the Injective Subcategory
Problem, Cahiers Topologie Geom. Differentielle Categoriques 43
(2002) 83106, with J. Ada'mek, H. Herrlich, and J. Rosicky'.
ps 
 Free Quillen factorization systems, Georgian J. Math. 9 (2002)
807820, with A. Pultr.
pdf. 
 Essential weak factorization systems Contributions to General
Algebra 13 (2001) 321333.
ps 
 Perfect Maps are exponentiable  categorically, Theory Appl.
Categories 8 (2001) 321333, with G\"unther Richter.
ps 
 A note on local compactness, Rendiconti Ist. Mat. Univ. Trieste
Suppl. 2, 32 (2001) 1731, 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 351357. pdf 
 Factorizations, fibres and connectedness, in: Proc. Conf.
Categorical Topology, Toledo 1983 (Heldermann, Berlin 1984), pp
549566. pdf 
 Concrete dualities, in: Category Theory at Work (Heldermann,
Berlin 1991), pp 111136, with H.E. Porst. pdf 
General Mathematical Interest Articles
 Saunders Mac Lane 19092005, Meeting a Grand Leader. Scientiae
Matematicae Japonicae 19 (2006) 1324 pdf

 Mathematics: Beauty and the Beast. ppt

Upcoming and Recent Conferences
 Workshop
on Algebra, Logic and Topology, Coimbra (Portugal), September 2729,
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 0814, 2018,
University of Azores, organized by M. M. Clementino et al. Presentation:
Remarks on weighted categories and the nonsymmetric
PompeiuHausdorffGromov 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, 69
July 2006, Georgia Southern University, organized by Martha Abell, Francis
Jordan, Frederic Mynard, and SzeMan Ngai. Presentation:
Macro and MicroAspects of Categorical Topology . 
 Summer School on Contemporary Categorical Methods in Algebra and
Topology, HauteBodeux (Belgium), 310 June 2007, Université
Catholique de Louvain, organized by Francis Borceux. Lectures on
Laxalgebraic methods in General Topology:
Lecture 1, Lecture 2. 
 Category Theory 2007 (CT07), Algarve (Portugal),
1723 June, University of the
Algarve, organized by Diana Rodelo et al. Presentation:
Topology for Vcategories and (T,V)categories. 
 Categorical Methods in
Algebra, Topology and Computer Science, Coimbra (Portugal), 2628
October 2007, University of Coimbra, organized by Maria Manuel Clementino
and Lurdes Sousa. 
 Mathematical
Applications of Category Theory, London (Ontario), 810 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), 915 December 2007,
University of Antwerp, organized by Eva Colebunders , Bob Lowen, Mark
Sioen and Stijn Verwulgen. 
 Advances in
SetTheoretic Topology, Erice (Sicily, Italy), 919 June 2008,
International School of Mathematics "G. Stampacchia", organized by Gino
Tironi et al. 
 International Category Theory Conference (CT08), Calais (France),
2328 June 2008, Université du Littoral,
organized by Dominique Bourn and Marino Gran. Presentation: Injectivity,
exponentiability, and completeness (Slides
14,
58, 912,1316,
1720,
2124,
2527). 
 Conference in honour of Francis Borceux and Dominique Bourn, Brussels
(Belgium), 1011 October 2008. Organized by Marino Gran, Rudger Kieboom
and Enrico Vitale. Presentation: On the categorical meaning of Hausdorff
and Gromov distances (Slides 02,
36,
711). 
 88th Peripatetic
Seminar on Sheaves and Logic  in Honour of Martin Hyland and Peter
Johnstone, Cambridge (UK), 45 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), 1417 July 2009. Organized by Josef Slapal. 
 Aspects of Contemporary Topology IV, Antwerp (Belgium), 1418 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), 1820
March 2010. Organized by Margerida Dias, et al. 
 91st
Peripatetic Seminar on Sheaves and Logic, Amsterdam (The
Netherlands), 2728 November 2010, University of Amsterdam. Organized
by Raul Leal Rodriguez, et al. 
 AMS Sectional
Meeting (#1068), Section on Categorical Topology, Statesboro (GA),
1213 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), 1823 July 2011, University of
British Columbia. Organized by John MacDonald, et al. 
 Workshop
on Category Theory (Conference in honour of George Janelidze), Coimbra (Portugal),
913 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 AMSEMSPortuguese 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 PanPacific Conference on Topology and Applications, Zhang Zhou
(China), 2530 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. 
