Centre of Australian Category Theory

Report for 2002

The Centre of Australian Category Theory CoACT develops an algebra of widespread applicability for the synthesis and analysis of systems and processes in fields as diverse as physics and computer science, and also mathematics itself. Although having operated as a coherent group since the founding of the on-going Australian Category Seminar in 1971, CoACT was formally established in 1999.


To provide the environment for the top international centre for Higher-dimensional Category Theory and a major international centre for general Category Theory.


To pursue vigorously research into those parts of mathematics and computer science which find natural expression and advancement in terms of Category Theory and to train the highest-quality research students.

Advisory Board

Professor Ross Street

Director CoACT

Professor Michael Johnson

Associate Director CoACT

Emeritus Professor Max Kelly

University of Sydney

Dr Wesley Phoa

Capital Strategy Research, USA

Associate Professor Dominic Verity

Division of ICS, Macquarie University

Professor Di Yerbury

Vice Chancellor, Macquarie University

Professor Ray Offen

Dean, Division of ICS, Macquarie University

The Advisory Board met on 1 May 2002 and a meeting is set for 3 June 2003.


Research in 2002 and early 2003

Grants and funding

Personnel matters


Visitors in 2002 and early 2003

John Baez

University of California, Riverside

January-March 2003

Isar Stubbe

Université Catholique de Louvain-la-Neuve, Belgium

January 2003

Eric Goubault

Commissariat à l'Energie Atomique, Saclay, France

December 2002

Shahn Majid

Queen Mary, University of London

December 2002

Yefim Katsov

Hanover College, Indiana

April 2002

George Janelidze

Universidade de Aveiro, Portugal and Mathematical Institute of the Academy of Science, Tbilisi

Nov 2001 - Mar 2002

Bob Rosebrugh

Mt Allison University, Canada

Mar 2002

Jürgen Koslowski

Technische Universität Braunschweig, Germany

Mar 2002

Anne Heyworth

University of Leicester

Feb 2002

Kostas Tourlas

University of Edinburgh

Jan 2002

Documented Research Activity since early 2002


1. M. Batanin, On the Penon method of weakening of algebraic structures, J. Pure Appl. Algebra 172 (2002) 1-23.

2. G.M. Kelly, A. Labella, V. Schmitt and R. Street, Categories enriched on two sides, J. Pure Appl. Algebra 168 (2002) 53-98.

3. S. Lack and R. Street, The formal theory of monads II, J. Pure Appl. Algebra 175 (2002) 243-265.

4. B.J. Day and R. Street, Lax monoids, pseudo-operads, and convolution, in: "Diagrammatic Morphisms and Applications", Contemporary Mathematics 318 (American Math Soc. 2003) 75-96.

5. R. Street, Trees, permutations and the tangent function, Reflections 27 (2) (Math. Assoc. of NSW, May 2002) 19-23; also arXiv: math.HO/0303267.

6. R. Street, Weak omega-categories, in: "Diagrammatic Morphisms and Applications", Contemporary Mathematics 318 (American Math Soc. 2003) 207-213.

7. B.J. Day and R. Street, Abstract substitution in enriched categories, J. Pure Appl. Algebra 179 (2003) 49-63.

8. A. Davydov and R. Street, Roots of unity as a Lie algebra, Georgian Mathematical Journal 9(4) (2002) 683-690.

9. A. Davydov, K-theory of braided monoidal categories, K-Theory 27 (2002) 371-389.

10. J.R.B. Cockett and S. Lack, Restriction categories I: categories of partial maps, Theoretical Computer Science 270 (2002) 223-259.

11. J. Adamek, F. Borceux, S. Lack and J. Rosicky, A classification of accessible categories, J. Pure Appl. Algebra 175 (2002) 7-30.

12. S. Lack, Codescent objects and coherence, J. Pure Appl. Algebra 175 (2002) 223-241.

13. S. Lack, A Quillen model structure for 2-categories, K-Theory 26 (2002) 171-205.

14. J.R.B. Cockett and S. Lack, Restriction categories II: partial map classification, Theoretical Computer Science 294 (2003) 61-102.

15. A. Carboni, G. Janelidze and R. Street, Foreword [on the 70th birthday of Gregory Maxwell Kelly]. Special volume celebrating the 70th birthday of Professor Max Kelly. J. Pure Appl. Algebra 175 (2002) 1-5.

16. G. Janelidze, G.M. Kelly, A note on actions of a monoidal category. Theory Appl. Categ. 9 (2001/2), 61-91.

17. P. McCrudden, Tannaka duality for Maschkean Categories, J. Pure. Appl. Algebra 168 (2002) 265-307.

18. Paddy McCrudden, Opmonoidal monads, Theory and Applications of Categories 10 (2002) 469-485.

19. Michael Johnson and Robert Rosebrugh, Database Interoperability Through State Based Logical Data Independence, International Journal of Computer Applications in Technology 16 (2-3) (2003) 97-102.

20. Michael Johnson, Robert Rosebrugh and Richard Wood, Entity Relationship Attribute Designs and Sketches, Theoy and Application of Categories 10 (2002) 94-112.

21. Michael Johnson and Robert Rosebrugh, Sketch Data Models, Relational Schema and Data Specifications, ENTCS 61 (6) (2002) 1-13.

22. C.N.G Dampney and Michael Johnson, Enterprise Information Systems: Specifying the links among project data models using category theory, Enterprise Information Systems III (Eds J. Filipe, B. Sharp, and P. Miranda; Kluwer 2002) 191-197.

23. Richard Buckland, Michael Johnson and Dominic Verity, On the specification of Higher Dimensional Automata, ENTCS 68 (2002) 1-13.

24. Michael Johnson and Rosebert Rosebrugh, Three approaches to partiality in the sketch data model, ENTCS 78 (2003) 1-18.


25. J. Bichon and R. Street, Militaru's D-equation in monoidal categories, Applied Categorical Structures (to appear).

26. R. Street, Functorial calculus in monoidal bicategories, Applied Categorical Structures (to appear).

27. B.J. Day, P. McCrudden and R. Street, Dualizations and antipodes, Applied Categorical Structures (to appear).

28. M. Bunge and S. Lack, Van Kampen theorems for toposes, Advances in Math. (to appear).

29. George Ivanov and Peter Vamos, A characterization of FGC rings, Contemporary Math. (Amer. Math. Soc. 2002).

30. P.H. Butler, W.P. Joyce, L.F. McAven and B.G. Searle, Recursive calculation of non-primitive coupling and recoupling brakets, Canadian Journal of Physics


31. M. Batanin, The Eckmann-Hilton argument, higher operads and -spaces, math.CT/0207281; submitted to Advances in Math.

32. M. Batanin, Computads and slices of operads, math.CT/0209035; submitted to Theory and Appl. of Categories.

33. M. Batanin, The combinatorics of iterated loop spaces, math.CT/0301221; submitted to Topology and its Appl.

34. B.J. Day and R. Street, Quantum categories, star autonomy, and quantum groupoids, math.CT/0301209; submitted to an American Math Soc. publication "Categories, Algebras, and Galois Theory - Proceedings of the Workshop on Categorical Structures for Descent and Galois Theory, Hopf Algebras and Semiabelian Categories, Toronto 2002";.

35. R. Street, Categorical and combinatorial aspects of descent theory, math.CT/0303175; submitted to Applied Categorical Structures.

36. R. Street, The monoidal centre as a limit, math.CT/0304053.

37. G.M. Kelly and S. Lack, Monoidal functors generated by adjunctions, with applications to transport of structure.

38. William Joyce, Natural Associativity without the Pentagon condition.

In Preparation

39. Michael Batanin and Mark Weber, Multitensors and higher dimensional operads.

40. Michael Batanin, Coherence, cooperative games and shuffle polytopes.

41. Michael Batanin, Brian Day and Ross Street, Lax globular monoidal functors out of Omega (working title).

42. Michael Batanin, Clemens Berger, and Sjoerd Crans, Contractibility of the operad for Crans' 4-categories (working title).

43. Alexei Davydov, Nuclei for pseudo-monoidal categories.

44. Alexei Davydov, Gerstenhaber structures on extensions.

45. Alexei Davydov, A_{infinity}-structures and Hochschild cohomology.

46. Michael Johnson, Rewriting techniques and coherence theorems.

47. Michael Johnson, David Naumann and John Power, Category Theoretic Models of Data Refinement.

48. Michael Johnson and Robert Rosebrugh, Universal view updatability.

49. G.M. Kelly, S. Lack and A.J. Power, Flexibility for 2-monads.

50. G.M. Kelly and M.-C. Pedicchio, On one-sortedness of algebraic categories.

51. G.M. Kelly and A.J. Power, Enrichment for monads on the category of categories.

52. F. Borceux and G.M. Kelly, On accessibility for enriched categories.

53. B.J. Day and G.M. Kelly, On categories with a distributive law.

54. C. Kennett, M. Roy and M. Zaks, When does skeletal imply coskeletal?

55. G.M. Kelly and B. Mesablishvili, On enriched monads of descent type and of effective descent type (28 page working note, 2002).

56. C. Dampney and M. Johnson, Experience in developing inteoperations among legacy information systems using partial reverse engineering (Manuscript, February, 2003).