Completed PhD Students

1. Mei Chee SHUM

            Thesis title: Tortile Tensor Categories (Macquarie University, November 1989); published in full in Journal of Pure and Applied Algebra 93 (1994) 57-110.

2. Scott R. JOHNSON died 8 December 1988; posthumous PhD 1994;

            Thesis title: Cauchy Completion in Enriched Categories (Australian National University, 1993).

            Publications forming the thesis:

            1. Monoidal Morita equivalence, Journal of Pure & Appl. Algebra 59 (1989) 169-177;

            2. Small Cauchy completions, Journal of Pure & Appl. Algebra 62 (1989) 35-45;

            3. Modulated bicategories (with A. Carboni, R. Street and D. Verity), Journal of Pure & Appl. Algebra 94 (1994) 229-282.

3. Paddy McCRUDDEN

            Thesis title: Categories of Representations of Balanced Coalgebroids (Macquarie University, 22 February 1999) ; awarded a Letter of Commendation from the Dean of Graduate Students.

            Publications arising from the thesis:

            1. Balanced coalgebroids, Theory and Appl. of Categories 7 (2000) 71-147;

            2. Categories of Representations of Coalgebroids, Advances in Math. 154 (2000) 299-332;

            3. Tannaka duality for Maschkean Categories, Proceedings of the Category Theory Conference in Coimbra (July 1999), J. Pure. Appl. Algebra 168 (2002) 265-367.

4. Mark WEBER

            Thesis title: Symmetric Operads for Globular Sets (Macquarie University, May 2001).

5. Isar STUBBE

            Thesis title: Categorical structures enriched in a quantaloid: categories and semicategories (Principal Supervisor Francis Borceux, Universit\'e Catholique de Louvain, Belgium, 2003).


            Thesis title: Categories of Mackey Functors (Macquarie University, 10 April 2007;

7. Craig PASTRO

            Thesis title: Hopf algebras and related structures in a categorical environment (Macquarie University, 10 June 2008).


            Thesis title: Elements of enriched and quantum category theory (Macquarie University, submitted 2 July 2010; PhD awarded 28 September 2010).

            Publications arising from the thesis:

            1. Barr's Embedding theorem for enriched categories, Journal of Pure and Applied Algebra 215 (2011) 2148-2153.

            2. Category of quantum categories, Theory and Applications of Categories 25 (2011) 1-37.

            3. (with S. Lack and R. Street) Hopf monoidal comonads, Theory and Applications of Categories 24 (2010) 554-563.

            4. The Tannaka representation theorem for separable Frobenius functors, Algebras and Representation Theory (accepted on 22 February 2011).

9. David OURY

            Thesis title: Duality for Joyal's category $\Theta $ and homotopy concepts for ${\Theta }_{2}$-sets (Macquarie University, submitted 18 March 2011; PhD awarded 4 October 2011).

            Publication arising from the thesis:

  1. On the duality between trees and disks,  Theory Appl. Categ. 24 (2010) 418-450.

10. Thomas BOOKER

            Thesis title: Structures in and on monoidal categories with a view towards Tannaka duality  (Macquarie University, submitted 15 December 2011; PhD awarded 3 April 2012).

            Publication arising from the thesis:

  1. Torsors, herds and flocks (with R. Street), Journal of Algebra 330 (2011) 346-374
  2. Commutative algebras in Fibonacci categories (with A. Davydov), Journal of Algebra 355 (2012) 176-204

11. Camell KACHOUR

            Thesis title: Aspects of Globular Higher Category Theory (Principal Supervisor Michael Batanin; Macquarie University, PhD awarded 5 November 2013).

12. Mitchell A. BUCKLEY

            Thesis title: Three studies in higher category theory: fibrations, skew monoidal structures and excision of extremals (Main Supervisors Dominic Verity and Richard Garner; Macquarie University, PhD awarded 2015).

13. Alexander CAMPBELL

            Thesis title: A higher categorical approach to Giraud's non-abelian cohomology (Macquarie University, PhD awarded 6 October 2016).

14. Ram\'on ABUD ALCAL\'A

            Thesis title: Oplax actions and enriched icons with applications to coalgebroids and quantum categories (Principal Supervisor Stephen Lack; Macquarie University, PhD awarded ~November 2017).

15. Christopher NGUYEN

            Thesis title: Parity structure on associahedra and other polytopes (Principal Supervisor Stephen Lack; Macquarie University, PhD awarded March 2018).

16. Branko NIKOLI\'C

            Thesis title: Morphisms of 2-dimensional structures with applications (Macquarie University, PhD awarded May 2018).

17. Charles R. WALKER

            Thesis title: Structures in two dimensional category theory and applications to polynomial functors (Principal Supervisor Richard Garner; Macquarie University, PhD awarded March 2019).

18. Yuki MAEHARA

            Thesis title: The Gray tensor product for 2-quasi-categories (Principal supervisor Dominic Verity ; Macquarie University, PhD awarded September 2020).

Partially supervisor of: Tim Brook PhD ANU 1974; Greg Bird PhD USyd 1984; Andrew Solomon PhD USyd 1997. Geoffrey Lewis PhD UNSW 1974 was a student of Max Kelly


Current Higher Degree Students (Macquarie University)

Hardy Hulley (Principal supervisor Richard Garner);

Eli Hazel (Principal supervisor Richard Garner);

Ruben Zilibowitz (MResYear2; Associate supervisor Richard Garner).


Visiting Masters Students

Steve Bennoun (\'Ecole Polytechnique F\`ed\'erale de Lausanne), Tannaka Duality for Comodules over a Hopf Algebra (October 2006 -- March 2007)


Jean-Baptiste Boyer (\'Ecole Normale Superieure de Cachan, antenne de Bretagne), Categories and Algebraic Topology (June 2010 -- July 2010)


Basile Pillet (\'Ecole Normale Superieure de Cachan, antenne de Bretagne), Tangle with categories: Presentation and Report (July 2011 -- August 2011)


Honours Students

Frank Sharpe, Sheaves as Generalized Sets (1973)

Colin Hill, Sets with Operations from a Categorical Point of View (1974)

Mark Weber, A Mathematical Analogy (1996)

Amy Young, Traced Monoidal Categories (June 1998)

Dilshara Abayasekara, Species of Structure (1999)

Simon Byrne, Groupoids and Stuff Types (2005)

Thomas Booker, Non-Standard Numbers as Global Sections of a Dedekind Reals Object (2007)

Mitchell Buckley, Lawvere Theories (2008)


Vacation Scholars

1994: Heidi Manning (Knot theory)

1995: Paddy McCrudden (Quantum groups) and Stephen Warburton (Links formed in fencing wire)

1996: Stuart Lawrence (String diagrams in linear algebra)

1997: Daniel O'Neil and Paul Batten (Representations of the finite general linear groups)

2001: Ryan Crompton and Thi Minh Tam Pham (The Taylor expansions of tanx and secx; also see )

2002: Ben Odgers and Hanh Nguyen Vo (Efficient development of number systems and trigonometry)

2004: James Douglas and Rony Kirollos (Number systems, TeX and categories)

2005: Simon Byrne (Quantum groups)

2006: Mitchell Buckley (String diagrams in algebra)