- (with Aurelio Carboni and R.F.C. Walters)
Introduction to extensive and distributive
categories,
*Journal of Pure and Applied Algebra*84(2):145-158, 1993.

- (with G.M. Kelly) Finite-product-preserving
functors, Kan extensions, and strongly-finitary monads,
*Applied Categorical Structures*1(1):84-94, 1993.

- (with G.M. Kelly and R.F.C. Walters)
Coinverters and categories-of-fractions
for categories with structure,
*Applied Categorical Structures*1(1):95-102, 1993.

- (with G.M. Kelly) On
property-like structures,
*Theory and Applications of Categories*3:213-250, 1997.

- On
the monadicity of finitary monads,
*Journal of Pure and Applied Algebra*140(1):65-73, 1999.

- A note on the exact
completion of a regular category, and its infinitary generalizations,
*Theory and Applications of Categories*, 5:70-80, 1999.

- A coherent approach to pseudomonads,
*Advances in Mathematics*, 152(2):179-202, 2000.

- (with G.M. Kelly) On
the monadicity of categories with chosen colimits,
*Theory and Applications of Categories*7:148-170, 2000.

- (with E.M. Vitale) When do completion processes
give rise to extensive categories?,

*Journal of Pure and Applied Algebra*, 159(2-3):203-230, 2001.

- (with J.R.B. Cockett) The extensive
completion of a distributive category,
*Theory and Applications of Categories*, 8:541-554, 2001.

- (with G.M. Kelly)
**V-Cat**is locally presentable or locally bounded if**V**is so,*Theory and Applications of Categories*, 8:555-575, 2001.

- (with J.R.B. Cockett) Restriction categories I:
categories of partial maps,
*Theoretical Computer Science*, 270(1-2):223-259, 2002.

- (with J. Adamek, F. Borceux, and J. Rosicky) A
classification of accessible categories,
*Journal of Pure and Applied Algebra*, 175(1-3):7-30, 2002.

- Codescent objects and coherence,
*Journal of Pure and Applied Algebra*, 175(1-3):223-241, 2002.

- (with Ross Street) The formal theory of monads II,
*Journal of Pure and Applied Algebra*, 175(1-3):243-265, 2002.

- A Quillen model structure for 2-categories,
*K-Theory*, 26(2):171-205, 2002.

- (with J.R.B. Cockett) Restriction categories
II: partial map classification,
*Theoretical Computer Science*, 294(1-2):61-102, 2003.

- (with Marta Bunge) Van Kampen theorems for
toposes,
*Advances in Mathematics*, 179(2):291-317, 2003.

- The 3-by-3 lemma for regular Goursat
categories,
*Homology, Homotopy and Applications*, 6:1-3, 2004.

- (with G.M. Kelly) Monoidal functors
generated by adjunctions, with applications to transport of structure,
*Fields Institute Communications*43, 319--340, 2004.

- (with Pawel Sobocinski)
Adhesive categories, in
*Foundations of Software Science and Computation Structures: 7th International Conference, FOSSACS 2004*(=Lecture Notes in Computer Science 2987), Springer, 2004, pp. 273--288.

- (with Stefano Kasangian and Enrico M. Vitale)
Coalgebras, braidings, and distributive laws,
*Theory and Applications of Categories*, 13:129-146, 2004.

- Composing PROPs,
*Theory and Applications of Categories*, 13:147-163, 2004.

- A Quillen model structure for
bicategories,
*K-theory*, 33(3):185--197, 2004.

- (with Pawel Sobocinski)
Adhesive and quasiadhesive categories,
*Theoretical Informatics and Applications*, 39(3):511-546, 2005.

- Limits for lax morphisms,
*Applied Categorical Structures*, 13(3):189-203, 2005.

- (with Simona Paoli) An operadic approach to
internal structures,
*Applied Categorical Structures*, 13(3):205-222, 2005.

- (with Pawel Sobocinski) Toposes are adhesive, International Conference on Graph Transformation, 184-198, (Lecture Notes in Comput. Sci. 4178), Springer, Berlin, 2006.

- (with B.J. Day) Limits of small functors,
*Journal of Pure and Applied Algebra*, 210(3):651-663, 2007; also`arXiv:math.CT/0610439`. - (with J.R.B. Cockett) Restriction categories
III: colimits, partial limits, and extensivity,
*Mathematical Structures in Computer Science*, 17(4):775-817, 2007; also`arXiv:math.CT/0610500`.

- Homotopy-theoretic aspects of 2-monads,
*Journal of Homotopy and Related Structures*2(2):229-260, 2007; also`arXiv:math.CT/0607646`.

- Bicat is not triequivalent
to Gray,
*Theory and Applications of Categories*, 1:1-3, 2007; also`arXiv:math.CT/0612299`.

- (with P.T. Johnstone and Pawel Sobocinski) Quasitoposes, quasiadhesive
categories, and Artin gluing, in
*2nd Conference on Algebra and Coalgebra in Computer Science*(CALCO 2007),*Lecture Notes in Computer Science*4624:312-326, 2007. - (with Simona Paoli) 2-nerves
of bicategories,
*K-theory*, 38(2):153-175, 2008; also`arXiv:math.CT/0607271`.

- (with John Power), Gabriel-Ulmer duality and Lawvere theories enriched
over a general base,
*Journal of Functional Programming*, 19(3-4):265-286, 2009. - A 2-categories companion, in
*Towards Higher Categories*, eds. John C. Baez and J. Peter May, Springer, 2009; also`arXiv:math.CT/0702535`.

- Icons,
*Applied Categorical Structures*, 18(3):289-307, 2010; also`arXiv:0711.4657`. - Note on the construction of free monoids,
*Applied Categorical Structures*, 18(1):17-29, 2010; also`arXiv:0802.1946`. - (with R.F.C. Walters and R.J. Wood) Bicategories of spans as
cartesian bicategories,
*Theory and Applications of Categories*, 24(1):1-24, 2010; also`arXiv:0920.2996`. - (with Dimitri Chikhladze and Ross Street)
Hopf monoidal comonads,
*Theory and Applications of Categories*, 24(19):554-563, 2010; also`arXiv:1002.1122`. - (with Jiri Rosicky), Notions of Lawvere theory,
*Applied Categorical Structures*, 19(1):363-391, 2011; also`arXiv:0810.2578`. - A Quillen model
structure for Gray-categories,
*Journal of K-theory*, 8(2):183-221, 2011; also`arXiv:1001.2366`. - (with Alain Bruguières and Alexis Virelizier) Hopf monads on monoidal categories,
*Advances in Mathematics*, 227(2):745-800, 2011; also`arXiv:1003.1920`. - (with Gabriella Böhm and Ross Street) Weak bimonads and weak Hopf monads (previously known as "Weak bimonads"),
*Journal of Algebra*, 328(1):1-30, 2011; also`arXiv:1002.4493`. - An embedding theorem for adhesive categories,
*Theory and Applications of Categories*, 25(7):180--188, 2011; also`arXiv:1103.0600`. - (with Gabriella Böhm and Ross Street)
On the 2-category of weak distributive laws,
*Communications in Algebra*; 39(12):4567-4583, 2011; also`arXiv:1009.3454`. - (with Mike Shulman) Enhanced 2-categories and limits for lax morphisms,
*Advances in Mathematics*, 229(1):294-356, 2012; also`arXiv:1104.2111`. - (with Gabriella Böhm and Ross Street)
Idempotent splittings, colimit completions, and weak aspects of the theory of monads,
*Journal of Pure and Applied Algebra*, 216(2):385-403, 2012; ; also`arXiv:1102.4931`. - Non-canonical
isomorphisms,
*Journal of Pure and Applied Algebra*, 216(3):593-597, 2012 ; also`arXiv:0920.2996`. - (with Jiri Rosicky), Enriched weakness,
*Journal of Pure and Applied Algebra*, 216(8-9):1807-1822, 2012; also`arXiv:1009.1678`. - (with Richard Garner) Grothendieck quasitoposes,
*Journal of Algebra*, 355(1):111-126, 2012; also`arXiv:1106.5331`. - (with Richard Garner) Lex colimits,
*Journal of Pure and Applied Algebra*, 216(6):1372-1396, 2012; also`arXiv:1107.0778`. - (with Richard Garner) On the axioms for adhesive and quasiadhesive categories,
*Theory and Applications of Categories*, 27(3):27-46, 2012; also`arXiv:1108.2934`. - (with Ross Street) Skew monoidales, skew warpings, and quantum categories,
*Theory and Applications of Categories*, 26(15):385-402, 2012; also`arXiv:1205.2934`. - Morita contexts as lax functors,
*Applied Categorical Structures*, 22(2):311-330, 2014; also`arXiv:1209.4436`. - (with Ross Street) A skew-duoidal Eckmann-Hilton argument and quantum categories,
*Applied Categorical Structures*, 22(5):789-803, 2014; also`arXiv:1210.8192`. - (with Ross Street) Triangulations, orientals, and skew monoidal categories,
*Advances in Mathematics*, 258:351-396, 2014; also`arXiv:1302.4488`. - (with Ross Street) On monads and warpings,
*Cahiers de Topologie et Géometrie Différentielle Catégoriques*, LV(4):244-266, 2014; also`arXiv:1408.4953`. - (with Mitchell Buckley, Richard Garner, and Ross Street)
The Catalan simplicial set,
*Mathematical Proceedings of the Cambridge Philosophical Society*, 158(2):211-222, 2015; also`arXiv:1309.6120`.

See also the earlier version,*Skew-monoidal categories and the Catalan simplicial set*, available as`arXiv:1307.0265`. - (with Ross Street) Combinatorial categorical equivalences of Dold-Kan type,
*Journal of Pure and Applied Algebra*, 219:4343-4367, 2015; also available as`arXiv:1402.7151`. - (with Gabriella Böhm) Multiplier bialgebras in braided monoidal categories,
*Journal of Algebra*423:853-889, 2015; also`arXiv:1405.4668`. - (with Ross Street) Skew-monoidal reflection and lifting theorems,
*Theory and Applications of Categories*20:985-1000, 2015; also available as`arXiv:1410.6972`. - (with Jiri Rosicky) Homotopy locally presentable enriched categories,
*Theory and Applications of Categories*31:712--754, 2016; also available as`arXiv:1311.3712`. - (with Marino Gran) Semi-localizations of semi-abelian categories
,
*Journal of Algebra*454:206-232, 2016; also`arXiv:1405.1092`. - (with Gabriella Böhm) Monoidal comonads on naturally Frobenius map-monoidales,
*Journal of Pure and Applied Algebra*, 220:2177-2213, 2016; also available as`arXiv:1411.5788`. - (with Gabriella Böhm) A category of multiplier bimonoids,
*Applied Categorical Structures*, 25(2):279-301, 2017; also available as`arXiv:1509.07101`. - (with Gabriella Böhm) Multiplier Hopf monoids,
*Algebras and Representation Theory*, 20(1):1-46, 2017; also available as`arXiv:1511.03806`. - (with Gabriella Böhm) A simplicial approach to multiplier bimonoids,
*Bulletin of the Belgian Mathematical Society - Simon Stevin*, 24:107-122, 2017; also available as`arXiv:1512.01259`. - (with Richard Garner and Paul Slevin) Hochschild homology, lax codescent, and duplicial structure,
*Annals of K-Theory*, 3(1):1-31, 2018; also available as`arXiv:1510.08925`. - (with Gabriella Böhm and José Gómez-Torrecillas),
Weak multiplier bimonoids,
*Applied Categorical Structures*, to appear; also available as`arXiv:1603.05702`. - Operadic categories and their skew monoidal categories of collections,
*Higher Structures*, to appear; also available as`arXiv:1610.06282`. - (with John Bourke), Free skew monoidal categories,
*Journal of Pure and Applied Algebra*, to appear; also available as`arXiv:1708.06087`. - (with John Bourke), Skew monoidal categories and skew multicategories, preprint, 2017; available as
`arXiv:1708.06088`. - (with John Bourke), Braided skew monoidal categories, preprint, 2017; available as arXiv:1712.08276.

- Special volume dedicated to Aurelio Carboni on the occasion of his 60th birthday, editors G.Janelidze, S. Lack, F.W. Lawvere, E.M. Vitale, R.J. Wood,
*Theory and Applications of Categories*13, 2004. *Categories in Algebra, Geometry and Mathematical Physics*, Conference and Workshop in honor of Ross Street's 60th Birthday, Macquarie University 11-16 July 2005 and Australian National University 18-21 July 2005; edited by Alexei Davydov, Michael Batanin, Michael Johnson, Stephen Lack and Amnon Neeman; Contemporary Mathematics 431 (American Math. Society, 2007).- Special issue dedicated to the memory of Professor Gregory Maxwell Kelly, editors Martin Hyland, George Janelidze, Michael Johnson, Peter Johnstone, Stephen Lack, Walter Tholen and Richard Wood,
*Applied Categorical Structures*19(1), 2011. - Proceedings of CT2011 at UBC (Vancouver), editors Marino Gran, George Janelidze, Stephen Lack, John MacDonald, Walter Tholen,
*Theory and Applications of Categories*27, 2013.