nLab Stephen Lack

Stephen Lack (commonly known as ‘Steve’) is an Australian category theorist with notable contributions to 2-category theory and the theory of monoidal categories.

He was winner of The Australian Mathematical Society Medal for 2009.

He is on the Steering Board of the Journal ‘Compositionality’.

• Homepage of Steve Lack.

Selected writings

On extensive categories and distributive categories:

• Aurelio Carboni, Stephen Lack, R. F. C. Walters, Introduction to extensive and distributive categories, JPAA 84 (1993) pp. 145-158 (doi:10.1016/0022-4049(93)90035-R)

On accessible categories via doctrines of limits:

• Jiří Adámek, Francis Borceux, Stephen Lack, Jiri Rosicky, A classification of accessible categories, Journal of Pure and Applied Algebra 175 1–3 (2002) 7-30 [doi:10.1016/S0022-4049(02)00126-3]

On toposes as adhesive categories:

• Stephen Lack, Pawel Sobocínski, Lemma 18 in: Toposes are adhesive, in: Graph Transformations ICGT 2006, Lecture Notes in Computer Science 4178, Springer (2006) 184-198 [doi:10.1007/11841883_14, pdf]

On the 2-category theory of monads and their Eilenberg-Moore categories:

• Stephen Lack, Ross Street, The formal theory of monads II, Journal of Pure and Applied Algebra

  175 1–3 (2002) 243-265 [doi:10.1016/S0022-4049(02)00137-8]

On descent:

• Stephen Lack. Codescent objects and coherence. Journal of Pure and Applied Algebra 175 1-3 (2002) 223-241 [doi:10.1016/S0022-4049(02)00136-6]

On Hopf monads:

• Alain Bruguières, Steve Lack, Alexis Virelizier, Hopf monads on monoidal categories, Adv. Math. 227 2 (2011) 745-800 [arXiv:1003.1920, doi:10.1016/j.aim.2011.02.008]

On adhesive categories:

• Richard Garner, Steve Lack: On the axioms for adhesive and quasiadhesive categories, Theory and Applications of Categories, 27 3 (2012) 27-46 [arXiv:1108.2934, tac:27-03]

On (enriched) accessible categories:

• Stephen Lack, Giacomo Tendas, Virtual concepts in the theory of accessible categories, Journal of Pure and Applied Algebra 227 2 (2023) 107196 [arXiv:10.1016/j.jpaa.2022.107196, arXiv:2205.11056]

See also:

• John Bourke and Stephen Lack, Skew monoidal categories and skew multicate- gories, Journal of Algebra, 506:237–266, 2018.

• John Bourke and Stephen Lack, Free skew monoidal categories, Journal of Pure and Applied Algebra, 222:3255–3281, 2018.

• Stephen Lack, Operadic categories and their skew monoidal categories of collections, Higher Structures, accepted 30 July 2017, 29 pages; available as arXiv:1610.0628.

• Gabriella Böhm, Stephen Lack, and José Gómez-Torrecillas, Weak multiplier bi- monoids, Applied Categorical Structures, 65 pages, published online; also available as arXiv:1603.05702.

• Richard Garner, Stephen Lack, 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.

• Gabriella Böhm and Stephen Lack, A simplicial approach to multiplier bimonoids, Bulletin of the Belgian Mathematical Society - Simon Stevin, 24:107–122, 2017.

• Gabriella Böhm and Stephen Lack, Multiplier Hopf monoids, Algebras and Representation Theory, 20(1):1–46, 2017; also available as arXiv:1511.03806.

• Gabriella Böhm and Stephen Lack, A category of multiplier bimonoids, Applied Categorical Structures, 25(2):279–301, 2017; and available as arXiv:1509.07171.