Alexander Campbell

email: acampbell@msri.org

I am an Australian category theorist.
My research interests are in category theory, especially higher and enriched category theory, and categorical aspects of homotopy theory.
I am a member of the Centre of Australian Category Theory at Macquarie University, where I was a PhD student (2013--2016) and a Postdoctoral Research Fellow (2017--2019).
In Spring 2020 I was a Postdoctoral Fellow in the Higher Categories and Categorification program at MSRI.
Next year I will begin a Postdoctoral Research Fellowship at Johns Hopkins University.

Publications

10. Fiat lax, in preparation.
11. A Chevalley criterion for 2-fibrations, in preparation.
12. The gregarious model structure for double categories, in preparation. (abstract, slides)
13. The model category of algebraically cofibrant 2-categories, in preparation. (abstract, slides)
14. Joyal's cylinder conjecture, arXiv:1911.02631.
15. A homotopy coherent cellular nerve for bicategories, arXiv:1907.01999, Advances in Mathematics 368 (2020), 107138.
16. A counterexample in quasi-category theory, arXiv:1904.04965, Proceedings of the American Mathematical Society 148 (2020), no. 1, 37--40.
17. On truncated quasi-categories (with Edoardo Lanari), arXiv:1810.11188, Cahiers Topol. Géom. Différ. Catég. 61 (2020), no. 2, 154--207.
18. How strict is strictification?, arXiv:1802.07538, Journal of Pure and Applied Algebra 223 (2019), no. 7, 2948--2976.
19. Skew-enriched categories, arXiv:1709.01222, Applied Categorical Structures 26 (2018), no. 3, 597--615.
20. A higher categorical approach to Giraud's non-abelian cohomology, PhD thesis, Macquarie University, 2016. Supervisor: Ross Street.
21. Linear algebra via complex analysis (with Daniel Daners), The American Mathematical Monthly 120 (2013), no. 10, 877--892.

Talks

See here for a list of my talks at the Australian Category Seminar.

Slides:

• The gregarious model structure for double categories, talk at the Masaryk University Algebra Seminar, 18 June 2020.
• Joyal's cylinder conjecture, talk at the MSRI Online Seminar, 8 April 2020.
• The model category of algebraically cofibrant 2-categories, talk at the Category Theory 2019 conference.
• Enriched algebraic weak factorisation systems, talk at the Category Theory 2017 conference.

Notes:

• Equivalences of complicial sets, handwritten notes, Australian Category Seminar, 28 August & 4 September 2019.
• The fundamental theorem of n-quasi-category theory, handwritten notes, Australian Category Seminar, 26 September 2018.
• Change of base for enriched model categories, an expository talk given at the Australian Category Seminar, 14 February 2018.

Blog post: An exegesis of Yoneda structures, written for the Kan Extension Seminar.

Teaching

I was a co-organiser with Emily Riehl and Brendan Fong of the Kan Extension Seminar II, an online graduate reading course in category theory.

Other material

• AustMS Lift-Off Fellowship Report.