Alexander Campbell

email: campbell@maths.usyd.edu.au

I used to be a category theorist. Now I spend most of my time learning Ancient Greek.
I was a member of the Centre of Australian Category Theory (CoACT) at Macquarie University, where I was a postgraduate student (2013–2016), a Postdoctoral Research Fellow (2017–2019), and a Research Officer (2020–2021). In 2021, I held Postdoctoral Fellowships in the Mathematical Sciences Institute at the Australian National University and in the School of Mathematics and Statistics at the University of Melbourne. In 2020, I was the Viterbi Endowed Postdoctoral Fellow in the Higher Categories and Categorification program at MSRI. I was an undergraduate student (2009–2012) at the University of Sydney, where I graduated with First Class Honours and the University Medal in Pure Mathematics, and where I am currently working as a Casual Academic.

Publications

6. Joyal's cylinder conjecture, Advances in Mathematics 389 (2021), 107895, 40 pp.
7. A homotopy coherent cellular nerve for bicategories, Advances in Mathematics 368 (2020), 107138, 67 pp.
8. A counterexample in quasi-category theory, Proceedings of the American Mathematical Society 148 (2020), no. 1, 37–40.
9. On truncated quasi-categories (with Edoardo Lanari), Cahiers Topol. Géom. Différ. Catég. 61 (2020), no. 2, 154–207.
10. How strict is strictification?, Journal of Pure and Applied Algebra 223 (2019), no. 7, 2948–2976.
11. Skew-enriched categories, Applied Categorical Structures 26 (2018), no. 3, 597–615.
12. A higher categorical approach to Giraud's non-abelian cohomology, PhD thesis, Macquarie University, 2016. Supervisor: Ross Street.
13. 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:

• On weighted homotopy limits in Kan-enriched categories, talk at the Australian Category Seminar, 26 May 2021.
• The model category of algebraically cofibrant 2-categories, talk at the AustMS 2020 Annual Meeting, 11 December 2020.
• The Gray monoidal structure for (∞,2)-categories via Day's extension theorem (with Yuki Maehara), talk at the Melbourne Topology Seminar, 20 October 2020.
• A modular proof of the straightening theorem, talk at the Australian Category Seminar, 29 July 2020.
• The gregarious model structure for double categories, talk at the Masaryk University Algebra Seminar, 18 June 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.