Alexander Campbell
email: alexander.campbell@anu.edu.au
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 currently a Postdoctoral Fellow in the Mathematical Sciences Institute at the Australian National University.
I am also a member of the Centre of Australian Category Theory at Macquarie University, where I was a PhD student (2013--2016), a Postdoctoral Research Fellow (2017--2019), and a Research Officer (2020--2021).
I was the Viterbi Endowed Postdoctoral Fellow in the Higher Categories and Categorification program at MSRI in (Northern Hemisphere) Spring 2020.
Publications
- Joyal's cylinder conjecture, arXiv:1911.02631.
- A homotopy coherent cellular nerve for bicategories, arXiv:1907.01999, Advances in Mathematics 368 (2020), 107138, 67 pp.
- A counterexample in quasi-category theory, arXiv:1904.04965, Proceedings of the American Mathematical Society 148 (2020), no. 1, 37--40.
- On truncated quasi-categories (with Edoardo Lanari), arXiv:1810.11188, Cahiers Topol. Géom. Différ. Catég. 61 (2020), no. 2, 154--207.
- How strict is strictification?, arXiv:1802.07538, Journal of Pure and Applied Algebra 223 (2019), no. 7, 2948--2976.
- Skew-enriched categories, arXiv:1709.01222, Applied Categorical Structures 26 (2018), no. 3, 597--615.
- A higher categorical approach to Giraud's non-abelian cohomology, PhD thesis, Macquarie University, 2016. Supervisor: Ross Street.
- Linear algebra via complex analysis (with Daniel Daners), The American Mathematical Monthly 120 (2013), no. 10, 877--892.
Papers in preparation:
- The model category of algebraically cofibrant 2-categories. (abstract, slides)
- A modular proof of the straightening theorem. (abstract, slides)
- The gregarious model structure for double categories. (abstract, slides)
- (with Yuki Maehara) A model-independent construction of the Gray monoidal structure for (∞,2)-categories. (slides)
- The new normal lax functors.
- A Chevalley criterion for 2-fibrations.
- A convenient model category for tricategories.
Talks
See here for a list of my talks at the Australian Category Seminar.
Slides:
- A model-independent construction of the Gray monoidal structure for (∞,2)-categories, 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.
- 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:
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.