Alexander Campbell

email: alexanderpcampbell@gmail.com

I am a member of the Centre of Australian Category Theory at Macquarie University.
My research interests are in category theory, especially higher and enriched category theory, and categorical aspects of homotopy theory.
In 2017--2019, I was a Postdoctoral Research Fellow in the Department of Mathematics and Statistics at Macquarie University.
In January--May 2020, I will be a Postdoctoral Fellow in the Higher Categories and Categorification program at MSRI.

Publications

7. The model category of algebraically cofibrant 2-categories, in preparation. (abstract, slides)
8. Joyal's cylinder conjecture, arXiv:1911.02631.
9. A homotopy coherent cellular nerve for bicategories, arXiv:1907.01999.
10. A counterexample in quasi-category theory, arXiv:1904.04965, Proceedings of the American Mathematical Society 148 (2020), no. 1, 37--40.
11. On truncated quasi-categories (with Edoardo Lanari), arXiv:1810.11188.
12. How strict is strictification?, arXiv:1802.07538, Journal of Pure and Applied Algebra 223 (2019), no. 7, 2948--2976.
13. Skew-enriched categories, arXiv:1709.01222, Applied Categorical Structures 26 (2018), no. 3, 597--615.
14. A higher categorical approach to Giraud's non-abelian cohomology, PhD thesis, Macquarie University, 2016. Supervisor: Ross Street.
15. 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 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:

• 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.