Alexander Campbell

email: alexander.campbell@mq.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 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), and where I am currently employed as a Research Officer.
I was the Viterbi Endowed Postdoctoral Fellow in the Higher Categories and Categorification program at MSRI in (Northern Hemisphere) Spring 2020.
Next year I will begin a Postdoctoral Research Fellowship at Johns Hopkins University.

Publications

  1. Joyal's cylinder conjecture, arXiv:1911.02631.
  2. A homotopy coherent cellular nerve for bicategories, arXiv:1907.01999, Advances in Mathematics 368 (2020), 107138.
  3. A counterexample in quasi-category theory, arXiv:1904.04965, Proceedings of the American Mathematical Society 148 (2020), no. 1, 37--40.
  4. On truncated quasi-categories (with Edoardo Lanari), arXiv:1810.11188, Cahiers Topol. Géom. Différ. Catég. 61 (2020), no. 2, 154--207.
  5. How strict is strictification?, arXiv:1802.07538, Journal of Pure and Applied Algebra 223 (2019), no. 7, 2948--2976.
  6. Skew-enriched categories, arXiv:1709.01222, Applied Categorical Structures 26 (2018), no. 3, 597--615.
  7. A higher categorical approach to Giraud's non-abelian cohomology, PhD thesis, Macquarie University, 2016. Supervisor: Ross Street.
  8. Linear algebra via complex analysis (with Daniel Daners), The American Mathematical Monthly 120 (2013), no. 10, 877--892.

Papers in preparation:

Talks

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

Slides:

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.