Pure (higher) category theory

I sometimes work on pure category theory.

• In Cocompactness and Presentability, with Thorger Geiß and Phil Pützstück we revisited a classical category theory fact that only existed as "folklore" in \(\infty\)-categories about categories that are both presentable and op-presentable. We proved a stronger result generally about cocompact objects in presentable \(\infty\)-categories that seems new even for ordinary categories, see arXiv link.
• A monoidal Grothendieck construction for \(\infty\)-categories. arXiV link. Nagoya Mathematical Journal. Published online 2025:1-32. doi:10.1017/nmj.2025.10086
• Universality of Barwick's unfurling construction, with Bastiaan Cnossen and Tobias Lenz. arXiv link. International Mathematical Research Notices, Volume 2025, Issue 18, September 2025
• An elementary proof of the naturality of the Yoneda embedding. arXiV link. Proceedings of the American Mathematical Society. 151, 10, p. 4163-4171
• Fully faithful functors and pushouts of \(\infty\)-categories, with Peter Haine and Jan Steinebrunner. arXiv link. (submitted)