Emily Riehl is rewriting the foundations of higher category theory (2020)
6 comments
·October 22, 2025TimorousBestie
Emily Riehl is one of the best category theory writers in the business. Lurie’s opus was basically unreadable for me until I found her notes on (inf, 1)-categories and enrichment.
More recently, she wrote https://arxiv.org/abs/2510.15795 on how univalence drives some approaches to synthetic topology/homotopy.
libraryofbabel
One of the things I liked about her interview was how she candidly says her strengths are less in opening up new areas or proving new theorems and more reworking and clarifying existing areas (i.e. Lurie’s work) with cleaner approaches and new proofs to make them more accessible and therefore more useful.
This seems to me to be admirable, and perhaps under-appreciated. Although it is probably much more valued in mathematics than most other fields, perhaps because mathematicians place more value than other fields on simplicity and clarity of exposition for its own sake, and because it is just so hard to read unfamiliar mathematics. Her north star goal of making her field accessible to mathematics undergraduates was a nice one.
I would like to learn category theory properly one day, at least to that kind of "advance undergraduate" level she mentions. It's always seemed to me when dipping into it that it should be easier to understand than it is, if that makes sense - like the terminology and notation and abstraction are forbidding, but the core of "objects with arrows between them" also has the feeling of something that a (very smart) child could understand. Time to take another crack at it, perhaps?
moralestapia
>2021
Was
gus_massa
I guess the ceremony was programed for 2021, but the winner was anounced in 2020. (Like the Nobel, not like the Oscar.)
null
This title is a bit ironic when you consider the fact that one of the motivations of inventing category theory is to provide a foundation for many branches of mathematics