Emily Riehl is rewriting the foundations of higher category theory (2020)
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Re: Emily Riehl is rewriting the foundations of higher category theory (2020)
#2>2021
Was
Re: Emily Riehl is rewriting the foundations of higher category theory (2020)
#3>2021 Was
[deleted]
Re: Emily Riehl is rewriting the foundations of higher category theory (2020)
#4>2021 Was
I guess the ceremony was programed for 2021, but the winner was anounced in 2020. (Like the Nobel, not like the Oscar.)
Re: Emily Riehl is rewriting the foundations of higher category theory (2020)
#5Emily 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.
Re: Emily Riehl is rewriting the foundations of higher category theory (2020)
#6This 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
Re: Emily Riehl is rewriting the foundations of higher category theory (2020)
#7Emily 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.
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?
Re: Emily Riehl is rewriting the foundations of higher category theory (2020)
#8>2021 Was
I guess the ceremony was programed for 2021, but the winner was anounced in 2020. (Like the Nobel, not like the Oscar.)
Information about this prize: https://awm-math.org/awards/awm-birman-research-prize/
"Nomination Period: April 1 through May 15 of an even numbered year. The prize will be awarded the January after nominations close, which falls in an odd year."
See for example the dates on the various announcement notices as given in the notes in the Wikipedia article: https://en.wikipedia.org/wiki/Joan_%26_Joseph_Birman_Researc...
(Note also that 2020 may have been unusual because pandemic.)
Re: Emily Riehl is rewriting the foundations of higher category theory (2020)
#9This 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
Can you elaborate what's ironic (what is "this" - higher CT)?
A note on the motivations - CT was not originally intended as a foundations. This is clear from both the name (General Theory of Natural Equivalences) and construction (based on set theory, which is was and still is the foundation for most of mathematics). There was indeed work in the foundational direction and there are relevant aspects, but I don't think that's even today the core aspect of it.
Re: Emily Riehl is rewriting the foundations of higher category theory (2020)
#10Emily 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.
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 math…
You might also find the work of David I. Spivak (no relation to the _Calculus on Manifolds_ Spivak) helpful in this endeavor.
John Baez (who is distantly related to Joan Baez, if memory serves) has also written a lot of introductory category theory and applied category theory.