Emily Riehl is rewriting the foundations of higher category theory (2021)

6 months ago

Emily Riehl compares her work in higher category theory to playing the viola, seeing both as foundational 'glue' in their fields.
Category theory, introduced by Eilenberg and Mac Lane in 1945, replaces equality with the concept of equivalence, revolutionizing mathematics.
Higher category theory extends this by considering equivalences between equivalences, captured in structures called infinity categories.
Riehl and Dominic Verity are finalizing a book to make higher category theory more accessible, aiming to rewrite its technical foundations.
Riehl won the 2021 AWM-Joan and Joseph Birman Research Prize for her contributions to topology and geometry.
She discusses her early career inspiration from 'Jurassic Park' and her passion for abstract algebra and category theory.
Riehl highlights the importance of community in mathematics, likening her role to a 'categorical consultant' supporting others.
She co-founded Spectra, an association for LGBTQ mathematicians, to provide visibility and support within the community.
Riehl advocates for social justice in mathematics, addressing issues like inclusivity and the impact of language on learning.
Her work with Mike Shulman aims to simplify higher category theory for future undergraduate education.

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