Emily Riehl

eriehl at math dot jhu dot edu

Johns Hopkins University
Department of Mathematics
3400 N. Charles Street
Baltimore, MD 21218

312 Krieger Hall

New Research Exposition Talks Teaching
I am an associate professor in the department of mathematics at Johns Hopkins University working on a variety of topics in category theory related to homotopy theory. From 2015-2019, I was an assistant professor in the department of mathematics at Johns Hopkins University. From 2011-2015, I was a Benjamin Peirce and NSF postdoctoral fellow at Harvard University. In 2011, I completed my PhD at the University of Chicago under the direction of Peter May. I frequently collaborate with Dominic Verity at the Centre of Australian Category Theory. I am a host of the n-Category Café and founder of the Kan Extension Seminar, which recently completed its second iteration. I spent the spring of 2014 at MSRI as a member of the program on Algebraic Topology, the summer of 2015 at the Hausdorff Institute of Mathematics as a participant in the Homotopy theory, manifolds, and field theories program, and part of the winter of 2016 at the Max Planck Institute for Mathematics as part of the Program on Higher Structures in Geometry and Physics. I was in residence at the Center for Advanced Study at the Norwegian Academy of Science and Letters in May/June 2019 as part of the Homotopy Type theory and Univalent Foundations Program and am the lead organizer for an MSRI semester program Higher Categories and Categorification that took place in Spring 2020. Here is my CV.

I am the author of Categorical Homotopy Theory, published by Cambridge University Press in their New Mathematical Monographs series. (This material has been published by Cambridge University Press as Categorical Homotopy Theory by Emily Riehl. This version is free to view and download for personal use only. Not for re-distribution, re-sale or use in derivative works. © Emily Riehl 2014.) I am grateful to them for a special arrangement that also allows me to host a free PDF copy with the preceding disclaimer. More information can be found on the book website and in this blog post.

I am also the author of Category Theory in Context, published by Dover Publications in the Aurora: Modern Math Originals series. Once again, I am very grateful for a special arrangment with the publishers that allows me to host a free PDF copy. More information can be found on the book website and in this blog post.

Dominic Verity and I are in the process of writing a book developing the model-independent foundations of ∞-category theory, the most recent draft of which can be found here:

The original draft, which is no longer actively being edited, contained several additional chapters, which will re-appear later in a separate volume. For now, the original combined version can be found here: The 2018 MIT Talbot workhop was on the same topic and various additional resources can be found on the conference website.

I am a member of the editorial boards for Homology, Homotopy, and Applications, the Journal of Homotopy and Related Structures, and the Journal of Pure and Applied Algebra. I organize the Johns Hopkins Category Theory Seminar. There is a rapidly expanding group of PhD students at Johns Hopkins who are interested in category theory, abstract homotopy theory, and homotopy type theory. If you are interested in joining us, more information about graduate admissions can be found here.






∞-categories Homotopy type theory New model structures Algebraic model structures Reedy categories Miscellaneous  


Formal writing: Miscellaneous mathematical notes: n-Category Café posts:  


Research lecture notes: Slides: Video: General audience: University of Chicago Topology Proseminar lecture notes: (written hastily with little editing)  


Johns Hopkins: Harvard: