eriehl at math.harvard.edu

Harvard University
Department of Mathematics
1 Oxford Street
Cambridge, MA 02138

Science Center 320

I am a Benjamin Peirce and NSF postdoctoral fellow at Harvard University working on various topics in category theory related to homotopy theory. In 2011, I completed my PhD at the University of Chicago under the direction of Peter May. As a graduate student, I began work with Dominic Verity at Macquarie University in Sydney. I am a host of the n-Category Café. I am currently based at MSRI as a member of the program on Algebraic Topology.


In the spring of 2014, I will lead an online graduate reading course in category theory modeled after the Kan seminar at MIT. More information can be found on the course website.

In the fall of 2012, I taught Math 131: Topology I. The course website is here.

In the spring of 2012, I taught Math 266x: Categorical Homotopy Theory. More information can be found on the course website. Lecture notes written at the time have been assembled into a book that will appear in the New Mathematical Monographs series published by Cambridge University Press. Cambridge has graciously allowed me to host a free PDF copy in perpetuity, which can be found here.



My “topic” proposal: A model structure for quasi-categories

My Part III essay: Model categories and weak factorisation systems

My undergraduate senior thesis: Lubin-Tate formal groups and local class field theory


A document to accompany an n-Category Café post: Associativity data in an (∞,1)-category.

A formalist's introduction to simplicial sets, intended to establish a firm foundation for understanding the categorical and topological applications: A leisurely introduction to simplicial sets.

Lecture notes for talks given by Mike Shulman in the fall of 2008 introducing weighted limits, with some preliminary ideas about homs and tensors of bimodules expanding into their full gorey detail. The level is appropriate for someone whose knowledge of enriched category theory is more-or-less contained in the first three pages of Max Kelly's Basic concepts of enriched category theory: Weighted limits and colimits.

A short note, originally written for my advisor, proves the equivalence between an alternative (and my preferred) definition of a model structure on a category and the usual axioms: A concise definition of a model category.

Notes describing the appropriate topologies for spaces constructed as products, subspaces, quotients, or by gluing, written to accompany a series of lectures in an undergraduate point-set topology course taught at Harvard in the fall of 2012: On the construction of new topological spaces from existing ones.

A less-abridged version of an “extended conference abstract” to be published by the Centre de Recerca Matemàtica following their Conference on Type Theory, Homotopy Theory, and Univalent Foundations: Made-to-order weak factorization systems.

Comments are always welcome.


The following notes were written — usually quite hastily and with sparce, if any, editing — to accompany talks I gave as a PhD student in the University of Chicago Topology Proseminar.


Finally, here is my CV.