I am an Assistant Professor in the Department of Mathematics at Johns Hopkins University.
My webpages can be found here and here.
On rigidification of quasi-categories:
On topos levels in simplicial sets and cubical sets:
On Reedy model structures via weighted colimits:
An introductory category theory textbook for beginning graduate students or advanced undergraduates with an emphasis on applications of categorical concepts to a variety of areas of mathematics.
Textbooks on (simplicial) homotopy theory and (∞,1)-category theory with emphasis on tools from category theory and 2-category theory (via ∞-cosmoi and the homotopy 2-category of (∞,1)-categories):
Emily Riehl, Categorical Homotopy Theory, Cambridge University Press (2014) [doi:10.1017/CBO9781107261457, pdf]
Emily Riehl, Dominic Verity, Elements of ∞-Category Theory, Cambridge studies in advanced mathematics 194, Cambridge University Press (2022) [doi:10.1017/9781108936880, ISBN:978-1-108-83798-9, pdf]
On directed homotopy type theory via a form of simplicial type theory
Survey of homotopy theory from homotopical categories to (∞,1)-categories:
A new proof of the Strøm model structure using algebraic weak factorization systems:
On monads in computer science:
On left-transferred model structures and model structures on functors:
Marzieh Bayeh, Kathryn Hess, Varvara Karpova, Magdalena Kedziorek, Emily Riehl, Brooke Shipley, Left-induced model structures and diagram categories, in: Women in Topology: Collaborations in Homotopy Theory, Contemporary Mathematics 641 American Mathematical Society (2015) [arXiv:1401.3651, ISBN:978-1-4704-2495-4]
Kathryn Hess, Magdalena Kedziorek, Emily Riehl, Brooke Shipley, A necessary and sufficient condition for induced model structures, J. Topology 10 2 (2017) 324-369 [arXiv:1509.08154, doi:10.1112/topo.12011]
(this contains an error which is corrected in Garner, Kedziorek & Riehl 2018)
Richard Garner, Magdalena Kedziorek, Emily Riehl, Lifting accessible model structures, J. Topology 13 1 (2020) 59-76 [arXiv:1802.09889, doi:10.1112/topo.12123]
On (∞,1)-category theory via the homotopy 2-category of (∞,1)-categories (formal -category theory):
Emily Riehl, Dominic Verity, The 2-category theory of quasi-categories, Advances in Mathematics Volume 280, 6 August 2015, Pages 549-642 (arXiv:1306.5144, doi:10.1016/j.aim.2015.04.021)
Emily Riehl, Dominic Verity, Infinity category theory from scratch, Higher Structures Vol 4, No 1 (2020) (arXiv:1608.05314, pdf)
Emily Riehl, The formal theory of ∞-categories, talk at Categories and Companions Symposium June 8–12, 2021 (video)
On (∞,1)-functors and (∞,1)-monads:
On the Yoneda lemma for (∞,1)-categories:
On (discrete) Grothendieck fibrations and profunctors:
On the categorical semantics of univalent homotopy type theory in -topoi (proof of Awodey's conjecture):
Exposition of (∞,1)-category theory with an eye towards homotopy type theory:
On teaching (∞,1)-category theory to undergraduate students:
Formalization of the -Yoneda lemma via simplicial homotopy type theory (in Rzk):
On formalization of -cosmoi in the proof assistant Lean:
A constructive model of homotopy type theory in a Quillen model category of cubical sets that classically presents the usual homotopy theory of spaces:
Last revised on June 30, 2025 at 12:54:05. See the history of this page for a list of all contributions to it.