nLab Emily Riehl

I am an Assistant Professor in the Department of Mathematics at Johns Hopkins University.

My webpage can be found here.

Selected writings

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.

• Emily Riehl, Category Theory in Context

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 (pdf, doi:10.1017/CBO9781107261457)

• 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$]$

Survey of homotopy theory from homotopical categories to (∞,1)-categories:

• Emily Riehl, Homotopical categories: from model categories to (∞,1)-categories, in: Andrew J. Blumberg, Teena Gerhardt, Michael A. Hill (eds,) Stable categories and structured ring spectra, MSRI Book Series, Cambridge University Press (arXiv:1904.00886)

A new proof of the Strøm model structure using algebraic weak factorization systems:

• Tobias Barthel, Emily Riehl, On the construction of functorial factorizations for model categories, Algebr. Geom. Topol. 13 (2013) 1089-1124 (arXiv:1204.5427, doi:10.2140/agt.2013.13.1089)

On monads in computer science:

• Emily Riehl, A categorical view of computational effects, talk at C$\circ$mp$\circ$se$\colon\!\colon$Conference (2017) [pdf, pdf]

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 $(\infty,1)$-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:

• Emily Riehl, Dominic Verity, Homotopy coherent adjunctions and the formal theory of monads, Advances in Mathematics, Volume 286, 2 January 2016, Pages 802-888 (arXiv:1310.8279, doi:10.1016/j.aim.2015.09.011)

On the Yoneda lemma for (∞,1)-categories:

• Emily Riehl, Dominic Verity, Fibrations and Yoneda’s lemma in an $\infty$-cosmos, Journal of Pure and Applied Algebra Volume 221, Issue 3, March 2017, Pages 499-564 (arXiv:1506.05500, doi:10.1016/j.jpaa.2016.07.003)

On the categorical semantics of univalent homotopy type theory in $\infty$-topoi (proof of Awodey's conjecture):

• Emily Riehl, On the $\infty$-topos semantics of homotopy type theory, lecture at Logic and higher structures CIRM (Feb. 2022) $[$pdf, pdf$]$

Exposition of (∞,1)-category theory with an eye towards homotopy type theory:

• Emily Riehl, $\infty$-Category theory for undergraduates, talk at CQTS (Dec. 2022) [video: rec]

category: people