Papers
Published Research
- M. Carneiro, E. Riehl, Formalizing colimits in Cat, In 16th International Conference on Interactive Theorem Proving (ITP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 352, pp. 20:1-20:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025), arXiv:2503.20704
- E. Riehl and D. Verity, Cartesian exponentiation and monadicity, Cahiers de Topologie et Geometrie Differential Categoriques, (2024), 1–60, arXiv:2101.09853
- S. Hazratpour and E. Riehl, A 2-categorical proof of Frobenius for fibrations defined from a generic point, Mathematical Structures in Computer Science, Published online 2024:1-23, arXiv:2210.00078
- N. Kudasov, E. Riehl, and J. Weinberger, Formalizing the ∞-categorical Yoneda lemma, CPP 2024: Proceedings of the 13th ACM SIGPLAN International Conference on Certified Programs and Proofs, 274-290, arXiv:2309.08340
- P. Hackney, V. Ozornova, E. Riehl, and M. Rovelli, Pushouts of Dwyer maps are (∞,1)-categorical, Algebraic & Geometric Topology 24-4 (2024), 2171–2183. arXiv:2205.02353
- P. Hackney, V. Ozornova, E. Riehl, M. Rovelli, An (∞, 2)-categorical pasting theorem, Trans. Amer. Math. Soc. 376 (2023), 555–597, arXiv:2106.03660
- E. Riehl and M. Wattal, On ∞-cosmoi of bicategories, La Matematica 1, (2022), 740–764, arXiv:2108.11786
- E. Riehl and D. Verity, On the construction of limits and colimits in ∞-categories, Theory Appl. Categ. 35 (2020), no. 30, 1101–1158, arXiv:1808.09835
- E. Riehl and D. Verity, Recognizing quasi-categorical limits and colimits in homotopy coherent nerves, Appl. Categ. Struct., 28(4), (2020), 669–716, arXiv:1808.09834
- E. Riehl and D. Verity, ∞-category theory from scratch, Higher Structures 4(1):115–167, 2020, arXiv:1608.05314
- R. Garner, M. Kędziorek, and E. Riehl, Lifting accessible model structures, J. Topology, 13 (2020), no. 1, 59–76, arXiv:1802.09889
- E. Riehl and D. Verity, The comprehension construction, Higher Structures 2 (2018), no. 1, 116-190, arXiv:1706.10023
- K. Bauer, B. Johnson, C. Osborne, E. Riehl, and A. Tebbe, Directional derivatives and higher order chain rules for abelian functor calculus, Topology Appl. Women in Topology II: Further collaborations in homotopy theory 253 (2018), 375–427, arXiv:1610.01930
- E. Riehl and M. Shulman, A type theory for synthetic ∞-categories, Higher Structures 1 (2017), no. 1, 116–193, arXiv:1705.07442
- K. Hess, M. Kędziorek, E. Riehl, and B. Shipley, A necessary and sufficient condition for induced model structures, J. Topology 10 (2017), no. 2, 324–367, arXiv:1509.08154
- E. Riehl and D. Verity, Kan extensions and the calculus of modules for ∞-categories, Algebr. Geom. Topol. 17 (2017), no. 1, 189–271, arXiv:1507.01460
- E. Riehl and D. Verity, Fibrations and Yoneda’s lemma in an ∞-cosmos, J. Pure Appl. Algebra 221 (2017), no. 3, 499–564, arXiv:1506.05500
- M. Ching and E. Riehl, Coalgebraic models for combinatorial model categories, Homol. Homotopy Appl. 16 (2014), no. 2, 171–184, arXiv:1403.5303
- E. Riehl and D. Verity, Completeness results for quasi-categories of algebras, homotopy limits, and related general constructions, Homol. Homotopy Appl. 17 (2015), no. 1, 1–33, arXiv:1401.6247
- M. Bayeh, K. Hess, V. Karpova, M. Kędziorek, E. Riehl, and B. Shipley, Left-induced model structures and diagram categories, Contemp. Math. 641 (2015), 49–81. arXiv:1401.3651
- E. Riehl and D. Verity, Homotopy coherent adjunctions and the formal theory of monads, Adv. Math 286 (2016), 802–888, arXiv:1310.8279
- T. Barthel, J.P. May, and E. Riehl, Six model structures for DG-modules over DGAs: model category theory in homological action, New York J. Math 20 (2014), 1077-1159, arXiv:1310.1159
- E. Riehl and D. Verity, The 2-category theory of quasi-categories, Adv. Math. 280 (2015), 549–642, arXiv:1306.5144
- E. Riehl and D. Verity, The theory and practice of Reedy categories, Theory Appl. Categ. 29 (2014), no. 9, 256–301, arXiv:1304.6871
- E. Cheng, N. Gurski, and E. Riehl, Cyclic multicategories, multivariable adjunctions and mates, J. K-theory 13 (2014), no. 2, 337–396, arXiv:1208.4520
- A.J. Blumberg and E. Riehl, Homotopical resolutions associated to deformable adjunctions, Algebr. Geom. Topol. 14 (2014), no. 5, 3021–3048, arXiv:1208.2844
- T. Barthel and E. Riehl, On the construction of functorial factorizations for model categories, Algebr. Geom. Topol. 13 (2013), no. 2, 1089–1124, arXiv:1204.5427
- E. Riehl, Monoidal algebraic model structures, J. Pure Appl. Algebra 217 (2013), no. 6, 1069–1104, arXiv:1109.2883
- C. Kennett, E. Riehl, M. Roy, M. Zaks, Levels in the toposes of simplicial sets and cubical sets, J. Pure and Appl. Algebra 215 (2011), no. 5, 949–961, arXiv:1003.5944
- E. Riehl, On the structure of simplicial categories associated to quasi-categories, Math. Proc. Camb. Phil. Soc. 150 (2011), no.3., 489–504, arXiv:0912.4809
- E. Riehl, Algebraic model structures, New York J. Math. 17 (2011), 173–231, arXiv:0910.2733
- J. D’Angelo, S. Kos, E. Riehl, A Sharp Bound for the Degree of Proper Monomial Mappings Between Balls, J. Geom. Anal. 13 (2003), no. 4, 581–593.
- E. Graham Evans, Jr. and E. Riehl, On the intersections of polynomials and the Cayley-Bacharach theorem, J. Pure and Appl. Algebra 183 (2003), no. 1–3, 293–298.
Published Exposition
- E. Riehl, Synthetic perspectives on spaces and categories, to appear in the ICM Conference Proceedings, arXiv:2510.15795.
- E. Riehl, On the ∞-topos semantics of homotopy type theory, Bulletin of the London Mathematical Society, Volume 56, Issue 2, Feb 2024, 461-879, arXiv:2212.06937.
- E. Riehl, Could ∞-category theory be taught to undergraduates?, Notices of the AMS 70(5). May 2023, 727–736.
- E. Riehl, Homotopy coherent structures, Expositions in Theory and Applications of Categories 1 (2023), 1-31, arXiv:1801.07404, also available via AMS Open Math Notes OMN:201901.110786.
- E. Riehl, Homotopical categories: from model categories to (∞, 1)-categories, to appear in a forthcoming volume on spectra to appear in the MSRI Publications Series with Cambridge University Press, (2019), 1–67, arXiv:1904.00886
- F. Loregian and E. Riehl, Categorical notions of fibration, Expositiones Mathematicae 38 (2020), no. 4, 496–514, arXiv:1806.06129
- E. Riehl, Made-to-Order Weak Factorization Systems, Extended Abstracts Fall 2013, Research Perspectives CRM Barcelona, 2015.
- E. Riehl, Complicial sets, an overture, 2016 MATRIX Annals, (2017), 49–76, arXiv:1610.06801
- E. Riehl, The Kan Extension Seminar: An Experimental Online Graduate Reading Course, Notices Amer. Math. Soc. 61 (2014), no. 11, 1357–1358.
- A.M. Bohmann, A comparison of norm maps, with an appendix by A.M. Bohmann and E. Riehl, Proc. Amer. Math. Soc. 142 (2014), no. 4, 1413–1423, arXiv:1201.6277
Popular writing
- E. Riehl Mathematics is hard for mathematicians to understand too, my first column for Science Magazine’s Expert Voices series.
- E. Riehl AI Took on the Math Olympiad—But Mathematicians Aren’t Impressed: AI models supposedly did well on International Math Olympiad problems, but how they got their answers reminds us why we still need people doing math, an opinion piece published by Scientific American, August 2025.
- E. Riehl Should all mathematical proofs be checked by a computer?, Lost in Space-Time Column, New Scientist, July 2023.
- E. Riehl Infinity-Category Theory Offers a Bird’s-Eye View of Mathematics, originally published with the title “Infinite Math” in Scientific American 325, 4, 32-41 (October 2021).
Preprints
