Papers

Published Research

• 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, 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 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

• S. Awodey, E. Cavallo, T. Coquand, E. Riehl, C. Sattler, The equivariant model structure on cartesian cubical sets, (2024), 1-87, arXiv:2406.18497
• E. Riehl and D. Verity, Cartesian exponentiation and monadicity, (2021), 1–71, arXiv:2101.09853
• E. Riehl, Inductive Presentations of Generalized Reedy Categories