Chris Kapulkin: Publications & Preprints

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  1. Synthetic approach to the Quillen model structure on topological spaces, with S. Ebel, Algebr. Geom. Topol. (to appear), 2023. [arXiv]
  2. Extensional concepts in intensional type theory, revisited, with Y. Li, submitted, 2023. [arXiv]
  3. Closed symmetric monoidal structures on the category of graphs, with N. Kershaw, Theory Appl. Categ. (to appear), 2023. [arXiv]
  4. Nonexistence of colimits in naive discrete homotopy theory, with D. Carranza and J. Kim, Appl. Categ. Structures 31 (2023), no.5, 41, 6 pp. [arXiv] [ACS]
  5. Calculus of Fractions for Quasicategories, with D. Carranza and Z. Lindsey, submitted, 2023. [arXiv]
  6. Diagonal Lemma for Presheaves on Eilenberg-Zilber Categories, with D. Carranza and L.-Z. Wong, submitted, 2023. [arXiv]
  7. The fundamental group(oid) in discrete homotopy theory, with U. Mavinkurve, Adv. Appl. Math. (to appear), 2023. [arXiv]
  8. Cofibration category of digraphs for path homology, with D. Carranza, B. Doherty, M. Opie, M. Sarazola, and L.-Z. Wong, Algebr. Comb. 7 (2024), no. 2, 475–514. [arXiv] [ALCO]
  9. The Hurewicz theorem for cubical homology, with D. Carranza and A. Tonks, Math. Z. 305, 61 (2023), 20 pages. [arXiv] [Math.Z.]
  10. Cubical setting for discrete homotopy theory, revisited, with D. Carranza, Compos. Math. (to appear), 2022. [arXiv]
  11. Homotopy groups of cubical sets, with D. Carranza, Expo. Math. 41 (2023) 125518, no. 4, 55 pp. [arXiv] [Expo.Math.]
  12. Equivalence of cubical and simplicial approaches to (∞,n)-categories, with B. Doherty and Y. Maehara, Adv. Math. 416 (2023) 108902, 81 pp. [arXiv] [Adv.Math.]
  13. 2-adjoint equivalences in homotopy type theory, with D. Carranza, J. Chang, and R. Sandford, Log. Methods Comput. Science 17 (2021), no. 1, Paper No. 3, 9 pp. [arXiv] [LMCS]
  14. A cubical model for (∞,n)-categories, with T. Campion and Y. Maehara, Geom. Topol. (to appear), 2020. [arXiv]
  15. Cubical models of (∞,1)-categories, with B. Doherty, Z. Lindsey, and C. Sattler, Mem. Amer. Math. Soc. 297 (2024), no. 1484, v+110 pp. [arXiv] [MAMS]
  16. The Law of Excluded Middle in the Simplicial Model of Type Theory, with P. LeF. Lumsdaine, Theory Appl. Categ. Vol. 35, 2020, No. 40, pp. 1546-1548. [arXiv] [TAC]
  17. A co-reflection of cubical sets into simplicial sets with applications to model structures, with Z. Lindsey and L.-Z. Wong, New York J. Math. 25 (2019), 627–641. [arXiv] [NYJM]
  18. Homotopical inverse diagrams in categories with attributes, with P. LeF. Lumsdaine, J. Pure Appl. Algebra 225 (2021), no. 4, 44 pp. [arXiv] [JPAA]
  19. Threshold Properties of Prime Power Subgroups with Application to Secure Integer Comparisons, with R. Carlton and A. Essex, Topics in Cryptology – CT-RSA 2018137-156, Lecture Notes Comput. Sci., 10808, 2018. [iacr] [LNCS]
  20. A Cubical Approach to Straightening, with V. Voevodsky, J. Topol. 13 (4), 1682-1700, 2020. [pdf] [J.Topol.]
  21. Internal Language of Finitely Complete (∞,1)-categories, with K. Szumiło, Selecta Math. (N.S.) 25 (2019), no. 2, Art. 33, 46 pp. [arXiv] [Sel.Math.]
  22. The Homotopy Theory of Type Theories, with P. LeF. Lumsdaine, Adv. Math. 337, 1-38, 2018. [arXiv] [Adv.Math.]
  23. Locally cartesian closed quasicategories from type theory, J. Topol. 10 (4), 1029-1049, 2017. [arXiv] [J.Topol.]
  24. Quasicategories of frames of cofibration categories, with K. Szumiło, Appl. Categor. Struct. 25 (2017), no. 3, 323–347. [arXiv] [ACS]
  25. Joyal's Conjecture in Homotopy Type Theory, PhD dissertation, 148 pp., 2014. [d-Scholarship] [award]
  26. Homotopy Type Theory (The HoTT Book), as part of the Univalent Foundations Project, 2013. [web]
  27. Homotopy limits in type theory, with J. Avigad and P. LeF. Lumsdaine, Math. Structures Comput. Science 25 (2015), no. 5, 1040–1070. [arXiv] [MSCS]
  28. Univalent categories and the Rezk completion, with B. Ahrens and M. Shulman, Math. Structures Comput. Science 25 (2015), no. 5, 1010–1039. [arXiv] [MSCS]
  29. The Simplicial Model of Univalent Foundations (after Voevodsky), with P. LeF. Lumsdaine, J. Eur. Math. Soc. (JEMS) 23 (2021), no. 6, 2071-2126. [arXiv] [JEMS]
  30. Univalence in Simplicial Sets, with P. LeF. Lumsdaine and V. Voevodsky, not intended for publication, 2012. [arXiv]
  31. Expressiveness of positive coalgebraic logic, with A. Kurz and J. Velebil, Advances in modal logic. Vol. 9, 368–385, Coll. Publ., London, 2012. [pdf] [AIML]
  32. Homotopy-theoretic models of type theory, with P. Arndt, Typed lambda calculi and applications, 45–60, Lecture Notes in Comput. Sci., 6690, Springer, Heidelberg, 2011. [arXiv] [LNCS]

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