Chris Kapulkin: Publications & Preprints

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  1. The Hurewicz theorem for cubical homology, with D. Carranza and A. Tonks, preprint, 2022. [arXiv]
  2. Cubical setting for discrete homotopy theory, revisited, with D. Carranza, preprint, 2022. [arXiv]
  3. Homotopy groups of cubical sets, with D. Carranza, preprint, 2022. [arXiv]
  4. Equivalence of cubical and simplicial approaches to (∞,n)-categories, with B. Doherty and Y. Maehara, submitted, 2021. [arXiv]
  5. 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]
  6. A cubical model for (∞,n)-categories, with T. Campion and Y. Maehara, submitted, 2020. [arXiv]
  7. Cubical models of (∞,1)-categories, with B. Doherty, Z. Lindsey, and C. Sattler, Mem. Amer. Math. Soc. (to appear), 2020. [arXiv]
  8. 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]
  9. 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]
  10. Homotopical inverse diagrams in categories with attributes, with P. LeF. Lumsdaine, J. Pure Appl. Algebra 225 (2021), no. 4, 44 pp. [arXiv] [JPAA]
  11. 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]
  12. A Cubical Approach to Straightening, with V. Voevodsky, J. Topol. 13 (4), 1682-1700, 2020. [pdf] [J.Topol.]
  13. 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.]
  14. The Homotopy Theory of Type Theories, with P. LeF. Lumsdaine, Adv. Math. 337, 1-38, 2018. [arXiv] [Adv.Math.]
  15. Locally cartesian closed quasicategories from type theory, J. Topol. 10 (4), 1029-1049, 2017. [arXiv] [J.Topol.]
  16. Quasicategories of frames of cofibration categories, with K. Szumiło, Appl. Categ. Structures 25 (2017), no. 3, 323–347. [arXiv] [ACS]
  17. Joyal's Conjecture in Homotopy Type Theory, PhD dissertation, 148 pp., 2014. [d-Scholarship] [award]
  18. Homotopy Type Theory (The HoTT Book), as part of the Univalent Foundations Project, 2013. [web]
  19. Homotopy limits in type theory, with J. Avigad and P. LeF. Lumsdaine, Math. Structures Comput. Science 25 (2015), no. 5, 1040–1070. [arXiv] [MSCS]
  20. Univalent categories and the Rezk completion, with B. Ahrens and M. Shulman, Math. Structures Comput. Science 25 (2015), no. 5, 1010–1039. [arXiv] [MSCS]
  21. 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]
  22. Univalence in Simplicial Sets, with P. LeF. Lumsdaine and V. Voevodsky, not intended for publication, 2012. [arXiv]
  23. 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]
  24. 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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