Preprints

• Awodey, Cavallo, Coquand, Riehl, Sattler, The equivariant model structure on Cartesian cubical sets (2024)
• Anel, Barton, Choice axioms and Postnikov completeness (2024)
• Barton, A short proof of Frobenius for generic fibrations (2024)
• Anel, Weinberger, Smooth and Proper Maps (2024)
• Anel, Biedermann, Finster and Joyal, Left-exact localization III : The Acyclic Product (2023)
• Frey,  Duality for Clans: a Refinement of Gabriel-Ulmer Duality  (2023)
• Awodey,  Cartesian cubical model categories, (May 2023)
• Awodey,  On Hofmann-Streicher universes (2022)
• Anel,  The elementary  ∞-topos of truncated coherent spaces (2021)
• Anel, Subramaniam,  Small object arguments, plus-construction, and left-exact localizations (2020)
• Swan, Definable and non-definable notions of structure (2022)
• Swan, Double negation stable h-propositions in cubical sets (2022)

Publications

• Anel, Biedermann, Finster and Joyal, Left-exact localization II : Grothendieck topologies, Journal of Pure and Applied Algebra, Volume 228, Issue 3 (2024) 107472.
• Awodey, Gambino, Hazratpour, Kripke-Joyal forcing for type theory and uniform fibrations, Selecta Mathematica, Volume 30 (2024).
• Frey, Rasekh,  Constructing Coproducts in locally Cartesian closed ∞-Categories.  Homotopy, Homology and Applications, Volume 25 (2023).
• Frey, J.,  Categories of partial equivalence relations as localizations.  Journal of Pure and Applied Algebra, 2022, doi:10.1016/j.jpaa.2022.107115
• Anel, Biedermann, Finster, Joyal,  Left-exact localizations of ∞-topoi I: Higher sheaves.  Advances in Mathematics, Volume 400, 2022, 108268.
  
• Swan, A.W. (2022). A class of higher inductive types in Zermelo-Fraenkel set theory. Mathematical logic quarterly, Volume 68, Issue 1. doi:10.1002/malq.202100040
• Swan, A.W. (2022). On the Nielsen-Schreier theorem in homotopy type theory. Logical Methods in Computer Science, Volume 18, Issue 1. doi:10.46298/lmcs-18(1:18)2022
• Frey, J., & Streicher, T. (2021). Triposes as a generalization of localic geometric morphisms.  Mathematical Structures in Computer Science,  1-10. doi:10.1017/S0960129520000304
• Awodey, S. (2021).  Sheaf representations and duality in logic. In: Joachim Lambek: The Interplay of Mathematics, Logic, and Linguistics, Claudia Casadio and Philip J. Scott (eds.), Springer-Verlag.

Slides

• Awodey, S. (2024) What is HoTT? Slides and video from a talk for the Hausdorff Institute for Mathematics program Prospects of Formal Mathematics in May 2024. HIM video
• Awodey, S. (2023) Homotopy type theory, Slides from CMU Philosophy Colloquium, September 2023.
• Frey, J. (2022)  Basic Combinatory Objects, Uniform Preorders and Partial Combinatory Algebras. Slides from the Category Theory Octoberfest 2022 online workshop. Video recording
• Awodey, S. (2022)  Kripke–Joyal Forcing for Martin-Löf Type Theory. Slides from the special session on  Homotopy Type Theory at the  2022 North American Annual Meeting of the  Association for Symbolic Logic.
• Frey, J. (2022) An Introduction to Cohesive Homotopy Type Theory. Slides from the special session on  Homotopy Type Theory at the  2022 North American Annual Meeting of the  Association for Symbolic Logic.
• Awodey, S. (2022) Tutorial on polynomial functors and type theory. Slides from the Workshop on Polynomial Functors, held at the Topos Institute, March 2022. Video of part I, video of part II.
• Frey, J. (2022)  Characterizing clan-algebraic categories, Slides from an invited talk at the  Homotopy Type Theory Electronic Seminar Talks series, February 2022.  Video
• Awodey, S. (2021) Univalence in infinity topoi.  Slides from the conference Category Theory 2021 held at the University of Genoa, August 2021.
• Frey, J. (2021) A refinement of Gabriel-Ulmer duality. Slides from the conference Category Theory 2021 held at the University of Genoa, August 2021.
•  Swan, A.W. (2021) Some remarks on locally representable algebraic weak factorisation systems. Slides from the conference Category Theory 2021 held at the University of Genoa, August 2021. Video of the talk.
• Frey, J. (2021) Coproducts in infinity-LCCCs with subobject classifier. Slides from the workshop HoTT/UF 2021 held at Buenos Aires, July 2021. Video of the talk.
• Swan, A.W. (2021) The Nielsen-Schreier theorem in homotopy type theory. Slides from the workshop HoTT/UF 2021 held at Buenos Aires, July 2021. Video of the talk.
• Awodey, S. (2021) Polynomial functors and natural models of type theory. Slides from the Workshop on Polynomial Functors held at the Topos Institute, March 2021.
• Awodey, S. (2019) Quillen model structures on cubical sets. Slides from the conference Homotopy Type Theory 2019 held at CMU, July 2019.

Sponsorship

The CMU HoTT Group gratefully acknowledges the support of the Air Force Office of Scientific Research through MURI grants FA9550-15-1-0053 and FA9550-21-1-0009, as well as award n umber FA9550-20-1-0305 .  Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the United States Air Force.