## Preprints

- 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)
- Awodey, Gambino, Hazratpour, Kripke-Joyal forcing for type theory and uniform fibrations
- 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. - 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. (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.*