- Awodey, Gambino, Hazratpour, Kripke-Joyal forcing for type theory and uniform fibrations
- Anel, The elementary ∞-topos of truncated coherent spaces
- Anel, Biedermann, Finster and Joyal, Higher Sheaves and Left-Exact Localizations of ∞-Topoi
- Swan, On the Nielsen-Schreier Theorem in Homotopy Type Theory
- Swan, A class of higher inductive types in Zermelo-Fraenkel set theory
- Anel, Subramaniam, Small object arguments, plus-construction, and left-exact localizations
- Frey, Categories of partial equivalence relations as localizations
- 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.
- 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.
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 number 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.