All Outputs (2)

Connecting Constructive Notions of Ordinals in Homotopy Type Theory (2021)
Conference Proceeding
Kraus, N., Nordvall Forsberg, F., & Xu, C. (2021). Connecting Constructive Notions of Ordinals in Homotopy Type Theory.

In classical set theory, there are many equivalent ways to introduce ordinals. In a constructive setting, however, the different notions split apart, with different advantages and disadvantages for each. We consider three different notions of ordinal... Read More about Connecting Constructive Notions of Ordinals in Homotopy Type Theory.

Coherence via Well-Foundedness: Taming Set-Quotients in Homotopy Type Theory (2020)
Conference Proceeding
Kraus, N., & Von Raumer, J. (2020). Coherence via Well-Foundedness: Taming Set-Quotients in Homotopy Type Theory. In LICS '20: Proceedings of the 35th Annual ACM/IEEE Symposium on Logic in Computer Science (662-675). https://doi.org/10.1145/3373718.3394800

Suppose we are given a graph and want to show a property for all its cycles (closed chains). Induction on the length of cycles does not work since sub-chains of a cycle are not necessarily closed. This paper derives a principle reminiscent of inducti... Read More about Coherence via Well-Foundedness: Taming Set-Quotients in Homotopy Type Theory.