All Outputs (2)

Free Higher Groups in Homotopy Type Theory (2018)
Presentation / Conference Contribution
Kraus, N., & Altenkirch, T. (2018, July). Free Higher Groups in Homotopy Type Theory. Presented at LICS '18: 33rd Annual ACM/IEEE Symposium on Logic in Computer Science, Oxford United Kingdom

© 2018 ACM. Given a type A in homotopy type theory (HoTT), we can define the free∞-group onA as the loop space of the suspension ofA+1. Equivalently, this free higher group can be defined as a higher inductive type F(A) with constructors unit : F(A),... Read More about Free Higher Groups in Homotopy Type Theory.

Quotient inductive-inductive types (2018)
Book Chapter
Altenkirch, T., Capriotti, P., Dijkstra, G., Kraus, N., & Nordvall Forsberg, F. (2018). Quotient inductive-inductive types. In C. Baier, & U. Dal Lago (Eds.), FoSSaCS 2018: Foundations of Software Science and Computation Structures (293-310). Springer Publishing Company. https://doi.org/10.1007/978-3-319-89366-2_16

Higher inductive types (HITs) in Homotopy Type Theory (HoTT) allow the definition of datatypes which have constructors for equalities over the defined type. HITs generalise quotient types and allow to define types which are not sets in the sense of H... Read More about Quotient inductive-inductive types.