Corpus ID: 236635088

Syllepsis in Homotopy Type Theory

@article{Sojakova2021SyllepsisIH,
  title={Syllepsis in Homotopy Type Theory},
  author={Kristina Sojakova},
  journal={ArXiv},
  year={2021},
  volume={abs/2107.14283}
}
Abstract It is well-known that in homotopy type theory (HoTT)[The Univalent Foundations Program, Institute for Advanced Study(2013)], one can prove the Eckmann-Hilton theorem: given two 2-loops p, q : 1⋆ = 1⋆ on the reflexivity path at an arbitrary point ⋆ : A, we have p q = q p. If we go one dimension higher, i.e., if p and q are 3-loops p, q : 11⋆ = 11⋆ , we show that a property classically known as syllepsis also holds in HoTT: namely, the Eckmann-Hilton proof for q and p is the inverse of… Expand

References

Homotopy Type Theory : Univalent Foundations of Mathematics
These lecture notes are based on and partly contain material from the HoTT book and are licensed under Creative Commons Attribution-ShareAlike 3.0.