Syllepsis in Homotopy Type Theory
Abstract
It is wellknown that in homotopy type theory (HoTT), one can prove the EckmannHilton theorem: given two 2loops p, q : 1 = 1 on the reflexivity path at an arbitrary point a : A, we have pq = qp. If we go one dimension higher, i.e., if p and q are 3loops, we show that a property classically known as syllepsis also holds in HoTT: namely, the EckmannHilton proof for q and p is the inverse of the EckmannHilton proof for p and q.
 Publication:

arXiv eprints
 Pub Date:
 July 2021
 arXiv:
 arXiv:2107.14283
 Bibcode:
 2021arXiv210714283S
 Keywords:

 Computer Science  Logic in Computer Science