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arXiv · 2107.14283

Syllepsis in Homotopy Type Theory

Kristina Sojakova
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Abstract

It is well-known that in homotopy type theory (HoTT), one can prove the Eckmann-Hilton theorem: given two 2-loops 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 3-loops, 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 the Eckmann-Hilton proof for p and q.

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Kristina Sojakova. 2021-07-29. Syllepsis in Homotopy Type Theory. https://arxiv.org/abs/2107.14283

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