Construction of the Circle in UniMath

18 Nov 2020 · Bezem Marc, Buchholtz Ulrik, Grayson Daniel R., Shulman Michael ·

We show that the type $\mathrm{T}\mathbb{Z}$ of $\mathbb{Z}$-torsors has the dependent universal property of the circle, which characterizes it up to a unique homotopy equivalence. The construction uses Voevodsky's Univalence Axiom and propositional truncation, yielding a stand-alone construction of the circle not using higher inductive types.