Construction of the Circle in UniMath [article]

Marc Bezem and Ulrik Buchholtz and Daniel R. Grayson and Michael Shulman
2020 arXiv   pre-print
We show that the type Tℤ of 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.
arXiv:1910.01856v2 fatcat:uz7ncjbd7bb7lg3unxbkdywuxy