1. Construction of the Circle in UniMath
- Author
-
Bezem, Marc, Buchholtz, Ulrik, Grayson, Daniel R., and Shulman, Michael
- Subjects
Mathematics - Logic ,Computer Science - Logic in Computer Science ,Mathematics - Algebraic Topology ,03B15, 03B70, 55U35 - Abstract
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., Comment: 27 pages; many improvements thanks to referee comments; added Shulman as co-author, who helped write a new section on the interpretation in higher toposes
- Published
- 2019