Corpus ID: 203734723

Construction of the Circle in UniMath

  title={Construction of the Circle in UniMath},
  author={M. Bezem and Ulrik Buchholtz and D. Grayson},
  • M. Bezem, Ulrik Buchholtz, D. Grayson
  • Published 2019
  • Mathematics, Computer Science
  • ArXiv
  • 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. 

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