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Construction of the Circle in UniMath (1910.01856v2)
Published 4 Oct 2019 in math.LO, cs.LO, and math.AT
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.