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.

中文翻译：

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在UniMath中构建圆

我们表明类型 $\mathrm{Ť}\mathbb{ž}$ 的 $\mathbb{ž}$-torsors具有圆的从属通用属性，该特性将其表征为唯一的同伦等效性。该构造使用了Voevodsky的Univalence公理和命题截断，从而产生了不使用更高归纳类型的圆的独立构造。