## Construction of the circle in UniMath.(English)Zbl 07357172

Summary: 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.

### MSC:

 03B38 Type theory 03B70 Logic in computer science 55U35 Abstract and axiomatic homotopy theory in algebraic topology 03G30 Categorical logic, topoi

UniMath
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### References:

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