The equivalence of the torus and the product of two circles in homotopy type theory

Kristina Sojakova

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arXiv · 1510.03918

The equivalence of the torus and the product of two circles in homotopy type theory

Kristina Sojakova

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Abstract

Homotopy type theory is a new branch of mathematics which merges insights from abstract homotopy theory and higher category theory with those of logic and type theory. It allows us to represent a variety of mathematical objects as basic type-theoretic constructions, higher inductive types. We present a proof that in homotopy type theory, the torus is equivalent to the product of two circles. This result indicates that the synthetic definition of torus as a higher inductive type is indeed correct.

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Kristina Sojakova. 2015-10-13. The equivalence of the torus and the product of two circles in homotopy type theory. https://arxiv.org/abs/1510.03918

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